Workshop on metrology, standardization and certification. Laboratory workshop on the discipline "metrology, standardization and certification" Workshop on metrology and standardization

MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA

Federal State Budgetary Educational Institution of Higher Professional Education "Ugra State University" (YSU)

NIZHNEVARTOVSK OIL TECHNICAL SCHOOL

(branch) of a federal state budgetary educational institution

higher professional education "Ugra State University"

(NNT (branch) of the Federal State Budgetary Educational Institution of Higher Professional Education "Southern State University")

METROLOGY, STANDARDIZATION AND CERTIFICATION

Guidelines for performing laboratory work

for students of all forms of education in secondary vocational education institutions.

Nizhnevartovsk 2015

SUBJECTS OF LABORATORY WORK ON DISCIPLINE

"METROLOGY STANDARDIZATION AND CERTIFICATION"

Number

Number and name of the lesson

Number of classroom hours

form of control

1.

Laboratory work No. 1 “Measuring parts with caliper tools”

2

2.

Laboratory work No. 2 “Measuring parts with a micrometer instrument

2

3.

Laboratory work No. 3 “Measuring parts with indicator devices”

2

4.

Laboratory work No. 4 “Measuring a plug gauge”

2

5.

Laboratory work No. 5 “Surface roughness”

2

Laboratory work No. 1

MEASUREMENT OF PARTS WITH PANEL TOOLS

Goal of the work

Study the device, measurement principle and metrological characteristics of caliper tools.

Measure the issued part with a caliper.

Draw a sketch of the part with actual dimensions.

PANEL TOOLS

To measure linear dimensions using the absolute method and to reproduce dimensions when marking parts, caliper tools are used, which combine under this name a large group of measuring instruments: calipers, calipers, calipers, calipers, calipers, etc.

The most common type of vernier tool is the caliper. There are several models of calipers (GOST 166-80).

Fig.1

Caliper ShTs-IA) for external and internal measurements and with a ruler for measuring depths (vernier division value 0.1 mm, measurement range from 0 to 125 mm) has a rod (ruler) 1 with a main scale, the divisions of which are marked every 1 millimeter. The rod has fixed double-sided measuring jaws with working surfaces perpendicular to the rod. The measuring frame moves along the ruler 2 with a second pair of sponges; there is a locking screw on the frame 4 to fix it in the required position. There is an additional scale on the measuring frame - vernier 3 . External dimensions are measured using lower jaws having flat working surfaces of small width. The upper jaws are used to measure internal dimensions. Depth ruler 5 designed for measuring the height of ledges, the depth of blind holes, etc.

Caliper ShTs-II with double-sided jaws (Fig. 1, b) is intended for external and internal measurements and marking work. Consists of the same main parts as ШЦ-I, but has an auxiliary microfeed frame 4 for precise frame movement 1 on the bar 5 . To do this, you must first fix the auxiliary frame 4 locking screw 3 , and then, rotating the nut 6 by microscrew 7 , move the measuring frame along the rod. As a rule, this feed is used to accurately set the size on a caliper when marking. The pointed jaws of the ShTs-II caliper are used for marking or measuring external dimensions in hard-to-reach places. The lower jaws for measuring internal dimensions have cylindrical working surfaces. The closed jaw size is usually 10 mm and determines the smallest internal dimension that can be measured with this caliper. For internal measurements, add the size of the jaws indicated on their side to the scale reading. ShTs-II type calipers have verniers with division values ​​of 0.1 and 0.05 mm and measurement limits of 0-160, 0-200, 0-250 mm.

Caliper ShTs-III does not have upper pointed jaws and a device for microfeeding the measuring frame. It is used for external and internal measurements using the same lower jaws as those of ShTs-II. Vernier divisions are 0.1 and 0.05 mm, measurement limits are from 0 to 2000 mm.

Vernier depth gauge(Fig. 2) is used to measure depths and protrusions. It consists of a base 1 , rods 6 with main millimeter scale, measuring frame 3 , locking screw 2 , micrometer feed devices 5 , locking screw 4 , nuts and screws 7 micrometric feed and vernier 8 .

Fig.2

Vernier depth gauges are produced with a vernier division value of 0.05 mm and measurement limits of 0-160, 0-200, 0-250, 0-315, 0-400 mm. The design of the depth gauge differs from a caliper in the absence of fixed jaws on the rod and the presence of a base instead 1 , which is a reference when measuring depth. The depth gauge shows the zero size when aligning the end of the rod (ruler) 6 and grounds 1 .

Fig.3

Shtangenreysmas used for marking, but it can also be used to measure the height of parts installed on the slab (Fig. 3). Gauge gauges have vernier divisions of 0.1 and 0.05 mm and a measurement limit of up to 2500 mm. They have a massive base 5 for installation on a stove. The rod is located perpendicular to the base 1 with millimeter scale. Movable frame 2 with vernier 3 has a holder 4 for installing a special measuring leg 6 for measuring height or marking leg 7 .

When marking vertical surfaces, the gauge with the size set according to the scale and vernier (it is recommended to use the microfeed of the frame) moves along the plate along the workpiece being marked. The tip of the marking leg marks a horizontal line on the surface of the workpiece.

READING DEVICE

The design of the reading device is based on a rod (measuring ruler) with a main scale printed on it with a division interval of 1 mm. Every fifth division of the bar scale is marked with an elongated stroke, and every tenth with a longer stroke with the corresponding number of centimeters.

A measuring frame moves freely along the rod, on the bevel of which (opposite the millimeter scale of the rod) there is an additional scale called a vernier. The vernier is used to count fractional fractions of a millimeter.

The measurement count in a vernier device is based on the difference in the division intervals of the main scale and additionally the vernier scale. Vernier has a small number of divisions n(10, 20 or 50 dash divisions). The zero line of the vernier acts as an arrow and allows you to read the size in millimeters on the main scale.

Vernier division price With equal to the division price of the main scale A=1 mm divided by the number of divisions on the vernier scale n :

.

Verniers with a division value of 0.1 are used; 0.05 mm and in rare cases 0.02 mm. Vernier scale division interval depends on the accepted modulus value , which is selected from the numbers 1; 2; 3; 4 or more. But we must keep in mind that as the module increases, the length of the additional vernier scale increases and the overall dimensions of the entire reading device increase. Vernier scale division interval taken as a multiple of the division interval of the main scale

,

Where - vernier module, characterizing the elongation of the vernier scale or the relationship between the values ​​of the intervals of the main scale and the vernier scale.

Vernier scale length

For example, take the price of vernier divisionWith =0.1 mm at modulus
, then the vernier scale division interval
mm. All subsequent vernier strokes are applied at the same interval. Due to the fact that the intervals of vernier divisions are smaller than on the main scale, the position of the vernier strokes gradually accumulates behind the strokes of the main scale, and the tenth stroke of the vernier coincides with the ninth stroke of the main scale (Fig. 4).

Fig.4

For the convenience of counting fractional fractions of a millimeter, vernier tools with a vernier scale module of 2 are often produced.

When determining the size of the part, proceed as follows. If the zero stroke of the additional vernier scale coincides with any stroke of the main scale, then the value of the measured quantity is counted only on the main scale in mm.

If the zero stroke of the vernier does not coincide with any stroke of the main scale, then the reading is obtained from two parts. An integer number in millimeters is taken from the main scale to the left of the zero line of the vernier scale and added to it are fractions of a millimeter obtained by multiplying the value of the vernier division by the serial number of the vernier scale line that coincides with the line of the main scale (Fig. 4, b,c).

Goal of the work.

Vernier caliper model and its main metrological characteristics. Method of measurement.

Control questions

Name the types of caliper tools.

Models of calipers, their design features and purpose.

How are whole and fractional fractions of millimeters counted in measurements? Vernier device.

For what purpose is the thickness of the jaws marked on some models of calipers?

What is a depth gauge used for?

What is the purpose of the height gauge?

Literature

Laboratory work No. 2

MEASUREMENT OF PARTS WITH MICROMETRIC INSTRUMENTS

Goal of the work

Study the device, measurement principle and metrological characteristics of micrometer instruments.

Measure the part with a smooth micrometer and give a conclusion about the suitability of the part.

MICROMETRIC INSTRUMENTS

Micrometric instruments are widely used means of measuring external and internal dimensions, groove depths and holes. The operating principle of these tools is based on the use of a screw-nut pair. A precise micrometric screw rotates in a stationary micro-nut. These instruments got their name from this node.

In accordance with GOST 6507-78, the following types of micrometers are produced:

MK – smooth for measuring external dimensions;

ML – sheet with a dial for measuring the thickness of sheets and tapes;

MT – pipe for measuring pipe wall thickness;

MZ – gear gauges for measuring the length of the common normal of gears;

MVM, MVT, MVP – micrometers with inserts for measuring various threads and parts made of soft materials;

MR, MRI – lever micrometers;

MV, MG, MN, MN2 – tabletop micrometers.

In addition to the listed types of micrometers, micrometric bore gauges (GOST 10-75 and GOST 17215-71) and micrometric depth gauges (GOST 7470-78 and GOST 15985-70) are produced.

Almost all manufactured micrometers have a division value of 0.01 mm. The exception is the MR, MP3 and MRI lever micrometers, which have a division value of 0.002 mm. The measurement ranges of smooth micrometers depend on the size of the staple and are: 0-25, 25-50, ..., 275-300, 300-400, 400-500, 500-600 mm

In Fig. 1, a, b The design and diagram of a smooth micrometer are shown. In the holes of the bracket 1 fixed measuring foot pressed on one side 2 , and on the other - the stem 5 with a hole that guides the micrometer screw 4 . Micrometer screw 4 screws into micro nut 7 , having cuts and external threads. A special adjusting nut is screwed onto this thread. 8 , which compresses the micronut 7 until the gap in the microscrew-micronut connection is completely selected. This device ensures precise axial movement of the screw relative to the micronut depending on its angle of rotation. In one revolution, the end of the screw moves in the axial direction by a distance equal to the thread pitch, i.e. by 0.5 mm. A drum is placed on the micrometer screw 6 , secured with an installation cap-nut 9 . A special safety mechanism is mounted in the cap-nut 12 , connecting the cap-nut 9 and a ratchet 10 , it is necessary to rotate the drum for it 6 when taking measurements. A safety ratchet mechanism, consisting of a ratchet wheel, a tooth and a spring, disconnects the ratchet if the force between the jaws exceeds 500-900 cN 10 from the installation cap 9 and drum 6 , and it begins to turn with a characteristic clicking sound. In this case, the micrometric screw 4 does not rotate. To secure the screw 4 in the required position, the micrometer is equipped with a locking screw 11 .

Fig.1

On the stem 5 micrometer scale marked 14 with divisions every 0.5 mm. For ease of reference, even strokes are placed above, and odd strokes are placed below the solid longitudinal line. 13 , which is used to measure the rotation angles of the drum. There is a circular scale on the conical end of the drum 15 , having 50 divisions. If we take into account that for one revolution of a drum with fifty divisions the end of the screw and the cut of the drum are moved by 0.5 mm, then turning the drum by one division will cause a movement of the end of the screw equal to 0.01 mm, i.e. graduation price on the drum is 0.01 mm.

When taking a reading, use the scales on the stem and drum. The cut of the drum is a longitudinal scale indicator and records readings with an accuracy of 0.5 mm. To these readings add a reading on the drum scale (Fig. 1, V).

Before measuring, check that the zero setting is correct. To do this, it is necessary to rotate the microscrew using the ratchet until the measuring surfaces of the heel and the screw come into contact or these surfaces come into contact with the setting standard 3 (Fig. 1, A).

Rotation by ratchet 10 continue until a characteristic clicking sound is heard. A correct installation is considered to be in which the end of the drum coincides with the leftmost stroke of the scale on the stem and the zero stroke of the circular scale of the drum coincides with the longitudinal line on the stem. If they do not coincide, it is necessary to secure the microscrew with a stopper 11 , unscrew the installation cap-nut half a turn 9 , turn the drum to the zero position, secure it with a cap-nut, and release the microscrew. After this, you should check again that the “zero setting” is correct.

Micrometric instruments also include a micrometric depth gauge and a micrometric bore gauge.

Micrometric depth gauge(Fig. 2, A) consists of a micrometer head 1 , pressed into the hole in the base 2 . The end of the microscrew of this head has a hole into which replaceable rods are inserted with split spring ends 3 with a spherical measuring surface. Replacement rods have four sizes: 25; 50; 75 and 100 mm. The dimensions between the ends of the rods are kept very precisely. The measuring surfaces in these devices are the outer end of the replaceable rod 3 and the lower supporting surface of the base 2 . When taking the countdown, you must remember that the main scale located on the stem has a countdown (from 25 mm to 0).

Fig.2

To adjust the depth gauge, the supporting surface of the base is pressed against the end of a special installation gauge (Fig. 2, b), which is placed on the surface plate. The microscrew with the insert is brought into contact with the plate using a ratchet, secured with a stopper, and then the same operations are performed as when setting the micrometer to zero.

Measuring the depth of holes, ledges, recesses, etc. perform as follows. The supporting surface of the base of the micrometric depth gauge is installed on the base surface of the part, relative to which the size is measured. With one hand, press the base against the part, and with the other, rotate the micrometer head drum by the ratchet until the rod touches the surface to be measured and the ratchet clicks. Then fix the microscrew with a stopper and take a reading from the head scales. Micrometric depth gauges have measurement limits from 0 to 150 mm and a division value of 0.01 mm.

Micrometric bore gauges designed for measuring the internal dimensions of products in the range from 50 to 6000 mm.

They consist of a micrometer head (Fig. 3, A), replaceable extension cords (Fig. 3, b) and measuring tip (Fig. 3, V).

The micrometer head of the bore gauge is slightly different from the head of the micrometer and depth gauge and does not have a ratchet. Into the stem 6 micrometer head has a measuring tip pressed onto one side 7 , and on the other there is a microscrew screwed in 5 which is connected to the drum 4 nut 2 and locknut 1 . The measuring tip of the microscrew protrudes outwards 5 .

The gap in the screw-nut connection is selected using an adjusting nut 3 , screwed onto a split micro-nut with an external conical thread. The set size is fixed with a locking screw. 9 . To extend the measuring range into the threaded hole of the coupling 8 extensions are screwed in (Fig. 3, b) and measuring tip (Fig. 3, V).

Fig.3

The extension is a rod with spherical measuring surfaces, having a precise size in the axial direction. The rod does not protrude beyond the body, which is threaded at both ends. A spring located inside the housing creates a forceful connection between the rods when screwing the extension with a micrometer head. Another extension can be screwed onto the free end of the extension, etc., until a bore gauge with the required measurement limit is obtained. The measuring tip is screwed into the last extension. During the measurement process, the measuring tip of the microscrew and the measuring tip of the extension come into contact with the workpiece. When using a bore gauge with multiple extensions, remember that the extensions should be connected in descending order of their sizes and the micrometer head should be connected to the longest of them.

The micrometric bore gauge assembled with the measuring tip is set to zero using a 75 mm adjusting bracket (Fig. 3, G). If the zero adjustment is unsatisfactory, loosen the lock nut by half a turn. 1 , turn the drum until the zero mark coincides with the longitudinal line of the stem, tighten the lock nut 1 and release the screw 9 . Then check the correct installation. After setting the bore gauge to zero, screw it with extensions to obtain the required size and begin measuring.

Measuring internal dimensions with a bore gauge is carried out as follows. Insert the tool into the space between the measuring surfaces (for example, into a hole). Place one measuring tip of the bore gauge on the surface and rotate the head drum until the second measuring tip touches the opposite surface. During the measurement process, it is necessary not only to rotate the drum, but also to rock the assembled bore gauge, measuring the diameter in a plane perpendicular to the axis of the hole and in the plane of the axial section. The largest size in the first position and the smallest size in the second position must match.

Goal of the work.

Design and metrological characteristics of a smooth micrometer. How are micrometer readings read when taking measurements?

Sketch of the part with actual dimensions.

Assessing the suitability of parts.

Control questions

Types of micrometric instruments.

Micrometer device.

How to take micrometer readings? Setting the micrometer to zero.

What is the ratchet used for?

Micrometric depth gauge device.

Micrometric bore gauge device.

Literature

Markov N.N., Ganevsky G.M. Design, calculation and operation of control and measuring instruments and instruments. – M.: Mashinostroenie, 1993.

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mechanical Engineering, 1987.

Vasiliev A.S. Fundamentals of metrology and technical measurements. –M.: Mechanical Engineering, 1980.

Laboratory work No. 3

MEASUREMENT OF PARTS WITH INDICATOR DEVICES

Goal of the work

Study the device, principle of operation and metrological characteristics of a dial indicator and indicator devices.

Gain skills in working independently with instruments by measuring parts with an indicator bracket and an indicator bore gauge.

MEASURING HEADS WITH GEAR MECHANISM
OR DIAL TYPE INDICATORS

Measuring heads are reading devices that convert small movements of the measuring rod into large movements of the pointer along the scale (dial indicators, lever-gear indicators, multi-turn indicators, lever-gear heads).

Fig.1. Dial indicator ICH-10

Heads cannot be used as a separate measuring device and for measurement they are installed on stands, tripods or equipped with instruments and measuring devices.

Measuring heads are designed primarily for relative measurements. If the dimensions of the parts are smaller than the range of readings of the device, then measurements can be made using the absolute method.

The most common gear-driven measuring heads are dial indicators.

The operating principle of the dial indicator is as follows (Fig. 1):

Measuring rod1 moves in precise guide bushings. A gear rack is cut on the rod, which meshes with the tribe4 (=16). In instrument making, a tribe is a gear of a small module with the number of teeth ≤18. On the same axis with the tribe4 gear installed3 (=100), which transmits rotation to the tribune2 (=10).On one axis there is a tribe2 big arrow fixed8 , which moves along the scale7 , counting tenths and hundredths of a millimeter of movement of the measuring rod with the tip12 .

When moving the measuring rod in the reading range, the large arrow makes several revolutions, so an additional arrow is installed in the design of the dial indicator 5 on the axis of the tribe 4 and wheels 3 . When moving the measuring rod by 1 mm, the large arrow 8 makes one revolution, and the arrow 5 moves one division of the small scale 6.

The number of divisions of the small scale determines the range of readings of dial indicators in mm.

With the tribe 2 the second gear is engaged9 (=100). A spiral spring is attached to the axis of this wheel at one end10 , the second end of which is fixed in the indicator body. The spring ensures that the gears operate in single-profile gearing mode, thereby reducing the influence of gaps in gear pairs on the measurement error.

The dial indicator has a helical spring 11 , one end of which is mounted on the measuring rod, and the other on the indicator body. This spring creates a measuring force on the rod R=150±60 cN.

All dial indicators have a large scale division value of 0.01 mm. Most indicators have an indication range of 2 mm (ICh-2), 5 mm (ICh-5), 10 mm (ICh-10), and indicators with a reading range of 25 mm (ICh-25) and 50 mm (ICh-50) are less commonly produced.

The measurement error with a dial indicator depends on the movement of the measuring rod. So, in the reading range of 1÷2 mm, the measurement error is in the range of 10÷15 microns, and in the range of 5÷10 mm, the error is in the range of 18÷22 microns.

MEASUREMENT WITH A CLOCK TYPE INDICATOR

Indicator 1 mounted on indicator stand 2 screw 3 (Fig. 2, A). Loosening the screw 5 , lower the indicator until the tip touches the measuring table 4 , after which we lower it an additional 1…2 mm (we create a “tension”). We fix this position by tightening the screw 5 . Turn by the rim 6 dial indicator until the “0” scale aligns with the large arrow. We record the indicator readings (for example, 1.00 mm with a tension of 1 mm).

Without changing the position of the indicator body, lift the measuring tip and place the part on the measuring table. Let go of the rod (Fig. 2, b) and record the indicator reading (for example, 2.15 mm) The difference between the indicator reading during measurement and during adjustment gives the value of the movement of the rod relative to the stage during measurement
(b=2.15-1.00=1.15 mm). This will be the size b. In this way, measurements are made using the absolute method.

In cases where the size of the part is larger than the range of instrument readings, the relative method is used. To do this, we determine the approximate size of the part (for example, about 42 mm), assemble a block of plane-parallel gauge blocks (also 42 mm), set the device to “0” relative to plane-parallel gauge blocks (PCMD) (Fig. 2, V) is similar to the setting for the absolute method. We record the indicator readings (for example, 1.00 mm), remove the PCMD block and install the part. We record the indicator readings (for example, 2.15 mm). We determine the movement of the rod when measuring relative to the PCMD ( = 2.15-1.00 = 1.15 mm) (Fig. 2, G). Actual part size d=PCMD+ (for example, d=42+1.15=43.15 mm). When adding, it is necessary to take into account the sign of the relative movement: if the size of the part turns out to be smaller than the PCMD block, then  will turn out to be negative. For example, if the indicator showed 1.00 mm when setting, and 0.42 mm when measuring, then
 =0.42-1.00=-0.58 mm.

Fig.2. Indicator measurement

The relative method is also used in cases where it is necessary to reduce the measurement error, i.e. reduce the measuring movement in order to get rid of the accumulating error of the device.

INDICATOR BRACKET

The bracket body (Fig. 3) contains a dial indicator and a movable heel 2 and replaceable adjustable heel 3 .

Movable heel 2 is constantly pressed towards the product by the measuring rod of the indicator and a special spring. Adjustable heel 3 with the screw released 4 and the cap removed can move up to 50 mm. The measurement ranges of indicator brackets are: 0÷50 mm, 50÷100 mm, 100÷200 mm, ..., 600÷700 mm, 700÷ 850 mm, 850÷1000 mm.

The main error of the device (depending on the standard size of the bracket) varies from 5 to 20 microns.

MEASUREMENT WITH INDICATOR BRACKET

INDICATOR NUTROMETER

Indicator bore gauges are designed to measure the internal dimensions and diameters of holes using the relative method.

The most commonly used bore gauges are standard sizes from the following range of measurement ranges: 6-10; 10-18; 18-50; 50-100; 100-160; 160-250; 250-450; 450-700; 700-1000 mm.

Let's look at the design and operation of indicator bore gauges using the example of bore gauge model NI-100 (Fig. 4).

An insert sleeve is inserted into the body of the bore gauge 2 , into which a replaceable fixed measuring rod is screwed on one side 3 , and on the other side there is a movable measuring rod 4, acting on a two-arm lever 5 , mounted on an axis 6 .

There is a rod inside the body 8 , pressed to the lever 5 dial indicator measuring rod and coil spring 10 . The latter create a measuring force ranging from 200 to 500 cN.

Fig.4.

Within the measurement range, bore gauges are equipped with a set of replaceable measuring rods. The position of the fixed measuring rod after adjustment is fixed with a nut 7 . Movable measuring rod 4 under the influence of the measuring force is in the extreme initial position. Centering bridge 12 , pressed by two springs 11 to the surface of the controlled hole, ensures alignment of the measurement line with the diameter of the hole.

The bore gauge is adjusted to the required nominal size using PCMD blocks with sidewalls installed in clamp holders, or using certified rings. The error of bore gauges is usually normalized to 1.5÷2.5 division values ​​of the reading head.

MEASUREMENT WITH AN INDICATOR NUTROMETER.

Calculate the nominal dimensions of the PMDC based on the nominal size of the hole of the part being measured. Prepare an installation kit (Fig. 5) from a PMKD block and two side panels 2 and clamps 1 . From the set of replacement adjustable rods (attached to the bore gauge), select a rod with a size range that contains the nominal size of the hole being measured. Screw the replaceable adjustable rod 3 into the bore gauge body 5 .

Insert the bore gauge with measuring rods into the installation kit between the sides and create a tension of 1÷2 mm for the dial indicator (Fig. 5).

By rocking the inside gauge away from you, turning it left and right around the vertical axis, you need to set the axis of the measuring rods (measurement axis) to a position that coincides with the shortest distance between the measuring surfaces of the sides. This position will be shown by the large indicator hand when it reaches the farthest (as it moves clockwise) division of the scale and begins to move back. Having given the correct position to the indicator, you need to tighten the lock nut 4 replaceable measuring rod 3 and set the zero division of the indicator scale until it coincides with the large arrow.

Fig.5. Indicator bore gauge when setting up ( A) (centering bridge not shown)
and when measuring ( b)

After setting the bore gauge to “0”, you can begin to measure deviations in the size of the part’s hole from the nominal value.

We insert the measuring head of the bore gauge into the hole of the part being measured. Spring-loaded centering bridge 8 orients the measuring axis of the bore gauge strictly in the diametrical plane of the hole being measured (Fig. 5, b).

By rocking the inside gauge in a vertical plane, we determine the indicator readings at the extreme right position of the large arrow.

When determining the actual deviations of hole sizes from the nominal value, they are guided by the following rule: the deviation is accepted with a minus sign (“-”) if the large indicator arrow deviates from the “0” scale division clockwise, and the counterclockwise deviation shows an increase in the diameter of the hole about the nominal size and the actual deviation is taken with a plus sign (“+”).

The value of the actual deviation is calculated by multiplying the number of divisions of the indicator scale (indicated by a large arrow from “0”) by the division value of 0.01 mm.

The actual size of the hole diameter will be equal to the nominal hole diameter plus (“+”) or minus (“-”) the actual deviation.

Goal of the work.

Types of indicator instruments used in work and their metrological characteristics. Method of measurement.

Sketches of measured parts with actual dimensions.

Assessing the suitability of parts.

Control questions

Design of dial indicators.

Metrological characteristics of indicator devices. Method of measurement.

How are readings read when measuring with indicator devices?

Indicator bracket. Setting up the measuring bracket.

What is the name of the value that the device records?

Indicator bore gauge. Setting up the bore gauge.

Measurement with a bore gauge.

Literature

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mechanical Engineering, 1987.

Vasiliev A.S. Fundamentals of metrology and technical measurements. –M.: Mechanical Engineering, 1980.

Laboratory work No. 4

MEASUREMENT OF GAUGE-PLUG

Goal of the work

Study the design, principle of operation and metrological characteristics of spring measuring heads IGP - microcators (GOST 6933-81).

Gain skills in independent work with instruments for precise measurements using the relative method.

Learn to build tolerance charts for calibers.

Measure the plug gauge using the IGP installed on the C-1 or C-2 stand.

Determine the suitability of the plug gauge.

SPRING MICROCATOR MEASURING HEADS

These devices are precision measuring instruments with mechanical conversion of small movements of the measuring tip into large movements of the pointer relative to the instrument scale. This group of devices is called “spring”, since a spring made of a thin bronze ribbon, curled from the middle in different directions, is used as a sensitive element.

14

A

b

Fig.1.

Ribbon spring 2 fixed on a square 1 and cantilever flat spring 4 , mounted on a rigid ledge (Fig. 1, A). Changing the position of the spring 4 , use screws to adjust the tension of the ribbon spring. Measuring rod 7 suspended on membranes 6 and rigidly connected to the square 1 . Moving the measuring rod causes the square to rotate around the point " A» and spring extension 2 . The measuring force is generated by a conical spring 5 . A quartz arrow is glued to the middle part of the bronze twisted band 3 . Spring stretch 2 causes the arrow to turn 3 relative to the scale.

Spring measuring heads are used for high-precision relative measurements of product dimensions, as well as deviations in the shape and location of surfaces. The accuracy of controlled products can be from 2 th until 6 th quality

For measurements, instruments are mounted in racks (Fig. 1, b) type S-1 and S-2 or in special devices for the tube 7 diameter 28 mm. When adjusting to the zero position on the block of gauge blocks, the microfeed of the rack table is used.

During transport, the measuring rod is clamped by turning the clamp into the base of the tube.

Spring measuring heads are produced in the following modifications: 01IGP; 02IGP; 05IGP; 1IGP; 2IGP; 5IGP; 10IGP and have a scale division value of the device, respectively: 0.0001; 0.0002; 0.0005; 0.001; 0.002; 0.005; and 0.01 mm.

PROCEDURE FOR PERFORMANCE OF THE WORK

1. Study the device, measurement principle and metrological characteristics of the microcator on the C-1 or C-2 rack. Write down in the report the main metrological characteristics of the device (scale division of the device, measurement range on the device scale).

2. Obtain a plug gauge for measurements from the teacher.

3. Based on the markings on the gauge, determine which hole it is intended for checking (nominal diameter of the hole, deviation of the tolerance field of the hole and quality).

4. According to GOST-25347-82 ( ST SEV 144-75) determine the maximum deviations of the hole size, and then construct a diagram of the location of the hole tolerance field (Fig. 2)

5. According to GOST-24853-81 (ST SEV 157-75) for a given plug gauge, find the tolerances, maximum deviations and construct a diagram of the location of the tolerance zone for the gauge.

7. Select according to the diagram the size relative to which the device is adjusted to zero using gauge blocks.

8. From a set of plane-parallel end measures of length, take a measure or several measures to compose a block, the size of which is equal to the size selected according to the diagram.

9. Wash the end gauges and the instrument table with gasoline and wipe with a soft cloth. Rub the rubbed measures together and onto the table.

10. Set the device to zero. For this (Fig. 1, b), releasing the locking screw 2 table 3 by rotating the micrometer nut 1 , the object table with the ground gauge block is lowered to the lower position. Then, releasing the locking screw 10 bracket 9 , by rotating the ring-nut 11 bracket lowers 9 with a microcator until the tip touches the surface of the gauge block or block. The moment of contact is judged by the beginning of the movement of the arrow. In this position the bracket 9 secured with a screw 10 .

Attention!!!

The bracket should be lowered smoothly, without allowing the tip to hit the gauge block! Do not touch the adjustment screws 14 table, as this will disturb the installation
table

The final zeroing of the device is carried out using a nut 1 ; table 3 rises until the microcator needle aligns with the zero division of the scale. In this position the table is locked with a screw 2 and the zero setting is checked by raising and lowering the measuring tip 4 using a locking device 5 .

Precise adjustment of the device to zero is carried out using a screw. 8 , which can shift the scale relative to the arrow within ±5 divisions.

11. By pressing the lock, lift the measuring tip and remove the gauge block or block (do not disassemble the gauge block).

12. Place a plug gauge on the object table and, pressing the gauge tightly with two fingers to the table, slowly roll it under the tip and watch the movement of the arrow. The greatest deviation of the pointer in “plus” or “minus” on the scale determines the actual deviation of the size of the plug in a given section relative to the adjustment size of the end block or block. To ensure that the resulting deviation is correct, measurements are repeated two to three times. Each time there should be clear repeatability of the instrument readings. Such measurements should be carried out in three sections along the length of the plug and in two planes (Fig. 3). Enter the measurement results into the report table.

13. Determine the actual dimensions of the plug in the controlled sections, which are equal to the algebraic sum of the size of the gauge block or block and the instrument reading. Enter the result into the report table.

14. Check the zero reading of the device. To do this, by pressing the lock, the gauge is removed from the table and the gauge block or block is again installed under the measuring tip. Raising and lowering the tip two or three times, make sure the arrow is set to zero.

The deviation of the arrow from the zero line should not exceed half a division of the instrument scale; if the deviation is greater, then the instrument must be adjusted to zero and the caliber measurements must be repeated.

The obtained data based on the measurement results are entered into the report.

1. Purpose of the work.

2. The name of the measuring device and its main metrological characteristics (measurement limits on the device scale, scale division value).

3. The type of caliber that is being controlled and its marking.

4. Scheme of tolerance fields for the product and caliber with the setting of maximum dimensions in mm and deviations in microns (Fig. 2).

Fig.2

5. Select a gauge block or gauge block to zero the instrument.

6. Scheme of caliber measurements (Fig. 3) and measurement results with filling out the table.

Fig.3.

Measurement results

Gauge block dimensions
or block

Passage side

R-PR

Non-passable side

R-NOT

Sections

Sections

Indications
device in microns

Plane

II-II

Actual caliber dimensions in mm

Plane

II-II

7. Conclusion on the suitability of the caliber.

Control questions

Design, principle of operation and metrological characteristics of spring microcator heads.

What are the areas of application for microcators?

Measuring method and setting up a microcator for measurements.

How are the tolerance fields of smooth limit plug gauges and clamp gauges located on the diagrams?

Why is it necessary to use microkator-type measuring instruments to assess the suitability of a plug gauge?

How is a conclusion about the suitability of a caliber formulated?

Literature

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mechanical Engineering, 1987.

Vasiliev A.S. Fundamentals of metrology and technical measurements. –M.: Mechanical Engineering, 1980.

Laboratory work No. 5

SURFACE ROUGHNESS

Goal of the work

Study the basic parameters of roughness and the designation of roughness in the drawings.

Get acquainted with measurement methods and instruments for assessing the surface roughness of machine parts.

BASIC CONCEPTS

Surface roughness is a set of surface irregularities with relatively small steps, identified using the base length (GOST 25142-82).

Base length - the length of the baseline used to highlight irregularities that characterize the surface roughness.

Numerical values ​​of surface roughness are determined from a single base, which is taken to be the middle line of the profilem , i.e., a base line in the shape of a nominal profile and drawn so that within the base length the standard deviation of the profile to this line is minimal. Evaluation length - length at which the actual profile is evaluated. It may contain one or more base lengths (Fig. 1).

Rice. 1. Profilogram and main parameters of surface roughness

NORMALIZED ROUGHNESS PARAMETERS

Roughness parameters in the direction of the roughness height. Arithmetic mean deviation of the profile
- arithmetic mean of the absolute values ​​of profile deviations within the base length:

or approximately
,

Where - base length; - number of selected profile points on the base length;y - the distance between any profile point and the center line. Standardized from 0.008 to 100 microns.

Height of profile irregularities at ten points
- the sum of the average absolute values ​​of the heights of the five largest protrusions of the profile and the depths of the five largest depressions of the profile within the base length:

,

Where
- heighti -th largest protrusion of the profile;
- depthi th largest depression in the profile.

Maximum height of profile irregularities
- the distance between the line of profile protrusions and the line of profile depressions within the base length . Standardized from 0.025 to 100 microns.

Roughness parameters in the direction of the profile length. Average pitch of profile irregularities
- arithmetic mean pitch of profile irregularities within the base length:

,

WhereP - number of steps within base length ;
- pitch of profile irregularities equal to the length of a segment of the center line intersecting the profile at three adjacent points and limited by two extreme points. Standardized from 0.002 to 12.5 mm.

Average pitch of local profile projections - arithmetic mean pitch of local profile protrusions within the base length:

,

Where P - number of steps of irregularities along the vertices within the base length ; - step of profile irregularities along the tops of the protrusions. Standardized from 0.002 to 12.5 mm.

Numerical values ​​of roughness parameters
,
,
,
And are given in GOST 2789-73, and Appendix 1 shows the values ​​of the base length , recommended for parameters
,
,
.

Roughness parameters associated with the shape of profile irregularities. Profile reference length - sum of segment lengths , cut off at a given levelR % in the profile material by a line equidistant to the center linem - m and within the base length (Fig. 1).

- ratio of the profile reference length to the base length:

.

Reference profile length determined at the level of the profile sectionR, those. at a given distance between the line of profile protrusions and a line intersecting the profile equidistant to the line of profile protrusions. The line of profile protrusions is a line equidistant to the center line, passing through the highest point of the profile within the base length. Profile section level valueR counted along the line of protrusions and selected from the row: 5; 10; 15; 20; 25; thirty; 40; 50; 60; 70; 80; 90% of
. Relative reference length of profile appointed from row 10; 15; 20; 25; thirty; 40; 50; 60; 70; 80; 90%.

The Interstate Council for Standardization, Metrology and Certification has made changes to GOST 2.309-73 “Designations of surface roughness” and set a deadline for introducing changes - from January 1, 2005.

The changes concern both the designation of surface roughness and the rules for applying them to the drawing.

The interstate standard GOST 2.309 fully complies with the ISO 1302 standard.

1. Designation of surface roughness

Surface roughness is indicated in the drawing for all product surfaces made according to this drawing, regardless of the methods of their formation, except for surfaces whose roughness is not determined by the design requirements.

Fig.2.

The structure of the surface roughness designation is shown in Fig. 2. When a sign is used without specifying the parameter and processing method, it is depicted without a shelf.

To indicate surface roughness, one of the signs shown in Fig. 3 is used. Height should be approximately equal to the height of the dimensional numbers used in the drawing. Height
equal to (1.5…5) . The thickness of the character lines should be approximately equal to half the thickness of the solid main line used in the drawing. To designate surface roughness, the processing method of which is not specified by the designer, use the sign according to Fig. 3,A . To designate surface roughness, which should be formed only by removing a layer of material, use the sign according to Fig. 3,b . To designate the surface roughness, which must be formed without removing a layer of material, use the sign according to Fig. 3,V indicating the value of the roughness parameter.

The surfaces of a part made of a material of a certain profile and size, which are not subject to additional processing according to this drawing, must be marked with the sign according to Fig. 3, V without specifying roughness parameters. The condition of the surface marked with such a sign must comply with the requirements established by the relevant standard or technical specifications, or other document, and this document must be referenced, for example, in the form of an indication of the material range in column 3 of the main inscription of the drawing according to GOST 2.104-68.

Fig.3.

The value of the roughness parameter according to GOST 2789-73 is indicated in the roughness designation after the corresponding symbol, for example: 0,4;
6,3;
0,63; 70; 0,032; 50. In the example 70 indicates the relative reference length of the profile =70% at profile section level =50%. . The thickness of the sign lines should be approximately equal to half the thickness of the solid main line.

The type of surface treatment is indicated in the roughness designation only in cases where it is the only one applicable to obtain the required surface quality (Fig. 5).

It is allowed to use a simplified designation of surface roughness with its explanation in the technical requirements of the drawing according to the example shown in Fig. 6.

2. Rules for applying roughness designations
surfaces in drawings

Indications of surface roughness in the product image are placed on contour lines, extension lines (as close as possible to the dimension line) or on the shelves of leader lines. If there is not enough space, it is allowed to place the roughness designation on the dimension lines or on their extensions, on the shape tolerance frame, and also to break the extension line (Fig. 7).

Fig.7

Fig.8

Fig.9

Indications of the surface roughness in which the sign has a flange are positioned relative to the main inscription of the drawing as shown in Figs. 8 and 9. When the surface is located in a shaded area, the designation is applied only on the flange of the leader line.

When specifying the same roughness for all surfaces of the product, the roughness designation is placed in the upper right corner of the drawing and is not applied to the image (Fig. 10). The dimensions and thickness of the sign lines in the roughness designation placed in the upper right corner of the drawing should be approximately 1.5 times larger than in the designations printed on the image. a-c), and for globoid worms and wheels associated with them - on the line of the calculated circle (Fig. 14, G).

The designation of the surface roughness of the thread profile is applied according to the general rules when depicting the profile (Fig. 15, A), or conditionally on the extension line to indicate the thread size (Fig. 15, b - d), on the dimension line or on its extension (Fig. 15, e).

If the roughness of the surfaces forming the contour must be the same, the roughness designation is applied once in accordance with Fig. 16. Diameter of auxiliary sign- 4…5 mm. In the designation of the same roughness of surfaces that smoothly transition into one another, the sign

Fig.16

Fig.17

Fig.18

In this case, the letter designation of the surface is applied on the shelf of a leader line drawn from a thick dash-dotted line, which is used to outline the surface at a distance of 0.8...1.0 mm from the contour line (Fig. 18).

MEASUREMENT AND CONTROL OF SURFACE ROUGHNESS

Certification of surface roughness is carried out using two types of control: qualitative and quantitative.

Qualitative control of surface roughness parameters is carried out by comparison with samples or reference parts visually or by touch. GOST 9378-75 establishes roughness samples obtained by mechanical processing, taking positive impressions by electroforming or coating plastic impressions. Sets or individual specimens have straight, arced, or intersecting arcuate arrangements of surface irregularities. Each sample shows the parameter value
(in microns) and type of sample processing. To increase accuracy, probes and comparison microscopes are used.

Quantitative control of roughness parameters is carried out using non-contact and contact measuring instruments.

To quantify surface roughness using a non-contact method, two methods are used - increasing them using an optical system or using the reflectivity of the treated surface.

Devices based on the assessment of surface irregularities while magnifying them using an optical system are “light section devices.” Instruments based on reflectivity are microinterferometers.

The principle of operation of light section devices is to obtain an enlarged image of the profile of the surface being measured using rays directed obliquely to this surface, and to measure the height of irregularities in the resulting image. The most common is a double microscope of the MIS-11 type, which allows you to determine three roughness parameters with the fact that many of their functional units coincide. These devices are intended primarily for laboratory use. The domestic industry produces several models of devices (201, 202, 252) based on the inductive method of converting needle vibrations into voltage fluctuations.

A profilograph is a device for recording the values ​​of surface roughness in a section normal to it in the form of a profilogram, the processing of which determines all the parameters characterizing the roughness and waviness of the surface.

A profilometer is a device for measuring surface irregularities in a section normal to it and presenting the measurement results on the instrument scale in the form of the value of one of the parameters used to evaluate these irregularities. Most profilometers evaluate surface irregularities using the parameter
and are used as workshop instruments. Roughness assessment by parameter
associated with signal processing difficulties.

Drawing of the profile of surface irregularities with the main parameters.

Estimation of roughness parameters for a given profile.

Instruments for assessing surface roughness on machine parts.

An example of roughness designation on a part drawing.

Control questions

What parameters are used to evaluate surface roughness?

What and how is surface roughness controlled?

What roughness parameter is measured by the MIS-11 device?

How is roughness indicated in drawings?

Why is low roughness achieved on critical machine parts?

Literature

Markov N.N., Ganevsky G.M. Design, calculation and operation of control and measuring instruments and instruments. – M.: Mashinostroenie, 1993.

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mechanical Engineering, 1987.

Vasiliev A.S. Fundamentals of metrology and technical measurements. –M.: Mechanical Engineering, 1980.

Â. Í. KAKNA, T. Í. GAMAN, Å. Â. TASSENKO, Å. À. CLASSIC MANAGEMENT, SYSTEM AND SYSTEM. REPORT Under the general editorship of V. N. Kainova ON THE OUTDOOR The State of the World about the world, about the world, about the world formalization of the world "SPA" SBK 30.10.73 K 12 Kaynova V.N., G Rebneva T. N., Teslenko E. V., Kulikova E. A. K 12 Metrology, standardization and certification: Workshop: Textbook / Ed. V. N. Kainovoy. - St. Petersburg: Lan Publishing House, 2015. - 368 pp.: ill. - (Textbooks for universities. Special literature). ISBN 9785811418329 The textbook contains theoretical and reference & methodological material on the standardization of geometric characteristics of products, as well as on the selection of measuring instruments and processing of the results of single and multiple measurements performed by direct and indirect methods. Variants of tasks have been developed that are used when performing practical classes and independent work in the discipline “Metrology, standardization and certification”. Intended for students of higher educational institutions studying in technical areas of training bachelors, masters and certified specialists. It may be useful for engineering and technical services of enterprises and organizations involved in the development and production of products in the field of mechanical engineering. BBK 30.10ya73 Reviewers: F. F. REPIN - Candidate of Technical Sciences, Professor of the Department of “Technology of Structural Materials and Mechanical Repair” of the Volga State Academy of Water Transport; P. M. KOROLEV - Candidate of Technical Sciences, Deputy. Chief Technologist of JSC NAZ "SOKOL". Cover by E. A. VLASOV Protected by Russian copyright law. Reproduction of the entire book or any part thereof is prohibited without written permission from the publisher. Any attempts to violate the law will be prosecuted. © Publishing house “La; н", 2015 © Team of authors, 2015 © Publishing house "Lan", artistic design, 2015 PREFACE The discipline "Metrology, standardization and certification" refers to the basic part of the professional cycle of full-time and part-time education for students of higher educational institutions studying in technical areas of training bachelors, masters and graduates. This textbook was developed for the first time in the form of a workshop; previous editions contained theoretical material and reference data. The authors of the manual have extensive experience in studying issues of standardization and control of the accuracy of geometric parameters, in matters of standardization in the field of preparation of design and technological documentation. Considering that modern curricula pay significant attention to students performing independent and practical work, the need arose to create an educational manual in the form of a workshop. The manual on all topics discussed briefly contains the theoretical part, variants of tasks and examples of their solutions. The manual consists of five chapters and appendices, which contain reference tables from the standards necessary to complete the tasks. T. N. Grebneva prepared the first chapter, sections on keyed and spline connections from the fourth chapter. The second and third chapters, as well as the section on the choice of means 4 Preface measurements from the fifth chapter were compiled by E. V. Teslenko. E. A. Kulikova developed a section on normalizing metric thread parameters from the fourth chapter and a section from the fifth chapter on calculating measurement errors. Sections of the fifth chapter on the fundamentals of probability theory, mathematical statistics and processing of measurement results were compiled by V. N. Kaynova. The general editing of the manual was carried out by Associate Professor, Candidate of Technical Sciences Valentina Nikolaevna Kaynova. The authors express deep gratitude for valuable suggestions and comments on improving the content of the textbook to the candidate of technical sciences, professor F. F. Repin and the chief technologist, candidate of technical sciences, associate professor of JSC NAZ "Sokol" P. M. Korolev. Exact science is unthinkable without measure. D.I. Mendeleev The further unreliability is discovered from the design board, the more expensive it is. A. A. Tupolev INTRODUCTION Design documentation determines the design quality of products. It is the main type of documents that are used for designing technological processes of processing and assembly, control and measurement operations, as well as when performing certification work. When developing design documentation, it is necessary to comply with the requirements of current standards. Accuracy significantly affects the quality of products, the labor intensity of their production, and, consequently, the cost. The purpose of this textbook is to help students solve these problems. The manual consists of five chapters and appendices, which contain reference tables from the standards necessary to complete the tasks. The first chapter provides general concepts about the tolerance system for smooth cylindrical joints (ESDC), as well as recommendations and examples for the selection and calculation of tolerances and fits, and methods for calculating dimensional chains. The second chapter is devoted to the issues of surface roughness, the accuracy of the shape and location of the surfaces of machine parts, and also contains recommendations for calculating the numerical values ​​of geometric tolerances and indicating them on the drawings. The third chapter examines connections with rolling bearings and provides recommendations for choosing fits and drawing up drawings. 6 Introduction Chapter Four contains information on parallel keys, straight splines, threaded connections and spur gears. The fifth chapter covers issues of metrological support for mechanical engineering production: analysis of measurement errors, recommendations for the selection of measuring instruments, fundamentals of probability theory and mathematical statistics, specific situations are considered. CHAPTER 1 STANDARDING THE ACCURACY OF SMOOTH CYLINDRICAL CONNECTIONS 1.1. ESDP. TOLERANCES AND FITMENTS FOR SMOOTH JOINTS 1.1.1. TERMS AND DEFINITIONS ACCORDING TO GOST 25346-89 THEORETICAL PART FOR PRACTICAL LESSON 1.1 Standardization of the accuracy of linear dimensions is carried out by the standards of the Unified System of Tolerances and Landings (USDP). The basic standard of this system is GOST 25346-89 “ONV. Unified system of admissions and landings. General provisions, series of tolerances and main deviations.” Size - the numerical value of a linear quantity in the selected units of measurement. It is customary to divide dimensions into free and mating, male (shafts) and female (holes). Hole is a term conventionally used to designate the internal elements of parts, including non-cylindrical elements. Shaft is a term conventionally used to designate the external elements of parts, including non-cylindrical elements. All shaft parameters are indicated in lowercase letters of the Latin alphabet, and all hole parameters are indicated in uppercase letters. The size can be real, nominal or limiting (largest or smallest). Actual size is the size of an element established by measurement with an acceptable error. Limit dimensions - two maximum permissible dimensions of an element (the largest and the smallest), between which the actual size of a suitable part should be: Dmax, Dmin - the largest and smallest limiting dimensions of the hole, respectively; dmax, dmin - the largest and smallest maximum shaft dimensions, respectively. Nominal size is the size relative to which deviations are determined. The value of the nominal size is determined by engineering calculations of the part for strength, rigidity, bending, etc. , taking into account the safety factor (equal to 2, 3 or more), with its further rounding according to the series of normal linear dimensions in accordance with GOST 6636-69: d - nominal shaft diameter; D is the nominal diameter of the hole. The nominal size serves as the starting point for measuring deviations - actual or limiting (upper and lower). All nominal sizes in the ESDP system are divided into a number of intervals, . Deviation is the algebraic difference between the size (actual, limit) and the corresponding nominal size. Limit deviation (upper or lower) - the algebraic difference between the limit and the corresponding nominal dimensions (Fig. 1.1): E, e - actual deviations of the hole and shaft, respectively; ES, es - upper limit deviations of the hole and shaft, respectively; EI, ei are the lower limit deviations of the hole and shaft, respectively. ES = Dmax – D; es = dmax – d; EI = Dmin – D; (1.1) ei = dmin – d. (1.2) From here, the maximum dimensions can be determined as the algebraic sum of the nominal size and the corresponding maximum deviation using the following formulas: Chapter 1. Standardization of the accuracy of smooth cylindrical joints 9 Fig. 1.1 Limit dimensions and deviations: a, b - shafts; c - holes. Dmax = D + ES; dmax = d + es; Dmin = D + EI; (1.3) dmin = d + ei. (1.4) The tolerance of the hole and shaft (T) can be represented as the difference in the maximum dimensions or as the algebraic difference in the maximum deviations: TD = Dmax – Dmin = ES – EI; (1.5) Td = dmax – dmin = es – ei. (1.6) The dependence of the tolerance on the nominal size is expressed through the tolerance unit, which for sizes up to 500 mm is denoted by the letter i (µm), and for sizes over 500 mm - I (µm). It is a characteristic of accuracy (a function of the nominal size). The rounded values ​​of the tolerance unit depending on the nominal size are presented in Table 1.1. In accordance with GOST 25346-89, a standard tolerance (IT) is any of the tolerances established by a given system of tolerances and landings, which is specified by quality (degree of accuracy) and is conventionally designated taking into account the quality number ITn. 10 Metrology, standardization and certification Table 1.1 Size intervals, mm Rounded values ​​of tolerance units i, µm up to 3 St. 3 to 6 St. 6 to 10 St. 10 to 18 St. 18 to 30 St. 30 to 50 St. 50 to 80 St. 80 to 120 St. 120 to 180 St. 180 to 250 St. 250 to 315 St. 315 to 400 St. 400 to 500 i 0.6 0.8 0.9 1.1 1.3 1.6 1.9 2.2 2.5 2.9 3.2 3.6 4 Quality is a set of tolerances considered as appropriate same level of accuracy for all nominal sizes. Size tolerances depending on size intervals and grades are given in Appendix B, Table B.1. The calculation was made for a normal temperature of 20°C with a probability of 0.997. Thus, quality is understood as the totality of tolerances of all nominal sizes of a given range, which are characterized by constant relative accuracy, expressed by coefficient a, called the number of tolerance units (Table 1.2). A series of values ​​of coefficient a corresponds to a series R5 of preferred numbers. Table 1.2 Quality Values ​​of the number of tolerance units a depending on the quality number 5 6 7 8 9 10 11 12 13 14 15 16 17 a 7 10 16 25 40 64 100 160 250 400 640 1000 1600 Number of tolerance units a for a given quality is constant throughout the entire range of sizes, and the tolerance value depends on the nominal size and quality number. Consequently, the tolerance value for qualifications from 5 to 17, depending on the nominal size, can be determined by the formula ITn = a⋅i; (1.7) where a is the number of tolerance units; i - tolerance unit, µm. Chapter 1. Standardization of accuracy of smooth cylindrical connections 11 The tolerance unit, which is a function of the nominal size (hyperbolic dependence), is calculated by the formula i = 0.453 D + 0.001D, where D = Dmax Dmin, i.e. the geometric mean of the extreme dimensions of each interval (Dmax and Dmin), in mm. The standard establishes 20 qualifications: 01, 0, 1, 2, ..., 18. Qualities from 01 to 4 are intended primarily for calibers. The executive dimensions in the drawings are specified by the nominal size and tolerance range. The tolerance field is limited by the largest and smallest maximum dimensions and is determined by the value of the tolerance and its position relative to the nominal size. When graphically depicting tolerance fields, the position of the nominal size is depicted by a line called zero. Deviations are counted perpendicular to the zero line: up - with a positive sign, and down - with a negative sign. The horizontal lines limiting the tolerance field from above and below are the upper generatrices of cylindrical surfaces with the largest and smallest diameters, respectively. The position of the tolerance field is specified by the main deviation, which in the ESDP is called one of the two maximum deviations (upper or lower), closest to the zero line. Thus, for tolerance fields located above the zero line, the main deviation will be the lower deviation, and for tolerance fields located below the zero line, the upper deviation will be. The main deviations are indicated by letters of the Latin alphabet: lowercase for shafts (a–zc), uppercase for holes (A–ZC). For sizes up to 500 mm, 27 options for the main deviations of shafts and holes are provided (Table 1.3). The layout of the main deviations is shown in Figure 1.2. 12 Metrology, standardization and certification Table 1.3 Designations of the main deviations of the hole and shaft Holes A B C D E EF F FG G H Js K Shafts a b c d e ef f fg g h js k m Holes N P R S T U V X Y Z ZA ZB ZC Shafts n p r s t u v x y z za zb zc M Fig. 1.2 Main deviations: a - holes; b - shafts; I - for landings with clearance; II - for transitional landings; III - for interference fits. Among the main deviations, a special place is occupied by deviations designated H, h, Js, js. The letters H, h Chapter 1. Standardization of accuracy of smooth cylindrical joints 13 indicate the tolerance fields of the main hole and the main shaft, respectively. Main shaft (h) - a shaft whose main upper deviation is zero: es = 0. Main hole (H) - a hole whose main lower deviation is zero: EI = 0. The tolerance fields of the main hole and the main shaft are directed towards the “body” parts and determine the size of the maximum material. The term maximum material size refers to that of the limit dimensions to which the larger volume of material of the part corresponds, i.e., the largest limit size of the outer (male) element (shaft) or the smallest limit size of the internal (female) element (hole). In GOST 25346, the term “maximum material limit” is used in approximately the same meaning as the term “maximum material size” according to GOST R 53090-2008. The designations Js, js correspond to the symmetrical (tolerance field) arrangement of deviations of the hole and shaft, respectively (Fig. 1.2). The value of the main deviation depends on the symbol and the value of the nominal size. The second deviation of the tolerance fields (Fig. 1.3) is defined as the algebraic difference or algebraic sum of the values ​​of the main deviation and the standard tolerance ITn of a hole or shaft, specified by the size grade, according to the following formulas (taking into account the sign of the main deviation and its location): ES = EI + ITn ( from A to H); (1.8) EI = ES – ITn (from K to ZC); (1.9) ei = es – ITn (from a to h); (1.10) es = ei + ITn (from k to zc). (1.11) Numerical values ​​of the main deviations are given in Appendix B, for shafts - in Table B.2, for holes - in Table B.3. 14 Metrology, standardization and certification Fig. 1.3 Layout of tolerance fields: a - holes (ES and EI - positive); b - shaft (es and ei - negative). Due to the fact that the tolerance field is determined by the value of the tolerance and its position relative to the nominal size, its symbol in accordance with GOST 25436 must include the value of the nominal size, the designation of the main deviation and the quality number. For example: ∅30F7 and ∅30f6. The first dimension refers to the hole and the second to the shaft. Indication of tolerance fields and maximum dimensional deviations in the drawings is carried out in accordance with ESKD in accordance with GOST 2.307-2011 as follows: 1) symbol of tolerance fields (letter and number); recommended for mass production: ∅20m6, ∅50H7, ∅100f8, etc.; 2) numerical values ​​of maximum deviations (upper and lower deviations) in mm; recommended for single production: +0.025 ; ∅100−0.036; ∅20++0.021 0.008 ; ∅50 −0.090 3) mixed method; recommended for mass production and for educational purposes: To write in a mixed way means to indicate the tolerance field twice: first with symbols (a letter and a number), and then in brackets with the values ​​of maximum deviations. A parenthesis separates one way of writing a tolerance field from another. When drawing dimensions with maximum deviations on drawings, the following rules should be observed: the upper and lower deviations are written in two lines in a font half the size of the main one, placing the upper deviation above the lower one: ∅30++0.075 0.051 ; the number of characters when recording the upper and lower deviations should be the same, for example ∅30−−0.007 0.040 ; deviations equal to zero do not indicate, for example +0.021 ∅30; ∅30–0.033; when the deviations are symmetrically located, their value is specified after the “±” sign in numbers equal in height to the numbers of the nominal size, for example ∅30 ± 0.026. PROCEDURE FOR COMPLETING THE PRACTICAL LESSON 1.1 Familiarize yourself with the theoretical part of the section. Receive an assignment (option) of practical work. The options are given in Table 1.4. Table 1.4 Options for tasks for practical lesson 1.1 Option number Dimensions Option number Dimensions Option number Dimensions 1 30F8 30h8 10 100K7 100h6 19 80U7 80h6 2 90f8 90H9 11 120k6 120H7 20 70u6 70H7 3 45G 7 45h6 12 85S7 85h6 21 50H11 50d10 4 65g6 65H7 13 75s6 75H7 22 150h10 150E9 5 112G6 112h5 14 102D8 102h7 23 12P5 12h5 6 35M5 35h4 15 135m5 135H6 24 240G7 240h 6 72E7 72h6 7 16 58e8 58H9 25 20s7 20H8 8 185m6 185H7 17 10Js9 10h9 26 24k6 24H7 9 28a11 18 32c11 32H12 27 210r6 210H7 28H12 Task. Calculate tolerances and maximum deviations of given dimensions and write down tolerance fields in a mixed way (1st level of complexity); at the 2nd level of complexity, construct diagrams of the location of tolerance fields. 16 Metrology, standardization and certification Solution. 1. Find from Table 1.1 the value of the tolerance unit for the given nominal dimensions. 2. Determine the number of tolerance units according to Table 1.2 depending on the specified quality number. 3. Calculate the tolerance value for given dimensions using formula (1.7). 4. Round the calculated tolerance value to the standard value according to Table B.1 of Appendix B. 5. Determine the type and value of the main deviations (Tables B.2 and B.3), as well as the second deviations of the tolerance fields for given dimensions using formulas (1.8) , (1.9) or (1.10), (1.11). 6. Write down the specified dimensions, indicating the tolerance fields in a mixed way. 7. Construct layout diagrams of tolerance fields for given dimensions similar to Figure 1.3. EXAMPLES OF PRACTICAL LESSON 1.1 Example 1 (1st level of difficulty) Assignment. Calculate the tolerances and maximum deviations of dimensions ∅30H7 and ∅30f6 and write down the tolerance fields in a mixed way. Solution. 1. For size ∅30, find from Table 1.1 the value of the tolerance unit i = 1.3 µm. 2. Determine the number of tolerance units according to Table 1.2: for the 7th qualification –a = 16; for the 6th qualification –a = 10. 3. Calculate the tolerance value for the given dimensions using formula (1.7): for hole IT7 = a ⋅ i = 1.3 ⋅ 16 = 20.8 µm; for shaft IT6 = a ⋅ i = 1.3 ⋅ 10 = 13 µm. 4. Using Table B.1, find the standard tolerance values: IT7 = 21 µm; IT6 = 13 µm. 5. Determine the type and value of the main deviations and the second deviations of the tolerance fields for given dimensions using formulas (1.8), (1.9) or (1.10), (1.11). Chapter 1. Standardization of accuracy of smooth cylindrical joints 17 5.1. The size ∅30H7 has a main deviation H (Table B.3), which corresponds to a lower deviation equal to EI = 0, the second deviation is determined by formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 5.2. The size ∅30f6 has a main deviation f, which corresponds to an upper deviation equal to es = –20 µm (Table B.2). Lower shaft deviation according to formula (1.10): ei = es – ITn = –20 – 13 = –33 µm. 6. Write down the specified dimensions, indicating the tolerance field in a mixed way: ∅30H7 (+0.021); ∅30f 6 (−−0.020 . 0.033) Example 2 (2nd level of difficulty) Task. Calculate maximum deviations, maximum dimensions ∅30H7 and ∅30f6, write down tolerance fields in a mixed way and construct layout diagrams of tolerance fields. Solution. For size ∅30H7 determine: 1. Type and value of the main deviation H: EI = 0 (Table B.3). 2. Standard tolerance value IT7 = 21 (Table B.1). 3. The value of the second deviation according to formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 4. Write down the tolerance field in a mixed way: ∅30H7(+0.021). 5. Calculate the maximum hole dimensions using formulas (1.3): Dmax = D + ES = 30.000 + 0.021 = 30.021; Dmin = D + EI = 30,000 + 0 = 30,000. For size ∅30f6 determine: 1. Type and value of the main deviation f: es = –20 (Table B.2). 18 Metrology, standardization and certification Fig. 1.4 Layout of tolerance fields: a - holes ∅30H7; b - shaft ∅30f6. 2. Standard tolerance value IT6 = 13 µm (Table B.1). 3. The value of the second deviation according to formula (1.10): ei = es – IT6 = –20 – 13 = –33 µm. 4. Write down the tolerance field in a mixed way: ∅30f 6 (−−0.020 . 0.033) 5. Calculate the maximum dimensions of the shaft using formulas (1.4): dmax = d + es = 30.000 – 0.020 = 29.980; dmin = d + ei = 30.000 – 0.033 = 29.967. 6. Construct a diagram of the location of tolerance fields for size ∅30H7 (Fig. 1.4a) and for size ∅30f6 (Fig. 1.4b). 1.1.2. LANDINGS AND THEIR CHARACTERISTICS. FITTING SYSTEMS THEORETICAL PART FOR PRACTICAL LESSON 1.2 Fitting is the connection of two parts, resulting in the formation of a gap or interference. The difference in sizes Chapter 1. Standardization of the accuracy of smooth cylindrical connections 19 of the hole and shaft before assembly determines the nature of the connection of the parts. There are clearance fits, interference fits and transition fits. To form landings, use either the main hole H or the main shaft h. The main shaft is a shaft whose upper (main) deviation is zero: es = 0 → h. The main hole is a hole whose lower (main) deviation is zero: EI = 0 → H. Nominal fit size is the nominal size common to the hole and shaft that make up the connection. Fit characteristics include interferences, clearances and fit tolerances. Gap (S) is the difference between the dimensions of the hole and the shaft before assembly, if the hole size is larger than the shaft size. Preference (N) is the difference between the dimensions of the shaft and the hole before assembly, if the shaft size is larger than the hole size. Fit tolerance is the sum of the tolerances of the hole and shaft that make up the connection: TS (TN) = TD + Td. Rice. 1.5 Layout of tolerance fields for clearance fits (1.12) 20 Metrology, standardization and certification A clearance fit is a fit in which a gap always forms in the connection, since the smallest limiting hole size is greater than or equal to the largest limiting shaft size. When depicting the fit graphically, the tolerance field of the hole is located above the tolerance field of the shaft (Fig. 1.5). The limiting characteristics of a clearance fit are the largest and smallest clearances and clearance tolerance: Smax = Dmax – dmin = ES – ei; (1.13) Smin = Dmin – dmax = EI – es; (1.14) TS = Smax – Smin = TD + Td. (1.15) An interference fit is a fit in which an interference is always formed in the connection, i.e., the largest limit size of the hole is less than or equal to the smallest limit size of the shaft. When shown graphically, the tolerance field of the hole is located below the tolerance field of the shaft (Fig. 1.6). The limiting characteristics of an interference fit are the maximum and minimum interference and interference tolerance: Fig. 1.6 Layout of interference fit tolerance fields Chapter 1. Standardization of accuracy of smooth cylindrical connections 21 Fig. 1.7 Layout of tolerance fields for transitional fit Nmax = dmax – Dmin = es – EI; (1.16) Nmin = dmin – Dmax = ei – ES; (1.17) TN = Nmax – Nmin = TD + Td. (1.18) Transitional fit - a fit in which both clearance and interference are possible in the connection, depending on the ratio of the actual dimensions of the hole and the shaft. When graphically depicting the tolerance fields of the hole and shaft, they overlap completely or partially (Fig. 1.7). The limiting characteristics of the transitional fit are the largest gap, the largest interference and fit tolerance: Smax = Dmax – dmin = ES – ei; (1.19) Nmax = dmax – Dmin = es – EI; (1.20) TS/N = Smax + Nmax = TD + Td. (1.21) The diagram in Figure 1.8 illustrates the calculation of the clearance fit tolerance, transition fit and interference fit through the limit characteristics. Since gaps and interference are of the opposite nature, it is customary to put gaps in the positive direction from zero, and interference in the negative direction. The problem, in accordance with the scheme, is solved as a geometric one, i.e., the fit tolerance is defined either as the difference of segments equal to the limiting characteristics of the fit (for clearance fits and interference fits), or as their sum (for a transitional fit). 22 Metrology, standardization and certification Fig. 1.8 Scheme for calculating fit tolerance based on limiting characteristics The fit designation is indicated after the nominal fit size. The fit is indicated by a fraction, the numerator of which indicates the symbol of the tolerance field of the hole, and the denominator - the symbol of the tolerance field of the shaft. With a mixed designation method, after the symbolic designation of the tolerance fields of the hole and shaft, the numerical values ​​of the maximum deviations of these tolerance fields are indicated, enclosed in brackets. For example: ∅40 H7/ k6; ∅40 H7 (+0.025) H7; ∅50. k6 k6 (+0.018 +0.002) The system of tolerances and landings is a set of series of tolerances and landings, naturally built on the basis of theoretical and experimental research. Landings can be assigned in two systems: in the hole system (CH) and in the shaft system (CH). Hole system fits are fits in which the required clearances and interferences are obtained by combining the tolerance fields of the shafts, which differ in the main deviation, with the tolerance field of the main hole H (EI = 0). Thus, in order to change the nature of the connection, it is necessary to change the position of the shaft tolerance field, i.e., the main shaft deviation (Fig. 1.9), leaving the hole tolerance field (H) unchanged. Examples of fits in the hole system: ∅30N/k6; ∅30Н7/f6; ∅30Н7/р6. Shaft system fits are fits in which the required clearances and tensions are obtained by combining tolerance fields of holes that differ in the main deviation with the tolerance field of the main shaft h (es = 0). Chapter 1. Standardization of accuracy of smooth cylindrical joints 23 Fig. 1.9 Tolerance fields of the hole system Thus, in order to change the nature of the connection, it is necessary to change the main deviation of the hole, i.e., the position of the tolerance field of the hole (Fig. 1.10), leaving the shaft tolerance field (h) unchanged. Examples of fits in the shaft system: ∅30M7/h6; ∅30F7/h6; ∅30R7/h6. Fittings of the same name from different systems with the same nominal size are interchangeable, since they have the same maximum characteristics. However, in some cases the use of a shaft system is necessary. Examples of application of the shaft system: 1) in connections of a smooth shaft with several holes for fits of various types; Rice. 1.10 Tolerance fields of the shaft system 24 Metrology, standardization and certification 2) in the connection of the outer ring of the bearing with the hole in the housing (the bearing is a standard product); 3) in connections of a key along the width with the grooves of the hole and shaft; 4) the use of smooth cold-drawn calibrated rods as axles or shafts without additional machining in agricultural machines. The standard allows any combination of tolerance fields for holes and shafts, but two narrower series of tolerance fields are recommended for use: the main series, in which an even narrower selection of preferred tolerance fields is highlighted (Tables 1.5 and 1.6), and an additional series of limited use. Table 1.5 Preferred tolerance fields in the hole system Main holes Shaft tolerance fields Number of fields Н7 e8, f7, g6, h6, js6, k6, n6, p6, r6, s6 10 Н8 d9, e8, h7, h8 4 Н9 d9, h9 2 Н11 2 d11, h11 Σ 18 Total Table 1. 6 Preferred tolerance fields in the shaft system Main shafts Hole tolerance fields h6 F8, H7, Js7, K7, N7, P7 6 h7 H8 1 h8 E9, H9 2 h11 H11 1 Total Number of fields Σ 10 The hole system (CH) is preferable, so how it allows you to reduce the cost of processing parts by reducing the range of standard sizes of measuring cutting tools (drills, countersinks, reamers) and measuring tools (bore gauges for holes). Chapter 1. Standardization of accuracy of smooth cylindrical joints 25 Fitments are called basic if the following conditions are met: the tolerance fields (main deviations) of the hole and shaft belong to the same system; the accuracy of the hole and shaft is the same, i.e. the quality numbers of the hole and shaft are the same or differ by one; in rare cases, a difference in qualification numbers of two is allowed. If these conditions or one of them are not met, the planting will be combined based on both characteristics or one of them. Examples of basic and combined fits: 1) fit ∅45Н7/k6 - main fit: tolerance fields belong to one system - the hole system, and the difference in quality numbers is equal to one; 2) landing ∅45Н7/h6 - combined landing according to the first sign. Tolerance fields belong to different systems: the hole tolerance field belongs to the hole system, the shaft tolerance field belongs to the shaft system. 3) landing ∅45F9/k6 - combined according to two characteristics. The hole and shaft tolerance fields belong to different systems: the hole tolerance field belongs to the shaft system, and the shaft tolerance field belongs to the hole system. The difference in qualification numbers is no more than three. The tolerance fields for holes recommended by the standard for nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.4. The largest number of tolerance fields (10) are in the zone of 7–11 qualifications. The standard tolerance ranges for shafts with nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.5. The largest number of tolerance fields (16) are in the zone of 6–11 qualifications. PROCEDURE FOR COMPLETING THE PRACTICAL LESSON 1.2 Level of first complexity - solving questions for one given landing, for two landings - the second level, and for three - the third level of complexity. 26 Metrology, standardization and certification Familiarize yourself with the theoretical part of the section. Receive an assignment (option) of practical work. The options are given in Table 1.7. Table 1.7 Plantings Option number Option number Options for tasks for practical lesson 1. 2 105Js7/h6 14 Landings 1 30H7/f6 62P7/h6 16H6/g5 50U8/h7 88H8/e7 2 45G7/h6 83H6/r5 58K7/h6 15 45H7/g6 76M7/h6 25H9/js9 22H7/r6 3 36G6/h5 85H8 /x8 100M6/h5 16 30F7/h6 180K8/h7 4 22C11/h10 230H6/t5 18 K8/h7 17 25F7/h6 10Js10/h9 45H7/s6 5 40D11/h10 60H7/p6 105H7/js 7 18 32F9/h8 28N8/ h7 175H6/t 5 6 118F10/h9 150H7/p6 130H6/m5 19 34D9/h8 240H5/k4 102H7/s6 7 76D8/h7 205H7/u7 90H7/m6 20 72F8/h7 18H8/z8 90H7/j s6 8 25H9/f8 210T7 /h6 55H7/k6 21 118U8/h7 15H10/h9 20H7/n7 9 90H8/g8 110H7/t6 65N7/h6 22 27M8/h7 36H10/f9 125H7/s7 10 185H8/k7 222N8/h7 70H10/ d9 27H7/r6 112Js7/ h7 23 95H11/d11 11 48H12/d11 42S7/h6 130H6/k5 24 114Js9/h9 50G7/h6 55H7/s6 12 80K8/h7 122H7/r6 25 145G7/h6 23H7/r6 108K7/h6 140H7/n6 40H9/x8 26 180H10 /e9 105R7/h6 215H6/k5 50F8/h7 13 90H12/b11 Note. When calculating the main deviations of holes (K, M, N, as well as for P–Z up to the 7th grade), use the “Note” to Table B.3 of Appendix B. Assignment. Determine the maximum deviations of the tolerance fields for three given fits (with clearance, interference and transition fit) for a given option. 1. Determine the maximum deviations of the tolerance fields of the given fits. To do this, use Tables B.1–B.3 of Appendix B to determine the tolerances and main deviations. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance, as was done during the first practical work. 3. Write down the tolerance fields for the dimensions of the parts using a mixed method. 4. Calculate the limiting characteristics of the given fits, find the fit tolerance in two ways: according to the maximum clearances or interference, and check according to the tolerances of the hole and shaft according to formula (1.12). 5. Construct three layout diagrams of the tolerance fields of all three landings. EXAMPLE OF A PRACTICAL LESSON 1.2 Assignment. Calculate the limiting characteristics of three given fits and construct diagrams of the location of tolerance fields for them: ∅40H7/f6; ∅40H7/k6; ∅40H7/r6. Solution. 1. Determine the maximum deviations of the tolerance fields of the given fits. To do this, use Table B.1 of Appendix B to determine the tolerances for size ∅40: tolerance IT7 = 25 µm; tolerance IT6 = 16 µm. The main deviations are determined from tables B.2, B.3 of Appendix B: for H → EI = 0; for f → es = –25 µm; for k → ei = +2 µm; for r → ei = +34 µm. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance: for H → ES = EI + IT7 = 0 + 25 = +25 µm; for f → ei = es – IT6 = –25 – 16 = –41 µm; for k → es = ei + IT6 = +2 + 16 = +18 µm; for r → es = ei + IT6 = +34 + 16 = +50 µm. 3. Write down the tolerance fields for the dimensions of the parts using a mixed method: +0.018 +0.050 ∅40H7 (+0.025); ∅40f 6 (−−0.025 0.041); ∅40k6 (+0.002); ∅40r 6 (+0.034). 4. Calculate the limiting characteristics of the given landings. 4.1. Calculate the limiting characteristics for H7 (+0.025) of the charger with a gap in the hole system ∅40 using f 6 (−−0.025) 0.041 formulas (1.13)–(1.15): Smax = ES – ei = +25 – (–41) = 66 µm ; 28 Metrology, standardization and certification Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; Perform the check using formula (1.12): TS = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transition fit in a hole system ∅40 lams (1.12), (1.19)–(1.21): Н7 (+0.025) according to form6 (++0.018 0.002) Smax = ES – ei = 25 – 2 = 23 µm; Nmax = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. Rice. 1.11 Layout of landing tolerance fields: a - with a gap; b - transitional; c - with interference. Chapter 1. Standardization of accuracy of smooth cylindrical joints 29 4.3. Calculate the limiting characteristics of an interference fit in a hole system ∅40 lams (1.12), (1.16)–(1.18): H7 (+0.025) r 6 (++0.050 0.034) according to the form - Nmin = ei – ES = 34 – 25 = 9 µm; Nmax = es – EI = 50 – 0 = 50 µm; TS/N = Nmax – Nmin = 50 – 9 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct layout diagrams of tolerance fields for given fits (Fig. 1.11). 1.1.3. GENERAL AND SPECIAL RULES FOR FORMING INTERCHANGEABLE FITTS THEORETICAL PART FOR PRACTICAL LESSON 1.3 GOST 25346 provides for the interchangeability of identical fits of the hole system and shaft system with the same nominal dimensions. Such fits have the same limiting characteristics due to the use of general and special rules that establish the values ​​of the same basic deviations of the shaft and hole. The general rule establishes the following relationships between the main deviations of the same name (i.e., having the same letter designation): EI = –es → from A (a) to H (h); (1.22) ES = –ei → from K (k) to ZC (zc). (1.23) In accordance with the general rule, the main deviations of the same name of the hole and shaft are equal in magnitude and opposite in sign, i.e., symmetrical with respect to 30 Metrology, standardization and certification Fig. 1.12 Layout of the main deviations of the zero line of the same name. A fragment of the location diagram of the main deviations of the same name is presented in Figure 1.12. The general rule applies to all clearance fits, transitional fits from 9th grade and coarser, and interference fits from 8th grade and coarser. A special rule applies to transitional landings up to the 8th grade inclusive and interference landings up to the 7th grade. It allows you to obtain the same maximum clearances and interference in the same fits, specified in the hole system and in the shaft system, in which a hole of a given quality is connected to the shaft of the nearest more accurate quality. Special rule: the main deviation of the hole is equal to the main deviation of the shaft, taken with the opposite sign, with the addition of the correction ∆: ES = –ei + ∆, (1.24) where ∆ = ITq – ITq–1 is the difference between the tolerances of adjacent grades, i.e. the difference between the tolerance of the quality in question (hole) and the tolerance of the nearest more accurate quality (shaft). The second deviation of the hole or shaft tolerance field is determined through the main deviation and the tolerance ITn in accordance with the tolerance calculation formula. When changing the system, the accuracy (quality) of the hole and shaft does not change. Chapter 1. Standardization of accuracy of smooth cylindrical joints 31 PROCEDURE FOR PERFORMING PRACTICAL LESSON 1.3 Familiarize yourself with the theoretical part of the section. Receive an assignment (option) of practical work. The options are given in Table 1.8. Table 1.8 Options for tasks for practical lesson 1.3 Option number Landing Option number Landing Option number Landing 1 30H7/f6 2 45G7/h6 10 60P7/h6 19 76D11/h10 11 83H6/r5 20 210T6/h5 3 100M6/ h5 12 58E9/h8 21 36G7/h6 4 25F9/h8 13 55K7/h6 22 12N9/h9 5 100F7/h6 14 60H7/p6 23 76H11/d10 6 45H7/g6 15 83R6/h5 24 210H6/t5 7 100H6/m5 16 105H7/f6 25 36H7/g6 8 25H9/f8 17 55H7/k6 26 20Js9/h9 9 130H6/k5 18 27H7/r6 27 28N8/h7 Task. For a given fit, form an interchangeable fit of the same name in another system. Calculate the limiting characteristics of both landings. Construct diagrams of the location of tolerance fields for landings of the same name. Solution. 1. Determine the system of a given landing and assign the landing of the same name to it in another system. 2. Determine the value of the tolerance value, the type and value of the value of the main and second deviations for all tolerance fields that form fits of the same name (see note to Table B.3). Designate plantings in a mixed way. 3. Calculate the limiting characteristics of both landings. 4. Construct layout diagrams of landing tolerance fields. 5. Draw a conclusion about the interchangeability of landings. 32 Metrology, standardization and certification EXAMPLES OF PRACTICAL LESSON 1.3 Example 1 for the general rule (2nd level of complexity) Assignment. For a given fit ∅40Н7/f6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Construct diagrams of the location of tolerance fields for landings of the same name and draw a conclusion. Solution. 1. The fit with a gap in the hole system is specified, since there is a tolerance zone for the main hole. It corresponds to the same fit in the shaft system ∅40F7/h6. 2. Determine the value of the tolerance value, the type and value of the value of the main and second deviations for all tolerance fields that form fits of the same name. 2.1. Calculate and round to standard values ​​according to Table B.1 the tolerance values ​​of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 40 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a⋅i = 10 ⋅1.6 = 16 µm; IT7 = a⋅i = 16⋅1.6 = 25 µm. 2.2. Determine the type (upper or lower) and values ​​of the main deviations of holes with ∅40 (Tables B.2 and B.3 of Appendix B): H → EI = 0; F → EI = +25 µm. 2.3. Since clearance fits are specified, based on the general rule (EI = –es) we find the values ​​of the same basic shaft deviations: h → es = 0; f → es = –25 µm. 2.4. The second deviations of the tolerance fields of the hole and shaft are calculated through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES – EI; Td = es – ei. Chapter 1. Standardization of accuracy of smooth cylindrical joints 33 Calculate the second deviation of the tolerance fields: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; h6 → ei = es – IT6 = 0 – 16 = –16 µm; F7 → ES = EI + IT7 = +25 + 25 = +50 µm; f6 → ei = es – IT6 = –25 – 16 = –41 µm. 2.5. Designate landings in a mixed way: 3. Calculate the limiting characteristics of both landings. 3.1. Calculate the limiting characteristics of the fit with a gap in the hole system ∅40 H7 (+0.025) f 6 (−−0.025 0.041): Smax = ES – ei = +25 – (–41) = 66 µm; Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 3.2. Calculate the limiting characteristics of the fit with a gap in the shaft system ∅40 F7 (++0.050 0.025) h6 (−0.016): Smax = ES – ei = +50 – (–16) = 66 µm; Smin = EI – es = +25 – 0 = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 4. Construct diagrams of the location of tolerance fields for landings of the same name (Fig. 1.13). 34 Metrology, standardization and certification Fig. 1.13 Layout of landing tolerance fields: a - in the hole system; b - in the shaft system. Conclusion. The considered examples showed that landings of the same name with the same nominal dimensions, specified in different systems, are interchangeable, since they have the same limiting characteristics. Thus, for fits ∅40Н7/f6 and ∅40F7/h6 the smallest and largest gaps are equal, respectively: Smin = 25 µm; Smax = 66 µm. Example 2 for a special rule (3rd difficulty level) Task. For a given fit ∅50H7/k6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Construct diagrams of the location of tolerance fields for landings of the same name. Solution. 1. The transitional fit in the hole system is specified to be no rougher than 8th grade: ∅50H7/k6. It corresponds to a fit of the same name in the shaft system ∅50K7/h6 2. Determine the value of the tolerance, the type and value of the main and second deviations for the tolerance fields forming the fits of the same name. 2.1. Calculate the tolerance values ​​of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 50 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a ⋅ i = 10 ⋅ 1.6 = 16 µm; Chapter 1. Standardization of accuracy of smooth cylindrical joints 35 IT7 = a ⋅ i = 16 ⋅ 1.6 = 25 µm. 2.2. Determine the type (upper or lower) and values ​​of the main deviations of the tolerance fields of the hole and shaft for fit ∅50H7/k6 (Table B.2, B.3 of Appendix B): H → EI = 0; k → ei = +2 µm. 2.3. The second deviations of the tolerance fields of the hole and shaft are calculated through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES – EI; Td = es – ei. Calculate the second deviation of the fit tolerance fields ∅50H7/k6: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; k6 → es = ei + IT6 = +2 + 16 = +18 µm. 2.4. For a fit in the shaft system ∅50K7/h6, determine the main deviation of the tolerance field of the hole K7 according to a special rule, since the fit is transitional, no rougher than 8th grade: ∆ = IT7 – IT6 = 25 – 16 = 9 µm; ES = –ei + ∆ = –2 + 9 = +7 µm, where ES is the main deviation of the tolerance field of hole K7; ei is the main deviation of the tolerance field of the same name for shaft k6. 2.5. Calculate the second deviation of the tolerance field of hole K7: EI = ES – IT7 = +7 – 25 = –18 µm. 2.6. The main deviation of the tolerance field of the main shaft h6 is es = 0. The second deviation: ei = es – IT6 = 0 – 16 = –16 µm. 36 Metrology, standardization and certification 3. Designate landings in a mixed way: 4. Calculate the limiting characteristics of these landings. 4.1. Calculate the limiting characteristics of the transition fit in the hole system ∅50H7/k6: Smax = Dmax – dmin = ES – ei = 25 – 2 = 23 µm; Nmax = dmax – Dmin = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transition fit in the shaft system ∅50K7/h6: Smax = Dmax – dmin = ES – ei = +7 – (–16) = 23 µm; Nmax = dmax – Dmin = es – EI = 0 – (–18) = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct diagrams of the location of tolerance fields for landings of the same name (Fig. 1.14). Rice. 1.14 Layout of landing tolerance fields: a - ∅50H7/k6; b - ∅50K7/h6. Chapter 1. Standardization of accuracy of smooth cylindrical joints 37 Conclusion. The considered examples showed that landings of the same name with equal nominal dimensions, specified in different systems, are interchangeable, since they have the same limiting characteristics. Thus, for fits ∅50H7/k6 and ∅50K7/h6, the largest gap and the largest interference, respectively, are equal to Smax = 23 µm; Nmax = 18 µm. 1.1.4. ASSIGNMENT OF FITTS BY THE SIMILARITY METHOD THEORETICAL PART TO THE PRACTICAL LESSON 1.4 Method of precedents (analogues) The method consists in the fact that the designer, when designing new components and mechanisms, assigns to them the same fits that were used in the same type of product previously designed and in use. Similarity method It is a development of the precedent method and is based on the classification of machine parts according to design and operational characteristics and the publication of reference books with examples of the use of fits (Appendix B.6). The disadvantage of this method is the qualitative rather than quantitative description of operational characteristics and the difficulty of identifying them with the characteristics of the newly designed structure. Recommendations for assigning fits using the similarity method. Assigning fits with a gap. The fits are characterized by a guaranteed minimum gap Smin, necessary for placing lubricant between the mating surfaces in movable joints, to compensate for temperature deformations, errors in shape and location in order to ensure the assembly of the product. Basic requirements for clearance fits: operating temperature should not exceed 50°C; 38 Metrology, standardization and certification the ratio of mating length to diameter should not exceed the ratio l:d ≤ 1:2; the linear expansion coefficients of the hole and shaft should be close to each other; The greater the angular velocity of rotation, the greater the guaranteed gap value should be. Purpose of interference fits. The fits are intended for fixed permanent connections without additional fastening with screws, pins, etc. Relative immobility is achieved due to the stresses arising in the material of the mating parts. The main methods of assembling parts with interference fit: longitudinal pressing - assembly under pressure due to axial force at normal temperature; transverse pressing - assembly with preheating of the female part or cooling of the female part to a certain temperature. Purpose of transitional landings. Transitional fits are designed for fixed but detachable connections of parts, provide good centering and are used with additional fastening. These landings differ from each other in the likelihood of obtaining gaps or interference (Table 1.9). Table 1.9 Probability of obtaining gaps or interference in transitional fits Designation of fit Name of fit Probability of gaps Probability of interference H7/n6 blind 1% 99% H7/m6 tight 20% 80% H7/k6 tense 60% 40% H7/ js6 dense 99% 1% ORDER OF PRACTICAL LESSON 1.4 (3RD LEVEL OF COMPLEXITY) Familiarize yourself with the theoretical part of the section. Receive an assignment (option) of practical work. The options are given in Appendix A (A.1–A.12) in size D1 or D2. Chapter 1. Standardization of accuracy of smooth cylindrical joints 39 Task. Determine the fit for a given connection (options A.1–A.12); taking into account the requirements for it, calculate the limiting characteristics and landing tolerances, construct a diagram of the location of the landing tolerance fields, record the landing using a mixed method. The task should be presented in the form of a map of initial data. Solution. 1. Determine which group the fit belongs to (according to the description of the nature of the connection and its purpose): with clearance, interference or transitional. 2. Determine the landing system based on the joint design analysis. 3. Select the type of interface (combination of the main deviations of the tolerance fields of the hole and shaft) according to Table B.6. 4. Determine the accuracy of the fit: the quality of accuracy, taking into account the preference for using fits and tolerance fields according to tables B.4 and B.5. 5. Determine maximum deviations and tolerances according to tables B.1–B.3. 6. Calculate the limiting characteristics and fit tolerance. 7. Construct a diagram of the location of the landing tolerance fields and record the landing using a mixed method. EXAMPLE OF PRACTICAL EXERCISE 1.4 Map of initial data Name of initial data Value of initial data Nominal size of the connection and its value D = 65 mm Name of parts included in the connection Helical gear 4 and spindle 6 Requirements for the operation of the connection (from the description to the drawing) Helical gear wheel 4 along D2 is well centered relative to the spindle axis and has two diametrically located feather keys. Solution. 1. Determine the planting group. A fixed connection with additional fastening with two keys is specified, in which it is required to ensure 40 Metrology, standardization and certification precise centering. These conditions correspond to a transitional landing (Table B.6). 2. Designate a landing system. The connection includes a helical gear and a spindle. Since a given diameter of the shaft is connected to one hole, and the internal surfaces are more difficult to process, we select the preferred hole system CH. Thus, we assign a tolerance field of the main hole H to the hole of the helical gear. 3. Select the type of mating. Using the similarity method, we assign the following type of landing H/js (Table B.6). For this type, gaps are more likely than interference. It provides easy assembly and disassembly, precise centering and is used for replacement parts that require additional fastening in precise grades: shafts from 4th to 7th, and holes from 5th to 8th. 4. Determine the accuracy of the fit. Analyzing the design and operating conditions of this connection, we assign the landing H7/js6. This fit is used in the following connections: bearing cups of 4th and 5th accuracy classes in housings, gears connected to the shaft with two keys, tailstock quill of a lathe (Table B.6). 5. Determine the maximum deviations and tolerances of the hole and shaft. Using Table B.1, find the tolerances of the 6th and 7th qualifications over the size range from 50 to 80: IT6 = 19 µm; IT7 = 30 µm. The upper deviation for ∅65Н7 is equal to the tolerance, i.e. 30 µm. The ∅65js6 shaft has a symmetrical tolerance field, i.e. ±9.5 µm. 6. Calculate the limiting characteristics and fit tolerance ∅65 H7(+0.030). js6(±0.0095) Limit hole dimensions: Dmax = D + ES = 65 + 0.030 = 65.030 mm; Chapter 1. Standardization of accuracy of smooth cylindrical joints 41 Dmin = D + EI = 65 + 0 = 65 mm. Limit shaft dimensions: dmax = d + es = 65 + 0.0095 = 65.0095 mm; dmin = d + ei = 65 + (–0.0095) = 64.9905 mm. Maximum interference: Nmax = dmax – Dmin = 65.0095 – 65 = 0.0095 mm. Maximum clearance: Smax = Dmax – dmin = 65.030 – 64.9905 = 0.0395 mm. Average probable gap: Sm = (Smax – Nmax)/2 = (0.0395 – 0.0095)/2 = 0.015 mm. Fit tolerance: TS/N = Smax + Nmax = 0.0095 + 0.0395 = 0.049 mm or TS/N = TD + Td = 0.030 + 0.019 = 0.049 mm. 7. Construct a diagram of the location of the landing tolerance fields (Fig. 1.15). Rice. 1.15 Location of fit tolerance fields 42 Metrology, standardization and certification 1.1.5. PURPOSE OF LANDING BY CALCULATION METHOD THEORETICAL PART FOR PRACTICAL LESSON 1. 5 The calculation method is the most reasonable method for assigning a landing. It is based on engineering calculations of joints for strength, rigidity, etc. However, the formulas do not always fully take into account the complex nature of the physical phenomena occurring in the joint. The disadvantage of this method is the need to test prototypes before launching mass production of a new product and adjust the fits in the developed product. The calculation method is used when, due to the operating conditions of the mechanism, the maximum values ​​of clearances or interference are limited, for example for plain bearings, critical press connections, etc. For example, when calculating a fit with a gap of the form H/h, used as a centering fit, determine first of all, the highest maximum permissible value of eccentricity or thermal deformation of parts, if the operating temperature differs significantly from normal. When calculating transitional fits (mainly test fits), the probability of obtaining gaps and interference in the connection, the largest gap according to the known maximum permissible eccentricity of the parts being connected, or the greatest assembly force at the highest fitting interference are determined, and for thin-walled bushings a strength calculation is performed. In interference fits, the minimum permissible interference is calculated based on the greatest possible forces acting on the mating, and the maximum interference is calculated from the strength of the parts. After calculating the limiting characteristics, it is necessary to select a standard fit with limiting characteristics close to the calculated ones. Chapter 1. Standardization of accuracy of smooth cylindrical joints 43 The selection of a standard fit is carried out in the following sequence. 1. Based on the results of the analysis of the assembly design, the landing system is determined. In most cases, plantings are assigned to the hole system as preferred. Typical cases of assigning landings in the shaft system - see paragraph 1.1.4. 2. The clearance, interference or transition fit tolerance is calculated according to the specified characteristics: Tpos = TS = Smax – Smin; (1.25) Tpos = TN = Nmax – Nmin; (1.26) Tpos = TS/N = Smax + Nmax. (1.27) 3. To determine the standard fit tolerance, it is necessary to determine the relative fit accuracy apos (the number of fit tolerance units), based on formulas (1.7) and (1.12): Tpos = TD + Td = aD ⋅ i + ad ⋅ i = i ⋅ (aD + ad), (1.28) where aD + ad = apos, i.e. the sum of the numbers of tolerance units of the hole and shaft is equal to the number of fit tolerance units; i = ipos - unit of fit tolerance, the value of which depends on the nominal size of the fit (Table. B.1). It follows that apos = Tpos/i. (1.29) 4. Based on a known number of fit tolerance units, the quality numbers for the hole and shaft are determined in accordance with the second sign of the main fit: the quality numbers of the hole and shaft are the same or differ by one (rarely by two). Thus, aD = ad = apos/2. Then, according to Table B.1, the closest to the calculated standard value of the number of tolerance units of the hole and shaft is determined, by which the quality number is determined. 5. If the value of the number of tolerance units falls between two standard values, grades corresponding to these standard values ​​are assigned to the hole and shaft (coarser - to the hole, more 44 Metrology, standardization and certification fine - to the shaft), with the sum aD + ad should be close to the calculated value of apos, for example apos = 35, then with aD = ad = 35/2 = 17.5 - the accuracy of the hole and shaft corresponds to ≈ IT7 (a = 16). 6. The fit can be combined according to quality if a rolling bearing shaft is installed on the same diameter. In this case, it is necessary to limit the accuracy of the shaft. For example, IT6 (ad = 10), then aD = 35 – 10 = 25, which corresponds to the hole accuracy of IT8. 7. Tolerance fields for the hole and shaft are assigned depending on the selected fit system (CH or CH), tolerances of the hole and shaft (Table B.1) and the value of one of the limiting characteristics of the fit, from which the main deviation of the tolerance field of the non-main part is calculated ( shaft or hole) in the following sequence: first, determine the tolerances of the hole and shaft according to Table B.1 and the second deviations of the main parts according to formulas (1.8) and (1.10) of practical lesson 1.1: ES = EI + ITn (from A to H); ei = es – ITn (from a to h); for clearance, interference and transition fits specified in the hole system, the main deviations are calculated accordingly according to the following formulas: es = EI – Smin; (1.30) ei = ES + Nmin; (1.31) ei = ES – Smax; (1.32) for clearance, interference and transition fits specified in the shaft system, the main deviations are calculated accordingly according to the following formulas: EI = es + Smin; (1.33) ES = ei – Nmin; (1.34) ES = ei + Smax. (1.35) Chapter 1. Standardization of accuracy of smooth cylindrical joints 45 Based on the calculated values ​​of the main deviations of the shaft or hole according to tables B.2 and B.3, the nearest standard values ​​are selected. 8. Then the second maximum deviations of the non-main shaft or hole are determined using formulas (1.8)–(1.10) of practical lesson 1.1, depending on the group of landings. ORDER OF PRACTICAL LESSON 1.5 (3RD LEVEL OF COMPLEXITY) Familiarize yourself with the theoretical part of the section. Receive an assignment (option) of practical work. The options are given in Appendix A (A.1–A.12) for size D3. Exercise. Select a standard fit for a given connection based on the specified limit characteristics using the calculation method. Calculate the limiting characteristics and standard fit tolerance, construct a layout diagram of the fit tolerance fields and record the fit using a mixed method. The task should be presented in the form of a map of initial data. Solution. 1. Determine which group the fit belongs to (according to the description of the nature of the connection and its purpose): with clearance, interference or transitional. 2. Determine the landing system by analyzing the connection design. 3. Determine the accuracy of the fit. 3.1. Calculate the landing tolerance depending on its group using formula (1.26), or (1.27), or (1.28). 3.2. Determine the relative accuracy of the fit (the number of fit tolerance units apos). Calculate the number of fit tolerance units using formula (1.29). 3.3. Using Table B.1, determine the quality of the shaft and hole. When assigning qualities to the hole and shaft, it is necessary to strive to ensure the fulfillment of the second sign of the main fit, i.e. assign the same qualities to the shaft and hole or with a difference in quality numbers equal to one. 46 Metrology, standardization and certification 3.4. Find the tolerances of the hole and shaft according to Table B.1. 4. Determine the main and second deviations of the hole and shaft. 4.1. The selected fit system determines the main part (main hole for CH and main shaft for Ch). The main part will have a main deviation equal to 0, and the second is determined depending on the type of main deviation (ES or ei) and tolerance. 4.2. Determine the position of the tolerance field of another (not the main) part using formulas (1.30)–(1.32) or (1.33)–(1.35) depending on the group of fits through the known values ​​of Smin; Smax or Nmin; Nmax and taking into account the accepted deviations of the main part. 4.3. Select the standard main and second deviations of the tolerance fields of the hole and shaft (Table B.2 or B.3). Write down tolerance fields in mixed form. 5. Calculate the limiting characteristics and landing tolerance using the formulas of practical exercise 1.2. 6. Construct a layout diagram of the landing tolerance fields. 7. Determine the error in selecting a fit based on the fit tolerance and limiting characteristics. The permissible error in selection based on fit characteristics can be ±10%. The formula for determining the error (∆Tpos) has the form: ∆Tpos Tset − Tst ⋅ 100% ≤ ±10%, Tset where ∆Tpos is the error in selecting the fit according to the fit tolerance, i.e. e. the relative magnitude of the difference between the assigned standard tolerance zone and the specified one; Tzad - specified fit tolerance; Tst - tolerance of the selected standard fit. Check the correctness of the selection of the fit by comparing the standard values ​​of the maximum clearances (preferences) with the specified ones: for fits with a gap Smax st ≤ Smax; Smin st ≈ Smin; for interference fits Nmax st ≈ Nmax; Nmin st ≥ Nmin. Chapter 1. Standardization of accuracy of smooth cylindrical joints 47 EXAMPLE OF PRACTICAL EXERCISE 1.5 Map of initial data to Figure A.12 Name of initial data Value of initial data Nominal size of the joint and its value Name of parts included in the joint D = 36 mm Mill 11 and spindle 6 Specified fit characteristics for the calculated method of assigning fits, µm: Smax= Smin= Requirements for the operation of the connection (from the description to the drawing) 42 2 At both ends of the spindle, cutters 11 are installed, which are periodically removed for sharpening or readjusting the machine Solution. 1. Determine the planting group. It is necessary to assign a standard fit with characteristics close to the specified ones. Limit clearances are specified, therefore a clearance fit must be assigned. 2. Determine the planting system. At both ends of the spindle there are 11 cutters installed, which are periodically removed for sharpening or readjusting the machine. Also along the diameter D at the same end of the spindle there is an adjusting washer and a protective ring for fits of a different nature. Thus, we assign the shaft system Ch (Table B.6). 3. Determine the accuracy of the fit. 3.1. Calculate the fit tolerance: TS = Smax – Smin = 42 – 2 = 40 µm. 3.2. Determine the relative accuracy of the fit (the number of fit tolerance units aS). Based on the nominal size, we find the tolerance unit (Table B.1) - i = 1.6 µm. Let's calculate the number of fit tolerance units: aS = TS 40 = ≈ 25. i 1.6 48 Metrology, standardization and certification 3.3. Determine the quality of the shaft and hole. Based on the fact that aS = aD + ad and in accordance with the principle of the basic fit that the accuracy of the hole and shaft is equal (the quality numbers of the hole and shaft are the same or differ by one), we accept aD = 16, ad = 10. This corresponds to the 7th grade for the hole and 6th grade for the shaft. 3.4. Find the tolerances of the hole and shaft. Using Table B.1, we determine the hole tolerance TD = IT7 = 25 µm and the shaft tolerance Td = IT6 = 16 µm. 4. Determine the main and second deviations of the hole and shaft. 4.1. Since the fit is assigned in the shaft system, we assign the tolerance field of the main shaft h6 with the main deviation es = 0 to the shaft. 4.2. We will determine the second shaft deviation taking into account the 6th grade tolerance according to Table B.2: ei = es – IT6 = 0 – 16 = –16 µm. Let's write the shaft tolerance field in a mixed way: 4.3. Let us determine the main deviation of the hole. Since a clearance fit in the shaft system is assigned, the main deviation of the hole tolerance field will be the lower limit deviation, which is determined by the specified minimum gap: EI = Smin + es = 2 + 0 = +2 µm. 4.4. According to GOST 25346-89 (Table B.3), we select the standard hole tolerance range. There is no standard tolerance range for a hole with a main deviation of EI = +2 µm. The closest to this arrangement will be the tolerance field of the main hole H7 with the main deviation EI = 0 µm. 4.5. We will calculate the second deviation of the hole tolerance field depending on the 7th grade tolerance: ES = EI + IT7 = 0 + 25 = +25 µm. Chapter 1. Standardization of accuracy of smooth cylindrical joints 49 Let's write the tolerance field of the hole in a mixed way: ∅36Н7 (+0.025). Thus, we will assign a fit to the “cutter-spindle” connection: ∅36 H7 (+0.025). h6 (−0.016) The fit is combined according to systems, since the hole is specified in the hole system, and the shaft is specified in the shaft system. 5. Calculate the limiting characteristics and fit tolerance. Calculation of characteristics consists of determining the maximum dimensions of the hole and shaft and determining the values ​​of the maximum clearances and fit tolerance. Limit hole dimensions: Dmax = D + ES = 36 + 0.025 = 36.025 mm; Dmin = D + EI = 36 + 0 = 36 mm. Limit shaft dimensions: dmax = d + es = 36 + 0 = 36 mm; dmin = d + ei = 36 + (–0.016) = 35.984 mm. Minimum clearance: Smin = Dmin – dmax = 36 – 36 = 0 mm. Maximum clearance: Smax = Dmax – dmin = 36.025 – 35.984 = 0.041 mm. Average probable gap: Sm = (Smax + Smin)/2 = (0.041 + 0)/2 = 0.0205 mm. Fit tolerance: TS = Smax – Smin = 0.041 – 0 = 0.041 mm = 41 µm; TS = TD + Td = 25 + 16 = 41 µm = 0.041 mm. 50 Metrology, standardization and certification 6. Construct a diagram of the location of tolerance fields for the designated fit (Fig. 1.16). 7. Checking the correctness of calculation and selection of landing. Determine the error ∆Tpos for selecting a fit according to the tolerance: ∆Tpos = Tset − Tst ⋅ 100%; Tback ∆Tpos = 40 − 41 ⋅ 100% = 2.5%< 10%. 40 Проверить правильность подбора посадки сравнением стандартных значений предельных зазоров (натягов) с заданными: Smaх ст = 41 ≤ Smax = 42; Smin ст = 0 ≈ Smin = 2. Следовательно, посадка назначена верно. Рис. 1.16 Схема расположения полей допусков вала и отверстия посадки Глава 1. Нормирование точности гладких цилиндрических соединений 51 1.2. ДОПУСКИ РАЗМЕРОВ, ВХОДЯЩИХ В РАЗМЕРНУЮ ЦЕПЬ 1.2.1. ОСНОВНЫЕ ПОНЯТИЯ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКОМУ ЗАНЯТИЮ 1.6 Размерная цепь - совокупность геометрических размеров (звеньев), расположенных по замкнутому контуру и определяющих взаимные положения и точность элементов деталей при изготовлении, измерении и сборке. По области применения размерные цепи можно разделить на конструкторские (сборочные), технологические (операционные, детальные) и измерительные. Звено размерной цепи - один из размеров, образующих размерную цепь. Звенья размерной цепи обозначаются заглавной буквой русского алфавита с числовым индексом, определяющим порядковый номер звена в цепи. Размерная цепь состоит из составляющих звеньев и одного замыкающего звена. Простейшей размерной цепью будет соединение вала с отверстием (рис. 1.17а). Эта размерная цепь содержит наименьшее число размеров (три), которые расположены параллельно и получены в результате обработки вала и втулки: диаметр вала d (А2), диаметр отверстия втулки D (А1). В результате сборки этих деталей получается замыкающее звено - зазор S (А∆), если размер отверстия будет больше размера вала до сборки, или натяг N (А∆), если размер вала будет больше размера отверстия до сборки. Простейшая технологическая размерная цепь двухступенчатого валика (рис. 1.17б) состоит из габаритного размера А1, ступени вала А2 и замыкающего звена, оставшейся части вала А∆, которая получается за счет обтачивания меньшего диаметра на длину А2. Схема размерной цепи - графическое изображение размерной цепи. Замыкающее звено - звено, получаемое в размерной цепи последним в результате решения поставленной задачи, 52 Метрология, стандартизация и сертификация Рис. 1.17 Виды размерных цепей: а - конструкторская (сборочная); б - технологическая (операционная). в том числе при изготовлении, сборке и измерении. В размерной цепи должно быть только одно замыкающее звено, которое получается последним в результате сборки, обработки или измерения (размер контролируемой детали). Составляющее звено - звено размерной цепи, изменение которого вызывает изменение замыкающего звена. Все составляющие звенья по характеру влияния на замыкающее звено делятся на увеличивающие и уменьшающие. Увеличивающие звенья - звенья, при увеличении которых замыкающее звено увеличивается. Уменьшающие - звенья, при увеличении которых замыкающее звено уменьшается. На рисунке 1.18 представлена схема размерной цепи, в которой звенья А1–А6 - составляющие звенья, А∆ - замыкающее звено. Для определения характера составляющего звена используют правило обхода по контуру размерной цепи. Для этого предварительно выбирают направление обхода размерной цепи (может быть любое). Оно совпадает с направлением левонаправленной стрелки (←), проставленной над замыкающим звеном. Обходя цепь в этом направлении, над Глава 1. Нормирование точности гладких цилиндрических соединений 53 составляющими звеньями расставляют стрелки в направлении обхода. Увеличивающие звенья обозначаются стрелкой над буквой, направленной вправо а уменьшающие - стрелкой, направленной влево Правило. Все составляющие звенья, имеющие такое же направление стрелок, которое имеет стрелка над замыкающим звеном, являются уменьшающими звеньями, а звенья, имеющие противоположное направление, - увеличивающими . По взаимному расположению размеров цепи делятся на плоские (звенья цепи расположены произвольно в одной или нескольких произвольных параллельных плоскостях) и пространственные (звенья цепи расположены произвольно в пространстве). В зависимости от вида звеньев цепи делятся на линейные (звенья цепи - линейные размеры, расположенные на параллельных прямых) и угловые (звенья цепи представляют собой угловые размеры, отклонения которых могут быть заданы в линейных величинах, отнесенных к условной длине, или в градусах). По месту в изделии цепи делятся на детальные (определяют точность относительного положения поверхностей или осей одной детали) и сборочные (определяют точность относительного положения поверхностей или осей деталей, образующих сборочную единицу). По характеру звеньев цепи делятся на скалярные (все звенья - скалярные величины), векторные (все Рис. 1.18 Схема размерной цепи 54 Метрология, стандартизация и сертификация звенья - векторные погрешности) и комбинированные (часть звеньев - векторные погрешности, остальные - скалярные величины). Перед тем как построить размерную цепь, следует выявить замыкающее звено. Для этого по чертежам общих видов и сборочных единиц выявляются и фиксируются все требования к точности, которым должно удовлетворять изделие или сборочная единица, например: точность взаимного расположения деталей, обеспечивающая качественную работу изделия при эксплуатации (перпендикулярность оси шпинделя станка к рабочей плоскости стола); точность взаимного расположения деталей, обеспечивающая собираемость изделия , . При выявлении замыкающих звеньев их номинальные размеры и допускаемые отклонения устанавливаются по стандартам, техническим условиям, на основании опыта эксплуатации аналогичных изделий, а также путем теоретических расчетов и специально поставленных экспериментов. Для нахождения составляющих звеньев после определения замыкающего звена следует идти от поверхностей (осей) деталей, образующих замыкающее звено, к основным базам (осям) этих деталей, от них - к основным базам деталей, образующих первые детали, и т. д. до образования замкнутого контура. В число составляющих звеньев необходимо включать размеры деталей, непосредственно влияющих на замыкающее звено, и стремиться к тому, чтобы от каждой детали в линейную цепь входил только один размер. Каждая размерная цепь должна состоять из возможно меньшего числа звеньев (принцип «кратчайшей» размерной цепи). 1.2.2. МЕТОДЫ РЕШЕНИЯ РАЗМЕРНЫХ ЦЕПЕЙ При решении размерных цепей могут быть использованы два метода расчета: метод расчета размерной цепи на max-min; вероятностный метод расчета. Глава 1. Нормирование точности гладких цилиндрических соединений 55 Метод расчета размерной цепи на max-min - метод расчета размерной цепи, при котором требуемая точность замыкающего звена размерной цепи получается при любом сочетании размеров составляющих звеньев. При этом предполагают, что в размерной цепи одновременно могут оказаться все звенья с предельными значениями, причем в любом из двух наиболее неблагоприятных сочетаний (все увеличивающие звенья имеют наибольшее предельное значение, а все уменьшающие звенья - наименьшее предельное значение или наоборот). В результате размер замыкающего звена будет максимальным или минимальным. Преимущества такого метода заключаются в простоте, наглядности, небольшой трудоемкости вычислительных работ, полной гарантии от брака из-за неточности замыкающего звена. Недостатком является то, что полученные по этому методу результаты часто не соответствуют фактическим. Метод экономически целесообразен лишь для цепей малой точности или для точных цепей с небольшим числом составляющих звеньев. Вероятностный метод расчета - метод расчета размерной цепи, учитывающий явление рассеяния и вероятность различных сочетаний отклонений составляющих звеньев. Этот метод допускает малый процент изделий, у которых замыкающее звено выйдет за рамки поля допуска. При этом расширяются допуски составляющих цепь размеров и тем самым снижается себестоимость изготовления деталей. В данном практическом занятии используется только метод расчета размерной цепи на max-min, а вероятностный метод расчета рассматривается в спецкурсах. Уравнения размерных цепей устанавливают взаимосвязь между параметрами замыкающего звена и составляющих звеньев. Для конструкторских (сборочных) линейных скалярных цепей передаточное отношение принимается для увеличивающих звеньев ξ = +1, для уменьшающих звеньев - ξ = –1. Тогда уравнения размерных цепей при расчете на max-min можно представить в следующем виде. 56 Метрология, стандартизация и сертификация 1. Уравнение номиналов. По определению размерной цепи следует, что сумма всех номинальных размеров, включая и замыкающее звено, равна нулю: Исходя из этого равенства, можно найти номинальный размер замыкающего звена: где ξ = ±1 - передаточное отношение; ρ - число составляющих звеньев. Или с учетом характера звена (передаточного отношения) получим уравнение номиналов для расчета размерной цепи на max-min (номинал замыкающего звена равен разности суммы номиналов увеличивающих звеньев и суммы номиналов уменьшающих звеньев): (1.36) где n - число увеличивающих звеньев; k - число уменьшающих звеньев. 2. Уравнение допусков. Допуск замыкающего звена (или поле рассеяния размера замыкающего звена) равен сумме допусков составляющих звеньев: (1.37) где p = n + k - число составляющих звеньев; 3. Уравнения предельных отклонений: верхнее отклонение замыкающего звена равно разности суммы верхних отклонений увеличивающих звеньев и суммы нижних отклонений уменьшающих звеньев: (1.38) Глава 1. Нормирование точности гладких цилиндрических соединений 57 нижнее отклонение замыкающего звена равно разности суммы нижних отклонений увеличивающих звеньев и суммы верхних отклонений уменьшающих звеньев: (1.39) При расчете конструкторских размерных цепей обычно решаются две задачи: прямая и обратная. Прямая задача заключается в том, что по предельным размерам и допуску замыкающего звена определяются допуски и предельные отклонения составляющих звеньев. Это основная задача, решаемая при проектировании. Дано: А∆; Т∆; ЕS∆; EI∆ (параметры замыкающего звена). Найти: Аj; Тj; ЕSj; EIj (параметры составляющих звеньев). Обратная задача заключается в том, что по размерам, предельным отклонениям и допускам составляющих звеньев определяется размер, допуск и предельные отклонения замыкающего звена. Эта задача используется при проверочных расчетах. Дано: Аj; Тj; ЕSj; EIj (параметры составляющих звеньев) Найти: А∆; Т∆; ЕS∆; EI∆ (параметры замыкающего звена). Нахождение точности составляющих звеньев при решении прямой задачи может осуществляться двумя способами: 1. Способ равных допусков. Этот способ применим в случае, когда все размеры цепи входят в один интервал размеров. Тогда допуски составляющих звеньев будут равны среднему допуску Тm: ТА1 = ТА2 = ... = ТАp = Тm. Средний допуск определяется по формуле (1.40) 58 Метрология, стандартизация и сертификация 2. Способ одного квалитета. Все размеры могут быть выполнены по какому-либо одному квалитету (или двум ближайшим квалитетам), который определяется нахождением среднего числа единиц допуска аm (средней относительной точности). Величины допусков при этом будут определены в зависимости от номинального размера (табл. Б.1). Известно, что допуск есть произведение единицы допуска на число единиц допуска. Это справедливо для любого звена размерной цепи: Tj = ijaj, где ij - единица допуска для каждого звена, мкм; aj - число единиц допуска каждого звена. Следовательно, уравнение допусков размерной цепи можно представить в следующем виде при условии, что число единиц допуска a у всех звеньев одинаковое (т. е. точность звеньев одинаковая): Так как допуски составляющих звеньев неизвестны, на основании уравнения размерных цепей (1.37) сумму допусков составляющих звеньев заменим допуском замыкающего звена, который задан по условию задачи. Определим среднее число единиц допуска размерной цепи - аm: (1.41) Если в размерную цепь включены стандартные звенья (ширина подшипника), необходимо из допуска замыкающего звена исключить сумму допусков стандартных звеньев, так как допуск этих звеньев уже известен и изменять его нельзя. В этом случае число единиц допуска определяется только для нестандартных звеньев - аmнест: Глава 1. Нормирование точности гладких цилиндрических соединений 59 (1.42) где t - число стандартных звеньев; p - число всех составляющих звеньев; (ρ − t) - число нестандартных звеньев; Tjст - допуск стандартного звена; ijнест - единица допуска нестандартного звена. Для определения полей допусков на размеры составляющих звеньев, кроме квалитета, необходимо назначить основные отклонения в зависимости от вида размеров: для охватываемых - h, охватывающих - H, остальных - js. Например, на рисунке 1.17а размер - охватывающий, размер - охватываемый; на рисунке 1.17б размер - охватывающий, относится к группе остальных размеров, т. е. не относится ни к охватываемым, ни к охватывающим. ПОРЯДОК ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 1.6 (РАСЧЕТ РАЗМЕРНОЙ ЦЕПИ НА MAX-MIN) (3-Й УРОВЕНЬ СЛОЖНОСТИ) Задание. По предельным размерам и допуску замыкающего звена определить допуски и предельные отклонения составляющих звеньев. Выполнить проверку, решив обратную задачу. Даны предельные размеры замыкающего звена и номинальные размеры составляющих звеньев. Варианты заданий указаны в Приложении А.13. 1. Решить прямую задачу. 1.1. Представить схему размерной цепи и указать, какие звенья охватываемые, а какие охватывающие. 1.2. Определить номинальный размер, предельные отклонения и допуск замыкающего звена. 1.3. Определить номинальный размер (номинал) замыкающего звена по уравнению номиналов размерной цепи (1.36). 60 Метрология, стандартизация и сертификация 1.4. Определить предельные отклонения через предельные размеры и номинал замыкающего звена. 1.5. Рассчитать допуск замыкающего звена по предельным размерам или предельным отклонениям. 1.6. Определить характер составляющих звеньев (увеличивающие или уменьшающие звенья). 1.7. Определить точность составляющих звеньев, используя способ равных квалитетов (формулы 1.41 и 1.42). Назначить одинаковый квалитет на все звенья. 1.8. Определить вид и значения (табл. Б.1) основных отклонений полей допусков составляющих звеньев в зависимости от вида размера (для охватываемых - h; охватывающих - H; остальных - js). 2. Решить обратную задачу. 2.1. Выполнить проверку по уравнению допусков (1.37). При большой разнице между полем рассеяния и допуском замыкающего звена выполнить согласование по квалитетам (изменить квалитет у одного звена). 2.2. Выполнить проверку по предельным отклонениям (1.38), (1.39). Для корректировки расположения поля рассеяния замыкающего звена выбрать самое простое по конструкции согласующее звено. Рассчитать новые предельные отклонения согласующего звена, подставив в левую часть Т а б л и ц а 1.10 Номинальный размер звена, мм Значение единицы допуска ij, мкм Обозначение размеров размерной цепи, Аj Расчет размерной цепи методом на «максимум - минимум» после назначения полей допусков по расчетному значению аm 55 1,9 55Js10(±0,06) 55Js10(±0,06) 3 0,6 3h10(–0,04) 3h10(–0,04) 22 1,3 22h10(–0,084) 22h11(–0,13) 22h11(–0,13) 32 1,6 32h10(–0,10) 32h10(–0,10) 32h10(–0,10) ω∆ = 0,344 ω∆ = 0,39 ω∆ = 0,4 Т∆ 0,4 A∆ 2–0,4 - Принятые значения звеньев размерной цепи ω∆ < T∆ после согласования значений допусков после согласования предельных отклонений 55Js10(±0,06) 2–0,4 Глава 1. Нормирование точности гладких цилиндрических соединений 61 уравнений требуемые значения предельных отклонений замыкающего звена. 2.3. Представить результаты расчета размерных цепей в виде таблицы (табл. 1.10). ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 1.6 (РАСЧЕТ РАЗМЕРНОЙ ЦЕПИ НА MAX-MIN) Задание. Необходимо обеспечить собираемость деталей с валом (Приложение А.13, табл. А.25, рис. А.13; вариант 13-1). Исходные данные: 1) предельные размеры замыкающего звена (зазор между торцами вала 13 и зубчатого колеса 3): А∆min = 1,6 мм; A∆max = 2,0 мм; 2) номинальные размеры составляющих звеньев: длина ступени вала 13 - А1 = 53 мм; буртик втулки 7 - А2 = 3 мм; длина втулки 7 - А3 = 22 мм; длина (высота) зубчатого колеса 3 - А4 = 32 мм. Решение. 1. Решить прямую задачу. 1.1. На рисунке 1.19 представлена схема размерной цепи, в которую включены размеры, влияющие на замыкающее звено, по одному от каждой детали. Размеры А2, А3, А4 - охватываемые; размер А1 не относится ни к охватываемым, ни к охватывающим (группа остальных размеров). Рис. 1.19 Схема размерной цепи 62 Метрология, стандартизация и сертификация Для обеспечения полной взаимозаменяемости сборки решение следует вести методом расчета на max-min, так как цепь невысокой точности. 1.2. Определить номинальный размер, предельные отклонения и допуск замыкающего звена. 1.3. Определить номинальный размер замыкающего звена: А∆ = (32 + 22 + 3) – 55 = 2 мм. 1.4. Определить предельные отклонения замыкающего звена через его предельные размеры и номинал: ES∆ = A∆max – А∆ = 2 – 2 = 0; EI∆ = А∆min – A∆ = 1,6 – 2 = –0,4 мм. 1.5. Определить допуск замыкающего звена: Т∆ = A∆max – А∆min = 2 – 1,6 = 0,4 мм = 400 мкм. Записать номинал и предельные отклонения замыкающего звена в виде исполнительного размера: А∆ = 2–0,4 (нулевое отклонение не обозначается). 1.6. Определить характер составляющих звеньев. Для этого обходим цепь слева направо в соответствии с левонаправленной стрелкой, указанной над замыкающим звеном. Расставляем стрелки над составляющими звеньями в направлении обхода. В соответствии с правилом обхода по контуру размерной цепи определяем характер составляющих звеньев: звено - уменьшающее; звенья - увеличивающие. 1.7. Определить точность составляющих звеньев. Так как номинальные размеры составляющих звеньев относятся к разным интервалам размеров, для определения точности составляющих звеньев используем способ одного квалитета, т. е. рассчитаем среднее число единиц допуска с учетом отсутствия в цепи стандартных звеньев по формуле (1.41): Глава 1. Нормирование точности гладких цилиндрических соединений 63 Ближайшее к рассчитанному значению аm = 74 стандартное число единиц допуска равно аm = 64, что соответствует 10-му квалитету. Поэтому принимаем для всех звеньев 10-й квалитет. 1.8. Определить вид и значения основных отклонений полей допусков составляющих звеньев в зависимости от вида размера (для охватываемых - h; охватывающих - H; остальных - js). Так как звено А1 относится к третьей группе размеров, назначим на него поле допуска js10, а для звеньев А2, А3, А4 (как на охватываемые) поле допуска h10. Составляющие звенья будут иметь следующие размеры: 2. Решить обратную задачу 2.1. Выполним проверку по допускам. Рассчитаем поле рассеяния замыкающего звена: ω∆ = 120 + 40 + 84 + 100 = 344 = 0,344 < 0,4 на 0,056 мм. Так как разница между полем рассеяния ω∆ = 0,344 мм и заданным допуском замыкающего звена T∆ = 0,4 мм получилась слишком большая, изменим 10-й квалитет звена А3 на 11-й квалитет. Тогда Это позволяет расширить поле рассеяния замыкающего звена на следующую величину: IT11 – IT10 = 0,130 – 0,084 = 0,046 мм, т. е. поле рассеяния при этом будет равно ω∆ = 0,39 мм. Примечание. Звено А3 выбрано потому, что разница между допусками 10-го и 11-го квалитетов для номинального размера этого звена наиболее близко приближает поле 64 Метрология, стандартизация и сертификация рассеяния замыкающего звена к полю допуска замыкающего звена. 2.2. Выполним проверку по предельным отклонениям: ES∆ = – [–0,060] = +0,060 мм; EI∆ = [(–0,040) + (–0,13) + (–0,10)] – [(+0,06)] = –0,33 мм. Следовательно, поле рассеяния замыкающего звена по предельным отклонениям равно: ω∆ = ES∆ – EI∆ = 0,06 – (–0,33) = 0,39 мм. Это совпадает со значением поля рассеяния, полученным по уравнению допусков: ω∆ = 0,39 мм, т. е. расчет предельных отклонений замыкающего звена выполнен правильно. Однако расположение поля рассеяния замыкающего звена, полученное по отклонениям (рис. 1.20а), не соответствует заданному положению поля допуска (рис. 1.20б). 2.3. Для обеспечения заданного расположения поля допуска замыкающего звена выберем самое простое по конструкции согласующее звено. Таким звеном будет звено А2 (высота буртика втулки). Принимаем его отклонения за неизвестные и решаем уравнения отклонений размерной цепи относительно этих неизвестных, подставив в левую часть уравнений требуемые отклонения (А∆ = 3–0,4) замыкающего звена. 0 = – [(–0,06)]; Рис. 1.20 Расположение поля допуска замыкающего звена: а - полученное по отклонениям; б - заданное. Глава 1. Нормирование точности гладких цилиндрических соединений 65 ESA2 = –0,06 мм; –0,4 = – [(+0,06)]; EIA2 = –0,11 мм. В результате для звена А2 получили новые предельные отклонения и допуск звена: TA2 = 0,05 мм. Таким образом, расширение допуска компенсирующего звена и изменение его предельных отклонений позволили получить замыкающее звено в заданных пределах (рис. 1.20б). Все расчеты внесем в таблицу 1.10. ГЛ А В А 2 НОРМИРОВАНИЕ ТРЕБОВАНИЙ К ШЕРОХОВАТОСТИ ПОВЕРХНОСТИ И ГЕОМЕТРИЧЕСКИМ ДОПУСКАМ 2.1. ШЕРОХОВАТОСТЬ ПОВЕРХНОСТИ И ЕЕ НОРМИРОВАНИЕ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЮ 2.1 Н а поверхности детали после обработки остаются следы от кромок режущего инструмента в виде неровностей и гребешков, близко расположенных друг от друга. Шероховатостью поверхности называется совокупность неровностей с относительно малыми шагами, выделенная на базовой длине (l). Нормирование шероховатости поверхности по ГОСТ 2789-73 выполнено с учетом рекомендаций международных стандартов. Установлены (рис. 2.1) шесть параметров: три высотных (Ra; Rz; Rmax), два шаговых (Sm; S) и параметр относительной опорной длины профиля (tp) , , . Рис. 2.1 Профилограмма шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 67 Характеристика параметров шероховатости: Ra - среднее арифметическое отклонение профиля, мкм: (2.1) где yi - расстояние между любой точкой профиля и средней линией m, cредняя линия имеет форму номинального профиля и проводится так, что в пределах базовой длины среднее квадратическое отклонение профиля до этой линии минимально; n - количество рассматриваемых точек профиля на базовой длине. Rz - высота неровностей профиля по 10 точкам, мкм: (2.2) где Himax; Himin - высота наибольшего выступа и глубина наибольшей впадины, мкм. Соотношение между Ra и Rz колеблется в пределах от 4 до 7 раз; Rz больше, чем Ra. Rmax - наибольшая высота профиля - расстояние между линией выступов и линией впадин, мкм; Sm - средний шаг неровностей профиля по средней линии в пределах базовой длины, мм: (2.3) где n - количество шагов в пределах базовой длины; Smi - шаг неровностей профиля по средней линии. S - средний шаг местных выступов профиля (по вершинам) в пределах базовой длины, мкм: (2.4) где n - количество шагов в пределах базовой длины; Si - шаг местных выступов профиля. tp - относительная опорная длина профиля в %: 68 Метрология, стандартизация и сертификация (2.5) где p - уровень сечения профиля в процентах - это расстояние между линией выступов и линией, пересекающей профиль эквидистантно линии выступов; за 100% принимается Rmax; bi - длина отрезка, отсекаемая на заданном уровне в материале, мм; l - базовая длина, мм. Направления неровностей обработки зависят от метода и технологии изготовления, влияют на работоспособность, износостойкость и долговечность изделия. Условные обозначения направления неровностей (табл. 2.1) указывают на чертеже при необходимости. Т а б л и ц а 2.1 Условное обозначение направлений неровностей Тип направления неровностей Обозначение Тип направления неровностей Параллельное Произвольное Перпендикулярное Кругообразное Перекрещивающееся Радиальное Обозначение Точечное Выбор параметров производится в зависимости от эксплуатационных свойств поверхности. Предпочтительным принят параметр Ra - среднее арифметическое отклонение профиля, так как он определяет шероховатость по всем точкам профиля (табл. В.1). Глава 2. Нормирование требований к шероховатости поверхности 69 Точечное направление неровностей дают поверхности, полученные методом порошковой металлургии, электроискровым методом, травлением и др. Средняя высота неровностей по 10 точкам Rz используется в тех случаях, когда нельзя измерить Ra на приборах типа профилометр путем ощупывания поверхности алмазной иглой (острые кромки, мягкий материал, особо чистая поверхность). Шаговые параметры влияют на виброустойчивость, сопротивление в волноводах и электропроводность в электротехнических деталях. Параметр tp необходимо учитывать при высоких требованиях к контактной жесткости и герметичности. В ГОСТ 2789-59 предусматривалось 14 классов шероховатости в порядке уменьшения значений параметров. В сравнительной таблице В.1 даны соотношения между классами шероховатости и другими высотными параметрами. С 1983 г. для всех классов введен ряд значений Ra предпочтительного применения по 1-му варианту. Определение значений параметров шероховатости может быть выполнено методом подобия и расчетным методом. Метод подобия (табл. В.2) ориентируется на экономическую точность, которая устанавливает зависимость шероховатости и формы поверхности от допуска размера и применяемого отделочного метода обработки. Минимальные требования к шероховатости поверхности в зависимости от допусков размера и формы даны в таблице В.3 . Примеры выбора числовых значений Ra в зависимости от вида соединения даны в таблице В.4. При расчетном методе учитывается зависимость параметров шероховатости поверхности от допуска размера, так как при обеспечении требуемой точности размера изменяется шероховатость и точность геометрической формы поверхности. Для деталей жесткой конструкции (L ≤ 2d) соотношение допусков размера (Т) и формы поверхности (Тф) установлены три уровня относительной геометрической точности (ГОСТ 24643-81): А - нормальный, используемый наиболее часто в машиностроении для поверхностей без особых требований 70 Метрология, стандартизация и сертификация к точности формы при низкой скорости вращения или перемещения; В - повышенный, используемый для поверхностей, работающих при средних нагрузках и скоростях до 1500 об/мин, при оговоренных требованиях к плавности хода и герметичности уплотнений. Поверхности, образующие соединения с натягом или по переходным посадкам при воздействии больших скоростей и нагрузок, при наличии ударов и вибраций; С - высокий, рекомендуемый для поверхностей, работающих в подвижных соединениях при высоких нагрузках и скоростях свыше 1500 об/мин, при высоких требованиях к плавности хода, герметичности уплотнения и при необходимости трения малой величины; при высоких требованиях к точности центрирования, прочности соединения в условиях воздействия больших нагрузок, ударов и вибраций. Значения коэффициентов формы (Kф) и шероховатости (Kr) приведены в таблице 2.2. Т а б л и ц а 2.2 Значения коэффициентов Kф и Kr Уровень относительной геометрической точности цилиндрические поверхности плоские поверхности Значение коэффициента Kф Значение коэффициента Kr А 0,3 0,6 0,05 В 0,2 0,4 0,025 С 0,12 0,25 0,012 Значение Ra можно рассчитать по формуле Ra = KrТ, (2.6) где Т - допуск на размер, ограничивающий данную поверхность (Td или TD); Kr - коэффициент шероховатости поверхности по таблице 2.2. Расчетное значение округлить в сторону уменьшения до величины, указанной в таблице В.1, вариант 1. Указание требований к шероховатости поверхностей производится на чертежах согласно ЕСКД по ГОСТ 2.30973 «ЕСКД. Обозначения шероховатости поверхностей». Глава 2. Нормирование требований к шероховатости поверхности 71 Рис. 2.2 Место и порядок записи параметров шероховатости Обозначение шероховатости состоит из условного значка и числовых значений . Структура обозначения шероховатости поверхности приведена на рисунке 2.2. При применении знака без указания параметра и способа обработки его изображают без полки. В обозначении шероховатости применяют один из знаков: - основной знак, когда метод обработки поверхности чертежом не регламентируется; - знак, соответствующий поверхности, полученной удалением слоя металла (точением, сверлением, фрезерованием, шлифованием и т. д.); - знак, соответствующий поверхности в состоянии поставки, без удаления слоя металла (литье, штамповка, поковка и т. д.). Согласно ГОСТ 2.309-73 с 01.01.2005 г. при задании параметров шероховатости: обязательно указывать символы (Ra, Rz, S, tp) перед их числовым значением; все параметры записывать под полочкой. Под полочкой могут быть указаны: условные обозначения неровностей, базовая длина и все параметры шероховатости по строчкам, начиная с Ra; над полочкой указывают способ обработки и другие дополнительные требования (например, полировать); 72 Метрология, стандартизация и сертификация знак «остальное» для поверхностей, обрабатываемых с одинаковыми требованиями, указывать в верхнем правом углу чертежа, например, или; обработку поверхностей сложного контура «кругом» указывать так: . Знак шероховатости может указываться на контурной линии чертежа, на размерных линиях или на их продолжениях, на рамке допуска формы, на полках линий - выносок (рис. 2.3а). При указании двух и более параметров шероховатости поверхности в обозначении шероховатости значения параметров записывают сверху вниз в следующем порядке (рис. 2.3б): параметры высоты неровностей профиля; параметры шага неровностей профиля; относительная опорная длина профиля. При нормировании требований к шероховатости поверхности параметрами Ra, Rz, Rmax базовую длину в обозначении шероховатости не приводят, если она соответствует ГОСТ 2789-73 для выбранного значения параметра шероховатости (табл. В.1). В данном примере указано (рис. 2.3б): среднеарифметическое отклонение профиля Ra не более 0,1 мкм на базовой длине l = 0,25 мм (в обозначении Рис. 2.3 Примеры обозначения шероховатости: а - возможное размещение знака шероховатости; б - указание нескольких параметров. Глава 2. Нормирование требований к шероховатости поверхности 73 Рис. 2.4 Варианты обозначения шероховатости в правом углу чертежа: а - все поверхности имеют одинаковую шероховатость; б - часть поверхностей имеет одинаковую шероховатость (остальные); в - часть поверхностей по данному чертежу не обрабатывается (полочка не рисуется, параметры не указываются. базовая длина не указана, так как соответствует значению, определенному стандартом для данной высоты неровностей); средний шаг неровностей профиля Sm должен находиться в пределах от 0,063 до 0,040 мм на базовой длине l = 0,8 мм; относительная опорная длина профиля на 50%-ном уровне сечения должна находиться в пределах 80 ± 10% на базовой длине l = 0,25 мм. Примеры задания требований к шероховатости поверхности: означает Ra ≤ 1,6 мкм, метод обработки поверх ности чертежом не регламентируется; означает Rz≤ 40 мкм, обработка резанием; означает Ra ≤ 12,5 мкм, поверхность без удале ния слоя металла (литье, штамповка, поковка и т. д.). Обозначение шероховатости поверхностей повторяющихся элементов изделия (отверстий, пазов, зубьев и т. д.), количество которых указано на чертеже, а также обозначение шероховатости одной и той же поверхности, независимо от числа изображений или поверхностей, имеющих одинаковую шероховатость и образующих контур, наносят один раз. В правом верхнем углу чертежа указывают общие требования к поверхностям детали, варианты задания таких требований указаны на рисунке 2.4. 74 Метрология, стандартизация и сертификация ПОРЯДОК ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 (1-Й УРОВЕНЬ СЛОЖНОСТИ) Ознакомиться с теоретической частью раздела. Получить задание (вариант) практической работы. Варианты заданы в таблице 2.3. Т а б л и ц а 2.3 Варианты заданий к практическому занятию 2.1 № варианта Обозначение шероховатости поверхности № варианта 1 15 2 16 3 17 4 18 5 19 6 20 Обозначение шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 75 П р о д о л ж е н и е т а б л. 2.3 № варианта Обозначение шероховатости поверхности № варианта 7 21 8 22 9 23 10 24 11 25 12 26 13 27 14 28 Обозначение шероховатости поверхности 76 Метрология, стандартизация и сертификация Задание. По заданному варианту расшифровать условное обозначение шероховатости. Решение. 1. Указать вид условного значка, обозначающего требования к шероховатости поверхности. 2. Определить тип направления неровностей. 3. Определить наименование параметров шероховатости, их условное обозначение и числовое значение. 4. Указать базовую длину и объяснить ее назначение. ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 Задание. По заданному варианту расшифровать условное обозначение шероховатости. Дано: Решение. 1. Использован знак - метод обработки поверхности чертежом не регламентируется. 2. Направление неровностей не регламентируется, т. е. соответствует методу обработки. 3. Шероховатость нормируется по: параметру Ra (среднее арифметическое отклонение профиля), значение которого не должно превышать 0,1 мкм; средний шаг неровностей профиля по средней линии Sm в пределах (0,063–0,040) мм; относительная опорная длина профиля tp, задана на уровне 50% и должна составлять 80 ± 10%; 4. Базовая длина l = 0,25 мм для Ra не указывается, так как ее числовое значение соответствует числовому значению параметра Ra (табл. В.1); базовая длина l = 0,8 мм для Sm указана, базовая длина l = 0,25 мм для tp указана, так как эти параметры на приборах профилометр - профилограф измеряются на больших базовых длинах. Глава 2. Нормирование требований к шероховатости поверхности 77 2.2. НОРМИРОВАНИЕ ОТКЛОНЕНИЙ ФОРМЫ ПОВЕРХНОСТИ 2.2.1. ТЕРМИНЫ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЯМ 2.2, 2.3, 2.4 В ГОСТ 24642 (не действует в РФ) даны термины и определения, относящиеся к допускам формы; на территории России введен в действие с 01.01.2012 г. ГОСТ Р 53442, который устанавливает определения и правила указания на чертежах геометрических допусков (формы, ориентации, месторасположения и биения). Однако необходимо рассмотреть некоторые понятия ГОСТ 24642-81, так как аналогичных им в новом стандарте нет. Отклонением формы EF (∆ф) называется отклонение формы реального элемента от номинальной формы, оцениваемое наибольшим расстоянием от точек реального элемента по нормали к прилегающему элементу (рис. 2.5). Шероховатость поверхности в отклонение формы не включается. Номинальная поверхность - это идеальная поверхность, форма которой задана чертежом или другой технической документацией. Реальная поверхность - это поверхность, ограничивающая тело и отделяющая его от окружающей среды. Отклонения формы оцениваются по всей поверхности (по всему Рис. 2.5 Схема к определению отклонения формы поверхности 78 Метрология, стандартизация и сертификация профилю) или на нормируемом участке, если заданы площадь, длина или угол сектора, а в необходимых случаях и расположение его на поверхности. Если расположение участка не задано, то его считают любым в пределах всей поверхности или профиля. Отсчет отклонений формы поверхности производится по нормали к прилегающей поверхности как наибольшее расстояние от точек реальной поверхности до прилегающей, которая рассматривается как номинальная. Прилегающая поверхность - поверхность, имеющая форму номинальной поверхности, соприкасающаяся с реальной поверхностью и расположенная вне материала детали так, чтобы отклонение от нее наиболее удаленной точки реальной поверхности в пределах нормируемого участка имело минимальное значение. Отклонения формы профиля оцениваются аналогично - от прилегающей линии. Допуск формы TF (Тф) - это наибольшее допускаемое значение отклонения формы. Допуски формы могут быть: комплексными (плоскостность, цилиндричность, круглость, допуск формы заданного профиля); элементарными (выпуклость, вогнутость, овальность, огранка, конусообразность, седлообразность, бочкообразность). Отклонение от круглости ∆кр - наибольшее расстояние от точек реального профиля до прилегающей окружности (рис. 2.6). Основные виды частных отклонений профиля поперечного сечения цилиндрических поверхностей - овальность (рис. 2.7а) и огранка (рис. 2.7б). Частные отклонения профиля продольного сечения - конусообразность (рис. 2.8а), бочкообразность (рис. 2.8б), седлообразность (рис. 2.8в). Для всех случаев отклонение формы определяется в радиусном выражении: (2.7) Допуски формы поверхности назначаются только в том случае, если они по условиям эксплуатации изделия должны Глава 2. Нормирование требований к шероховатости поверхности Рис. 2.6 Отклонение от круглости Рис. 2.7 Частные виды отклонений от круглости: а - овальность; б - огранка. Рис. 2.8 Частные виды отклонений формы профиля продольного сечения: а - конусообразность; б - бочкообразность; в - седлообразность. 79 80 Метрология, стандартизация и сертификация быть меньше допуска размера. Виды допусков формы и другие геометрические допуски представлены в таблице В.5. Наименование геометрического допуска состоит из слова «допуск» и геометрической характеристики элемента, нормируемой им, например «допуск прямолинейности». Исключение составляет допуск позиционирования, который в сложившейся практике имеет наименование «позиционный допуск». Числовые значения допусков формы и расположения поверхностей установлены ГОСТ 24643-81 по 16 степеням точности (табл. В.6 и В.7). В таблицах рассмотрены 12 степеней, т. к. для грубых поверхностей применяется ГОСТ 30893.2 на общие допуски. Числовые значения допусков формы поверхности могут быть определены расчетным методом и методом подобия. 2.2.2. ОПРЕДЕЛЕНИЕ ЧИСЛОВЫХ ЗНАЧЕНИЙ ДОПУСКОВ ФОРМЫ ПОВЕРХНОСТИ Метод подобия применяется при известном квалитете точности размера рассматриваемой поверхности. Определяется степень точности формы поверхности по условиям экономической точности для жесткой конструкции (табл. В.2). Степень точности снижается на одну, если L/d от 2 до 5; на две степени точности грубее, если L/d >5. The calculation method is based on the relationship between dimensional tolerances and shape tolerances and surface roughness. When considering the relationship between the size tolerance and the shape tolerance, for cylindrical parts the diameter of the surface under consideration is accepted, and for flat parts - a tolerance for the thickness of the part, since the largest error is equal to this tolerance, i.e. 100%. Tf max = Td. For cylindrical parts, the shape tolerance is specified in radius terms, so the largest shape error is taken to be 50% of the diameter tolerance: Tf max = Td/2. Chapter 2. Standardization of requirements for surface roughness 81 For level A, shape tolerance (

A.G.Sergeev

M.V.Latyshev

V.V. Teregerya

PRACTICUM

ON METROLOGY, STANDARDIZATION, CERTIFICATION

Vladimir 2005

A.G. Sergeev, M.V. Latyshev, V.V. Teregerya

PRACTICUM

ON METROLOGY, STANDARDIZATION, CERTIFICATION

Tutorial

Vladimir 2005

UDC 621.753(076) + 658.516(075.8)

Reviewer

Workshop on metrology, standardization, certification / Compiled by: A.G. Sergeev, M.V. Latyshev, V.V. Teregerya; Vladim. state univ. Vladimir, 2005. p.

Compiled in accordance with the course program “Metrology, standardization, certification” for specialties 120301, 114000, 210200

The sections of the textbook contain practical training materials on the following topics of the course “Metrology, standardization, certification”: legal foundations of standardization, classification of technical documentation, development of technical specifications for products and services, control of the accuracy of manufacturing parts, basic concepts of connections and fits, state standard ESDP , selection of methods and means for measuring linear dimensions, processing of results of direct multiple measurements, certification basics.

Intended for full-time students of the named specialties.

Il. Table . Bibliography name

UDC 621.753(076 + 658.516

1. STANDARDIZATION

1.1. LEGAL FRAMEWORK AND REGULATIVE DOCUMENTS FOR STANDARDIZATION OF THE RUSSIAN FEDERATION

Basic provisions. The main document in the Russian Federation on standardization is the law “On Technical Regulation”, as well as the laws “On Ensuring the Uniformity of Measurements”, “On the Protection of Consumer Rights” and the resolutions of the Government of the Russian Federation adopted to implement these Laws of the Russian Federation.

The Law “On Technical Regulation” establishes the legal basis for standardization in the Russian Federation, defines the rights and obligations of participants regulated by the Federal Law of Relations. It regulates the relations arising in the development, adoption, application and use of mandatory requirements for products, production processes, operation and disposal, as well as the development, adoption, application and use on a voluntary basis of requirements for products, production processes, operation, storage, transportation, sales and disposal, performance of work or provision of services. Other Federal laws and regulations of the Russian Federation relating to the field of standardization (including those directly or indirectly providing for monitoring compliance with the requirements of technical regulations) are applied to the extent that does not contradict the main document. Federal executive authorities have the right to issue acts of only a recommendatory nature in the environment of technical regulation, with the exception in the case of regulation in relation to defense products (works, services) and products (works, services) information about which constitutes a state secret. If an international treaty of the Russian Federation in the field of technical regulation establishes rules other than those provided for by the basic Federal Law, the rules of the international treaty are applied, and if it follows from the international treaty that its application requires the publication of an internal act, the rules of the international treaty are applied agreement and adoption of legislation of the Russian Federation on its basis (see Appendix 1).

To strengthen the role of standardization in scientific and technological progress, improve the quality of products and the efficiency of their production, the Russian National Standardization System (RNSS) was developed. The basis of the RNSS is the State Standardization System (GOST R 1.0 – 92.

GSS RF. Basic provisions; GOST 1.5 – 2002. State Standards of the Russian Federation. Standards. General requirements for construction, presentation, design, content and designation; GOST R 1.8 – 2002. GSS RF. Interstate standards. Rules for the development, application, updating and termination of work carried out in the Russian Federation; GOST R 1.9 – 95. GSS RF. The procedure for marking products and services with a sign of compliance with state standards; GOST R 1.12 – 99. GSS RF. Terms and Definitions. etc.) as amended in the light of the Federal Law “On Technical Regulation”. The RNSS establishes the legal basis for standardization in the Russian Federation, for all government bodies, as well as enterprises and entrepreneurs, public associations, and determines measures of state protection of the interests of consumers and the state through the development and application of regulatory documents on standardization.

Standardization, as defined by ISO/IEC, is the establishment and application of rules with the aim of streamlining activities in a certain area for the benefit and with the participation of all interested parties, in particular to achieve overall optimal savings while complying with operating conditions (use) and safety requirements.

According to the Federal Law “On Technical Regulation”, standardization is carried out for the purposes of: increasing the level of safety of life or health of citizens, property of individuals or legal entities, state or municipal property, environmental safety, safety of life or health of animals and plants and promoting compliance with requirements technical regulations; increasing the level of safety of facilities, taking into account the risk of natural and technical emergencies; ensuring scientific and technological progress; increasing the competitiveness of products, works and services; rational use of resources; technical and information compatibility; comparability of research (test) and measurement results, technical and economic-statistical data; interchangeability of products. Standardization is guided by the following principles: voluntary application of standards; maximum consideration when developing standards of the legitimate interests of interested parties; application of an international standard as the basis for the development of a national standard, except in cases where such application is recognized as impossible due to the inconsistency of the requirements of international standards with the climatic and geographical features of the Russian Federation, technical and (or) technological features or for other reasons or the Russian Federation in

in accordance with established procedures, opposed the adoption of an international standard or its individual provisions; inadmissibility of creating obstacles to the production and circulation of products, performance of work and provision of services to a greater extent than is minimally necessary to achieve the goals of standardization; the inadmissibility of establishing standards that contradict technical regulations; ensuring conditions for uniform application of standards.

Standardization activities are regulated by regulatory documents. A normative document on standardization is a document that establishes rules, principles, norms, characteristics relating to objects of standardization, various types of activities or their results, and is accessible to a wide range of users. The list of main regulatory documents on standardization is shown in Fig. 1.1.1.

International standards are developed and issued by the International Organization for Standardization. National standards are created on the basis of international standards; they are also used for international economic relations. The main purpose of these standards is to promote the favorable development of standardization in the world in order to facilitate the international exchange of goods and develop mutual cooperation in the field of intellectual, scientific, technical and economic activities.

International, as well as national foreign standards are introduced in the Russian Federation through the adoption of state standards or technical regulations.

International standards are widely used in the world, their number currently exceeds 12 thousand, and about a thousand standards are adopted or revised annually. They are not mandatory for use by member countries of the international organization for standardization. The decision to use them is related to the degree of participation of a particular country in the international division of labor and the state of its foreign trade. In Russia there is currently an active process of introducing international standards into the national standardization system.

In Fig. 1.1.2 provides a list of international standardization organizations.

Rice. 1.1.1. List of main regulatory documents on standardization

Regulations

STP is a standard for enterprises and organizations.

Rice. 1.1.1. Ending

Rice. 1.1..2. International standardization organizations

Work assignment. Study the main legal documents on standardization (Federal Law “On Technical Regulation”, see Appendix 1), categories and types of regulatory documents on standardization. Familiarize yourself

learn about the concept of “international standards” and the activities of international standardization organizations.

Practical tasks. Answer the questions:

concept of standardization.

standardization goals.

Russian national standardization system.

definition of standard.

international standardization.

international standardization bodies.

Determine the correct test control answers.

1. Name the regulatory document on the legal basis of standardization in the Russian Federation:

“Law on Technical Regulation”;

“Law on Ensuring the Uniformity of Measurements”;

"International Acts";

"Regulatory and technical documents on standardization."

2. What is the nature of the requirements of technical regulations:

Only some of them are mandatory;

they are mandatory for use;

3. Indicate the leading international organization in the field of standardization:

International Electrotechnical Commission (IEC);

European Committee for Standardization (CEN);

International Organization for Standardization (ISO).

4. What is called a standard:

a document in which, for the purpose of voluntary repeated use, the characteristics of products, rules for implementation and characteristics of the processes of production, operation, storage, transportation, sale and disposal, performance of work or provision of services are established;

This is a planned activity to establish mandatory rules, norms and requirements for the object of standardization.

5. What is called technical regulations:

a document indicating only the technical requirements for the object of standardization;

a regulatory document developed for specific production processes and their elements related to solving the problems of organizing and managing work on standardization, metrology, certification, accreditation, licensing, state control and supervision of compliance with mandatory requirements of technical regulations, state and international standards.

This is a planned activity to establish mandatory rules, norms and requirements for the object of standardization.

This collection of descriptions of practical and laboratory work in the discipline “Metrology, standardization and certification” was developed for students in specialties 150411, 240401, 220301, 140613. Assignments for practical work are compiled in accordance with the current program, taking into account the specifics of each specialty. The collection includes works that make it possible to analyze the structure and content of standards, carry out measurements and their mathematical processing, study standardization in the industrial sphere, the basic norms of product interchangeability in order to ensure its quality and competitiveness. The collection includes works to familiarize yourself with the basic standards of product interchangeability and standardization of GVC accuracy; on the conversion of non-metric units of measurement to SI units. It deals with issues related to the choice of measuring instruments and how they measure linear dimensions.

Due to the lack of literature on the discipline, the main theoretical material necessary for study during practical work is included in the manual. This material is studied independently in preparation for practical work and is consolidated during its implementation. To improve theoretical and practical knowledge, the collection includes test questions and business situations.

The teaching aid includes:

Assignments for class topics indicating the order of their completion;

As an appendix to the collection of tasks are:

1. Law of the Russian Federation “On ensuring the uniformity of measurements”;

2. Federal Law “On Technical Regulation”;

3. NSS standards: GOST R 1.0-2004, GOST R 1.12-2004, GOST R 1.2-2004, GOST R 1.4-2004, GOST R 1.5-2004, GOST R 1.9-2004, GOST 2.114-95.

4. GOST R certification system

5. Fragments of ESDP standards.

6. Answers to tasks with solutions.

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Transcript

1 MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous Educational Institution of Higher Education "NATIONAL RESEARCH TOMSK POLYTECHNIC UNIVERSITY" A.S. Spiridonova, N.M. Natalinova PRACTICUM ON METROLOGY, STANDARDIZATION AND CERTIFICATION Recommended as a textbook by the Editorial and Publishing Council of Tomsk Polytechnic University Publishing House of Tomsk Polytechnic University 2014

2 UDC (076.5) BBK ya73 S72 S72 Spiridonova A.S. Workshop on metrology, standardization and certification: textbook / A.S. Spiridonova, N.M. Natalinova; Tomsk Polytechnic University. Tomsk: Publishing house of Tomsk Polytechnic University, p. The manual contains six laboratory works and four practical classes, which include the necessary theoretical materials and test questions to prepare for the defense of completed work. Designed for students of all directions to consolidate the theoretical foundations of metrology, measurement methods, the procedure for measuring the values ​​of physical quantities and the rules for processing measurement results, assessing the uncertainty of measurements, the legal framework of metrology, as well as the theoretical provisions of standardization activities, the principles of construction and rules for using standards, complexes standards and other regulatory documentation. UDC (076.5) BBK ya73 Reviewers Candidate of Technical Sciences, Associate Professor TGASU A.A. Alekseev Candidate of Chemical Sciences, Associate Professor of TSU N.A. Gavrilenko FSAOU VO NI TPU, 2014 Spiridonova A.S., Natalinova N.M., 2014 Design. Tomsk Polytechnic University Publishing House, 2014

3 INTRODUCTION Metrology and standardization are tools for ensuring the quality and safety of products, works and services of an important aspect of multifaceted activities. Quality and safety are the main factors in the sale of goods. The purpose of teaching the discipline “Metrology, standardization and certification” is to present concepts, develop students’ knowledge, skills and abilities in the areas of standardization, metrology and conformity assessment to ensure the efficiency of production and other activities. As a result of studying the discipline, the student must have the following competencies: know the goals, principles, scope of application, objects, subjects, means, methods, legal framework of standardization, metrology, activities to confirm conformity; be able to apply technical and metrological legislation; work with regulatory documents; recognize compliance confirmation forms; distinguish between international and national units of measurement; have experience working with current federal laws, regulatory and technical documents necessary for carrying out professional activities. The work meets the requirements of the state educational standard of higher professional education (FSES HPE and TPU OOP standards) in the discipline “Metrology, standardization and certification” for students of all specialties. This manual is intended to consolidate the theoretical foundations of metrology, measurement methods, the procedure for measuring the values ​​of physical quantities and the rules for processing measurement results, the legal framework of metrology, as well as the theoretical provisions of standardization and certification activities, the principles of construction and rules for using standards, sets of standards and other regulatory documentation. 3

4 SECTION 1. METROLOGY LABORATORY WORK 1 CLASSIFICATION OF MEASUREMENT INSTRUMENTS AND NORMALIZED METROLOGICAL CHARACTERISTICS 1.1. Basic concepts and definitions In accordance with the RMG, a measuring instrument is a technical instrument intended for measurements, having standardized metrological characteristics, reproducing and (or) storing a unit of physical quantity, the size of which is assumed to be unchanged (within the established error) for a known time interval. Measuring instruments (MI) used in various fields of science and technology are extremely diverse. However, for this set it is possible to identify some common features that are inherent in all SIs, regardless of the field of application. These features form the basis for various SI classifications, some of which are given below. Classification of measuring instruments By technical purpose: Measure of a physical quantity, a measuring instrument designed to reproduce and (or) store a physical quantity of one or more specified sizes, the values ​​of which are expressed in established units and are known with the required accuracy; The following types of measures are distinguished: unambiguous measure - a measure that reproduces a physical quantity of the same size (for example, a 1 kg weight, a capacitor of constant capacity); multi-valued measure - a measure that reproduces a physical quantity of different sizes (for example, a line measure of length, a variable capacitor); a set of measures is a set of measures of different sizes of the same physical quantity, intended for use in practice both individually and in various combinations (for example, a set of end length measures); a store of measures is a set of measures structurally combined into a single device, which contains devices for connecting them in various combinations (for example, a store of electrical resistances). 4

5 Measuring device is a measuring instrument designed to obtain the values ​​of a measured physical quantity within a specified range. A measuring device, as a rule, contains a device for converting the measured quantity into a signal of measuring information and indexing it in a form that is most accessible to perception. In many cases, the indicating device has a scale with a pointer or other device, a diagram with a pen, or a digital display, thanks to which the values ​​of a physical quantity can be read out or recorded. Depending on the type of output value, analogue and digital measuring instruments are distinguished. An analog meter is a measuring device whose readings (or output signal) are a continuous function of the quantity being measured (for example, a pointer voltmeter, a glass mercury thermometer). A digital meter is a measuring device whose readings are presented in digital form. In a digital device, the input analog signal of measuring information is converted into a digital code, and the measurement result is reflected on a digital display. According to the form of presentation of the output value (according to the method of indicating the values ​​of the measured value), measuring instruments are divided into indicating and recording measuring instruments. indicating meter a measuring instrument that allows only reading of the values ​​of the measured quantity (micrometer, analog or digital voltmeter). recording measuring device a measuring device that provides recording of readings. Registration of the values ​​of the measured quantity can be carried out in analog or digital form, in the form of a diagram, by printing on paper or magnetic tape (thermograph or, for example, a measuring instrument interfaced with a computer, display and device for printing readings). Based on their action, measuring instruments are divided into integrating and summing. There are also direct-acting devices and comparison devices. Measuring transducer is a technical device with standard metrological characteristics that serves to convert the measured value into another value or measuring signal, convenient for processing, storage, further transformations, indication or transmission. The resulting value of the transformation is 5

6 or the measuring signal are not available for direct perception by the observer; they are determined through the conversion coefficient. A measuring transducer is either part of any measuring device (measuring installation, measuring system), or is used together with any measuring instrument. Based on the nature of the conversion, analog, digital-to-analog, and analog-to-digital converters are distinguished. Based on their location in the measuring circuit, primary and intermediate converters are distinguished. There are also scale and transmission converters. Examples: thermocouple in a thermoelectric thermometer, measuring current transformer, electro-pneumatic converter. A measuring installation is a set of functionally combined measures, measuring instruments, measuring transducers and other devices, intended for measuring one or more physical quantities and located in one place. The measuring installation used for verification is called a verification installation. The measuring setup included in the standard is called the reference setup. Some large measuring installations are called measuring machines, designed for precise measurements of physical quantities characterizing a product. Examples: installation for measuring resistivity of electrical materials, installation for testing magnetic materials. A measuring system is a set of functionally combined measures, measuring instruments, measuring transducers, computers and other technical means located at different points of a controlled object, etc. for the purpose of measuring one or more physical quantities characteristic of this object and generating measuring signals for various purposes . Depending on the purpose, measuring systems are divided into measuring information, measuring control, measuring control systems, etc. A measuring system that is rebuilt depending on changes in the measuring task is called a flexible measuring system (GIS). Examples: measuring system of a thermal power plant, which makes it possible to obtain measurement information about a number of physical quantities in different power units. It can contain hundreds of measurement channels; a radio navigation system for determining the location of various objects, consisting of a number of measuring and computing complexes spaced in space at a considerable distance from each other. 6

7 Measuring and computing complex is a functionally integrated set of measuring instruments, computers and auxiliary devices, designed to perform a specific measuring task as part of a measuring system. Comparator is a comparison tool designed for comparing measures of homogeneous quantities (lever scales, comparator for comparing normal elements). According to their metrological purpose, all measuring instruments are divided into standards, working standards and working measuring instruments. A standard of a unit of physical quantity (standard) is a measuring instrument (or a set of measuring instruments) intended for reproducing and (or) storing a unit and transferring its size to subordinate measuring instruments in the verification scheme and approved as a standard in the prescribed manner. The design of the standard, its properties and the method of reproducing the unit are determined by the nature of a given physical quantity and the level of development of measuring technology in a given field of measurement. The standard must have at least three closely related essential features: immutability, reproducibility and comparability. Working standard is a standard designed to convey the size of a unit to working measuring instruments. If necessary, working standards are divided into categories (1st, 2nd,..., nth). In this case, the transmission of the unit size is carried out through a chain of subordinate working standards by rank. In this case, from the last working standard in this chain, the unit size is transferred to the working measuring instrument. A working measuring instrument is a measuring instrument intended for measurements not related to the transfer of unit size to other measuring instruments. According to the significance of the measured physical quantity, all measuring instruments are divided into main and auxiliary measuring instruments. The main means of measuring the SI of that physical quantity, the value of which must be obtained in accordance with the measurement task. Auxiliary measuring instruments SI of that physical quantity, the influence of which on the main measuring instrument or measurement object must be taken into account in order to obtain measurement results of the required accuracy (thermometer for measuring gas temperature in the process of measuring the volumetric flow rate of this gas). 7

8 The classification of measuring instruments by technical purpose is the main one and is presented in Fig. Fig. 1.1 Metrological characteristics of a measuring instrument (MX SI): Characteristics of one of the properties of a measuring instrument that affects the measurement result and its error. For each type of measuring instrument, its own metrological characteristics are established. Metrological characteristics established by regulatory and technical documents are called standardized metrological characteristics, and those determined experimentally are called actual metrological characteristics. The nomenclature of metrological characteristics and methods for their standardization are established by GOST. All metrological characteristics of measuring instruments can be divided into two groups: characteristics that influence the measurement result (determining the scope of application of measuring instruments); characteristics affecting the accuracy (quality) of measurement. The main metrological characteristics that influence the measurement result include: measurement range of measuring instruments; 8

9 the meaning of a single-valued or multi-valued measure; transducer conversion function; the price of division of the scale of a measuring instrument or a multi-valued measure; type of output code, number of code digits, unit price of the smallest code digit of measuring instruments intended for issuing results in a digital code. The measurement range of a measuring instrument (measurement range) is the range of values ​​of a quantity within which the permissible error limits of the measuring instrument are normalized (for converters this is the conversion range). Values ​​that limit the measurement range from below and above (left and right) are called, respectively, the lower limit of measurement or the upper limit of measurement. For measures, the limits of reproduction of quantities. Unambiguous measures have a nominal and actual value of the reproducible quantity. Nominal value of a measure is the value assigned to a measure or batch of measures during manufacture. Example: resistors with a nominal value of 1 ohm, a weight with a nominal value of 1 kg. Often the nominal value is indicated on the measure. The actual value of a measure is the value assigned to a measure based on its calibration or verification. Example: the state standard of a unit of mass includes a platinum-iridium weight with a nominal mass of 1 kg, while the actual value of its mass is 1. kg, obtained as a result of comparisons with the international standard of the kilogram stored at the International Bureau of Weights and Measures (BIPM) (in in this case it is calibration). The range of readings of a measuring instrument (reading range) is the range of values ​​of the instrument scale, limited by the initial and final values ​​of the scale. The measurement range of a measuring instrument (measurement range) is the range of values ​​of a quantity within which the permissible error limits of the measuring instrument are normalized. Values ​​that limit the measurement range from below and above (left and right) are called, respectively, the lower limit of measurement or the upper limit of measurement. Scale division value (division price) is the difference in the values ​​of quantities corresponding to two adjacent marks on the scale of a measuring instrument. The metrological characteristics that determine the measurement accuracy include the error of the measuring instrument and the SI accuracy class. 9

10 Error of a measuring instrument is the difference between the reading of a measuring instrument (x) and the true (actual) value (x d) of the physical quantity being measured. x x x d. (1.1) x d is either a nominal value (for example, a measure) or the value of a quantity measured by a more accurate (at least an order of magnitude, i.e. 10 times) SI. The smaller the error, the more accurate the measuring instrument. SI errors can be classified according to a number of characteristics, in particular: in relation to the measurement conditions, basic, additional; according to the method of expression (according to the method of normalization of MX) absolute, relative, reduced. Basic error of a measuring instrument (basic error) is the error of a measuring instrument used under normal conditions. As a rule, normal operating conditions are: temperature (293 5) K or (20 5) ºС; relative air humidity (65 15)% at 20 ºС; mains voltage 220 V 10% with a frequency of 50 Hz 1%; atmospheric pressure from 97.4 to 104 kPa. Additional error of a measuring instrument (additional error) is a component of the error of a measuring instrument that arises in addition to the main error due to the deviation of any of the influencing quantities from its normal value or due to its departure from the normal range of values. When normalizing the error characteristics of measuring instruments, the limits of permissible errors (positive and negative) are established. The limits of permissible main and additional errors are expressed in the form of absolute, reduced or relative errors, depending on the nature of the change in errors within the measurement range. The limits of permissible additional error can be expressed in a form different from the form of expressing the limits of permissible main error. The absolute error of a measuring instrument (absolute in x, expressed in unit error) is the error of a measuring instrument in relation to the physical quantity being measured. The absolute error is determined by formula (1.1). 10

11 The limits of the permissible basic absolute error can be specified in the form: a (1.2) or a bx, (1.3) where the limits of the permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x the value of the measured quantity at the input (output) of the measuring instruments or the number of divisions counted on the scale; ab, positive numbers independent of x. Reduced error of a measuring instrument (reduced error) is a relative error expressed as the ratio of the absolute error of a measuring instrument to a conventionally accepted value of a quantity (normalizing value), constant over the entire measurement range or part of the range. The reduced error of the measuring instrument is determined by the formula: 100%, (1.4) x N where the limits of the permissible reduced basic error, %; limits of permissible absolute basic error, established by formula (1.2); x N normalizing value expressed in the same units as. The limits of the permissible given basic error should be set in the form: p, (1.5) where p is an abstract positive number selected from the series 1 10 n ; 1.5 10 n; (1.6 10 n); 2 10 n; 2.5 10 n; (3 10 n); 4 10 n; 5 10 n; 6 10 n (n = 1, 0, 1, 2, etc.). The normalizing value x N is taken equal to: the final value of the working part of the scale (x k), if the zero mark is on the edge or outside the working part of the scale (uniform or power); the sum of the final values ​​of the scale (without taking into account the sign), if the zero mark is inside the scale; module of the difference between measurement limits for measuring instruments, the scale of which has a conventional zero; the length of the scale or its part corresponding to the measurement range, if it is significantly uneven. In this case, the absolute error, like the length of the scale, must be expressed in millimeters. eleven

12 Relative error of a measuring instrument (relative error) is the error of a measuring instrument, expressed as the ratio of the absolute error of the measuring instrument to the measurement result or to the actual value of the measured physical quantity. The relative error of the measuring instrument is calculated by the formula: 100%, (1.6) x where the limits of the permissible relative main error, %; limits of permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x the value of the measured quantity at the input (output) of the measuring instruments or the number of divisions counted on the scale. If bx, then the limits of the permissible relative basic error are set in the form: q, (1.7) where q is an abstract positive number selected from the series given - a bx, then in the form: above; or if x cd k 1, (1.8) x where x k is the largest (in absolute value) of the measurement limits; cd, positive numbers chosen from the series above. In justified cases, the limits of the permissible relative basic error are determined using more complex formulas or in the form of a graph or table. The characteristics introduced by GOST 8.009 most fully describe the metrological properties of measuring instruments. However, a fairly large number of measuring instruments are currently in use, the metrological characteristics of which are standardized somewhat differently, namely on the basis of accuracy classes. Accuracy class of measuring instruments (accuracy class) is a generalized characteristic of a given type of measuring instrument, usually reflecting the level of their accuracy, expressed by the limits of permissible main and additional errors, as well as other characteristics affecting accuracy. The accuracy class makes it possible to judge the limits within which the measurement error of this class lies. This is important when choosing measuring instruments depending on the specified measurement accuracy. 12

13 The designation of SI accuracy classes is assigned in accordance with GOST. Construction rules and examples of designation of accuracy classes in documentation and on measuring instruments are given in Appendix B. The designation of the accuracy class is applied to dials, shields and SI housings, and is given in the regulatory documentation for SI. The range of standardized metrological characteristics of measuring instruments is determined by the purpose, operating conditions and many other factors. Standards for basic metrological characteristics are given in standards, technical specifications (TS) and operational documentation for measuring instruments. The purpose of the work is to familiarize yourself with the technical documentation for measuring instruments and determine from it the main classification characteristics and standardized metrological characteristics of the measuring instruments used; acquiring the skills to determine the main classification characteristics, the measuring instruments used and their standardized metrological characteristics directly from the measuring instruments; consolidation of theoretical knowledge in the section “Classification of measuring instruments” of the studied discipline “Metrology, standardization and certification” Equipment and instruments used 1) oscilloscope; 2) digital voltmeter; 3) analog voltmeter; 4) generator; 5) amplifier; 6) power source; 7) normal thermostated element; 8) source of calibrated voltages, programmable Work program Determine the classification characteristics indicated in table. 1.2 from among the measuring instruments (MI) located at the workplace. Familiarize yourself with the technical documentation for the MI (operation manual, technical description with operating instructions or passport). 13

14 Determine the standardized metrological characteristics of measuring instruments directly from the measuring instruments and from the technical documentation for them and fill out the table for each measuring instrument. Draw up a report on the work done (for an example of the title page, see Appendix A). Table 1.2 Classification characteristics Measuring instrument (specify the type of measuring instrument) By type (by technical purpose) By type of output quantity By form of information presentation (only for measuring instruments) By purpose By metrological purpose Standardized metrological characteristics 1.5. Test questions 1. Name the types of measuring instruments. 2. By what classification criteria are SIs divided? 3. Characterize each type of SI. 4. What groups are the metrological characteristics of measuring instruments divided into? 5. What are metrological characteristics? 6. What are standardized and actual metrological characteristics and how do they differ from metrological characteristics? 7. Name the metrological characteristics that determine: the scope of SI; measurement quality. 8. Name the types of errors. 9. What characteristic determines the accuracy of SI? 10. What function do standards perform? 11. What is the difference in the purpose of working SI and working standards? 1.6. Literature 1. RMG GSI. Metrology. Basic terms and definitions. Recommendations for interstate standardization. 2. GOST GSI. Standardized metrological characteristics of measuring instruments. 3. GOST GSI. Accuracy classes of measuring instruments. 4. Sergeev A.G., Teregerya V.V. Metrology, standardization and certification. M.: Yurayt Publishing House: Yurayt Publishing House,

15 LABORATORY WORK 2 INDIRECT SINGLE MEASUREMENTS 2.1. Basic concepts and definitions Measurement is a set of operations involving the use of a technical means that stores a unit of physical quantity, ensuring that the relationship (explicitly or implicitly) of the measured quantity with its unit is found and the value of this quantity is obtained. Measurements are the main source of information about product compliance with regulatory requirements. Only the reliability and accuracy of measurement information ensures the correctness of decision-making on product quality, at all levels of production when testing products, in scientific experiments, etc. Measurements are classified: a) by the number of observations: single measurement - measurement performed once. The disadvantage of these measurements is the possibility of gross miss errors; multiple measurement is a measurement of a physical quantity of the same size, the result of which is obtained from several successive measurements, i.e., consisting of a number of single measurements. Usually their number is n 3. Repeated measurements are carried out in order to reduce the influence of random factors on the measurement result; b) by the nature of the accuracy (according to the measurement conditions): equal-precision measurements are a series of measurements of any quantity performed by measuring instruments of equal accuracy under the same conditions with the same care; unequal measurements a series of measurements of any quantity performed by several measuring instruments differing in accuracy and (or) under different conditions; c) by expressing the measurement result: absolute measurement measurement based on direct measurements of one or more basic quantities and (or) use of the values ​​of physical constants (for example, the measurement of force F m g is based on the measurement of the basic quantity of mass m and the use of the physical acceleration constant of gravity g (at the point of mass measurement); relative measurement, the measurement of the ratio of a quantity to a quantity of the same name, which plays the role of a unit, or the measurement of a quantity 15

16 definition of a value in relation to the same value, taken as the initial one; d) by the method of obtaining the measurement result: direct measurement is a measurement in which the desired value of a physical quantity is obtained directly (for example, measuring mass on a scale, measuring the length of a part with a micrometer); indirect measurement is the determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the desired quantity; cumulative measurements are measurements of several quantities of the same name carried out simultaneously, in which the desired values ​​of the quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations (for example, the value of the mass of individual weights of a set is determined from the known value of the mass of one of the weights and from the measurement results ( comparisons) of the masses of various combinations of weights); joint measurements are measurements taken simultaneously of two or more quantities of different names to determine the relationship between them; e) according to the nature of the change in the measured physical quantity: static measurement is a measurement of a physical quantity accepted in accordance with a specific measurement task as unchanged throughout the measurement time. They are carried out with practical constancy of the measured value; dynamic measurement measurement of a physical quantity changing in size; f) according to the metrological purpose of the measuring instruments used: technical measurements, measurements using working measuring instruments; metrological measurements measurements using standard measuring instruments for the purpose of reproducing units of physical quantities to transfer their size to working measuring instruments. The measurement results are approximate estimates of the values ​​of quantities found by measurements, since even the most accurate instruments cannot show the actual value of the measured quantity. There is definitely a measurement error, which can be caused by various factors. They depend on the method of measurement, on the technical means with which the measurements are made, and on the perception of the observer carrying out the measurements. 16

17 The accuracy of the measurement result is one of the characteristics of the quality of the measurement, reflecting the proximity to zero error of the measurement result. The smaller the measurement error, the greater its accuracy. Measurement error x deviation of the measurement result x from the true or actual value (x i or x d) of the measured quantity: xx x id. (2.1) The true value of a physical quantity is the value of a physical quantity that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms. It does not depend on the means of our knowledge and is the absolute truth. It can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. The actual value of a physical quantity is the value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the given measurement task. Measurement errors can also be classified according to a number of characteristics, in particular: a) according to the method of numerical expression; b) by the nature of the manifestation; c) by type of source of occurrence (causes of occurrence). According to the method of numerical expression, the measurement error can be: The absolute measurement error (x) is the difference between the measured value and the actual value of this value, i.e. x x x d. (2.2) Relative measurement error () is the ratio of the absolute measurement error to the actual value of the measured quantity. The relative error can be expressed in relative units (in fractions) or as a percentage: x or x 100%. (2.3) x x The relative error shows the accuracy of the measurement. 17

18 Depending on the nature of the manifestation, systematic (s) and random (0) components of the measurement error are distinguished, as well as gross errors (misses). Systematic measurement error (c) is a component of the measurement result error that remains constant or changes naturally with repeated measurements of the same physical quantity. Random measurement error (0) is a component of the measurement result error that changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. Gross errors (misses) arise due to erroneous operator actions, SI malfunctions, or sudden changes in measurement conditions (for example, a sudden drop in voltage in the power supply network). Depending on the type of source of error, the following components of the overall measurement error are considered: Method errors are errors caused by the imperfection of the measurement method, methods of using measuring instruments, incorrect calculation formulas and rounding of results, resulting from the error or insufficient development of the accepted theory of the measurement method as a whole or from simplifications made during measurements. Instrumental components of error are errors that depend on the errors of the measuring instruments used. The study of instrumental errors is the subject of a special discipline in the theory of accuracy of measuring devices. Subjective components of error are errors caused by the individual characteristics of the observer. Errors of this kind are caused, for example, by a delay or advance in recording a signal, incorrect counting of tenths of a scale division, asymmetry that occurs when placing a line in the middle between two marks, etc. Approximate error estimation Single measurements. The vast majority of technical measurements are one-time. Carrying out single measurements is justified by the following factors: production necessity (destruction of the sample, impossibility of repeating the measurement, economic feasibility, etc.); 18

19 the possibility of neglecting random errors; random errors are significant, but the confidence limit of the measurement result error does not exceed the permissible measurement error. A single reading value of the instrument reading is taken as the result of a single measurement. Being essentially random, a single reading x includes instrumental, methodological and personal components of the measurement error, in each of which systematic and random components of the error can be distinguished. The components of the error in the result of a single measurement are the errors of the SI, method, operator, as well as errors caused by changes in measurement conditions. The error in the result of a single measurement is most often represented by systematic and random errors. The error of measuring instruments is determined on the basis of their metrological characteristics, which must be specified in regulatory and technical documents, and in accordance with the RD. The errors of the method and operator must be determined during the development and certification of a specific MVI. Personal errors in single measurements are usually assumed to be small and are not taken into account. Indirect measurements. In indirect measurements, the desired value of a quantity is found by calculation based on direct measurements of other physical quantities that are functionally related to the desired quantity by the known dependence y f x1, x2,..., xn, (2.4) where x1, x2,..., x n are subject to direct measurements function arguments y. The result of the indirect measurement is an estimate of the value y, which is found by substituting the measured values ​​of the arguments x i into formula (4). Since each of the arguments x i is measured with some error, the task of estimating the error of the result comes down to summing up the errors in measuring the arguments. However, the peculiarity of indirect measurements is that the contribution of individual errors in the measurement of arguments to the error of the result depends on the type of function (4). 19

20 To assess errors, it is essential to divide indirect measurements into linear and nonlinear indirect measurements. For linear indirect measurements, the measurement equation has the form: y n bi xi, (2.5) i1 where b i are constant coefficients for the arguments x i. The result of a linear indirect measurement is calculated using formula (2.5), substituting the measured values ​​of the arguments into it. Errors in measuring arguments x i can be specified by their boundaries xi. With a small number of arguments (less than five), a simple estimate of the error of the result y is obtained by simply summing the maximum errors (without taking into account the sign), i.e., substituting the boundaries x 1, x 2, x n into the expression: y x1x2... xn. (2.6) However, this estimate is unnecessarily overestimated, since such summation actually means that the measurement errors of all arguments simultaneously have a maximum value and coincide in sign. The probability of such a coincidence is practically zero. To find a more realistic estimate, proceed to the static summation of the error of the arguments according to the formula: n 2 2 i i, (2.7) i1 yk b x where k is the coefficient determined by the accepted confidence probability (at P = 0.9 at k = 1.0; P = 0 .95 at k = 1.1; P = 0.99 at k = 1.4). Nonlinear indirect measurements any other functional dependencies other than (2.5). With a complex function (2.4) and, especially, if it is a function of several arguments, determining the law of distribution of the error of the result is associated with significant mathematical difficulties. Therefore, the basis for approximate estimation of the error of nonlinear indirect measurements is the linearization of function (2.4) and further processing of the results, as in linear measurements. Let us write the expression for the total differential of the function y in terms of partial derivatives with respect to the arguments x i: y y y dy dx1 dx2... dxn. (2.8) x x x 1 2 n 20

21 By definition, the total differential of a function is the increment of a function caused by small increments of its arguments. Considering that the errors in the measurement of arguments are always small compared to the nominal values ​​of the arguments, we can replace in formula (2.8) the differentials of the arguments dx n with the measurement error xn, and the differential of the function dy with the error of the measurement result y: y y y y x x... xn. (2.9) x x x If we analyze formula (2.9), we can obtain a simple rule for estimating the error of the result of a nonlinear indirect measurement. Errors in works and particulars. If the measured values ​​x1, x2,..., x n are used to calculate y x... 1x2 xn or y 1, x2, then the relative errors y x1x2... xn are summed up, where y y. y 2.3. Error in recording (rounding) a number. Error in recording (rounding) a number is defined as the ratio of half the unit of the least significant digit of the number to the value of the number. For example, for the normal acceleration of falling bodies g = 9.81 m/s 2, the least significant unit is 0.01, therefore, the error in recording the number 9.81 will be equal to 0.01 5, = 0.05%. 29, Goal of work n x mastering methods for conducting single direct and indirect measurements; mastering the rules for processing, presenting (recording) and interpreting the results of measurements; acquisition of practical skills in the use of measuring instruments of varying accuracy, as well as analysis and comparison of the accuracy of the results of indirect measurements with the accuracy of measuring instruments used in direct measurements; identification of possible sources and causes of methodological errors; 21

22 consolidation of theoretical material in the “Metrology” section of the studied discipline “Metrology, standardization and certification” The equipment used is a vernier caliper (hereinafter SC); micrometer; ruler. When recording the measuring instruments used, indicate their standardized metrological characteristics using the measuring instruments Work program Make single measurements of the diameter and height of the cylinder with measuring instruments of varying accuracy: calipers, micrometers and rulers. Record the measurement results in the table. For cylinder 1, select a cylinder of smaller height. Write down the results of direct measurements of the diameter and height of the cylinders in a table with the accuracy with which the measuring instrument allows you to measure. Table 2.1 Measurement results Measured Cylinder 1 (small) Cylinder 2 (large) parameter Diameter d, mm Height h, mm Volume V, mm Relative error. V Abs. error V, mm 3 micrometer ШЦ ШЦ ruler Determine the volume of the cylinder using the ratio: 2 V d h, mm 3, (2.10) 4 where = 3.14 numerical coefficient; d cylinder diameter, mm; h cylinder height, mm Determine the relative measurement error, expressed in relative units V V. (2.11) V 22

23 To determine the relative measurement error V, it is necessary to transform formula (2.11) into a convenient one for calculation using formula (2.9) (see paragraph 2.2). In the resulting formula d, h are the errors of the measuring instruments used in the measurements. When indirectly measuring physical quantities, tabular data or irrational constants are very often used. Because of this, the value of the constant used in calculations, rounded to a certain sign, is an approximate number that contributes its share to the measurement error. This fraction of the error is defined as the error in recording (rounding) the constant (see paragraph 2.3) Determine the error in calculating the volume using the formula V V, mm 3. (2.12) V Round off the measurement errors and write down the result of measuring the volume of the cylinders V V V mm 3. (2.13) For in order to record the final result of indirect measurements, it is necessary to round the measurement error V in accordance with MI 1317, agree on the numerical values ​​of the result and measurement errors (see paragraph 2.4) Draw in the figures the areas in which the results of volume measurements obtained by different measuring instruments are located for each of the cylinders. An example is shown in Figure 2.1. V 2 ΔV 2 V 2 V 1 ΔV 1 V 1 V 1 + ΔV 1 V 2 + ΔV 2 Fig Areas of cylinder volume measurement results The first point (for example, V 2) is placed arbitrarily; it is assigned the value of the cylinder volume, the measurement error of which is greater. Then you need to select a scale and put in all the other points. The figure shows the error of the method. 23

24 2.6.7 Prepare a report and draw a conclusion (for an example of a title page, see Appendix A). In the conclusion, evaluate the obtained measurement results, identify possible sources and causes of methodological errors. Test questions 1. Name the main types of measurements. 2. By what criteria are measurement errors classified? 3. Name and characterize the main types of measurement errors. 4. How to determine the error in recording a number? 5. How to determine the error of the result of an indirect measurement? 2.8. Literature used 1. RMG Recommendations for interstate standardization. GSI. Metrology. Basic terms and definitions. 2. R Recommendations for metrology. GSI. Single direct measurements. Estimation of errors and uncertainty of measurement results. M., Standards Publishing House, Borisov Yu.I., Sigov A.S., Nefedov V.I. Metrology, standardization and certification: textbook. M.: FORUM: INFRA-M, MI Methodological instructions. GSI. Results and characteristics of measurement error. Forms of submission. Methods of use when testing product samples and monitoring their parameters. 24

25 LABORATORY WORK 3 PROCESSING RESULTS OF DIRECT MULTIPLE MEASUREMENTS 3.1. Introduction The need to perform direct multiple measurements is established in specific measurement techniques. When statistically processing a group of results of direct multiple independent measurements, the following operations are performed: known systematic errors are excluded from the measurement results; calculate an estimate of the measured value; calculate the standard deviation of the measurement results; check for gross errors and, if necessary, eliminate them; check the hypothesis that the measurement results belong to a normal distribution; calculate the confidence limits of the random error (confidence random error) of the estimate of the measured value; calculate the confidence limits (boundaries) of the non-excluded systematic error in estimating the measured value; calculate the confidence limits of the error in estimating the measured value. The hypothesis that the measurement results belong to a normal distribution is tested with a significance level q from 10% to 2%. Specific significance levels must be specified in a specific measurement procedure. To determine the confidence limits of the error in estimating the measured value, the confidence probability P is taken equal to 0. Basic concepts and definitions Depending on the nature of the manifestation, systematic (C) and random (0) components of the measurement error, as well as gross errors (misses), are distinguished. Gross errors (misses) arise due to erroneous operator actions, SI malfunctions, or sudden changes in measurement conditions, for example, a sudden drop in voltage in the power supply network. Closely adjacent to them are error slips, depending on 25

26 observers and related to improper handling of measuring instruments. Systematic measurement error (systematic error C) is a component of the measurement result error that remains constant or changes naturally with repeated measurements of the same physical quantity. It is believed that systematic errors can be detected and eliminated. However, in real conditions it is impossible to completely eliminate the systematic component of the measurement error. There are always some factors that need to be taken into account, and which will constitute an inevitable systematic error. Non-excluded systematic error (NSE) is a component of the error of a measurement result, due to errors in the calculation and introduction of corrections for the influence of systematic errors or a systematic error, the correction for which is not introduced due to its smallness. The non-excluded systematic error is characterized by its boundaries. The limits of the non-excluded systematic error Θ with the number of terms N 3 are calculated by the formula: N i, (3.1) i1 where the boundary of the i-th component of the non-excluded systematic i error. When the number of non-excluded systematic errors is N 4, the calculation is carried out according to the formula k N 2 i, (3.2) i1 where k is the coefficient of dependence of individual non-excluded systematic errors on the selected confidence probability P when they are uniformly distributed (at P = 0.95, k = 1.1 ; at P = 0.99, k = 1.4). Here Θ is considered as a confidence quasi-random error. Random measurement error (0) is a component of the measurement result error that changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. 26

27 To reduce the random component of the error, multiple measurements are carried out. The random error is estimated by the confidence interval tp Sx, (3.3) where t P is the Student coefficient for a given confidence level P d and sample size n (number of measurements). Confidence limits of the error of the measurement result are the boundaries of the interval within which, with a given probability, the desired (true) value of the error of the measurement result is located. A sample of x measurement results (x i), i = 1,..., n (n > 20), from which known systematic errors are excluded. The sample size is determined by the requirements for measurement accuracy and the ability to make repeated measurements. Variation series is a sample ordered in ascending order. A histogram of the dependence of the relative frequencies of measurement results falling into grouping intervals on their values, presented in graphical form. Assessment of the distribution law assessment of the correspondence of the experimental distribution law to the theoretical distribution. It is carried out using special statistical criteria. At n< 15 не проводится. Точечные оценки закона распределения оценки закона распределения, полученные в виде одного числа, например оценка дисперсии результатов измерений или оценка математического ожидания и т. д. Средняя квадратическая погрешность результатов единичных измерений в ряду измерений (средняя квадратическая погрешность результата измерений) оценка S рассеяния единичных результатов x измерений в ряду равноточных измерений одной и той же физической величины около среднего их значения, вычисляемая по формуле: 1 n S 2 x x 1 i x n, (3.4) i1 где i x результат i-го единичного измерения; x среднее арифметическое значение измеряемой величины из n единичных результатов. Примечание. На практике широко распространен термин среднее квадратическое отклонение (СКО). Под отклонением в соответствии с приведенной выше формулой понимают отклонение единичных результатов в ряду измерений от их среднего арифметического значения. В метрологии это отклонение называется погрешностью измерений. 27

28 Root mean square error of the measurement result of the arithmetic mean estimate S x of the random error of the arithmetic mean value of the measurement result of the same quantity in a given series of measurements, calculated by the formula 2 i S Sx 1 x x x n nn1, (3.5) where S x root mean square error of the results of single measurements obtained from a series of equal-precision measurements; n number of single measurements in a series Elimination of gross errors To exclude gross errors, the Grubbs statistical criterion is used, which is based on the assumption that the group of measurement results belongs to a normal distribution. To do this, calculate the Grubbs criteria G 1 and G 2, assuming that the largest x max or smallest x min measurement result is caused by gross errors: xmax x x x G1, min S G. (3.6) x 2 Sx Compare G 1 and G 2 with the theoretical value G T Grubbs test at the selected significance level q. The table of critical values ​​of the Grubbs criterion is given in Appendix B. If G 1> G T, then x max is excluded as an unlikely value. If G 2 > G T, then x min is excluded as an unlikely value. Next, the arithmetic mean and standard deviation of a number of measurement results are again calculated and the procedure for checking the presence of gross errors is repeated. If G1 G T, then x max is not considered a miss and is retained in the series of measurement results. If G 2 G T, then x min is not considered a miss and is retained in the series of measurement results. Confidence limits for the error in estimating the measured value. Confidence limits for the error in estimating the measured value are found by constructing a composition of distributions of random errors and NSPs, considered as random variables. The error limits for estimating the measured value (without taking into account the sign) are calculated using formula 28

29 K S, (3.7) where K is a coefficient depending on the ratio of the random component of the error and the NSP. The total standard deviation S of the estimate of the measured value is calculated using the formula S S2 S2 x, (3.8) where S is the standard deviation of the NSP, which is estimated depending on the method of calculating the NSP using the formula S, (3.9) 3 where the boundaries of the NSP, which are determined by one from formulas (3.1), or P S, (3.10) k 3 where P are the confidence limits of the NSP, which are determined by one of the formulas (3.2); k is a coefficient determined by the accepted confidence probability P, the number of NSP components and their relationship to each other. The coefficient K for substitution into formula (3.7) depending on the number of non-reinforcing stations is determined by the empirical formulas K, P K, respectively. (3.11) S S S x x S 3.5. Algorithm for processing observation results Processing of observation results is carried out in accordance with GOST “GSI. Measurements are direct and multiple. Methods for processing measurement results. Basic provisions" Determination of point estimates of the distribution law x 1 n x i ; 1 n S 2 x x 1 i x n ; S S x x. n n i Construction of an experimental distribution law for the results of multiple observations a) in Table 3.2 write down the variation series of the results of multiple observations x ; i i1 29

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