Yakushev interchangeability standardization and technical measurements. Interchangeability, standardization and technical measurements. Interference fit calculation

Introduction

In order to improve the technical level and quality of products, increase labor productivity, save labor and material resources, it is necessary to develop and improve standardization systems in all sectors of the national economy based on the introduction of the achievements of science, technology and practical experience.

It is necessary to strengthen the effective and active influence of standards on the production of products that correspond in their technical and economic indicators to the highest world level

Today, when the production of one machine requires cooperation between hundreds of enterprises various industries industry, product quality issues cannot be resolved without expanding work to improve the system of interchangeability, metrological support, and improve methods and means of product control. Therefore, the training of a modern engineer includes the development of a wide range of issues related to standardization, interchangeability and technical measurements.

The course "Interchangeability, standardization and technical measurements" is the logical conclusion of the cycle of general technical courses on the theory of mechanisms and machines, metal technology, strength of materials, machine parts. If other cycle courses serve theoretical basis designing machines and mechanisms, using typical machine parts, calculating their strength and rigidity, then this course considers the issues of ensuring the accuracy of geometric parameters as a necessary condition for interchangeability and such important quality indicators as reliability and durability. The tasks of improving the quality of manufacturing, operation and repair of agricultural machinery can be considered comprehensively, using the principles of standardization, interchangeability and control of established technical conditions.

The purpose of the discipline is to develop the knowledge and practical skills of future engineers to use and comply with the requirements of complex systems of general technical standards, perform accurate calculations and metrological support in the manufacture, operation and repair of agricultural machinery.

As a result of studying the course and in accordance with qualification characteristic mechanical engineer Agriculture must know: basic provisions, concepts and definitions in the field of standardization; the state standardization system and its role in accelerating scientific and technological progress, intensifying production, improving the quality of agricultural machinery and the economic efficiency of its use; the main issues of the theory of interchangeability and technical measurements, the rules for designating accuracy standards in design and technological documentation; methods of calculation and selection of standard fits of typical connections of machine parts; calculation of dimensional chains; arrangement of measuring instruments for linear and angular quantities, their setting, operating rules and selection methodology.

1. Calculation and selection of fits of smooth cylindrical joints with a gap

Calculation and selection of landings of smooth cylindrical joints is carried out in the following sequence.

2. Select universal measuring instruments for the parts to be joined.

The initial data for the calculation are:

Nominal connection diameter, d H =30 mm;

Connection (bearing) length, l=50 mm;

Angular velocity, =70 rad/s;

Absolute viscosity of oil at operating temperature, = 0.03 N-s / m 2;

Average specific pressure on the support, g \u003d 0.45 N / M 2

R zD =4 μm and R zd =2. 5 µm - the surface roughness of the bushing and shaft.

Rice. 1.1 Scheme for the calculation of landings for a movable connection

It is known from the hydrodynamic theory of lubrication that the ratio between the values h and S (Fig. 1. 1) in bearings of finite length is expressed by the dependence = (1.1)

where h is the thickness of the oil layer at the point of closest approach of the surfaces of the shaft and the bearings in working condition, m; - the gap between the shaft and the bearing at rest, m.

hS= (µm 2)

Knowing the value of the product hS, determine the value of the most advantageous gap in the connection:

=79 (µm)

Taking into account the presence of surface roughness of the parts to be joined, the value of the calculated gap is found:

Spac= (1.3)

According to the size of the calculated gap according to the tables of maximum deviations of holes and shafts (appendices 4 and 5), a fit is selected that satisfies the condition

The given condition is satisfied by the standard fit 30 made in the hole system: limit deviations for the hole 30H8() ; limit deviations for the shaft 30e8 ().

For the specified landing:

S max = ES-ei=33-(-0.073)=106 (µm) (1.5)

S min \u003d EI- es \u003d 0 - (- 40) \u003d 40 (μm) (1.6)

The selected fit should be checked for fluid friction. The smallest thickness of the lubricant layer is determined with the largest gap of the selected fit

(1.7)

We check for the sufficiency of the lubricant layer that provides liquid friction, it is checked by the condition

(1.8)

The fluid friction condition is satisfied, which means that the fit is chosen correctly.

We determine the limiting dimensions and tolerances for the processing of connection parts according to the selected fit:

a) holes

D max \u003d D H +ES (1. 9)

max=30+0. 033=30. 033 (mm)

mln =D H +EI (1.10)

mln=30+0=30 (mm);

D = D max - D mln =ES-EI ; (1.11)

D=30. 033-30=0.033 (mm)

max = d H +es (1.12)

max \u003d 30 + (- 0.040) \u003d 29. 96(mm)

min = d H + ei (1.13)

min =30+(-0.073) =29. 927mm)

d = d max -d mln = es-ei (1.14)

d=29. 96-29.927=0.033(mm)

Determine landing tolerance:

s \u003d S max -S min \u003d T D + Td (1.5)

Ts = 33+33 = 66 (mm).

We choose universal means of measuring the parts to be joined, considering that the measurement is carried out in individual production.

The choice of universal measuring instruments is made taking into account metrological, design and economic factors. When choosing universal measuring instruments, it is necessary that the marginal error of measuring instruments lim be equal to or be less than the permissible measurement error . i.e., so that the condition is met:

For the connection under consideration, d H = 30 mm, T D = 33 µm, T d = 33 µm, select from the table in Appendix 3 for holes 30H8 = 10 µm; for the shaft 30e8 = 10 µm.

These requirements are met (Appendix 4) for the hole - an indicator caliper with a measuring head with a division value of 0.001 mm, and for the shaft a lever micrometer with a division value of 0.002 mm, the characteristics of which are entered in Table. eleven.

Table 1. 1. Initial data and characteristics of the selected measuring instruments

	Part tolerance value, IT parts, µm	Permissible error, µm	Limit error of measuring instruments, μm Name of measuring instruments and their metrological characteristics
Hole				Bore gauge indicator with an indicator of zero accuracy class when working within one turn of the arrow with a valuable division of 0. 01 mm
				Bracket indicator with valuable division 0. 01 mm

1.2 Calculation of the executive dimensions of smooth calibers

In the manufacture of limit calibers, their executive dimensions must be maintained within the tolerances for calibers established by the standards of GOST 24853 - 81 (Article SEV 157 - 75).

Let's calculate the working gauges to control the details of the connection:

Since for parts manufactured with an accuracy of more than 6-20 qualifications (shaft according to IT6), control using calibers (clip calibers) is carried out according to individual, limiting and executive dimensions of the cork caliber.

We determine the limiting and executive dimensions of the caliber - plugs:

According to Appendix 1 for IT6 and the size range of 18 ... 30 mm, we find data for calculating the caliber - plugs. =5µm, Y=4µm, H=4µm.

Passage side of the caliber - traffic jams.

PR max =D min +Z+H/2=30+0. 005+0. 004/2=30. 007 (mm). (1.16)

PR min \u003d D min + Z-H / 2 \u003d 30 + 0.005-0.004 / 2 \u003d 30. 001 (mm). (1.17)

PR meas = D min -Y=30 - 0. 004=29. 996 (mm). (1.18)

The executive dimensions of the passage and non-passage sides of the caliber - plugs are their largest limiting dimensions with a tolerance numerically equal to the tolerance for the manufacture of the caliber (minus).

Then for the passage side of the caliber - plugs, the executive size:

PR use \u003d 30. 007-0. 004 (mm).

Non-going side of the plug gauge:

NOT max =D max +H/2=30. 033+0. 004/2=30. 035 (mm). (1.19)

NOT min = D max -H/2=30. 033-0. 004/2=30. 031 (mm). (1.20)

Then for the impassable side of the caliber - plugs, the executive size:

NOT Spanish =30. 035 -0.004 (mm).

We calculate the caliber - brackets for shaft control ø25f6. According to Appendix 1 for IT6 and size range 18…30mm. we find data for calculating the caliber - staples. 1 \u003d 5 microns. Y 1 = µm. H 1 \u003d 4 μm.

Passing side of the caliber - brackets:

PR max \u003d d max -Z 1 + H 1 / 2 \u003d 29. 96-0. 005+0. 004/2=29. 957 (mm). (1.21)

PR min \u003d d max -Z 1 -H 1 / 2 \u003d 29. 96-0.005-0.004/2=29. 953 (mm). (1.22)

PR meas \u003d d max + Y 1 \u003d 29. 96+0. 004=29. 964 (mm). (1.23)

For the passing side of the bracket, the execution size:

PR Spanish \u003d 29. 957+0. 004 (mm).

The impassable side of the caliber - staples:

NOT max =d min +H 1 /2=29. 927+0. 004/2=29. 929 (mm). (1.24)

NOT min \u003d d min -H 1 / 2 \u003d 29. 927-0. 004/2=29. 925 (mm). (1.25)

For the non-going side of the bracket, the execution size:

NOT Spanish =29. 929+0. 004 (mm).

Limiting executive gauges - plugs and brackets are summarized in table 1. 2

Table 1.2 Results of calculations of measuring instruments

control part

The meaning of the elements of working calibers

passing side

Bad side

Nominal size

Limit dimensions, mm.

Executive size

Nominal size

Limit size in, mm.

Executive size

Hole

2. Calculation and selection of fits for rolling bearings

1 General information

Rolling bearings operate in a wide variety of operating conditions and are designed to provide the required accuracy and uniformity of rotation of the moving parts of machines. Being standard units, rolling bearings have complete external interchangeability in terms of connecting surfaces, determined by the outer diameter of the outer and inner diameter of the inner rings. Full interchangeability of rolling bearings on the connecting surfaces ensures their lightness and quick installation and dismantling while maintaining good quality machine nodes.

The quality of the rolling bearings themselves is determined by a number of indicators, depending on the size of which, according to GOST standards. 520-71, five accuracy classes are established, designated in order of increasing accuracy: O, 6, 5, 4 and 2. The bearing accuracy class is selected based on the requirements for rotation accuracy and operating conditions of the mechanism. In mechanical engineering and instrumentation under medium and low loads, normal rotation accuracy, bearings of accuracy class O are usually used. For the same conditions, but with increased requirements for rotation accuracy, bearings of accuracy class 6 are used. Bearings of accuracy classes 5 and 4 are used only at high speeds and strict requirements for rotational accuracy, and accuracy class 2 - only in special cases. The accuracy class (except class 0) is indicated with a dash before the bearing symbol, for example: 6 - 209

In order to reduce the range of bearings, bearings are manufactured with deviations in connecting diameters, which do not depend on the fits on which they are mounted on shafts and in housings. This means that the outer diameter of the outer ring and the inner diameter of the inner ring are taken as the diameters of the main shaft and the main hole, respectively, and, therefore, the outer ring is connected to the body according to the fit in the shaft system, and the inner ring to the shaft - according to the fit in the hole system. The hole diameter of the inner ring, taken as the main hole, has a tolerance direction similar to the tolerance direction of the main shaft. The inverted arrangement of the tolerance field for the inner ring hole diameter eliminates the need to develop and use special fits to obtain connections between rings and shafts with slight interference. In this case, the required interference values are provided as a result of using standard transitional fits according to GOST 25347-82.

Fittings of rolling bearings on shafts and housings are selected depending on their types and sizes, operating conditions, the magnitude and nature of the loads acting on them and the type of loading of the rings. There are three main types of loading of rolling bearing rings: local, circulation and oscillatory.

In practice, it most often happens that one of the bearing rings, usually rotating, experiences circulation loading, and the other (fixed) - local. The ring under circulating loading should be connected to the shaft or housing by fits that provide small preload values, and the stationary locally loaded ring should be connected to fits with a small gap.

Landings of circulation-loaded bearing rings on shafts and in housings are selected according to the intensity of the radial load on the seating surface, which is determined by the following formula:

(2.1)

K p - dynamic landing coefficient, depending on the nature of the load (with strong shocks and vibrations, overload up to 300% Kp = 1.8); - coefficient taking into account the degree of weakening of the landing interference with a hollow shaft or thin-walled housing (for a shaft F varies from 1 up to 3, for the body - from 1 to 1.8; with a solid shaft and a massive thick-walled body F=l); A is the coefficient of uneven distribution of the radial load R between rows of rollers in double-row tapered roller bearings or between double ball bearings in the presence of axial load A on the support (factor F A varies from 1 to 2, and in the absence of axial load F A = 1).

For locally loaded bearing rings, the fit is selected depending on the operating conditions and, first of all, on the nature of the load and the speed of rotation.

Mounting surfaces of shafts and housing bores for rolling bearings are subject to increased requirements in terms of shape deviations and roughness.

2.2 The order of calculation and selection of landings

According to the initial data, you must do the following:

Set the main dimensions of the bearing and determine the nature of the loading of its rings.

Determine the numerical values of the limit deviations of the connecting diameters of the bearing and seats shaft and body. Determine the numerical values of limit deviations.

3. Mounting diameters of the bearing and shaft and housing seats according to the selected fit.

5. Determine the deviations of the shape, relative position, roughness of the surfaces of the shaft and housing seats.

Ball bearing No. 209. The housing rotates, the shaft is stationary. The case is cast iron, one-piece. Radial load on the support R=19. 5 kH. The operating mode of the bearing is normal. According to Appendix 2, we find the main dimensions of the bearing:

outer diameter D =85mm,

inner diameter d = 45 mm,

ring width H=19 mm,

chamfer radius r=2 mm

We determine the type of loading of the rings, a given bearing. Since the housing rotates and the shaft is stationary, the outer ring of the bearing will experience circulation loading, internal-local.

We calculate and select the fit of a circulation-loaded ring.

We determine the intensity of the radial load of the landing surface by the formula

According to the table in Appendix 4, we find the tolerance field for the hole in the body of the part corresponding to the obtained value R R. The fit of the outer ring into the hole in the body of the part in the conditional notation has the form.

According to the table in Appendix 5, we accept the tolerance field for the shaft diameter.

Then the fit of the inner ring on the shaft of the part in general view let's write it like this:

According to the tables of GOST 25347-82, Appendix 6, we find numerical. values of limit deviations of connecting diameters of bearing rings and shaft and housing seats. We have:

inner ring

shaft neck

outer ring .

hole in the body.

The calculation of the limit values of the connecting diameters, their tolerances, as well as the gaps and interferences obtained in the joints, and we demolish in table 2. 1.

a) inner ring

Dmax=D H +ES=45+0=45 (mm) (2.2)=D H +EI = 45+(-0.012) = 44.988(mm) (2.3)

T D = D max -D mln =ES-E (2.4)

D=45-44. 988=0. 012 (mm)

b) shaft neck

D H+es=45+0. 018=45. 018 (mm) (2.5)

dmin = dH +ei = 45+0. 002=45. 002 (mm) (2.6)

T d = D max -D mln = es - ei (2.7)

d=45.018-45. 002=0. 016 (mm)

c) a hole in the body

ax=D H +ES=85+(-0.010)=84. 99 (mm) (2.8)

Dmin=D H +EI = 85+(-0.045) =84. 955 (mm) (2.9)

T D \u003d D max -D mln \u003d ES-EI (2.10)

T D =84. 99-84. 955=0.035 (mm)

d) outer ring

D H +es=85+0=85(mm) (2.11)

d min \u003d d H + ei \u003d 85 + (-0.020) \u003d 84. 98 (mm)

T d \u003d D max -D mln \u003d es - ei

T d = 85-84. 98=0.02 (mm)

Determine the limit clearance (preload) of the inner ring-shaft neck

N max \u003d es-EI \u003d -0. 012-0.018=-0.03(mm) (2.12)

S max = ES - ei = 0-0. 002=-0. 002 (mm) (2.13)

Determine landing tolerance;

T s (N) \u003d S max + N max \u003d T D + T d (2.14)

Ts(N) = -0. 002+(-0.03)= -0. 032 (mm). body bore - outer ring

max=ES-ei=-0. 010-(-0.020)=0.01 (mm) (2.15)

N max =es-EI=-0. 045-0=-0. 045(mm) (2.16)

Determine landing tolerance;

T s(N) =S max +N max =T D +T d (2.17)

Ts(N) = 0.01+(-0.045)= -0. 035 (mm).

According to the tables of applications 7 and 8, we establish the permissible deviations of the shape, the relative position of the seating surfaces, their roughness. We have:

a) deviation from the cylindricity of the shaft neck - 8 microns, holes in the housing - 15 microns;

b) runout of the ends of the shaft shoulders - 20 microns, holes in the body - 40 microns;

c) the roughness of the seating surfaces of the shaft R a 1.25 and the hole in the housing R a no more. 1.25 µm;

d) also the ends of the shaft shoulders R a 2.5 µm, and the holes in the body R a 2.5 µm.

Table 2.1 Dimensional characteristics of rolling bearings

Name of bearing connection elements	Limit deviations, mm	Limit dimensions, mm	Dopski, microns	Limit gaps, microns

Connecting diameters:
inner ring
Shaft journal
outer ring
case openings
Connections:
"inner ring-shaft"
"outer ring-housing"

3. Selection of keyway fits

3.1 General information

In general mechanical engineering, as well as in automotive and tractor and agricultural engineering, key connections with prismatic and segmented keys are most widely used.

The dimensions of the keyway elements depend on the shaft diameter and are regulated by the relevant standards.

To facilitate the conditions and ensure the required assembly quality, when creating movable or fixed joints, the key with its side faces (in size b) can simultaneously be connected to the grooves of the shaft and the complete sleeve in various fits.

Taking into account the technically feasible accuracy for the formation of various landings in the connection of a feather key with grooves in size b, the GOST 23360-78 standard establishes the following tolerance fields: for the width of the key - H9; on the shaft groove width - H9, N9, P9; on the width of the groove of the sleeve - D10, J S 9 and P9. The combination of groove tolerance fields with the key tolerance field must be such that the following three types of connections are formed:

a) a free connection that provides relative axial movement of the sleeve on the shaft (guide key) or is used to form fixed connections between the sleeves and the shafts under difficult assembly conditions and the action of small uniform loads;

b) a normal connection, used under favorable assembly conditions to ensure the relative immobility of the bushings and shafts connected to each other, operating without loads or with small irreversible loads;

c) a tight connection used to obtain fixed joints of bushings and shafts, which does not require frequent disassembly and works with significant alternating loads; this connection is characterized by the presence between the key and the grooves of approximately the same small interference.

In addition to size b, all other dimensions of the keyed connection elements are non-matching or non-fitting. The tolerances of these dimensions are also standardized.

The GOST 24071 80 standard establishes only two purposes for segment keys. They can be used to transmit torques or to simply hold parts. In this regard, for the formation of landings in the connection of a segmented key with grooves, the standard regulates the size b of the grooves not in three, as for feather keys, but in two tolerance fields: N9 and P9 - for the shaft groove and J b 9 and P9 - for the groove bushings. Tolerance field H9 is set for the width of the key. The preferred combination of the indicated groove tolerance fields with the segment key tolerance field is provided by two types of connections: normal and dense.

The GOST24071-80 standard also establishes tolerances for non-matching dimensions of connection elements with a segment key.

The quality of keyed connections depends on the presence of distortions and displacements in the location of the keyways of the shafts and bushings relative to the section plane. However, the tolerances for these errors are not standardized by the standards. The choice of their values is determined by the specific conditions of the assembly. Usually, with a symmetrical arrangement of the field, the tolerance for misalignment of the keyway along its length near the shaft and bushing is taken equal to 0.5 Tb, and the displacement tolerance is 2Tb, where Tb is the tolerance for the width of the groove of the shaft or bushing.

The standards do not standardize the surface roughness of the elements of keyed joints. Its values are determined by the accepted methods of finishing the keys and shafts. Usually, the roughness of the side (landing) surfaces of the grooves and keys is taken equal to R z 20 μm, and for shafts and surfaces of the key along the height h - R z 40 μm.

3.2. The procedure for selecting and calculating landings of a keyed connection

To solve the problem, the diameter of the shaft on which the key is arranged, the type of key (prismatic or segmented), the type of key connection (loose, normal or dense) must be known. In the presence of the specified initial data, the selection of landings and subsequent calculations must be performed in the following order:

1. Select the main design dimensions of the keyed connection elements with a parallel or segmented key.

2. In accordance with the type of keyed connection, select the fit of the key in the groove of the shaft and in the groove of the sleeve.

3. Find the numerical values of the maximum deviations of the width of the keys and grooves, tolerances and maximum deviations of incompatible dimensions.

4. Determine the limiting dimensions, as well as the interference gaps obtained in the joints of the keys with grooves according to the size b ;.

shaft diameter d = 16 mm;

key type - segmented,

type of keyed connection - normal,

appointment - 1.

Then, according to the table in Appendix 10, we find the main dimensions of the key and grooves:

key section bXhXd = (5X6. 5 X 16) mm;

shaft groove depth t 1 =4. 5 mm;

bushing groove depth t 2 =2. 3 mm.

We install the landing of the key in the groove of the shaft and in the groove of the bushing.

The width of the key and grooves with normal connection has the following tolerance fields: keys - b=5h9, shaft groove - b=5N9 and bushing groove - b=5Js9. Then the landing of the key in the groove of the shaft and in the groove of the sleeve in general terms can be written as follows:

In the groove of the shaft 5 and the groove of the sleeve 5

The numerical values of the maximum deviations of the width of the key and grooves are found from the standard table (Appendix 15)

for key 5h9

for shaft groove - 5N9

for bushing groove -5Js9

Tolerances and limit deviations of non-matching dimensions of the keyed connection elements are found from tables 1 and 12:

key height h= 6. 5h11 (-0.090)

key diameter d = 16h12 (-0.18)

shaft groove depth t 1 =4. 5(+0.2)

bushing groove depth t 2 =2. 3(+0.1)

We calculate the limit values of all the main dimensions and the gaps or tightness obtained in the connection of the key with grooves. the results of the calculations are summarized in Table. 3.1.

a) dowels

for key width

B H +es=5+0 =5 (mm) (3.1) min = bH +ei = 5+(-0.030) =4. 97 (mm) (3.2)

T b \u003d b max -b mln \u003d es-ei (3. 3)

T b = 5-4. 97=0. 03 (mm)

For key height

hmax = hH+es=6. 5+0=6. 5(mm) (3.4)

h min \u003d h H + ei \u003d 6. 5+ (-0.09) \u003d 6. 41(mm) (3.5)

T h \u003d h max -h mln \u003d es-ei (3.6)

T h = 6. 5-6. 41=0. 09(mm)

For key diameter d

d max = d H +es=16+0=16(mm) (3.7) min = d H +ei =16+(-0.18) =15. 82 (mm) (38)

T l \u003d d max - d mln \u003d es-ei (3.9)

T l \u003d 16-15. 82=0. 18(mm)

b) Shaft groove for shaft groove width

Bmax=B H +ES=5+0=5 (mm) (3.10)

Bmin=B H +EI = 5+(-0.03) =4. 97 (mm) (3.11)

T B \u003d B max -B mln \u003d ES-EI (3.12)

B=5-4. 97=0. 03 (mm)

For shaft groove depth

t 1 min \u003d t 1 +EI \u003d 4. 5 + 0 \u003d 4. 5(mm) (3.14)

T t 1 = t 1 max - t 1 mln =ES-EI (3.15)

1=4. 7-4. 5=0. 2(mm)

c) Bushing groove for bushing groove width

Bmax=BH+ES=5+0. 015=5. 015 (mm) (316)=B H +EI = 5+(-0.015) =4. 985 (mm) (3.17)

T B \u003d B max -B mln \u003d ES-EI; (3.18)

T B =5. 015-4. 985=0. 03 (mm)

For bushing groove depth 2max = t 2H +ES=2. 3+0. 1=2. 4 (mm) (3.9) 2min = t 2H +EI = 2. 3+0=2. 3 (mm) (3.20)

T t 2 \u003d t 2max - t 2mln \u003d ES-EI (3.21)

T H = 2. 4-2. 3=0.1(mm)

We determine the gaps

a) Shaft groove keys

Smax=ES-ei=0-(-0.03)=0. 03 (mm) (3.22)

N max \u003d es-EI \u003d 0- (-0. 03) \u003d 0.03 (mm) (3.23)

Determine landing tolerance;

T s (N) \u003d S max + N max \u003d T D + T d (3.24)

Ts(N) = 0.03+0. 03=0.06(mm).

b) Bushing groove keys

max=ES-ei=0.015-(-0.03)=0. 045 (mm) (3.25) max = es-EI =0-(-0.015) =0. 015(mm) (3.26)

Determine landing tolerance;

T s (N) \u003d S max + N max \u003d T D + T d (3.27)

Ts(N) = 0.015+ 0.045= 0.06 (mm).

Table 3-1 Dimensional characteristics of the key connection

Name of keyed connection elements	Nominal size in mm and tolerance field (fit)	Limit deviations, mm	Limit dimensions, mm	Tolerances, microns	Limit gaps, microns





Shaft groove:


Bushing Groove:


Connections:
"shaft key-groove"
"key-groove sleeve"

4. Choice of spline fit

4.1 General information

Spline connections are used for the same purposes as keyed connections, but unlike the latter, they have a number of advantages. Connections of this type are able to perceive significantly greater loads and provide more a high degree centering bushings on shafts.

Among the known types of spline joints, the most widely used, especially in automotive and tractor and agricultural engineering, are connections with a straight-sided tooth profile.

Nominal dimensions and number of teeth of spline connections of a straight-sided profile are regulated by the GOST 1139-80 standard. Depending on the magnitude of the transmitted loads, these standards establish three series of straight-sided splines: light, medium and heavy (Appendix 16). Light series connections have low height and number of teeth. These include fixed lightly loaded connections. Medium series connections have higher heights and number of teeth compared to light series connections and are used to transfer medium loads. The heavy series couplings have the largest height and number of teeth and are designed for heavy duty applications.

For straight-sided spline joints, depending on the operational and technical requirements for them, three methods are used to center the bushings on the shafts: on the outer diameter D, on the inner diameter d and on the side surfaces of the teeth b.

The system of tolerances and landings is regulated by standards and GOST 1139 - 80 and applies to critical movable and fixed joints of a straight-sided profile.

According to GOST 1139-80, landings are formed by combining bushings and shafts from the number of tolerance fields provided and are assigned, depending on the method of centering adopted, to the centering diameter and the side surfaces of the teeth. When centering on D, the fits are assigned to dimensions D and b. when centered on d - on d and b. If the parts of the spline connection are centered on the flanks of the teeth, the fit is assigned only to dimension b.

The tolerance fields of bushings and shafts for the formation of landings of centering surfaces for various methods of centering spline joints of a straight-sided profile are given in Appendix 18.

The GOST 1139-80 standard also provides tolerances for non-centering diameters of the shaft and bushing. Tolerances for non-centering diameters are given in Appendix 17.

The surface roughness of the elements of spline joints is not regulated by standards and can be selected depending on the purpose of the joint and the operational requirements for it, taking into account the applied methods of processing parts. Usually, for all methods of centering, the roughness of the centering surfaces of the shaft is recommended to be maintained within R and 1.25. . . 0.32 microns, and bushings - R and 2.5. . 1.25 µm. Roughness of non-centering surfaces of the shaft and bushing R z 20. . . 10 µm.

In the accepted designations of straight-sided spline joints, their shafts and bushings, the following must be indicated: the letter indicating the centering surface, the number of teeth, the nominal values of the inner d, outer D diameters and width b in the connection, tolerances or fits on diameters and size b, placed after the corresponding sizes. The standard allows not to indicate the tolerances of non-centering diameters in the designation.

4.2 Calculation procedure for spline fits

The choice of landings for the designed spline joints is a complex technical and economic task, as it requires performers to apply calculations taking into account all the data that comprehensively characterize the operation of the joints under operating conditions. Therefore, for educational purposes, course design the student is given a ready-made spline connection with the necessary fits, and the solution of the problem is reduced to the following:

According to the given symbol give a decoding of a straight-sided spline connection and determine the nominal dimensions of its elements.

2. According to the tables of standards, find the maximum deviations of the tolerance fields of the centering and non-centering diameters, as well as the size b.

3. Calculate the limiting dimensions of all elements, their tolerances and the limiting values of the gaps or interferences obtained in the joints along the centering diameter and the side surfaces of the teeth.

Given: Spline connection d-6x18x22 x 5

Let's decipher its conditional notation. The specified spline connection is centered on the inner diameter d, has the number of teeth z = 6, the nominal value of the inner diameter d = 18 mm with a fit, the outer diameter D = 22 with a fit, the thickness of the shaft tooth (width of the bushing cavity) b = 5 mm with a fit

According to the tables of the GOST 25347-82 standard, we find the maximum deviations of the diameters and size b of the bushing and shaft. We have:

a) for splined bushing:

inner diameter d=18H7(+0.018)

outer diameter D = 22H12 (+0.21)

trough width b= 5F8 ()

b) for a splined shaft:

inner diameter d=18h7(-0.018)

outside diameter D = 22a11()

tooth thickness b=5d8()

We calculate the limiting dimensions and tolerances of all elements, as well as the gaps obtained in the joints along the centering diameter and the side surfaces of the teeth.

a) for splined bushing

inner diameter

dmax=dH+ES=18+0. 018=18. 018(mm) (4.1)=d H +EI =18+0 = 18 (mm) (4.2) d = d max d=ES-EI (4.3)

d=18. 018-18=0. 018(mm)

outside diameter

Dmax=D H +ES=22+0. 21=22. 21 (mm) (4.4)=D H +EI = 22+0=22 (mm) (4.5) D = D max -D mln =ES-EI (4.6)

D=22. 21-22=0. 21(mm)

valley width

Bmax=BH+ES=5+0. 028=5. 028 (mm) (4.7)=B H +EI =5+0. 01=5. 01 (mm) (4.8)

T B \u003d B max -B mln \u003d ES-EI (4.9)

T B =5. 028-5. 01=0. 018 (mm)

b) for a splined shaft:

inner diameter

dmax = d H +es=18+0=18(mm) (4.10)

d min \u003d d H + ei \u003d 18 + (-0. 018) \u003d 17. 982(mm) (4.11)

T d = D max -D mln =ES-EI ;

T d =18-17. 982=0. 018 (mm) (4.12)

outside diameter

D H +es=22+(-0. 3)=21. 7(mm) (4.13)

D min \u003d D H + ei \u003d 22 + (-0.43) \u003d 21. 57(mm) (4.15)

T d \u003d D max -D mln \u003d ES-EI (4.16)

T d = 21. 7-21. 57=0. 13 (mm)

tooth thickness

BH +es=5+(-0.03)=4. 97(mm) (4.17)

b min \u003d b H + ei \u003d 5 + (-0. 048) \u003d 4. 952(mm) (4.18)

T b \u003d b max -b mln \u003d ES-EI (4.19)

b=4.97-4. 952=0.018(mm)

We determine the gaps

a) inner diameter

Smax=ES-ei=0. 018-(-0.018)=0. 036(mm) (4.20)

N max = es- EI=0- 0 =0 (mm) (4.21)

Determine landing tolerance;

T s(N) =N max +S max =T D +T d (4.21)

(N) = 0. 036+0=0. 036 (mm)

b) outside diameter

max=ES-ei=0.21-(-0.43)=0. 64(mm) (4.22)

S min =EI- es=0-(-0. 3) =0. 3(mm) (4.23)

Determine landing tolerance;

T s \u003d S max -S min \u003d T D + T d (4.24)

Ts = 0.64-0. 3= 0.34(mm)

c) size b

S max = ES-ei=0.028-(-0.048)=0.076 (mm) (4.25)

S min =EI- es=0.01-(-0.03)=0. 04(mm) (4.26)

Determine landing tolerance;

T s \u003d S max -S min \u003d T D + T d (4.27)

Ts = 0.076-0. 04= 0.036(mm)

5. Calculation of linear dimensional chains by the probabilistic method

For an assembly dimensional chain with a closing link G ∆, determine the tolerances and maximum deviations of the constituent links.

1. The closing link has a tolerance: Г ∆ = 1()

2. The scattering of the actual dimensions of all links obeys the normal law.

The percentage of the risk of the size of the closing link going beyond the tolerance limits is P = 0.1%.

Let's build a dimensional chain, i.e., find its constituent links. Making a bypass along the contour from the master link, we will establish the contact surfaces of the adjacent parts.

We write the dimensional relationships as follows:

the closing link - the cover of the right bearing;

right bearing cover - gasket;

gasket - housing;

body - body wall left;

housing wall left - sleeve left;

bushing left - drum;

drum - shaft neck;

shaft neck - right bearing;

right bearing - right spacer sleeve;

the right spacer is the master link.

The dimensional chain is made up of the dimensions between the contact surfaces of each of the specified parts:

G 1 = 334mm; G 2 =27 mm; G 3 =58 mm; D 4 \u003d 255mm; G 5 =24 mm; G 6 \u003d 23 -0. 1 mm; G 7 \u003d 6 mm; D 8 = 18 mm; D 9 = 24 mm.

The dimensional chain will include nine constituent links, of which the links G 1, G 2, G 9 and are decreasing, and the links G 3 ... G 8 are increasing.

Let's check the correctness of the dimensional chain according to the formula:

mm; (5.1)

Where m is the number of increasing links, n is the number of decreasing links.

G ∆ \u003d (G 1 + G 2 + G 9) - (G 3 + G 4 + G 5 + G 6 + G 7 + G 8) \u003d

\u003d (334 + 27 + 24) - (58 + 255 + 24 + 23 + 6 + 18) \u003d 1 mm.

The obtained value of the nominal size of the closing link corresponds to the given one. Therefore, the dimensional chain is drawn up correctly.

Define the tolerance of the closing link:

T ∆ = B ∆ - H ∆ = 300 - (-900) = 1200 µm.

Let's determine the accuracy factor of the dimensional chain by the formula:

(5.2)

where is the average value of the coefficient of relative dispersion of the dimensions of the constituent links. Since, according to the condition, the dispersion of the actual dimensions of the links obeys the normal law, we accept = 1/3;

Risk coefficient, = 3. 29 (see tab. 3. 1.).

The value of the tolerance units (see tab. 2. 1.), microns. 1=3. 54 µm; i 2 =1. 31 µm; i 3 =1. 86 µm; i 4 =3. 22 µm; i 5 =1. 31 µm; i 7 =0. 73 µm; i 8 =1. 08 µm; i 9 =1. 31 µm.

Then:

Comparing the obtained value and with the data of Table. 2. 2, we establish that it is somewhat different from the standard value a, corresponding to 12 quality. Therefore, we will assign unknown tolerances according to this quality, and we will perform the adjustment of tolerances due to the link that is the easiest to manufacture. Let us take as a corrective link the size of the hull length - link G 1 = 334 mm, and for the rest (except for G 6 we will assign standard tolerances).

s 1 = (s 2 + s 9) - (s 3 + s 4 + s 5+ s 6 + s 7 + s 8) - s ∆ =

\u003d (-0.105 -0.105) - (-0.15 + 0-0.26-0.05-0.06-0.09) + 0.3 \u003d 0.7 mm.

Now we set the limit deviations of the link E 3:

Thus, the corrective link has limit deviations:

We check the correctness of the calculation of the dimensional chain

The obtained value of the risk coefficient corresponds to the percentage of risk Р=0.1%, which is equal to the specified one.

This means that for a given accuracy of the closing link, the tolerances on the dimensions of the component links assigned according to the 12th grade are quite acceptable.

fit bearing clearance standardization

Literature

1. Interchangeability standardization and technical measurements. Part 1 Method. decree. /Comp. V. A. Orlovsky. , Belorusskaya s. -X. acad. . -Gorki, 1986. 47p.

Seriy I.S. Interchangeability standardization and technical measurements -M. : Agropromtizdat 1987. -365s.

Interchangeability standardization and technical measurements: Method. decree. Part 2 / Comp. N. S. Troyan, Belorusskaya p. -X. acad. . -Gorki, 1986. -48s. .

Interchangeability standardization and technical measurements: Method. decree. Part 3 / Comp. N. S. Troyan. , Belorusskaya s. -X. acad. . -Gorki, 1991. -36s.

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Introduction

1. Calculation and selection of fits of smooth cylindrical joints with a gap

2. Calculation and selection of fits for rolling bearings

3. Selection of keyway fits

4. Choice of spline fit

5. Calculation of linear dimensional chains

List of sources used

Introduction

It is necessary to strengthen the effective and active influence of standards on the production of products that correspond in their technical and economic indicators to the highest world level.

Today, when the production of one machine requires cooperation between hundreds of enterprises in various industries, product quality issues cannot be resolved without expanding work to improve the system of interchangeability, metrological support, and improve methods and means of product control. Therefore, the training of a modern engineer includes the development of a wide range of issues related to standardization, interchangeability and technical measurements. The course "Interchangeability, standardization and technical measurements" is the logical conclusion of the cycle of general technical courses on the theory of mechanisms and machines, metal technology, strength of materials, machine parts. If other cycle courses serve as a theoretical basis for the design of machines and mechanisms, the use of typical machine parts, their strength and rigidity calculations, then this course considers the issues of ensuring the accuracy of geometric parameters as a necessary condition for interchangeability and such important quality indicators as reliability and durability. The tasks of improving the quality of manufacturing, operation and repair of agricultural machinery can be considered comprehensively, using the principles of standardization, interchangeability and control of established technical conditions.

As a result of studying the course and in accordance with the qualification characteristics, an agricultural mechanical engineer must know: the main provisions, concepts and definitions in the field of standardization; the state standardization system and its role in accelerating scientific and technological progress, intensifying production, improving the quality of agricultural machinery and the economic efficiency of its use; the main issues of the theory of interchangeability and technical measurements, the rules for designating accuracy standards in design and technological documentation; methods of calculation and selection of standard fits of typical connections of machine parts; calculation of dimensional chains; device for measuring linear and angular values, their settings, operating rules and selection methods.

1. CALCULATION AND SELECTION OF FITS OF SMOOTH CYLINDRICAL JOINTS WITH A GAP

Initial data:

We define the product hS:

m2 or 4764 µm2.

We calculate the most advantageous gap:

We find the value of the calculated gap:

According to the table in Appendix 8, we select a fit that satisfies the condition:

The given condition is satisfied by the standard fit 40H8 / d8, made in the hole system according to the tenth grade: marginal deviations for the hole; marginal deviations for the shaft.

For the specified landing:

Determine the smallest thickness of the oil layer with the largest gap

We check for the sufficiency of the lubricant layer that provides fluid friction:

The fluid friction condition is satisfied, which means that the fit is torn out correctly.

We determine the limiting dimensions and tolerances for the processing of connection parts according to the selected fit:

a) holes

Determine landing tolerance:

The assembly and detailed sketches of the parts to be joined, indicating the fit, maximum deviations and roughness, are drawn on sheet 1.

The choice of universal measuring instruments. We choose universal measuring instruments, considering that measurements are made in individual production. In this case, the following condition must be met:

where is the maximum error of the measuring instrument, microns;

Permissible measurement error, µm.

The permissible error in measuring linear dimensions depends on the nominal size and quality.

For the considered connection DH(dH)=40 mm. Then, according to Appendix 3, it has:

for hole µm;

for shaft micron;

These requirements are met (appendix 4) for the hole - an indicator inside gauge, and for the shaft - a micrometer of the 1st class, the characteristics of which are given in table 1.1.

Table 1.1 - Characteristics of measuring instruments

Calculation of the executive dimensions of calibers. Limit gauges are special scaleless measuring instruments designed to determine the suitability of machine parts without determining the actual values of controlled dimensions.

Limit gauges are mainly used to control the dimensions of parts manufactured in large-scale and mass production. They are divided into calibers for checking holes and calibers for checking shafts, they have a pass-through and a non-passage side, denoted by the symbols PR and NOT, respectively.

Hole sizes are controlled by plugs. Structurally, they can be made double-sided or separately passable and non-passage side.

The dimensions of the shafts are controlled by brackets. Gauges-brackets can be double-sided or one-sided (in the latter case, the through and non-through sides are combined), sheet, stamped or cast, adjustable and non-adjustable. Adjustable clamp gauges are most often used to control parts in a repair shop. They are used when the size of the manufactured or repaired part does not fit into the dimensions of a standard rigid gauge. Adjustable shaft gauges can be adjusted to repair dimensions for which rigid gauges are not manufactured. Compared to rigid gauges, adjustable gauges have lower accuracy and reliability, so they are recommended for testing parts with dimensions up to 180 mm and accuracy starting from grade 8 and coarser.

In order to increase the service life of plug gauges and staple gauges, the lengths of their passing sides are made larger than the lengths of non-going sides. In addition, to reduce the cost of calibers and increase their service life, the through sides are provided with a hard alloy, thus increasing the wear resistance of calibers by 50 ... 150 times compared to the wear resistance of conventional steel calibers.

The nominal size of the passage side of the plug corresponds to the minimum size of the controlled hole (Dmin), and the non-passage side corresponds to its maximum size(Dmax). For a clamp, on the contrary, the nominal size of the passing side is equal to the maximum diameter of the controlled shaft (dmax), and the non-going side is equal to its minimum diameter (dmin). If, when inspecting a hole or a shaft, the passing side of the gauge does not pass, this means that the actual size of the hole is less than its minimum value (Dd dmax:) and, therefore, there is a correctable marriage. Correctable marriage is eliminated by additional processing of the hole or shaft. In the case when the non-passing side of the gauge passes during the control (Dd>Dmin or dd

According to the purpose, the limiting calibers are divided into working, receiving and control. Working gauges are used to control parts directly at the workplace in the process of their manufacture. Receiving calibers are used by customer representatives when accepting finished products. Unlike working calibers, it is customary to designate them: the through side through P-PR, and the impassable side through P-NOT. Control gauges, designated K-PR and K-NE, are used to check new working gauges-brackets. There are also control gauges (K-I) for checking the amount of wear on the through side of the working calibers-brackets. Counter-caliber plugs K-I are manufactured with dimensions corresponding to the maximum allowable wear of the working sides of the working brackets and are impassable. If the caliber K-I passes through the controlled bracket, then it is worn out over the established limit and is subject to withdrawal. There are no control gauges to check new and worn working plug gauges. The dimensions of the working gauges-plugs are checked by universal measuring instruments.

Executive call the limiting dimensions of the caliber, according to which a new caliber is made. Gauges control shafts and holes with tolerances of IT6 and coarser. The dimensions of parts made with tolerances more precisely than IT6 are checked by universal measuring instruments.

Caliber deviations are counted from the corresponding limiting dimensions of products. So, the deviations of through-pass calibers for shafts are counted from the largest limit size of the shaft, and the deviations of non-through calibers are counted from the smallest limit size of the shaft. Accordingly, the deviations of pass gauges for holes are counted from the smallest hole size limit, and the deviations of non-goal gauges are counted from the largest hole size limit.

The calculated parameters included in the formulas mean (respectively for the plug gauge and the staple gauge):

Dmax and d max - the largest limiting dimensions of the hole and shaft;

D min and d min - the smallest limit dimensions of the hole and shaft;

H and H1 - tolerances for the manufacture of calibers;

Z and Z1 are the coordinates of the midpoints of the tolerance fields for the manufacture of calibers;

Y and Y1 are the wear limits of the passing sides of the calibers.

Let's calculate the working gauges to control the details of the connection

We determine the limiting and executive dimensions of the plug gauge for hole control. According to the table of Appendix 2, we find data for calculating the caliber-cork:

H = 4 µm; Z = 6 µm; Y = 5 µm.

Passage side of the plug gauge

PRmax=Dmin+Z+ (1.2.1)

PRmax=40+0.006+=40.008 (mm)

PRmin=Dmin+Z- (1.2.2)

PRmin=40+0.006-=40.004 (mm)

PR=Dmin -Y (1.2.3)

PR=40-0.005=39.995 (mm)

The executive dimensions of the passage and non-passage sides of smooth working gauges for holes (plugs) are their largest maximum dimensions with a numerical tolerance equal to the manufacturing tolerance H, directed into the gauge body (minus).

Then for the passage side of the plug, the executive size

PRIsp. =40.008 -0.004

Non-going side of the plug gauge

HEmax=Dmax+ (1.2.4)

HEmax=40.039+=40.041 (mm)

HEmin=Dmax- (1.2.5)

HEmin=40.039-=40.037 (mm)

For the impassable side of the plug, the execution dimension

Passing side of the caliber-bracket

PRmax=dmax-Z1+ (1.2.6)

PRmax=39.92-0.006+=39.9175(mm)

PRmin=dmax-Z1- (1.2.7)

PRmin=39.92-0.006-=39.9105 (mm)

PR=dmax +Y1 (1.2.8)

PR=39.92+0.005=39.925 (mm)

The executive dimensions of the pass and non-pass sides of the working gauges for shafts (brackets) are their smallest limiting dimensions with a tolerance numerically equal to the tolerance for manufacturing H1 directed into the gauge body (plus).

Then for the passing side of the bracket, the executive size will be the following:

Prisp=39.9105+0.007.

Non-going side of the shackle gauge

HEmax=dmin+ (1.2.9)

HEmax =39.881+=39.8845 (mm)

HEmin=dmin- (1.2.10)

HEmin =39.881-=39.8775 (mm)

For the non-going side of the bracket, the executive size will be as follows:

FAILURE = 39.8775 +0.007.

When calculating the working and executive dimensions of calibers, dimensions ending in 0.25 and 0.75 microns should be rounded to multiples of 0.5 microns in the direction of reducing the manufacturing tolerance.

The layout of the tolerance fields and a sketch of the gauges for checking the hole and shaft are shown on sheet 2.

2. CALCULATION AND SELECTION OF FITTINGS FOR ROLLING BEARINGS

Ball bearing No. 410. The shaft rotates, the body is stationary. The case is cast iron, one-piece. Radial load on the support R = 16200 N. Bearing operation mode - normal (moderate shocks and vibrations, overload up to 150%).

According to Appendix 2 of the guidelines, we find the main dimensions of the bearing:

We determine the type of loading of the rings of a given bearing. Since the shaft rotates and the housing is stationary, the inner ring of the bearing will experience circulation loading, while the outer ring will experience local loading.

We calculate and select the fit of a circulation-loaded ring.

We determine the intensity of the radial load of the seating surface by the formula:

where is the dynamic landing coefficient, depending on the nature of the load, in our case we take KP = 1;

The coefficient taking into account the degree of weakening of the landing interference, in our case, we take F = 1;

The coefficient of uneven distribution of the radial load R between the rows of rollers in double-row tapered roller bearings or between double ball bearings in the presence of axial load A on the support, in our case there is no axial load, we take FA = 1;

B - ring width;

r - chamfer width.

According to the table in Appendix 4, we find the tolerance field for the shaft diameter corresponding to the obtained PR values. For a bearing of accuracy class 0, we accept the tolerance field k6. Then we can write the fit of the inner ring on the shaft as follows:

According to the table of Appendix 5, we accept the tolerance field of the hole in the H7 housing. The fit of the outer ring into the housing in conventional notation has the form.

According to tables 1 and 2 and Appendix 6 of the guidelines, we find the numerical values of the maximum deviations of the connecting diameters of the bearing rings and the shaft and housing seats. We have:

Let's calculate the limit value of connecting diameters and their tolerances. We summarize the calculation data in Table 2.1.

Inner ring:

Outer ring:

Body hole:

Connection: "inner ring - shaft"

Connection: "outer ring - body"

The diagrams of the relative position of the tolerance fields are shown on sheet 3.

According to the tables of Appendix 7 and 8, we set the permissible deviations in the shape, relative position of the seating surfaces, and their roughness. We have:

Deviations from the cylindricity of the neck of the shaft - 8 microns, holes in the housing - 20 microns.

Runout of the ends of the shaft shoulders - no more than 20 microns, holes in the housing - no more than 50 microns.

The roughness of the shaft seating surfaces Ra is not more than 1.25 microns; openings in the body Ra not more than 2.5 microns.

The roughness of the seating surfaces of the butt ends of the shoulders Ra is not more than 2.5 microns.

We draw sketches of the bearing assembly and the parts connected to the bearing with the application of all the necessary designations (sheet 3).

Table 2.1 - Dimensional characteristics of rolling bearings

Name of bearing connection elements	Limit deviations, mm	Limit dimensions, mm	Tolerances, microns	Limit gaps, microns

Connecting diameters:
inner ring
Shaft journal
outer ring
case openings
Connections:
"inner ring-shaft"
"outer ring-housing"

3 . SELECTION OF KEYJOIN FITS

Initial data:

According to Appendix 10, we find the main dimensions of the key and grooves.

Set the fit of the key in the groove of the shaft and in the groove of the sleeve from Appendix 13.

Then landing in the groove of the shaft and in the groove of the sleeve in general terms can be written as follows:

The numerical values of the maximum deviations of the width of the key and grooves are found from the tables of Appendix 15, we have:

Tolerances and limit deviations of incompatible dimensions of the elements of the keyed connection are found from Table. annexes 1 and 14 .

Let's calculate the limit values of all the main dimensions taught in the connection of the key with the grooves:

Bushing groove

We calculate the gaps and tensions obtained in the connection of the key with the grooves in width.

Compound:

"Key - Shaft Groove"

"Key - Groove Bushing"

The results of the calculations are summarized in Table. 3.1.

We draw sketches of the key connection and its details sheet 4.

Table 3.1 - Dimensional characteristics of the key connection

Name of keyed connection elements	Nominal size in mm and tolerance field (fit)	Limit deviations, mm	Limit dimensions, mm	Tolerances, microns	Limit gaps, microns





Shaft groove:


Bushing Groove:


Connections:
"shaft key-groove"
"key-groove sleeve"

4 . SELECTION OF SPLINE FITS

Spline connection:

We decipher its conditional notation. The given spline connection is centered on the outer diameter, has the number of teeth z=8, the nominal value of the inner (non-centering) diameter d=56 mm, the outer (centering) diameter is D=65 with fit H7/js6, the thickness of the shaft tooth (bush cavity width) b =10 with D9/f7 landing.

According to the tables of applications 1 and 2, as well as according to application 19, we find the maximum deviations of the dimensions of the spline connection:

We calculate the limiting dimensions and tolerances of all elements, as well as the gaps obtained in the joints by the centering diameter and dimension b:

for splined bushing:

inner diameter

outside diameter

valley width

for splined shaft:

inner diameter

outside diameter

tooth thickness

Connection: "sleeve - splined shaft":

centering diameter:

size b:

All dimensional characteristics of the spline connection are entered in the table. 4.1.

Table 4.1 - Dimensional characteristics of the spline connection

Name of spline connection elements	Nominal size in mm and tolerance field (fit)	Limit deviations, mm	Limit dimensions, mm	Tolerances, microns	Limit gaps, microns

A. Centering element.
bushing outer diameter
shaft outside diameter
bushing cavity width
shaft root width
B. Non-centering elements.
bushing inner diameter.
shaft inner diameter
B. Connection:
centering diameter
size b

bearing connection dimension chain

5. CALCULATION OF LINEAR DIMENSIONAL CHAINS BY THE METHOD OF COMPLETE INTERCHANGEABILITY

The sequence for calculating a dimensional chain when solving a direct problem by the method of complete interchangeability is as follows:

1. For the closing link specified in the assembly drawing, identify the constituent links of the dimensional chain;

2. Build a geometric diagram of a dimensional chain and determine the nature of the constituent links (determine which of them are increasing and decreasing);

3. Using the basic equation, check the correctness of the dimensional chain;

4. Determine the tolerance of the closing link, after which, using the formulas, calculate the value of the accuracy coefficient of the dimensional chain ac;

5. Comparing ac with the standard values of a, set the quality, assign tolerances for the dimensions of the constituent links, having previously selected the corrective link;

6. Determine the value of the tolerance of the corrective link, and set the limit deviations for the remaining component links according to the assigned tolerances;

7. Determine the coordinates of the midpoints of the tolerance fields of the closing and all component links, and then calculate the coordinate of the middle of the tolerance field of the corrective link;

For an assembly dimensional chain with a closing link = determine the tolerances and maximum deviations of the constituent links.

In a given dimensional chain, the closing link is the gap formed by the end of the body and the end of the sleeve. This gap is necessary to compensate for temperature changes in the dimensions of the assembly parts and, therefore, its value must be kept within strictly specified limits.

Let's build a dimensional chain, i.e., find its constituent links. Making a detour along the contour from the closing link, we will establish the contact surfaces (assembly bases) of adjacent parts, and through them - dimensional bonds. The gap value is determined by the mutual position of the end surface of the body and the end surface of the sleeve. The bushing with its left end touches the gear, which in turn rests against the shaft. The shoulder of the shaft is in contact with the bearing. Which rests on the body. We write the dimensional relationships as follows:

master link -- spacer sleeve

spacer sleeve - pinion

gear - shaft

shaft - body

body is the closing link.

The dimensional chain will be made up of dimensions between the contact surfaces of each of the indicated parts: the length of the spacer - link A1 \u003d 15 mm, the width of the gear link A2 \u003d 65 mm, the length of the shaft section link A3 \u003d 105 mm and the size of the housing (distance between the inner and outer surface of the sidewall) - link A4=22 mm.

Therefore, the dimensional chain includes nine constituent links, of which the links A1, A2, A4 are decreasing, and the A3 link is increasing. The geometric scheme of the dimensional chain is presented on sheet 5.

Let's check the correctness of the compilation of the dimensional chain, for which we use the formula:

A3- (A1 + A2 + A4) (5.1)

105-15--65--22=3mm.

The obtained value of the nominal size of the closing link corresponds to the given one. Therefore, the dimensional chain is drawn up correctly.

We now determine the accuracy coefficient of the dimensional chain, having previously calculated the tolerance of the closing link. Master link tolerance

ta =-- =200--(-200)= 400 µm.

We calculate the accuracy coefficient of the dimensional chain, since the dimensional chain contains links with known tolerances (rolling bearings):

In the denominator, under the sign of the sum, the values \u200b\u200bof the units of tolerance for the dimensions of the links A1, A2, A3, A4 which we find from Table. 2.1., Then

Comparing the obtained value of ac with the data in Table. 2.2., we establish that it is in the range of ac values corresponding to the 10th and 11th qualifications (a10=64, a11=100). In this case, it is advisable to assign tolerances for the 10th grade to the component links and, since ac\u003e a10, choose the most difficult link to manufacture as the corrective link. Let us take as a corrective link the size of the body - link A3 = 105 mm, and assign standard tolerances to the rest. According to the table 2.3., we have the following:

T1=70 µm, T2=120 µm; T4=84 µm. The non-standard tolerance of the corrective link T3 is found using the formula (2.10) .,:

Т3=Т-(Т1+Т2+ Т4) (5.3)

T3= 400--(70+120+84)=126 µm.

The limiting deviations of the constituent links (excluding the corrective one) are assigned following the above rule. Then A1 \u003d 15-0.07, A2 \u003d 65-0.12, A4 \u003d 22-0.084

We determine the coordinate of the middle of the tolerance field of the corrective link, having previously determined its value for all other links in the chain.

The coordinates of the middle of the tolerance fields of the closing and constituent links are found by the formula:

We have: s1 \u003d -0.035mm; c2 = -0.06 mm; с4=--0.042 mm;= 0 mm.

The coordinate of the middle of the tolerance field of the corrective link is found by the formula:

0.035-0.06-0.042-0=-0.137 mm.

Now we set the limit deviations of link A3

Thus, the corrective link has limit deviations

We check the correctness of the calculations made, for which we use the equations:

The obtained limit deviations of the closing link correspond to the given ones. Therefore, the dimensional chain is calculated correctly.

LIST OF USED SOURCES

1. Interchangeability, standardization and technical measurements. Part 1: Guidelines to the course design for the calculation and selection of landings of smooth cylindrical joints / Comp. V. A. Orlovsky; Belarusian agricultural acad. Gorki, 1986. - 47s.

2. Gray I.S. Interchangeability, standardization and technical changes. - M.: Agropromizdat, 1987. - 368 p.

3. Calculation of the executive dimensions of smooth working calibers: Guidelines for laboratory work on interchangeability, standardization and technical measurements / Comp. N. S. Troyan, V. A. Orlovsky; Belarusian agricultural acad. Gorki, 1987. - 16 p.

4. Interchangeability, standardization and technical measurements. Part 2. Guidelines for course design for the calculation and selection of landings of typical connections / Comp. N. S. Troyan; Belarusian agricultural acad. Gorki, 1986. - 48s.

5. Interchangeability, standardization and technical measurements. Part 3. Guidelines and tasks for the calculation of dimensional chains in course design / Comp. N. S. Troyan; Belarusian agricultural acad. Gorki, 1991. - 48s.

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3 Calculation of calibers

4 Calculation threaded connection

5 Fittings for rolling bearings

6 Calculation of dimensional chains

Literature

Introduction

At modern development science and technology, with organized mass production, standardization, based on the widespread introduction of the principles of interchangeability, is one of the most effective means of promoting progress in all areas of economic activity and improving the quality of products.

This course work was carried out in order to consolidate the theoretical provisions of the course, presented in lectures and teaching independent work with reference literature.

1 Purpose of work

1.1 For the pairing specified in the task, calculate and select a standard fit with interference or clearance

1.2 For a rolling bearing assembly with a load constant in direction, calculate the fit for a circulation-loaded ring and select a fit for a locally loaded ring.

1.3 Draw the layout of the tolerance fields for the bearing rings, shaft and housing. For a given threaded connection, determine all thread ratings, tolerances and deviations.

2 Interference fit calculation

The calculation of interference fits is performed in order to ensure the strength of the connection, that is, the absence of displacement of the mating parts under the action of external loads, and the strength of the mating parts.

The initial data for the calculation are taken from the task and summarized in Table 1.

Table 1 - Initial data for calculating interference fits

Value name	Designation in formulas	Numerical value	unit of measurement
Torque	T	256	H× m
Axial force	Fa	0	H
Nominal connection size	dn.s	50	mm
Shaft inner diameter	D 1	40	mm
Sleeve outer diameter	D 2	72	mm
Pairing length	l	40	mm
Friction coefficient	f	0,08
Modulus of elasticity of the sleeve material	E 1	0.9×10 11	N/m 2
Modulus of elasticity of the shaft material	E 2	2×10 11	N/m 2
Poisson's ratio math Rial bushings	m 1	0,33
Poisson's ratio math riala wala	m 2	0,3
Yield strength of sleeve material	sT 1	20×10 7	N/m 2
Yield strength of shaft material	sT 2	800×10 7	N/m 2
Bushing Roughness	RzD	2,5	micron
Shaft roughness	Rzd	1,3	micron

The smallest calculation of interference is determined from the condition of ensuring the strength of the connection (immobility), from the condition of ensuring the service purpose of the connection /1, p.333/.

Only on action T

(1)

only on action Fa

(2)

With simultaneous action Fa and T:

(3)

According to the received values R the required value of the smallest design interference is determined

(4)

where E 1, E 2- the modulus of elasticity of the materials of the male (shaft) and female (hole) parts, respectively, in N/m 2;

from 1, since 2 are the Lame coefficients determined by the formulas

(5)

The value of the minimum allowable interference is determined /1, p.335/

(6)

where gw- correction, taking into account the crushing of the roughness of the contact surfaces of the parts during the formation of the connection,

(7)

gt- correction taking into account the difference in the operating temperature of the parts t 0 and t d and assembly temperature tSat, the difference in the coefficients of linear expansion of the materials of the parts to be joined ( aD and ad),

(8)

Here DtD = tD - 20 ° - the difference between the operating temperature of the part with the hole and the normal temperature;

Dt d = t d - 20 ° is the difference between the shaft temperature and the normal temperature;

aD, ad – coefficients of linear expansion of materials for parts with a hole and a shaft.

gc- correction, taking into account the weakening of the tightness under the action centrifugal forces; for solid shaft and identical materials of connected parts

, (9)

where u- circumferential speed on the outer surface of the sleeve, m/s;

r is the density of the material, G/cm 3 .

gP- an additive that compensates for the decrease in tightness during repeated pressing; determined by experience.

Determine the maximum allowable specific pressure

, at which there is no plastic deformation on the contact surfaces of the parts.

take the smallest of the two values R 1 or R 2: , (10) , (11) and are the yield strengths of the materials of the male and female parts, H/m 2 ;

The value of the greatest design interference is determined

. (12)

The value of the maximum allowable tightness is determined, taking into account the amendments

, (13)

where goud- coefficient of increase in specific pressure at the ends of the female part;

gt- correction taking into account the operating temperature, which should be taken into account if the interference increases.

The landing is selected from the tables of the system of tolerances and landings / 1, p. 153 /.

The landing conditions are as follows:

- maximum tension

in the selected fit should be no more, that is; (fourteen)

- minimum tension

in a matched fit should be more, that is. (fifteen)

The required force is calculated when pressing the assembled parts,

, (16)

where f n– coefficient of friction during pressing, f n=(1,15…1,2)f;

Pmax- maximum specific pressure at maximum tension

, determined by the formula . (17)

According to the data obtained (Appendix B), we draw a diagram of the location of the tolerance fields of the “hole” and “shaft”.

The scheme for calculating the interference fit is shown in Figure 1.

Figure 1 - Scheme for calculating an interference fit

The calculation of landings with an interference fit was performed on a computer and the result of the calculation is given in (Appendix B).

We select the landing according to the tables of the system of tolerances and landings. The selection conditions are as follows:

a) the maximum interference N max in the selected fit should not be

over :

b) the minimum interference N min in the selected fit must be greater than:

Since the minimum condition is met, we choose this fit.

The graphic arrangement of the landing tolerance fields d50 H8 / g8 is shown in Figure 2.

	Test 22. The landing tolerance is determined by the formula:

Tests with answers in the discipline "Interchangeability, standardization and technical measurements" Option No. 2

	Test 7. Standards for control methods:
	establish organizational, methodological and, in general terms, technical provisions for a particular branch of standardization, as well as terms and definitions, in general terms technical requirements, norms and rules;
	establish requirements for a group of homogeneous or specific products, services that ensure its compliance with its purpose;
	establish basic requirements for the sequence and methods of execution various works in the processes that are used in the activities and ensure the conformity of the process to its purpose;
	establish the sequence of work, method and technical means performance for varieties and objects of control of products, processes, services.

	Test 8. Decipher the designation of the DSTU ISO standard
	state standards of Ukraine, approved by the State Standard of Ukraine;
	state standards through which the standards of the International Organization of Standardization are implemented;
	state standard of Ukraine adopted by the Interstate Council;
	state standards are approved by the Ministry of Construction and Architecture of Ukraine.

	Test 15. Which design group does the micrometric inside gauge belong to?
	To the group of lever-mechanical tools
	To the group of indicator instruments
	To the group of micrometer instruments
	To the group of opto-mechanical instruments

	Test 20. The micrometer screw has fine pitch threads

	Test 21. Complete interchangeability is characterized by the fact that ...
	Parts for high-precision joints are manufactured with deliberately reduced accuracy or allow fitting one of the parts
	The part, in addition to taking its place in the machine without additional processing operations, also performs its functions in accordance with the technical requirements.
	During the compilation process, there should be no fitting or adjustment operations.
	Interchangeability in size, shape, mutual arrangement of surfaces and axes of parts and roughness of their surfaces

	Test 22. The smallest landing interference is determined from the dependence:

Calculation tasks tests

69 In the detail drawing, the limit deviations are indicated as follows: D - 0.012. Specify the correct permission.

70 On the detail drawing, the size is indicated as follows: Ф 24 - 0.012. Specify the largest size limit.

71 On the detail drawing, the size is indicated as follows: Ф 24 - 0.012. Specify the smallest size limit.

72 Given: nominal size d n = 40 mm, maximum size limit d m a x = 40.016 mm, tolerance Td = 0.026 mm. Determine the smallest size limit

73 Given: nominal size d n = 230 mm, lower deviation - 0.016 mm, tolerance Td = 0.026 mm. Determine upper deviation

74 Given: nominal size d n \u003d 10 mm, smallest limit size d m i n \u003d 10.015 mm, tolerance Td \u003d 0.026 mm. Determine the largest size limit

75 On the drawing, the size of the hole is marked Ф 56 + 0.00 5, the actual size is 56.15 mm. Determine hole suitability

2) marriage is irreparable

3) fix the marriage

76 On the drawing, the size of the hole is marked Ф 56 + 0.00 5, the actual size is 56.010 mm. Determine hole suitability

2) marriage is irreparable

3) fix the marriage

77 On the drawing, the size of the hole is marked Ф 56 + 0.00 5, the actual size is 56.00 mm. Determine hole suitability

2) marriage is irreparable

3) fix the marriage

78 On the drawing, the size of the shaft is marked Ф 35, the actual size is 35.00 mm. Determine the suitability of the shaft

2) marriage is irreparable

3) fix the marriage

79 On the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the actual size is 35.00 mm. Determine the suitability of the shaft

2) marriage is irreparable

3) fix the marriage

80 On the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the actual size is 35.15 mm. Determine the suitability of the shaft

2) marriage is irreparable

3) fix the marriage

81 In the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

82 On the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.008 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

83 On the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.00 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

84 In the drawing, the size of the shaft is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.019 mm and 35.020 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

85 On the drawing, the size of the hole is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.005 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

86 On the drawing, the size of the hole is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.014 mm and 35.010 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

87 In the drawing, the size of the hole is marked Ф 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.018 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance.

2) marriage is irreparable

3) fix the marriage

88 The diameter of the hole in the drawing is marked 100 + 0.02. At which of the indicated actual dimensions should the part be rejected?

INTERCHANGEABILITY, STANDARDIZATION AND TECHNICAL MEASUREMENTS

You can download the book in pdf format at the end of the description.

Chapter 1. Basic concepts of interchangeability and systems of tolerances and landings

1.1. The concept of interchangeability and its types
1.2. The concept of nominal, actual and limit sizes, limit deviations x, tolerances and landings
1.3. Uniform principles for building tolerance and fit systems for standard connections of machine parts and other products
1.4. Functional interchangeability
1.5. Principles for choosing tolerances and landings

Chapter 2. Basic concepts of standardization

2.1. State system standardization
2.2. Brief information about international standardization

Chapter 3. Methodological foundations of standardization

3.1. Principles that determine the scientific organization of standardization work
3.2. Standardization of parametric series of machines
3.3. Unification and aggregation of machines. Indicators of the level of unification and standardization
3.4. Comprehensive to advanced standardization
3.5. Integrated systems of general technical standards
3.6. Classification and coding of technical and economic information
3.7. Standardization of products and assembly units according to non-geometric parameters
3.6. The role of unification, aggregation and standardization in improving the quality of machines and the efficiency of their production, Economic efficiency standardization

Chapter 4. Standardization and quality of machines

4.1. The concept of quality and product quality indicators
4.2. Methods for assessing the quality level of machines. Optimal quality level
4.3. Statistical indicators of product quality
4.4. Statistical methods of product quality control
4.5. Product quality management systems
4.6. Certification of the quality of industrial products
4.7. Mathematical model for optimizing the parameters of standardization objects

Chapter 5. Metrology and technical measurements

5.1. General concepts
5.2. Standards. Measures of length and angle measures
5.3. Universal measuring instruments
5.4. Measurement planning methods
5.5. Criteria for assessing measurement errors

Chapter 6

6.1. Choice of Precision
6.2. Inversion principle
6.3. Principles of construction of measuring and control instruments
6.4. The principle of combining control functions with process control functions

Chapter 7. Automation of the processes of measurement, control, selection and processing of results

7.1. Automated fixture
7.2. Control semi-automatic machines and automatic systems
7.3. Active control devices and self-adjusting control systems
7.4. Automation of measurement results processing and design of control processes

Chapter 8

6.1. Classification of deviations of the geometric parameters of parts
8.2. The system of normalization of deviations in the form and location of the surfaces of parts
8.3. Designation in the drawings of the tolerances of the shape and location of the surfaces of parts
8.4. The system of normalization and designation of surface roughness
8.5. The waviness of the surfaces of parts
8.6. The effect of roughness, waviness, deviations in the shape and location of parts surfaces on the interchangeability and quality of machines
8.7. Methods and means for measuring and controlling deviations in shape, location and surface roughness

Chapter 9

9.1. Basic operational requirements and system of tolerances for fits of smooth cylindrical joints
9.2. Designation of limit deviations and landings in the drawings
9.3. Calculation and selection of landings
9.4. The use of computers to calculate landings
9.6. System of tolerances and fits for rolling bearings
9.6. Gauges smooth for sizes up to 600 mm

Chapter 10 Interchangeability of conical connections

10.1. Corner tolerance system
10.2. System of tolerances and fits of conical joints
10.3. Methods and means of controlling angles and cones

Chapter 11

11.1. Classification of dimensional chains. Basic terms and definitions
11.2. A method for calculating dimensional targets that ensures complete interchangeability
11.3. Theoretical and probabilistic method for calculating dimensional ice
11.4. Group interchangeability method. selective assembly
11.5. Adjustment and fit methods
116. Calculation of flat and spatial dimensional chains
11.7. The use of computers to solve dimensional chains

Chapter 12

12.1. Basic performance requirements for threaded connections
12.2. Basic parameters and a brief description of fixing cylindrical threads
12.3. General principles ensuring interchangeability of cylindrical threads
12.4. Tolerance and fit systems for metric threads
12.5. Influence of thread manufacturing accuracy on the strength of threaded connections
12.6. Characteristics and interchangeability of kinematic threads
12.7. Methods and means for monitoring and measuring the accuracy of cylindrical threads

Chapter 13

13.1. Basic performance and accuracy requirements for gears
13.2. Tolerance system for spur gears
13.3. Bevel Gear Tolerances
13.4. Tolerances of worm gears
13.5. Methods and means for measuring and controlling gear tracks and gears

Chapter 14

14.1. Tolerances and fits of keyed connections
14.2. Tolerances and fits of splined joints
14.3. Accuracy control of splines