Deviation- algebraic difference between the size (limit or actual) and the corresponding nominal size.

To simplify the setting of dimensions in the drawings, instead of the maximum dimensions, maximum deviations are indicated: upper deviation- algebraic difference between the largest limit and nominal sizes; lower deviation - algebraic difference between the smallest limit and nominal sizes.

The upper deviation is indicated ES(Ecart Superieur) for holes and es- for shafts; the lower deviation is indicated El(Ecart Interieur) for holes and ei- for shafts.

According to definitions: for holes ES=D max -D; EI= D min -D; for shafts es=d max –d; ei= d mln -d

The peculiarity of deviations is that they always have a sign (+) or (-). In a particular case, one of the deviations may be equal to zero, i.e. one of the maximum dimensions may coincide with the nominal value.

Admission size is the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations.

The tolerance is indicated by IT (International Tolerance) or T D - hole tolerance and T d - shaft tolerance.

According to the definition: hole tolerance T D =D max -D min ; shaft tolerance Td=d max -d min . The size tolerance is always positive.

The size tolerance expresses the spread of actual dimensions ranging from the largest to the smallest limiting dimensions; it physically determines the magnitude of the officially permitted error in the actual size of a part element during its manufacturing process.

Tolerance field- this is a field limited by upper and lower deviations. The tolerance field is determined by the size of the tolerance and its position relative to the nominal size. With the same tolerance for the same nominal size, there may be different tolerance fields.

For a graphical representation of tolerance fields, allowing one to understand the relationship between nominal and maximum dimensions, maximum deviations and tolerance, the concept of a zero line has been introduced.

Zero line is called the line corresponding to the nominal size, from which the maximum deviations of dimensions are plotted when graphically depicting tolerance fields. Positive deviations are laid upward, and negative deviations are laid down from it (Fig. 1.4 and 1.5)

Rice. 1.5. Layout of shaft tolerance fields

The smaller the tolerance, the more accurately the part element will be manufactured. The larger the tolerance, the rougher the part element. But at the same time, the smaller the tolerance, the more difficult, complex, and hence more expensive the production of a part element; The greater the tolerances, the easier and cheaper it is to produce a part element.

SURFACE ROUGHNESS.

BASIC CONCEPTS.

Surface roughness called a set of surface irregularities with relatively small steps, identified using the base length.

The microroughnesses under consideration are formed during the machining process by copying the shape of cutting tools, plastic deformation of the surface layer of parts under the influence of the processing tool, its friction against the part, vibration, etc.

The surface roughness of parts has a significant impact on wear resistance, fatigue strength, tightness and other performance properties.

Surface roughness in the form of a profilogram in Fig. 1.44.

Rice. 1.44. Surface profilogram

To separate surface roughness from other irregularities with relatively large steps (shape deviations and waviness), it is considered within a limited area, the length of which is called the base length L. The base length L is normalized depending on the roughness parameters within the range: 0.01; 0.03; 0.08; 0.25; 0.8; 2.5; 8; 25, i.e. the more micro-irregularities, the longer the base length.

The line on which the set of surface irregularities stands out is called the baseline. The base line is a line of a given geometric shape, drawn in a certain way relative to the profile and used to evaluate the geometric parameters of surface irregularities. The appearance of this line depends on the type of surface of the part element. Thus, the base line of the surface of a part element has the shape of a line of a nominal profile and is located equidistant to this profile.

The average line is used as a baseline when assessing surface irregularities, which is the basis for measuring profile deviation.

ROUGHNESS PARAMETERS.

1. Arithmetic mean deviation of profile Ra- arithmetic mean of the absolute values ​​of profile deviations within the base length:

where l is the base length;

n is the number of selected profile points along the base length;

y is the distance between any profile point and the center line (profile deviation).

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

or

where Himax, Himin are determined relative to the midline;

h jmax , h imin - relative to an arbitrary straight line parallel to the center line and not intersecting the profile.

3. Maximum height of profile irregularities R max - distance between line
profile protrusions and a line of profile depressions within the base length.

4. Average pitch of profile irregularities S m - arithmetic mean value
pitch of profile irregularities within the base length:

where S mi is the pitch of profile irregularities, equal to the length of the segment of the center line, enclosed between the points of intersection of adjacent protrusions and depressions of the profile with the center line.

5. Average pitch of profile irregularities along vertices S- arithmetic mean
step value of profile irregularities at the vertices within the base length:

where S i is the pitch of the profile irregularities, equal to the length of the segment of the center line enclosed between the projections onto it of the highest points of two adjacent local protrusions of the profile.

6. Relative reference length of profile t p - ratio of the reference length of the profile to the base length:

where h p - profile reference length- the sum of the lengths of the segments cut off at a given level in the profile material by a line equidistant to the center line t within the base length.

Of the listed roughness parameters, the parameters Ra and Rz are most often used. The Ra parameter is preferable, since it is determined from a significantly larger number of profile points than Rz. The use of the Rz parameter as a control parameter is largely determined by the methods of measuring the parameters under consideration. Ra values ​​are predominantly measured using instruments equipped with diamond stylus probes. Determining Ra on rough surfaces is associated with the risk of breaking the diamond needle, and on very smooth surfaces - with low reliability of the results due to the fact that the radius of the tip of the needle cannot detect very small irregularities. Therefore, Rz is recommended to be used for roughness heights of 320...10 and 0.1...0.025 microns, in other cases - Ra.

When calculating critical movable and press connections, it is necessary to take into account the parameter Rz, whereas in the drawings in most cases the Ra values ​​are specified. In these cases, you can use the dependency

Where K=4 at R a =80...2.5 µm; K=5 at Ra=1.25…0.02 µm.

Table 1.3 Correspondence of the numerical values ​​of Ra, Rz, Rmax to the numerical values ​​of the base length

For rubbing surfaces of critical parts, parameters Ra (or Rz), t p are assigned and the direction of irregularities is specified, for surfaces of cyclically loaded parts - R max, S m (or S) and the direction of irregularities, for connections with interference - only Ra (Rz). For non-critical parts, you can not indicate the roughness parameters, in which case it is not subject to control.

Table 1.4 Types of direction of roughness irregularities.

ON THE DRAWINGS.

The designation of roughness on drawings establishes the designations of surface roughness and the rules for applying them on product drawings.

Three symbols are used to indicate roughness:

When designating roughness only by parameter, a sign without a shelf is used.

The values ​​of all roughness parameters are indicated after the corresponding symbol, and the height parameters Ra, Rz, Rmax are indicated in micrometers, the step parameters Sm, S - in millimeters, the shape parameter t p - in percentages.

1. Signs indicating the requirements for surface irregularities - roughness are located (Fig. 1.46):

a) on the contour lines of the part elements,

b) on extension lines, as close as possible to the dimension line,

c) on the shelves of lines - callouts,

d) on dimension lines or on their extensions if there is not enough space, and it is allowed to break the extension line.

2. Signs indicating roughness requirements and having a shelf must be located relative to the main inscription of the drawing (stamp), as
indicated in Fig. 1.47.

4. If the requirements for surface roughness are the same for all elements of the part, then the roughness sign is applied once and placed in the upper right corner of the drawing, and is not applied to the surfaces of the elements of the part (Fig. 1.48).

This means that surfaces on which the roughness requirement is not specified are not processed according to this drawing at all, i.e. these surfaces will have the unevenness that the workpiece has.

Signs that indicate roughness requirements and placed in the upper right corner of the drawing must have dimensions and line thickness approximately 1.5 times larger than the signs applied directly to the surface of the part,

Rice. 1.50

6. When the surface of a part element has little space to place a sign, it is allowed to apply a simplified designation to surface irregularities (Fig. 1.) with an explanation of this designation in the technical requirements on the detail drawing.

7. When the surface of a part is a contour, for example a polyhedral figure, and the requirements for surface irregularities must be the same, then the roughness mark is applied once.

THREADED CONNECTIONS.

BASIC CONCEPTS AND CLASSIFICATION OF THREADS.

A threaded connection is the connection of two parts using a thread, i.e. elements of parts having one or more evenly spaced helical thread projections of constant cross-section formed on the side surface of a cylinder or cone.

The cross-sectional contour of grooves and projections in a plane passing through the thread axis, common to external and internal threads, is called a thread profile.

Classification of threads.

Various conditions for using threads have led to a variety of their types according to design characteristics and purpose.

· Depending on the shape of the surface on which the threads are formed:

Cylindrical; - conical threads;

· According to the section profile (i.e., depending on the type of figure in the section), threads are divided into:

Rice. 1.51.

Triangular (Fig. 1.51 a)

Trapezoidal (Fig. 1.51 b)

Sawtooth (Fig. 1.51 c)

Round (Fig. 1.51 d)

Rectangular (Fig. 1.51 d)

by number of visits:

Single pass; - multi-pass

· in the direction of the turns:

Right; - left;

· by unit of measurement of linear quantities

To metric; - inch.

· According to their purpose, threads are divided into general purpose and special threads.

TO general purpose include fastening, kinematic, pipe and reinforcement.

Mounting threads used for detachable fixed connections of machine parts. Their main purpose is to ensure the strength of the joints and maintain the tightness (non-opening) of the joint during operation.

Kinematic threads used for moving connections in screw-nut type gears (lead screws and caliper screws of metal-cutting machines, screws of measuring instruments, screws of presses, jacks, etc.).

Pipe and reinforcement threads having a triangular profile, they are used for pipelines and fittings with the main purpose of ensuring the tightness of connections.

To threads special purpose These include those that are used only in certain products of certain industries (for example, threads for bases and sockets of electric lamps, backlash-free threads in lead screws of jig boring machines, etc.).

General requirements are complete interchangeability, those. ensuring unconditional screwability of parts forming a threaded connection when manufactured independently without adjustment or selection, and reliable performance of prescribed operational functions.

METRIC THREADS.

The basics of this system of tolerances and fits, including degrees of accuracy, accuracy classes of threads, normalization of make-up lengths, methods for calculating tolerances of individual thread parameters, designation of accuracy and fits of metric threads on drawings, control of metric threads and other issues.

Degrees of accuracy and classes of thread accuracy.

A metric thread is determined by five parameters: average, outer and inner diameters, pitch and thread profile angle.

Tolerances are assigned only for two parameters of an external thread (bolt); middle and outer diameters and for two parameters of internal thread (nut); middle and inner diameters. For these parameters, for metric threads, degrees of accuracy are set to 3... 10 (Table 1.5).

Table 1.5. Degrees of accuracy of external and internal thread diameters.

In accordance with established practice, degrees of accuracy are grouped into 3 accuracy classes:

accurate (3-5 degree of accuracy),

average (5-7 degree of accuracy),

rude. (7-9 degree of accuracy),

The concept of accuracy class is conditional. When assigning degrees of accuracy to an accuracy class, the make-up length is taken into account, since during manufacturing the difficulty of ensuring a given thread accuracy depends on the make-up length available to it.

Installed three groups of make-up lengths:

S - short ( less than normal)

N - normal ( make-up length from 2.24Pd 0.2 mm to 6.7Pd 0.2 mm),

L - long(more than normal).

WHEELS AND GEARS.

Each of the operational groups is characterized by its main indicator of accuracy. Yes, for counts gears, the main accuracy requirement is kinematic accuracy; For high speed - smooth operation; For heavily loaded low-speed- completeness of contact teeth; For reversible(especially reference ones) - limiting the size and fluctuations of the side clearance.

Taking into account the operating conditions, the tolerance standards for gear and worm gears establish accuracy standards:

- Kinematic accuracy,

- smooth operation;

- tooth contact;

- side clearance.

According to manufacturing accuracy, all gears and gears are divided into 12 degrees.

Smooth transmission operation

This transmission characteristic is determined by parameters, the errors of which appear many times (cyclically) per revolution of the gear wheel.

The cyclic nature of errors that disrupt the smooth operation of the transmission, and the possibility of harmonic analysis, made it possible to determine and normalize these errors according to the spectrum of the kinematic error.

Under the cyclic transmission error f zkor(Fig. 1.72, A) And gear wheel f zkr(Fig. 1.72, b) understand the double amplitude of the harmonic component of the kinematic error of the gear or wheel, respectively. To limit the cyclic error, the following tolerances are established:

□ f zok - for cyclic transmission error;

□ f zk - on the cyclic error of the gear.

Rice. 1.73

To limit the cyclic error with a repetition frequency equal to the frequency at which the teeth engage f zzor And f zzr Tolerances have been established for the cyclic error of tooth frequency in the transmission f zzo And fzz. These tolerances depend on the frequency of the cyclic error (equal to the number of gear teeth z), the degree of accuracy, the axial overlap coefficient ε β and the modulus T.

Submitting your good work to the knowledge base is easy. Use the form below

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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. Coursework 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

At a 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 interaxle 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, profile error tolerance 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 dimensions 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.

References

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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The organization of serial production of products required a reduction in the embodied labor invested in them. It was possible to achieve a reduction in the cost of products by simplifying the design (primarily by eliminating excesses - expensive materials, labor-intensive decorations, low-tech parts and assembly units) and changing technology (providing division of labor and cooperation production).

The division of labor in its most extreme form can be represented as dividing the technological process of manufacturing a product into operations - the simplest actions, each of which is performed by one worker (operator). You can learn how to perform such an operation within a few minutes, and acquire sufficient work skills in 2...3 work shifts. The benefit from such an organization of work is high productivity with minimal requirements for worker qualifications.

To ensure a certain level of quality for mass-produced products, it is necessary that all processed parts for the same purpose (nomenclature, standard size) are practically the same. The differences between the parts must be so insignificant that any of them is assembled with the corresponding ones, and when assembled together they form a product that is indistinguishable from others in operation. Parts and more complex products, if they meet the specified requirements, are called interchangeable.

In the everyday sense, interchangeability can be considered as the sameness of products, but since absolutely identical products do not exist, it is obvious that during production one should only prevent such differences that go beyond the agreed standards. These standards are recorded in documentation (design documentation, technical descriptions, passports, etc.). Standardization is widely used to give the most frequently used norms official status. They standardize complex products and processes, their components, down to the elementary ones. Everyone knows not only standard houses and cars, but also standard voltage of the electrical network, standard sizes of magnetic tape, magnetic and optical disks, speed of recording and playback of information.

To obtain standard products of a given level of quality, it is necessary to organize an extensive regulatory framework. Standardization is regulatory framework for interchangeability mass-produced products and repeatedly reproducible processes.

In technology, the interchangeability of products implies the possibility of equivalent (from the point of view of specified conditions) replacement of one with another during the manufacturing or repair process. The more detailed and rigidly the parameters of products are standardized, the easier the replacement is, but the more difficult it is to ensure interchangeability.

The interchangeability of products and their components (assemblies, parts, elements) should be considered as the only possibility of ensuring economical serial and mass production of products of a given level of quality. The same (fluctuating within the limits of differences negligible for the consumer) level of quality of the final products of a particular production is ensured by fulfilling a certain set of requirements. Requirements apply to all elements of parts and interfaces that ensure normal operation of the product. Ensuring interchangeability, and therefore a given level of product quality, implies:

Establishing a set of requirements for all parameters that affect the interchangeability and quality of products (standardization of nominal values ​​and accuracy of parameters);

Compliance with established standards during production, uniform for identical objects, and effective control of standardized parameters.

At the same time, gaps in the assignment of standards or an incorrect, unclearly defined choice of their boundaries can lead to a violation of the interchangeability of manufactured products, and, consequently, to non-compliance with the specified level of product quality. An incorrect or incomplete set when standardizing the nomenclature of parameters or their limit values ​​will lead to a violation of interchangeability (even to the point of bullying the customer: ... the dog could have grown up during the journey), in which the manufacturer cannot formally be accused of non-compliance with the standards.

So, the highest achievement of standardization of product parameters will be to ensure complete interchangeability of similar products in any manufactured batch. Full interchangeability implies the interchangeability of products according to all standardized parameters. Parameters and properties that are not of fundamental importance for the functioning of products are not standardized. For example, a housewife is of little interest in the particle size of granulated sugar, which is sold by weight, while for pasta, shape and size can be quite significant properties, since noodles and vermicelli are not cooked equally. Interchangeability (full interchangeability) implies compliance during the manufacturing process of a product with all its standardized parameters within specified limits. Standardized product parameters may include:

Geometric (size, shape, location and surface roughness);

Physico-mechanical (hardness, mass, reflectivity, etc.);

Economic (cost, limit price, productivity, etc.);

Other (ergonomic, aesthetic, environmental, etc.).

You can refuse interchangeability even during the design process by incorporating a compensator into the design, which ensures a change within certain limits (regulation) of the normalized parameter. Everyone knows the adjustable supports (legs) of appliances and furniture, which make it possible to compensate not only for inaccuracies in the manufacture of the products themselves, but also for the imperfections of the base surfaces (table, floor).

Functional interchangeability is an analogue of complete interchangeability, which is not understood in the literal sense (identicality of parameters), but is limited to a necessary and sufficient set of requirements for the operation (functions) of the product. For example, a pencil, a ballpoint or fountain pen, a piece of chalk, a typewriter, or a computer may be functionally interchangeable if you need to write down a short message (the list is compiled without taking into account economic costs and qualifications). The imposition of economic restrictions can sharply shorten such a list. The feature that the term functional interchangeability emphasizes is the priority of the functions performed by the product (pencil, chalk, pen...writing) with possible significant technical differences in the objects used. Functionally interchangeable under a certain formulation of the problem (timely attendance at work) such vehicles as a tram, trolleybus, bus, taxi, bicycle or one’s own legs can be considered functionally interchangeable.

Functionally interchangeable in terms of the content of recorded information for the computer owner can be files recorded on a hard disk, floppy disks, CDs (if appropriate drives are available), as well as a hard copy of the corresponding file, although the parametric differences between the storage media are very significant. In particular, a printout can also be used when the computer stops working due to a temporary lack of electricity, a technical malfunction, or a virus infection.

From the examples considered, two accentuated features of functional interchangeability emerge: focus on results with an almost indifferent attitude to the process (goal-providing interchangeability), or guaranteeing results by reproducing functions (procedural interchangeability). In particular, we may be indifferent to where and how to obtain the necessary textual information, as long as its completeness and accessibility are ensured. On the other hand, if this information is subject to editing or other modification (partial borrowing, combining with additional information, etc.), not only the form of its presentation (printout or electronic copy on a floppy disk), but also the system becomes very important for us its coding. An electronic copy of the text becomes useless if we do not have the appropriate environment on our computer (the so-called word processor, the version of which is compatible with the one used). In this case, we are talking about procedural interchangeability, since the fundamentally described operations can be implemented using typewriting, but without a computer there is a slide into incomplete interchangeability due to difficulties in using fonts, mathematical signs and other symbols. The picture drawn can be continued until a return to individual rewriting of texts with quill pens.

Parts for mechanical engineering products (as opposed to a number of radio-electronic, optical, etc.) products pass the first test of interchangeability during the assembly process. Imprecisely manufactured parts may not fit together or may break if you try to assemble them by force, so for mechanical parts and assemblies, the first aspect that is considered is geometric interchangeability.

The arrays of geometric parameter values ​​used for standardization are usually formatted as standards. For example, you can use the standards for parameters of macrogeometry of surfaces (dimensions, shape, location) and microgeometry (roughness). The standards are suitable for normalizing the geometric parameters of any standard parts and surfaces in a very wide range.

The suitability of a product for a given parameter Q is assessed by comparing the actual value of the parameter Q dstv with its maximum permissible values. Determining suitability is called parameter control, and if measuring instruments are used, then control is called measuring. Measurement control is usually carried out in two stages:

Determining the actual value of the parameter;

Comparison of the actual value of the parameter with normalized values ​​and determination of the suitability of the object based on the controlled parameter.

To obtain the actual value of a controlled parameter specified by a physical quantity, it is necessary to compare its real value with the unit of the corresponding physical quantity - this is the essence of any measurement. Units of physical quantities are standardized, they are reproduced using standard standards, and from them they are transferred to standard and non-standardized working measuring instruments.

"Regulation of accuracy in mechanical engineering"

For course work in the discipline “Normalization of accuracy in mechanical engineering.”

Initial data for option No. 23.

• 1. Calculate the parameters and graphically depict the fit of smooth joints.
• 2. Select bearing fits for the outer and inner rings.
• 3. Draw a sketch of the threaded connection and give an explanation of the thread symbol.
• 4. Draw sketches of a straight-sided spline connection and standardize for accuracy for three centering methods.
• 5. On the working drawing of the part, indicate the tolerances of linear dimensions, the necessary deviations of shape and location. Assign surface roughness. Decipher the notation.

Calculation of landings of smooth joints

The quality of mechanical engineering products depends on the geometric accuracy of the parts included in them. Accuracy is a collective concept, and can be assessed by the accuracy of the dimensions of the elements of a part, the accuracy of the shape of surfaces and their relative position, waviness and roughness. Standardization of dimensional accuracy is carried out by the standards of the Unified System of Tolerances and Landings (USDP) through the system of GOSTs (State Standards). Available in sizes: nominal- the size relative to which the maximum dimensions are determined and which serves as the starting point for deviations is assigned from among the standard ones according to GOST 6636 “Normal linear dimensions”, limit (largest and smallest)- two maximum permissible sizes, between which the actual size of a suitable part must lie; valid- size established by measurement with permissible error.

Accepted designations:

· - nominal size of the hole (shaft);

· , - hole (shaft) size, largest (maximum), smallest (minimum), actual;

· - upper deviation of the hole (shaft); - lower deviation of the hole (shaft);

· - gap, largest (maximum), smallest (minimal), average, respectively;

· - interference, greatest (maximum), smallest (minimum), average, respectively.

During processing, each part acquires its actual size and can be assessed as acceptable if it is within the range of maximum sizes, or rejected if the actual size is outside these limits.

The condition for the suitability of parts can be expressed by the following inequality:

The difference between the largest and smallest limit sizes is called size tolerance. Tolerance is always positive.

For hole;

For the shaft.

Tolerance is a measure of dimensional accuracy. The smaller the tolerance, the smaller the permissible fluctuation in actual dimensions, the higher the accuracy of the part and, as a result, the complexity of processing and its cost increase. The position of the tolerance relative to the nominal size is determined by the deviations.

Size deviation is called the algebraic difference between the size (real, limit) and the nominal size. From here, deviations can be real or maximum, and maximum deviations can be upper ES (es) and lower EI (ei):

for the hole,

for the shaft,

Deviations can be: positive (with a plus sign), if

negative (with a minus sign), if

and equal to zero if

In the connection of elements of two parts, one of them is internal (male), the other is external (male). In ESDP, every external element is called a shaft, every internal element is called a hole. The terms "hole" and "shaft" also apply to non-mating elements.

The difference between the sizes of the hole and the shaft before assembly determines the nature of the connection of the parts, i.e. landing. The gap characterizes greater or lesser freedom of relative movement of the parts of the connection, and the interference is the degree of resistance to the mutual displacement of the parts in the connection:

The designer assigns fits in the form of a certain combination of tolerance fields of the hole and shaft, and the nominal size of the hole and shaft is common (the same) and is called nominal connection size. There are three types of fits: with clearance, interference and transitional, which can be assigned in the hole system (CH) or in the shaft system (CH). The choice of system is dictated by design, technological or economic considerations.

In the system, landing holes are made between the main hole with the main deviation H and the shafts with different main deviations (a....zc).

In the shaft system, fits are made between the main shaft with the main deviation h and the holes with different main deviations (A....ZC).

Of the two systems, CH is preferable, since it is more expensive to machine an accurate hole than an accurate shaft, and to produce holes of different accuracy in the CH system, many measuring cutting tools (drills, countersinks, reamers, broaches, etc.) and control equipment are required .

The shaft system is used less frequently, in economically justified cases: on shafts made from calibrated cold-drawn rod without cutting the seating surfaces; in connecting a long section of a shaft of the same nominal size with holes in several parts with different fit characteristics; in connections of standard parts and assemblies made in the shaft system (bearing outer ring, width key, etc.). Fitments can be made with clearance -S, interference - N and transition - S(N).

They are distinguished, which quantify the landing and are calculated using the formulas:

Clearance fit tolerance

The value is sometimes called the guaranteed clearance. Landings with clearance also include landings in various grades, in which the lower limit of the hole tolerance field coincides with the upper limit of the shaft tolerance field. For them = 0.

IN interference fit The tolerance field of the hole is located below the tolerance field of the shaft, i.e. The actual size of the shaft before assembly is larger than the actual size of the hole. The use of force or heat is required (heating the sleeve or cooling the shaft).

Interference fit tolerance

where is the guaranteed interference.

Transitional landing called a fit in which, during assembly, it is possible to obtain both a gap and an interference fit. These fits ensure precise centering (coincidence of axes) of the bushing relative to the shaft axis. In such a fit, the tolerance fields of the hole and shaft partially or completely overlap each other

Transitional fits are characterized by the highest values ​​of interference and clearance

Transitional fit tolerance

In a transitional fit, the average interference fit (clearance) is calculated using the formula:

A result with a minus sign will mean that the average value for the fit corresponds to The fit tolerance is always equal to the sum of the hole and shaft tolerances.

Initial data:

Nominal diameter: D=20 mm.

Hole tolerance range: E8; F7; JS6; N8; P6; S7.

Shaft tolerance fields: d8; f7; js6; n6; p6; r6.

According to GOST 25347-82 “Unified system of tolerances and landings. Tolerance fields and recommended fits” we will describe the maximum upper (es, ES) and lower (ei, EI) deviations for the given tolerance fields.

1) For tolerance range E8:

Upper deviation ES = + 73 µm

Lower deviation EI = + 40 µm

Tolerance T = 33 µm

2) For tolerance range F7:

Upper deviation ES = + 41 µm

Lower deviation EI = + 20 µm

Tolerance T = 21 µm

3) For tolerance zone JS6:

Upper deviation ES = + 6.5 µm

Lower deviation EI = - 6.5 µm

Tolerance T = 13 µm

4) For tolerance zone N8:

Upper deviation ES = - 3 µm

Lower deviation EI = - 36 µm

Tolerance T = 33 µm

5) For tolerance range P6:

Upper deviation ES = - 18 µm

Lower deviation EI = - 31 µm

Tolerance T = 13 µm

6) For tolerance range S7:

Upper deviation ES = - 27 µm

Lower deviation EI = - 48 µm

Tolerance T = 21 µm

7) For tolerance range d8:

Upper deviation es = - 65 µm

Lower deviation ei = - 98 µm

Tolerance T=33 µm

8) For tolerance range f7:

Upper deviation es = - 20 µm

Lower deviation ei = - 41 µm

Tolerance T=21 µm

9) For tolerance field js6:

Upper deviation es = + 6.5 µm

Lower deviation ei = - 6.5 µm

Tolerance T=13 µm

10) For tolerance range n6:

Upper deviation es = + 28 µm

Lower deviation ei = +15 µm

Tolerance T=13 µm

11) For tolerance range p6:

Upper deviation es = + 35 µm

Lower deviation ei = + 22 µm

Tolerance T=13 µm

12) For tolerance range r6:

Upper deviation es = + 41 µm

Lower deviation ei = +28 µm

Tolerance T=13 µm

Figure 1. Layout of hole tolerance fields

Figure 2. Layout of shaft tolerance fields

Let us express the absolute values ​​of size deviations:

a) Through the maximum dimensions:

Hole Ш20Э8:

b) Through the maximum deviations of the hole (shaft):

Formation of landings in the hole system

Let us graphically depict three types of plantings.