1.1 Calculation of tolerances and fits of smooth cylindrical mates

1.2 Gauges for the control of smooth cylindrical joints

2. Calculation and selection of rolling bearing fits

3. Roughness, deviation of shape and location of surfaces

4. Tolerances and fits of keyed and splined connections

4.1 Keyed connection

4.2 Straight spline connection

4.3 Involute spline connection

Literature

1. Smooth mates and calibers

1. The specified landing is Æ56H6/k5.

Transitional landing.

Limit deviations of hole Æ56H6: upper ES=+19 µm; lower EI=0.

Maximum shaft deviations Æ56k5: upper es=14 µm; lower ei=+1 µm.

Dmax = D + ES = 56 + 0.019 = 56.019 mm;

Dmin = D + EI = 56 + 0 = 56 mm;

dmax = d + es = 56 +0.014 = 56.014 mm;

dmin = d + ei = 56 + 0.001 = 56.001 mm;

TD = IT6 = 19 µm;

Td = IT5 = 13 µm;

Smax = ES - ei = 19- 1 = 18 µm;

Smin = EI - es = 0 - 14 = -14 µm;

TS = Smax - Smin = 18 + 14 = 32 µm.

Check: TS = Td+TD 32= 19 + 13

2. The specified landing is Æ70S6/h7.

Landing with clearance.

Limit deviations of hole Æ70S6: upper ES=-59 µm; lower EI=-78.

Maximum shaft deviations Æ70h7: upper es=0 µm; lower ei=-30 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 70 + (-0.059) = 69.941 mm;

Dmin = D + EI = 70 + (-78) = 69.922 mm;

dmax = d + es = 70 + 0 = 70 mm;

dmin = d + ei = 70 + (0.030) = 69.970 mm;

Hole and shaft dimensional tolerances:

TD = IT6 = 19 µm;

Td = IT7 = 30 µm;

Fit parameters (with clearance).

Nmax = dmax - Dmin = -0.078 mm;

Nmin = dmin - Dmax = -0.029 mm;

TN = Nmax - Nmin = -0.0678 + 0.029 = -0.049 mm.

Check: TN = Td+TD 0.049 = 0.019 + 0.030

3. The landing is Æ105F7/h7.

Landing with clearance.

Limit deviations of hole Æ53H7: upper ES=+30 µm; lower EI=0.

Maximum shaft deviations Æ53k5: upper es=+15 µm; lower ei=+2 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 53 + 0.030 = 53.030 mm;

Dmin = D + EI = 53 + 0 = 53 mm;

dmax = d + es = 53 + 0.015 = 53.015 mm;

dmin = d + ei = 53 + 0.002 = 53.002 mm;

Hole and shaft dimensional tolerances:

TD = IT7 = 30 µm;

Td = IT5 = 13 µm;

Landing parameters (transitional).

Smax = Dmax - dmin = 53.030 - 53.002 = 0.028 mm;

Nmax = dmax - Dmin = 53.015 - 53 = 0.015 mm;

Smin = -Nmax = -0.015 mm;

Nmin = -Smax = -0.028 mm;

TS(N) = Smax + Nmax = 0.028 - 0.015 = 0.043 mm.

Check: TS(N) = Td+TD 0.043 = 0.013 + 0.030

4. The landing is set to Æ21H8/h7.

Landing with clearance.

Limit deviations of hole Æ21H8: upper ES=+33 µm; lower EI=0.

Maximum shaft deviations Æ21h7: upper es=0 µm; lower ei=-21 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 21 + 0.033 = 21.033 mm;

Dmin = D + EI = 21 + 0 = 21 mm;

dmax = d + es = 21 + 0 = 21 mm;

dmin = d + ei = 21 + (-0.021) = 20.979 mm;

Hole and shaft dimensional tolerances:

TD = IT8 = 33 µm;

Td = IT7 = 21 µm;

Landing parameters (with clearance).

Smax = Dmax - dmin = 21.033 - 20.979 = 0.054 mm;

Smin = Dmin - dmax = 21 - 21 = 0;

TS = Smax - Smin = 0.054 - 0 = 0.054 mm.

Check: TS = Td+TD 0.054 = 0.021 + 0.033

We enter the obtained data for all landings in Table 1.1.

Table 1.1 Types and parameters of plantings

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Federal Agency for Education

Siberian State Aerospaceuniversitythem. Academician M.F.Reshetnyova

Department of UKS

Coursework for the course

« Standardization of accuracy in mechanical engineering»

Option No. 14

Completed: student

Checked by the teacher:

Krevina T.E.

Krasnoyarsk 2008

• Introduction 3
• 4
• 1.1 Standardization of interference fits 4
• 1.2 Transitional landings 7
• 11
• 3. Selection of fits for spline connections 15
• 4. Gear connections 18
• 5. Calculation of dimensional chains 21
• 5.1 Calculation by the method of complete interchangeability 21
• 5 .2 24
• References 28

Introduction

Mechanical engineering is the most important leading industry. But mechanical engineering plays an equally important role in other areas such as science, culture, education, public utilities and housing. Humanity is growing and developing, thereby providing food for the development of mechanical engineering and the expansion of its range. The main emphasis these days is on electrification, as well as mechanization and automation of production and labor; in general, everything is done to facilitate human physical labor.

The course work for the course “Normalization of accuracy in mechanical engineering” is the student’s first independent design work. Course work allows you to consolidate the theoretical principles of the course presented in lectures, instills skills in using reference material, ESKD standards, and introduces students to the main types of calculations.

An important place in the course work is occupied by issues related to ensuring the accuracy of interchangeable parts of assembly units. Standards for the accuracy of interchangeability of connections of all types are regulated by a unified system of tolerances and landings (USDP).

The purpose of the course work is to instill the skills of assigning the accuracy of parts and assemblies and the skills of indicating it in drawings.

When performing course work, the basic standards for tolerances and fits of typical interfaces are worked out, and issues of dimensional control and technical requirements are addressed.

1. Smooth cylindrical joints

1. 1 Standardization of interference fits

Nominal connection diameter, mm……………………………..75;

Maximum ultimate tension N max p, µm………………………80;

Minimum limit tension N min p , µm………………………..60.

The calculated nominal diameter d = 75 mm corresponds to the Ra40 series and there is no need to round it.

We determine the average tightness of the limiting tightnesses given in the problem:

where N max p and N min p are the calculated maximum tensions given in the problem, µm.

Based on the average interference, we select the fit in any system (shaft system or hole system) according to Table 5 and write out the table interferences N max T = 72 µm and N min T = 40 µm for the selected fit.

where N max T and N min T are the tabulated maximum tensions, µm.

The tabulated average interference is close to the calculated one and the fit in the hole system corresponds to it

We find deviations for the tolerance fields of the hole and shaft according to tables 6,9,14.

We write down the combined designation of landing with deviations

We build a diagram of the location of the tolerance fields of the selected fit. We indicate the tension. Deviations in the tolerance diagram are indicated in micrometers.

Fig.1 . Tolerance fields for interference fit

We calculate the maximum and minimum interference (check) for the selected fit, according to the tolerance zone diagram using the formulas:

Where ES, es, EI, ei- upper and lower deviations of the hole and shaft, respectively.

The resulting maximum interference fits coincide with the tabulated maximum interference.

Determine the shaft tolerance and hole tolerance:

The fit is chosen so that if the tolerances of the shaft and hole are unequal, the hole has a larger tolerance.

Rice. 2 . Connection sketch

TN = TD+Td = N max -N min = 72-40=32

The connection is not guaranteed to remain stable under load.

1. 2 Transitional settlementski

Given:

Nominal di connection diameter……………………………… 209 mm;

Maximum limit interference N nb ……………………………40 µm;

Maximum limit gap S nb ………………….……........14 µm

Solution:

1) Round the given connection diameter to a value of 210 mm, corresponding to the Ra40 series according to GOST 6636-69

2) Table values ​​of transitional landings:

N nm = - S nb N nb =40 µm N nm = -14 µm

These values ​​correspond to the fit in the shaft system

3) Limit deviations of the hole and shaft:

210

210 h5

4) Layout of tolerance fields in the fit:

S nb = ES - ei S nb = -8 - (-20) = 12 µm

S nm = EI - es S nm = -37 - 0 = - 37 µm

S nm = - N nb N nb = 37 µm

The table values ​​of the gap and interference coincide with the specified ones

Rice. 3 . Tolerance fields for transitional fit

5) Full landing designation:

6) Transitional fit tolerance:

T(S,N) = TD + Td

T(S,N) = (-0.008-(-0.037))+(0-(-0.02)) = 0.029+0.02 = 0.049 µm

7) The hole tolerance is greater than the shaft tolerance, which means the hole is made less accurately than the shaft.

9) Calculations for constructing a Gaussian curve:

a) standard deviation of landing:

b) zone of dispersion of interference gaps and maximum ordinate:

c) relative deviation:

actual ordinate deviation with zero clearance

d) probable number of mates with a gap:

e) probable number of interference fits:

10) Gaussian curve:

Along the y-axis we plot the number of mates, i.e. number of landings.

Along the x-axis is the dispersion of gaps or interference. On this curve, the landing grouping center corresponds to the landing center N avg.

Rice. 4 . Gauss curve

On distance X=12.5 µm from the grouping center there is an ordinate corresponding to zero interference (gap). Let us agree to count this ordinate to the left of the grouping center when the transition fit has an average gap and to the right when there is interference. The entire area under the curve limited along the ordinate by the scattering interval R, corresponds to the total number of mates of a given fit, i.e. the probability is from 1 to 100%. The probability of occurrence of mates with interference corresponds to the shaded area on the left, and with a gap - to the shaded area on the right.

2. Calculation of fits for rolling bearings

Given:

Bearing 97516, accuracy class 60, inner ring rotates, radial load 30000 N, moderate, with low vibration, axial load 10000 N, =0.6

Solution:

1) Bearing type: tapered ball bearing, double row, light series.

Dimensions: d=80mm, D=140mm, T=80mm,

The inner ring rotates, therefore, it is circulation-loaded.

2) The shaft is solid, the body is thin-walled, as the ratios are indicated

3) Radial load intensity:

a) R=30000 N, radial load

b) b=0.08 m, ring width

c) - coefficient depending on the nature of the load. =1

d) - coefficient that takes into account the weakening of the landing tension with a hollow shaft or thin-walled housing. =1.1, since the problem gives a solid shaft and a thin-walled housing. e) - coefficient of uneven distribution of radial load R between rows of rollers in double-row bearings. To find, calculate the expression

, then =2

e) let's calculate:

4) Tolerance range for mounting hole:

A load of 825 and a diameter of the outer ring D=140 mm corresponds to a tolerance zone G. Since according to the condition the accuracy class of the bearing is 6, then the quality for the hole in the housing is 7, then we write G7

5) Tolerance range for a circulation-loaded inner ring:

Shaft diameter 80mm corresponds to fit on k6 shaft

6) Deviations for tolerance fields of the mounting hole:

ES=+54; EI= 14 µm

7) Deviations for a circulation-loaded ring:

es=21; ei=2 µm

8) Deviations for the tolerance ranges of the inner and outer rings of the rolling bearing:

For the inner ring: ES=0; EI= -15µm

For the outer ring: es=0; ei= -12 µm

10) Fit for the inner ring-shaft connection:

80, where L0 is the tolerance field of the inner ring (0 is the designation of the accuracy class)

11) Fit for connection “hole in housing - outer ring”: 140, where l 0-tolerance field of the outer ring (0-accuracy class)

12) Layout of tolerance fields for the “shaft - inner ring” connection:

13) Layout of tolerance fields for the “hole in the housing - outer ring” connection:

Since the body will not rotate.

14) Sketch of the housing and shaft for a rolling bearing:

3. Selectionspline joint sediment

Determine the type of centering, accuracy and nature of mating for a spline connection.

Construct a diagram of the location of tolerance fields indicating deviations, determine the maximum dimensions of all mating elements.

1) Number of splines Z =10, internal diameter d =72, external diameter D =82

2) Tooth (slot) width b=12mm, smallest internal diameter d 1 = 67.4mm, series - average.

3) Type of centering: centering along b (side surfaces of the teeth)

4) According to the table. 3.1 we are looking for a fit for the centering parameter b .

Since the connection is movable, we choose a fit with a gap

5) For non-centering diameters d and D select plantings 5, according to the table. 3.4.] For D - , for inner diameter d: for bushing H 11, and for the shaft we find the tolerance d - d 1.

6). Let's find deviations for all parameters using table. 6, 7, 12.

For N 12ES = +350µm ; EI= 0 (D=82 mm)

ForN 11 ES =+ 190µm , EI= 0 (d =72 mm);

For F8 ES = +43µm ; EI= +16 (b =12 mm)

For f 87 es = - 16 µm ; ei = - 43 µm (b =12 mm);

Fora11 es = -380 µm ; ei = -600 µm (D = 82 mm);

for the internal diameter of the shaft we findd - d 1 =72- 67.4= 4.6mm = 4600 microns.

7) We build diagrams for the location of tolerance fields:

8) Let’s write down the symbol for the spline connection given in the problem with the corresponding fits.

Where b - type of centering; 10 - number of teeth; 72 - internal diameter of the connection. The landing is not indicated in the designation, since there is no tolerance field in the denominator; 82 - outer diameter of the connection;

Fit for outer diameter of connection; 12 - tooth width (splines);

Fit for slot width.

Let's write down the designations for the splined shaft and splined bushing separately

Bushing designation

In this designation, the internal diameter d = 72 mm is indicated by the tolerance field of the bushing H 11.

Shaft designation.

4. Gear connections

Type of gears - cylindrical, spur, uncorrected. Options : m =4, Z 1 = 60, Z 2 =35. Purpose: aircraft wheels.

1. According to the purpose of the gear transmission, we determine that tooth contact and lateral clearance are a group of indicators of smooth operation, which is of greatest importance for this transmission (see subsection 4.1 3).

2. Determine the degree of accuracy for the selected group of indicators according to the table. 24 5. From the same table we write down the peripheral speed.

The degree of accuracy for the smoothness group is 6, the peripheral speed is 15 m/s.

3. In this problem, for the accuracy and tooth contact groups we assign the same degrees of accuracy one lower than for the smoothness group, i.e., accuracy degree 7.

4. Based on the value of the peripheral speed, we determine the type of coupling, taking into account that the smallest lateral clearance is assigned for low-speed gears, and the largest for high-speed gears.

In this problem, the transmission is high-speed, because the speed is 15 m/s , Therefore, we choose the type of conjugation B

5. Using the table. 4.1, we will assign a tolerance for the lateral clearance and indicate the class of deviation of the center-to-center distance.

Side clearance tolerance -b, center distance deviation class -V.

6. Let us write down the designation for the accuracy of a cylindrical gear transmission:

7-7-6 B GOST 1643-81,

where 7 is the degree of accuracy of the contact of the teeth of the indicators; 7 - degree of accuracy of the accuracy group; 6 - degree of accuracy of the smoothness group; B - type of interface; b- side clearance tolerance.

7. For one group of smoothness indicators, which is of greatest importance for a given gear, we determine the standardized indicators. We write out the indicators according to tables 28 and 29 1. To do this, we need to calculate the dividing diameters of the two data in the wheel problem d 1 and d 2 ,width of each gear b 1 and b 2, center-to-center transmission distance a w. Let us set the width of the gear rim equal to 1/3 of the pitch diameter.

According to the table 28 5 determine the total contact patch along the height and length of the tooth, tolerances for parallelism f, axis misalignment f y and tooth tension F .

The total contact patch for the 6th degree of accuracy for the height of the teeth is not less than 50, for the length of the teeth is not less than 70.

To determine the following indicators, we calculate the pitch diameters d 1 And d 2 .

d 1 = mz 1 = 4 60= 240mm ;

d 2 = mz 2 = 4 35 = 140 mm

Gear ring width

b 1 = 1/3d 1 ;

b 2 = 1/3d 2 ;

b 1 = 80 mm ;

b 2 = 46,6 mm,

For 6th degree of accuracy f x 1 = 12 µm, f x 2 = 12 microns, f y 1 = 6.3 µm; f y 2 = 6.3 microns,

F 1 = 10 µm, F 2 = 10 µm.

According to the table 29 5 write down the values ​​of the guaranteed side clearance j n min and deviations of the center distance f a. To do this, we calculate the interaxle distance.

Type of pairing IN, class of center distance V, its value equal to 190 mm, deviation of center distance f a = ± 90 µm, corresponds to guaranteed lateral clearance j n min = 185 µm.

Standards for smooth operation: kinematic error μm, tolerance for profile error μm, maximum step deviations μm.

5 .Calculation of dimensional chains

5 .1 Calculationmehcompletely interchangeable

Given:

;; ; ; ; ; ;

Solution:

1) Nominal size of closing link:

,

where is A? - closing link, A I B has an increasing size, A I UM - reducing size, m- number of increasing links, n - number of constituent links.

Table 1

2) Average accuracy rate a:

where TA is the tolerance of the closing link; I- tolerance unit; n- number of constituent links.

For this task i 1 =i 2 =1.31µm; i 3 = 1.56 µm; i 4 =i 5 =1.31, i 6 =1.86µm; i 7 =2.17 µm; i 8 =3.23 µm.

3) Tolerance units for size intervals are entered into the table

4) Accuracy rating 7

5) The tolerance values ​​of the component links according to quality and size are entered into the table

6) Tolerance check:

; µm;

The sum of the tolerances of the constituent links is less than the tolerance of the closing link, therefore, an adjustment is necessary.

In this case (when? TA i < ТА?) рекомендуется провести корректировку следующим образом. Поскольку вычисленное значение среднего коэффициента A was between the 7th and 8th qualifications, then part of the tolerances can be taken according to the 8th qualification and thus increase? TA i to the required value.

For example, let’s assign tolerances for dimensions A 6 according to quality 8 (see Table 5.4).

In this case TA 6 =46, then?TA i = 238 µm.

?TA i < ТА? на 0.8 % , что находится в пределах допустимого.

7) We enter the dimensions of the reducing links with deviations in the table. Since the dimensions are covered, we assign deviations as for shafts.

8) Dimensions of the increasing link:

We will consider the deviation of the closing link to be symmetrical, that is

;

;

5 .2 Calculation using the theoretical-probabilistic method

Draw up a diagram of a dimensional chain indicating increasing and decreasing sizes. To do this, carry out an analysis and identify decreasing and increasing sizes.

Nominal dimensions, mm: ;; ; ; ; ; ; .

Distribution laws A 1 =3; A 2 =3; A 3 =2; A 4 =2; A 5 =1; A 6 =1; A 7 =1; A 8 =1.

Tolerance of the closing link TA = 240 µm.

1) We draw up a table in which we enter the dimensions of the links and the numerical values ​​of the tolerance units of the component links

table 2 .

2) The average accuracy coefficient is calculated using the formula

where is the average accuracy coefficient;

TA - tolerance of the closing link;

Coefficient corresponding to the distribution law;

Unit of tolerance.

1-for the law of normal distribution;

2-for the law of equal probability;

3-for the triangle law.

3) Denominator of the expression for A will look like this:

Substituting the tolerance values, we get

4) According to the average accuracy coefficient A we find the quality (see table 5.3 3). We choose 9th quality.

5) According to the quality and size of the links, we find the tolerances for the component dimensions (Table 5.4 3) and enter them into the table.

6) We check using the formula

The sum of the tolerances of the component links may be less than the tolerance of the closing link by 5 ... 6%, which is not fulfilled under these conditions.

We are making adjustments. To do this, we will assign tolerances according to quality 13 for dimensions A 4, A 5 and enter the values ​​of these tolerances into the table. We check again.

The check showed compliance with the condition.

7) Let us enter the dimensions with deviations in Table 2 (except for the increasing link), using the following rule: we assign deviations for all covered dimensions (as for shafts) with tolerances of “minus”. These are the dimensions A 1 ... A 7

We calculate the deviations for the magnifying link A8. To do this, we determine the average deviations for reducing sizes from A1 to A7:

Where? With A - average size deviation; ES A i, - upper limit deviation of size; EI A i, - lower limit deviation of size.

The calculation is carried out taking into account the signs of deviations in microns:

8) For the closing link (A?), let’s set the upper deviation equal to the tolerance, and the lower one equal to 0. ES A? =TA? = 1300 µm; EI A? = 0. Then the average deviation for the closing link

The average deviation for increasing size A 8 is found by the equation

Where c Ay m . - the sum of the average deviations of the reducing links;

c A y m = (- 75)*2 + (- 125) + (-230)*2 + (- 175) + (-200) = -1110 µm;

c A 8 = - 1110 + 650 = - 460 µm.

9) The upper and lower deviations for increasing size A 8 are determined from the following equations:

E S A8 = c A8 + 1/2TA8; EI A8 = c A8 - 1/2TA8.

Take the tabular tolerance for A 8 from Table 2. Then

the calculated values ​​of link deviations will be:

ES A 8 = - 460 + 1/2570 = -175 µm; EI A 8 = - 460 - 1/2570 = - 745 µm.

Let's write down size A 8 with calculated deviations in Table 2.

Tolerances calculated by the method of complete interchangeability are less stringent, i.e., the accuracy is lower than when calculating using the theoretical-probabilistic method.

Bibliography

1. Tolerances and landings: Handbook: In 2 hours / M.A. Paley, A.B. Romanov, V.A. Braginsky. -8th ed., revised. and additional -SPb.: Mechanical Engineering, 2001. - Part 1.

2. Tolerances and landings: Directory: In 2 hours / V.D. Myagkov, M.A. Paley, A.B. Romanov, V.A. Braginsky. -8th ed., revised. and additional -SPb.: Mechanical Engineering, 2001. - Part 2.

3. Metrology, standardization and certification: Guidelines for completing course work for students of technical specialties of a given form of study / Compiled by: Belik G.I., Pshenko E.B.; SibSAU.- Krasnoyarsk, 2003.

4. Metrology, standardization and certification: Handouts for course work for students of all forms of education / Compiled by: Belik G.I., Pshenko E.B.; SAA.-2002.

5. Standardization of accuracy in mechanical engineering. Collection of reference materials / Comp. G.I. Belik. - Krasnoyarsk: SAA, 1998..

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Content

• 1 . Smooth mates and calibers
• 1.1 Calculation of tolerances and fits of smooth cylindrical mates
• 1.2 Gauges for the control of smooth cylindrical joints
• 2. Calculation and selection of rolling bearing fits
• 3. Roughness, deviation of shape and location of surfaces
• 4. Tolerances and fits of keyed and splined connections
• 4.1 Keyed connection
• 4.2 Straight spline connection
• 4.3 Involute spline connection
• Literature
• 1. Smooth mates and calibers
• 1. The specified landing is 56H6/k5.
• Transitional landing.
• Limit deviations of hole 56H6: upper ES=+19 µm; lower EI=0.
• Maximum shaft deviations 56k5: upper es=14 µm; lower ei=+1 µm.
• Dmax = D + ES = 56 + 0.019 = 56.019 mm;
• Dmin = D + EI = 56 + 0 = 56 mm;
• dmax = d + es = 56 +0.014 = 56.014 mm;
• dmin = d + ei = 56 + 0.001 = 56.001 mm;
• TD = IT6 = 19 µm;
• Td = IT5 = 13 µm;
• Smax = ES - ei = 19- 1 = 18 µm;
• Smin = EI - es = 0 - 14 = -14 µm;
• TS = Smax - Smin = 18 + 14 = 32 µm.
• Check: TS = Td+TD 32= 19 + 13
• 2. The landing is set to 70S6/h7.
• Landing with clearance.
• Limit deviations of hole 70S6: upper ES=-59 µm; lower EI=-78.
• Maximum shaft deviations 70h7: upper es=0 µm; lower ei=-30 µm.
• Limit dimensions of hole and shaft:
• Dmax = D + ES = 70 + (-0.059) = 69.941 mm;
• Dmin = D + EI = 70 + (-78) = 69.922 mm;
• dmax = d + es = 70 + 0 = 70 mm;
• dmin = d + ei = 70 + (0.030) = 69.970 mm;
• Hole and shaft dimensional tolerances:
• TD = IT6 = 19 µm;
• Td = IT7 = 30 µm;
• Fit parameters (with clearance).
• Nmax = dmax - Dmin = -0.078 mm;
• Nmin = dmin - Dmax = -0.029 mm;
• TN = Nmax - Nmin = -0.0678 + 0.029 = -0.049 mm.
• Check: TN = Td+TD 0.049 = 0.019 + 0.030
• 3. The landing is set to 105F7/h7.
• Landing with clearance.
• Limit deviations of hole 53H7: upper ES=+30 µm; lower EI=0.
• Maximum shaft deviations 53k5: upper es=+15 µm; lower ei=+2 µm.
• Limit dimensions of hole and shaft:
• Dmax = D + ES = 53 + 0.030 = 53.030 mm;
• Dmin = D + EI = 53 + 0 = 53 mm;
• dmax = d + es = 53 + 0.015 = 53.015 mm;
• dmin = d + ei = 53 + 0.002 = 53.002 mm;
• Hole and shaft dimensional tolerances:
• TD = IT7 = 30 µm;
• Td = IT5 = 13 µm;
• Landing parameters (transitional).
• Smax = Dmax - dmin = 53.030 - 53.002 = 0.028 mm;
• Nmax = dmax - Dmin = 53.015 - 53 = 0.015 mm;
• Smin = -Nmax = -0.015 mm;
• Nmin = -Smax = -0.028 mm;
• TS(N) = Smax + Nmax = 0.028 - 0.015 = 0.043 mm.
• Check: TS(N) = Td+TD 0.043 = 0.013 + 0.030
• 4. The landing is set to 21H8/h7.
• Landing with clearance.
• Limit deviations of hole 21H8: upper ES=+33 µm; lower EI=0.
• Maximum shaft deviations 21h7: upper es=0 µm; lower ei=-21 µm.
• Limit dimensions of hole and shaft:
• Dmax = D + ES = 21 + 0.033 = 21.033 mm;
• Dmin = D + EI = 21 + 0 = 21 mm;
• dmax = d + es = 21 + 0 = 21 mm;
• dmin = d + ei = 21 + (-0.021) = 20.979 mm;
• Hole and shaft dimensional tolerances:
• TD = IT8 = 33 µm;
• Td = IT7 = 21 µm;
• Landing parameters (with clearance).
• Smax = Dmax - dmin = 21.033 - 20.979 = 0.054 mm;
• Smin = Dmin - dmax = 21 - 21 = 0;
• TS = Smax - Smin = 0.054 - 0 = 0.054 mm.
• Check: TS = Td+TD 0.054 = 0.021 + 0.033
• We enter the obtained data for all landings in Table 1.1.
• Table 1.1 Types and parameters of plantings

Designation Landing	Limit dimensions	Limit dimensions	Fit type	Fit tolerance
	Holes
									transitional

Figure 1.1 - Scheme of fit No. 1 with a gap Figure 1.2 - Scheme of fit No. 2 with interference Figure 1.4 - Scheme of fit No. 4 with a gap) b) Figure 1.5 - Sketches of mating parts: a) holes; b) shafts; 1.2 Gauge for monitoring smooth cylindrical joints We will develop limit gauges for monitoring the 34H7/s7 mating. We set tolerances for the production of limit gauges according to tables 3 and 4. Initial data: For hole 34H7: H = 4 µm; Z=3.5 µm; b = 0. For shaft: 34s7: H 1 = 4 µm, Z1 = 3.5 µm, H p = 1.5 µm, b 1 = 0, Y1 = 3 µm.

Executive size of the passage side of the plug gauge:

Prmax= Dmin+Z+=34+0.0035+0.004/2=34.0055 mm;

the size in the drawing is 34.0055 -0.004 mm.

The standard size of the non-pass side of the plug gauge:

Notmax= Dmax- b +=34.025-0+0.004/2=34.027 mm;

the size in the drawing is 34.027 -0.004 mm.

Executive size of the passage side of the staple gauge:

Prmin= dmax-Z 1 - =34.068-0.0035-0.004/2=34.0625 mm;

the size in the drawing is 34.0625 +0.004 mm.

The standard size of the non-pass side of the staple gauge:

Notmin= dmin+ b 1 - =34.043+0-0.004/2=34.041 mm;

the size in the drawing is 34.041 +0.004 mm.

Executive size of control gauge:

K-Imax= dmax+ Y 1 - b 1 +=34.068+0.003-0+0.0015/2=34.07025 mm;

the size in the drawing is 34.0702 -0.0015 mm.

Executive size of the pass-through control gauge:

K-Prmax= dmax-Z 1 +=34.068-0.0035+0.0015/2=34.06525 mm;

the size in the drawing is 34.0652 -0.0015 mm.

Executive size of a no-go control gauge:

K-Hemax= dmin+ b 1 +=34.043+0+0.0015/2+0=34.04375 mm;

the size in the drawing is 34.0437 -0.0015 mm.

Roughness of working surfaces of calibers:

R a ? 0.012T size (H 1 ,H), H 1 =H=4 µm;

R a = 0.012?4 = 0.048 µm;

We accept R a from the standard series

For both calibers: R a =0.05 µm.

Figure 1.6 Schemes of tolerance fields of maximum calibers

2. Calculation and selection of bearing fits

Initial data:

bearing 409;

accuracy class 0;

radial force F=4000 N;

It is the inner ring that rotates.

1. Bearing parameters 409: d=45 mm; D=120 mm; B=29 mm; r=3.0 mm.

In the unit under consideration, the rotating ring is the inner ring of the bearing, so we fit it onto the shaft with an interference fit, and install the outer ring in the housing with a gap.

2. Determination of the minimum required interference for the inner ring of the bearing:

where coefficient k=2 for the heavy bearing series.

3. Determination of the maximum permissible tension of the inner ring of the bearing:

Using Table 9, we determine the maximum size deviations:

for hole: ES=0; EI=-12 µm;

for the shaft: es=+25 µm; ei=+9 µm;

5. Determination of the minimum and maximum interference in the connection:

Since >(9 µm > 4.522 µm), and >(37 µm< 205,2 мкм), можно заключить, что посадка внутреннего кольца подшипника выполнена правильно.

6. Select the fit for the outer ring of the bearing from the recommended ones: 120H7/l0. Limit deviations:

for hole:

for shaft:

Maximum clearance for selected fit:

S max =ES-ei=35-(-15)=50 µm.

Minimum clearance for selected fit:

Smin=EI-es=0-0=0 µm.

7. We build a diagram of the tolerance fields of the selected fits for the rolling bearing rings:

8. Sketch of the assembly unit

Figure 2.2 Assembly

3. Roughness, deviations in shape and location of surfaces

Initial data:

1. 45k6; Td=16 µm;

2.50n7; Td=25 µm;

3. 45k6; Td=16 µm;

4.25r7; Td=21 µm;

5. 53 -0.3; Td=300 µm;

6. 55 -0.3; Td=300 µm;

7. 18h6; Td=11 µm;

8. 9h15; Td=580 µm;

9.14N9; Td=43 µm;

3.1 We find the roughness of the marked surfaces in accordance with the purpose of these surfaces and the tolerance of their size

3.1.1 Determine the roughness for the seats of rolling bearings

Surface 45k6: Td=16 µm;

we take R a =0.63 μm from the standard series.

Surface 45k6: Td=16 µm

Similar to the previous surface R a =0.63 µm.

3.1.2 Roughness for critical surfaces that form certain fits with the mating surfaces of other parts

In the general case, the selected surfaces can be considered surfaces of normal geometric accuracy, for which the roughness parameter T .

Surface 50n7: Td=25 µm;

we take R a =1.25 µm from the standard series.

Surface 25r7: Td=21 µm;

we take R a =1.00 µm from the standard series.

Surface 18h6: Td=11 µm;

we take R a =0.32 µm from the standard series.

3.1.3 Determination of the roughness of surfaces that do not have high requirements

Surface 53 -0.3: Td=300 µm;

Surface 55 -0.3: Td=300 µm;

we take R a =12.5 µm from the standard series.

Surface 9h15: Td=580 µm;

we take R a =25 µm from the standard series.

The roughness of the keyway surfaces is assumed to be within the range R a =3.6...12.5 µm, with larger values ​​corresponding to the bottom of the groove.

3.2 Tolerances for deviation of the shape and location of surfaces will also be determined using an approximate method

3.2.1 Calculation of tolerances for deviations from roundness and cylindricity of surfaces

Surface 45k6: Td=16 µm;

T µm, take T = 4 µm from the standard series.

T µm, take T = 4 µm.

Surface 50n7: Td=25 µm;

T µm, take T = 6 µm.

Surface 25r7: Td=21 µm;

T µm, take T = 6 µm.

3.2.2 Tolerance for radial runout of the surface relative to the AB surface

Surface 50n7:

T mm, take T =0.02 mm;

Surface 25r7:

T mm, take T =0.02 mm;

3.2.3 The tolerance for deviation from the perpendicularity of the surface end 50 -0.3 for fixing the bearing depends on the size tolerance for the width of the bearing

T µm, take T = 6 µm.

Tolerance for deviation from perpendicularity of the surface 9h15:

T µm, take T = 120 µm.

3.2.4 Tolerance for deviation from the symmetry of the keyway location

T µm, take T = 120 µm,

3.2.5 Tolerance for deviation from parallelism of the keyway

T // µm, take T // =120 µm.

where T B - when determining the perpendicularity tolerance, is the tolerance for the width of the bearing; when determining the tolerance for deviation from the symmetry of the sides of the keyway, this is the tolerance for the width of the shaft groove.

Draw a sketch of the shaft

4. Tolerances and fits of keyed and splined joints.

4.1 Keyed connections.

Initial data: d=35 mm, connection type 3 (tight connection).

According to GOST 23360-78, we select the main connection dimensions:

b=10 mm, h=8 mm;

The depth of the groove of the shaft and sleeve, respectively: t 1 = 5 mm, t 2 = 3.3 mm;

Type of execution 1;

Key length l=50 mm;

Key designation: Key 1-10 h 8 h 50 GOST 23360-78.

Application conditions - tight, characterized by the probability of obtaining approximately the same small interference in the connection of the keys with both grooves; assembly is carried out by pressing, used for rare disassembly and reverse loads.

For a given connection type, we assign tolerance fields for keyed connection parts:

shaft tolerance field s6,

hole tolerance H7,

key width tolerance range b - h9,

key height tolerance range h - h11,

tolerance range of key length l - h14,

tolerance range of groove width on the shaft and in the bushing - P9,

We determine the maximum deviations using the standard for smooth joints:

shaft diameter 35

sleeve diameter 35

key width 10

key height 8

key length 50

width of the groove on the shaft 10

groove width in sleeve 10

shaft groove depth

* sleeve groove depth

We build diagrams of the location of tolerance fields (Figure 4.1).

4.2 Straight spline connection

Initial data: b-6 h 28H11/ ? 26.7 h 32H12/a11 h7F8/js7 GOST 1139-80

Straight spline connection: centering along the side surfaces of the teeth b;

tolerance range of centering diameter D=32 mm

H12 - bushings,

number of straight-sided splines 6;

internal diameter of connection d=28 mm;

slot width b=7 mm,

bushing spline width tolerance range F8,

Shaft spline width tolerance range js7.

Centering along b is used when special alignment accuracy is not required, when transmitting significant moments, in cases where large gaps between the side surfaces of the shaft and bushing are unacceptable; the simplest and most economical way.

According to GOST 1139-80, we assign tolerance fields for the bushing and shaft according to the non-centering diameter:

H11 bushings,

maximum shaft deviation along the non-centering diameter d is not less than 26.7 mm.

Values ​​of maximum deviations of diameters and widths of straight-sided splines:

For bushing b-6 h 28H11 h 32H12 h7F8 GOST 1139-80

centering diameter;

non-centering diameter;

groove width;

For shaft b-6 h? 26.7 h 32a11 h7js7 GOST 1139-80

centering diameter;

non-centering diameter mm;

groove width;

We build diagrams of the location of tolerance fields (Figure 4.2).

4.3 Involute spline connections

Initial data: 48 h H7/h6 h 2 GOST 6033-80

Nominal diameter D=48 mm,

Module m=2 mm,

type of centering along the outer diameter,

tolerance range of the outer diameter of the bushing D f - H7,

tolerance range of the outer diameter of the shaft d a - h6.

Centering along the outer diameter D is the most technologically advanced, since in this case, the final operation of the hole is broaching, and when processing the shaft, grinding is performed. This centering is used in parts with a non-hardened hole.

We determine according to GOST 6033-80 the missing parameters of the involute connection:

Number of teeth Z=22;

Pitch diameter:

Diameter of spline shaft grooves

Inner sleeve diameter

We assign a tolerance field for the bushing cavity width e - 9H, a tolerance field for the shaft tooth thickness S - 9d: fit 9H/9d.

The tolerance field of the bushing and shaft for non-centered diameter with a flat shape of the bottom of the cavity: for bushing D a - H11, for shaft d f - h16, fit H11/h16.

Values ​​of maximum deviations of diameters, maximum deviations on the sides of the teeth:

For bushing 48 h H7 h 2 GOST 6033-80:

centering diameter;

depression width

e - 9H: ES=+71µm;

EJ e =+26 µm;

For shaft 48 h h6 h 2 GOST 6033-80:

centering diameter;

tooth thickness

S - 9d: es=-44 µm;

es e = -70 µm;

We build diagrams of the location of tolerance fields (Figure 4.3).

Literature

1. Markov N.N., Osipov V.V., Shabalina M.B. Standardization of accuracy in mechanical engineering: Textbook. for mechanical engineering specialist. universities / Ed. Yu.M. Solomentseva. - 2nd ed., revised. and additional - M.: Higher. school; Publishing center "Academy", 2001. - 335 pp.: ill.

2. Yakushev A.I. and others. Interchangeability, standardization and technical measurements: Textbook for colleges / A.I. Yakushev, L.N. Vorontsov, N.M. Fedotov. - 6th ed., revised. and additional - M.: Mechanical Engineering, 1987. - 352 p.: ill.

3. V.I. Anuriev "Handbook of mechanical engineering designer": in 3 volumes - 8th edition: - M.: Mechanical Engineering, 2001.

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higher professional education

"Altai State Technical University

named after I.I. Polzunov"

V.A. Wagner,

V.P. Zvezdakov,

V.V. Sobachkin

STANDARDING PRECISION IN MECHANICAL ENGINEERING

Tutorial

in the discipline "Metrology, standardization and certification"

Approved by the Educational and Methodological Association of Universities for University Polytechnic Education as a manual for students of higher educational institutions studying in mechanical engineering areas of training

From AltSTU

Barnaul – 2011

Vagner V.A. Standardization of accuracy in mechanical engineering. Textbook for the discipline “Metrology, standardization and certification” / V.A. Wagner, V.P. Zvezdakov, V.V. Sobachkin. - Barnaul: Publishing house Alt.gos.tekhn. University named after I.I. Polzunova. - 2011, 84 p.: ill.

The textbook provides information on the standardization of accuracy in mechanical engineering when developing machine parts and assemblies.

The purpose of the work is to study theoretical issues in the “interchangeability” section of the discipline “Metrology, standardization and certification”, to develop students’ independent activity skills to practically consolidate the tasks discussed in the theoretical part of the course, as well as work with reference literature and standards.

The textbook is intended for students of higher educational institutions of all specialties, studying in mechanical engineering areas of full-time, part-time and correspondence courses, studying the course “Metrology, standardization and certification”.

Reviewers:
Professor of the Department of Metrology and Interchangeability, MSTU. N.E. Bauman,

Doctor of Technical Sciences Pronyakin V.I.
Professor of the Department of Machine Parts, Ural Federal University,

Doctor of Technical Sciences Chechulin Yu.B.

1 Determination of the nominal dimensions of parts of an assembly unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 General information about dimensions, tolerances, fits and maximum deviations. . . . . . . . . . . . . . . . . . . . . .

3 Tolerances and landings in the “Unified System of Tolerances and Landings”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Choice of landings when designing structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1 Landings with clearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Transitional landings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Interference fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Calculation of interference fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Tolerances and fits of keyed joints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Connections with parallel keys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2 Connections with segmental keys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Tolerances and fits of gear (spline) connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.1 Toothed connection with straight splines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.2 Gear connection with involute splines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 Fittings of rolling bearings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 Dimensional chains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Standardization of the accuracy of the shape and location of surfaces of typical machine parts, determination of the required surface roughness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1 Tolerances of shape and relative position of surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2 Roughness of surfaces of parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 Tolerances for the location of the axes of holes for fasteners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12 Justification of the technical requirements for the drawing of the assembly unit. . . . . . . . . . . . . . . . . . . . . . . . . . .

12.1 General provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2 Determination of technical requirements values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2.1 Determination of the values ​​of lateral clearances in engagement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2.2 Determination of the completeness of contact of the mating side surfaces of the teeth. . . . . . . . . . . . . . . . . .

13 Instructions for drawing up technical requirements and preparing a working drawing of a gear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13.2 Recommendations for drawing up technical requirements for spur and bevel gears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 Instructions for drawing up technical requirements and preparing a working drawing of the gearbox shaft

15 Recommendations for drawing up technical requirements, developing and designing a drawing of the bearing cover and cup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In accordance with the educational standard for students of technical specialties in mechanical engineering, studying the discipline “Metrology, standardization and certification” in the interchangeability section, a course work or calculation assignment is provided.

The purpose of the course work (calculation assignment) is to consolidate the knowledge gained from the theoretical course and acquire skills in their practical application, therefore this work provides both theoretical information on the main sections of the discipline and examples of solving typical course problems. The appendix to the work provides reference material necessary for solving problems.

Coursework is completed according to individual assignments issued by the teacher.

Requirements for the content and design of the course work (calculation assignment) are set out in the methodological recommendations.

1 Determination of the nominal dimensions of parts of an assembly unit

The dimensions of the parts that make up the assembly unit depend on the assignment and option for the course work. To determine their nominal values, it is necessary to calculate the scale factor. It is calculated as follows. In the drawing of the course work assignment, the size corresponding to the diameter of the shaft under the rolling bearing (d 3 measured) is measured. The target size (d 3 given) is divided by this measured size to obtain the scale factor μ

By measuring all other dimensions of the parts of the assembly unit and multiplying them by this scale factor, the calculated dimensions are determined.

To reduce the number of standard sizes of workpieces and parts, cutting and measuring tools, the values ​​of nominal dimensions obtained by calculation must be rounded to the values ​​​​specified in GOST 6636-69 “Normal linear dimensions” (Table A.1). After this, the rounded values ​​of nominal sizes should be entered in Table 1.1. The dimensions associated with the rolling bearing should be taken according to the standard for this product, regardless of the design size. To do this, you should decipher the symbol of a given rolling bearing, determining its series, type and design features, and then, according to GOST 520-2002 or reference books, write down all the parameters of the rolling bearing necessary for further calculations (connecting diameter of the outer ring, width of the rings, dynamic load capacity of the bearing ).

Then the dimensions associated with the rolling bearing are assigned. These dimensions are size d 1 (fitting diameter of the through bearing cap), d 2 (diameter of the hole in the housing for installing the bearing), d 4 (inner diameter of the spacer sleeve), d 5 (fitting diameter of the blind bearing cap). Designations according to .

For example, if according to the assignment it is known that d 3 = 30 mm, bearing type 7300, then this means that the bearing size is 7306 (d 3 /5 = 30/5 = 6), tapered roller bearing and its outer diameter D = 72 mm . In accordance with this, the dimensions d 1 = d 2 = d 5 = 72 mm, and d 4 = d 3 = 30 mm.

When filling out Table 1.1, you should pay attention to the dimensions of standardized and standard parts, which must also be accepted in accordance with the relevant regulatory documents. Such parts include seals of bearing units, keys, round spline nuts, through and blind bearing caps, bearing cups.

Based on the obtained dimensions, an assembly unit is drawn on the appropriate scale.

2 General information about dimensions, tolerances, fits and maximum deviations

Size– numerical value of a linear quantity (diameter, length, etc.) in selected units of measurement. In the drawings, all linear dimensions are indicated in millimeters.

Actual size – element size established by measurement with permissible error.

Limit dimensions– two maximum permissible sizes, between which the actual size of a suitable part must be or can be equal to. The larger one is called the largest limit size, and the smaller one is called the smallest limit size. They are designated D max and D min for the hole and d max and d min for the shaft.

Nominal size– the size relative to which deviations are determined. The size indicated in the drawing is nominal. The nominal size is determined by the designer as a result of calculations for strength and rigidity or taking into account design and technological features. For parts forming a landing connection, the nominal size is common.

IN
Table 1.1 - Assembly unit dimensions