The concept of size deviations, tolerances and landings. Basic concepts of dimensions, limit deviations and tolerances. Surface location deviations

16.05.2020

The surfaces along which parts are connected during assembly are called conjugated , the rest - incompatible, or free . Of the two mating surfaces, the female surface is called hole , and the covered shaft (Fig. 7.1).

In this case, in the designations of the parameters of the holes, capital letters of the Latin alphabet are used ( D, E, S), and shafts - lowercase ( d, e,s).

The mating surfaces are characterized by a common size called nominal connection size (D, d).

Valid part size is the size obtained during manufacture and measurement with an allowable error.

Limit dimensions are the maximum ( D max and d max) and minimum ( D min and d min ) allowable dimensions, between which the actual size of a suitable part must be located. The difference between the largest and smallest limit sizes is called admission hole size TD and shaft Td .

TD(Td)=D max (d max ) – D min (d min ).

The size tolerance determines the specified boundaries (limit deviations) of the actual size of the good part.

Tolerances are depicted as fields limited by the upper and lower size deviations. In this case, the nominal size corresponds to zero line . The deviation closest to the zero line is called main . The main deviation of the holes is indicated in capital letters of the Latin alphabet A, B, C, Z, shafts - lowercase a, b, c, … , z.

Hole tolerances TD and shaft Td can be defined as the algebraic difference between the upper and lower limit deviations:

TD(Td) = ES(es) – EI(ei).

The amount of tolerance depends on the size and the required level of precision in the manufacture of the part, which is determined by quality (degree of accuracy).

quality is a set of tolerances corresponding to the same degree of accuracy.

The standard establishes 20 qualifications in decreasing order of accuracy: 01; 0; one; 2…18. Qualities are indicated by a combination of capital letters IT with serial number of qualification: IT 01, IT 0, IT 1, …, IT 18. With an increase in the qualification number, the tolerance for the manufacture of a part increases.

The cost of manufacturing parts and the quality of the joint work depend on the correct appointment of the quality. The following are recommended areas for applying qualifications:

- from 01 to 5 - for standards, gauge blocks and gauges;

- from 6 to 8 - for the formation of landings of critical parts, widely used in mechanical engineering;

- from 9 to 11 - to create landings of irresponsible nodes operating at low speeds and loads;

- from 12 to 14 - for tolerances on free dimensions;

- from 15 to 18 - for tolerances on workpieces.

On the working drawings of parts, tolerances are affixed next to the nominal size. In this case, the letter specifies the main deviation, and the number specifies the degree of accuracy. For example:

 25d6;  25 H7;  30 h8 ;  30 F8 .

7.2. The concept of landings and landing systems

landing called the nature of the connection of two parts, determined by the freedom of their relative movement. Depending on the relative position of the tolerance fields, the hole and the landing shaft can be of three types.

1. With guaranteed clearance S given that: D min ≥ d max :

- maximum clearance S max = D max – d min ;

- minimum clearance S min = D min – d max .

Landings with a gap are designed to form movable and fixed detachable connections. Provide ease of assembly-disassembly of nodes. In fixed connections, they require additional fastening with screws, dowels, etc.

2. With guaranteed tension N given that: D max < d min :

- maximum tension N max = d max – D min ;

- minimum tension N min = d min – D max .

Interference fits provide the formation of permanent connections more often without the use of additional fastening.

3. transitional landings , at which it is possible to obtain both a gap and an interference fit in the joint:

- maximum clearance S max = D max – d min ;

- maximum tension N max = d max – D min .

Transition fits are designed for fixed detachable connections. Provide high centering accuracy. Require additional fastening with screws, dowels, etc.

ESDP provides landings in the hole system and in the shaft system.

Landings in the hole system main hole H with different shaft tolerance fields: a, b, c, d, e, f, g, h(landing with a gap); j S , k, m, n(transitional landings); p, r, s, t, u, v, x, y, z(pressure landings).

Fits in the shaft system are formed by a combination of the tolerance field main shaft h with different hole tolerances: A, B, C, D, E, F, G, H(landing with a gap); J s , K, M, N(transitional landings); P, R, S, T, U, V, X, Y, Z(pressure landings).

Landings are put down on the assembly drawings next to the nominal size of the conjugation in the form of a fraction: in the numerator, the tolerance for the hole, in the denominator, the tolerance for the shaft. For example:

30or30
.

It should be noted that in the designation of the landing in the hole system in the numerator, the letter H, and in the shaft system in the denominator - the letter h. If the designation contains both letters H and h, for example  20 H6/h5 , then in this case the hole system is preferred.

1. Basic concepts and definitions: nominal size, limit dimensions, limit deviations, tolerance, fit, clearance, tightness. Give a diagram of the location of the tolerance fields of the hole and shaft for transitional fit. Indicate on it the indicated concepts and give formulas for the connection between them.

Dimensions are divided into true, actual, limit, nominal.

true size- some absolute value, to which we strive, improving the quality of products.
actual size- the size of the element set by measurements with an allowable error.

In practice, the actual size is used instead of the true size.

Nominal size- the size with respect to which the limiting dimensions are determined and which also serves as the starting point for deviations. For mating parts, the nominal size is common. It is determined by calculations for strength, stiffness, etc., rounded up to the greatest value taking into account the "normal linear dimensions".

Normal linear dimensions.

Normal linear dimensions are used to reduce the variety of dimensions assigned by the designer with all the ensuing advantages (narrowing the range of materials, the range of measuring, cutting and measuring tools, etc.).

Rows of normal linear dimensions are geometric progressions with a denominator. There are five values in the row. These ratios are stored for various numerical intervals.

First row Ra 5 g = 10 = 1.6

0.1; 0.16; 0.25; 0.4; 0.63

1; 1.6; 2.5; 4; 6.3

10; 16; 25; 40; 63

100; 160; 250; 400; 630

Second row Ra 10 g = 10 = 1.25

1; 1.25; 1.6; 2.0; 2.5; 3.2; 4.0; 5.0; 6.3; 8.0

Each next row includes members of the previous one.

Third row Ra 20 g = 10 = 1.12

Fourth row Ra 40 g = 10 = 1.06

When choosing nominal sizes, the previous row is preferable to the next.

The nominal size is indicated for holes D and shaft d.

Limit sizes: two maximum allowable sizes of the element, between which it must be located, or which can be equal to the actual size.

Largest size limit: the largest allowable element size, nominal vice versa.

Dmax, Dmin, dmax, dmin

In order to simplify the designation of the limiting dimensions in the drawings, limit deviations from the nominal size are introduced.

The upper limit deviation ES(es) is the algebraic difference between the largest limit size and the nominal size.

EI = dmax –D for hole

es = dmax – d for shaft

The lower limit deviation EI(ei) is the algebraic difference between the smallest limit deviation and the nominal size.

EI = dmin - D for hole

Ei = dmin – d for shaft

Valid deviation called the algebraic difference between the actual and nominal sizes.

Deviation values can be a positive or negative number.

On engineering drawings, linear, nominal, limiting dimensions, as well as deviations, are put down in millimeters.

Angular dimensions and their maximum deviations are put down in degrees, minutes, seconds, indicating the units.

When the absolute magnitude of the deviations is equal 42 + 0.2; 120+2

A deviation equal to zero is not put down on the drawings, only one deviation is applied - positive at the top, negative at the bottom.

Deviation is recorded up to the last significant digit. For production, it is not the deviation that is more important, but the width of the interval, which is called the tolerance.

Tolerance - the difference between the largest and smallest limit sizes or the absolute value of the algebraic difference between the upper and lower deviations.

TD = Dmax – Dmin = ES – EI

Td = dmax – dmin = es - ei

The tolerance is always positive, it determines the permissible dispersion field of the actual dimensions of the parts in the batch, which are recognized as suitable, i.e., it determines the specified manufacturing accuracy.

The appointment of a rational tolerance is an important task that combines the economic and quality requirements of production.

With increasing tolerance, the quality of products, as a rule, deteriorates, but the cost of manufacturing falls.

The space on the diagram, bounded by the lines of the upper and lower deviations is called tolerance field.

A simplified image of the tolerance fields, in which the hole and shaft patterns missing.

Example: Build a layout of tolerance fields for shafts with a nominal size of 20 and maximum deviations

1.es = + 0.02 2.es = + 0.04

ei = - 0.01 ei = + 0.01

T1 = + 0.0.01) = 0.03 mm T2 = 0.04 – 0.01 = 0.03 mm

The comparative accuracy of parts 1 and 2 is the same. The accuracy criterion is tolerance T1 = T2, but the tolerance fields are different, since they differ in location relative to the nominal size.

Designation of deviations in the drawings.

dmax = d + es

Related to the concept of interchangeability is the concept of the suitability of a part. Any real part will be good if:

dmin< dr < dmax

ei< er < es

For example: shafts

dr1 = 20.03 - good

dr2 \u003d 20.05 - defect is correctable

dr3 = 20.0 - irreparable marriage

The concept of landings.

Landing is the nature of the connection of parts, determined by the size of the gap or interference.

Gap - the difference between the dimensions of the hole and the shaft, if the size of the hole over size shaft.

Movable joints are characterized by the presence of gaps.

Preload - the difference between the dimensions of the shaft and the hole before assembly, if the size of the shaft is larger than the size of the hole.

Fixed joints are characterized, as a rule, by the presence of tension.

There are three types of landings: with a gap, with an interference fit and transient.

Transition landings.

Transitional - landings in which it is possible to obtain both a gap and an interference fit in the joints (the tolerance fields of the hole and the shaft overlap partially or completely).

Fixed connections.

Transitional landings are calculated for Smax and Nmax.

Smax = Dmax – dmin = ES – ei

Nmax = dmax – Dmin =es – EI

2. Deviations from parallelism, perpendicularity and inclination of surfaces and axes, their normalization and examples of designation in the drawing.

Deviations in the location of the surface.

Deviation of the actual location of a surface from its smallest location.

Types of location deviations.

Deviation from parallelism- the difference between the largest and smallest distances between the planes within the normalized area.

Deviation from perpendicularity of planes- deviation of the angle between the planes from right angle, expressed in linear units on the length of the normalized section.

Misalignment is the largest distance (Δ1, Δ2) between the axis of the considered surface of revolution and the common axis of rotation.

Deviation from symmetry relative to the reference plane- called the largest distance between the plane of symmetry of the element under consideration and the plane of symmetry of the base element within the normalized area.

To control alignment, special devices are used.

Form deviations must be excluded from location deviations, so location deviations(from parallelism, perpendicularity, coaxiality, etc.) are measured from adjacent straight lines and surfaces reproduced using additional means: straightedges, rollers, squares or special devices.

To control alignment, special devices are used:

Coordinate measuring machines are widely used as universal means of controlling deviations.

3. Methods of measurement and their difference.

According to the method of obtaining the measurement result, they are distinguished into:

Direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data.

Indirect measurement- the desired value is found by the known relationship between the desired value and the values \u200b\u200bdetermined by direct measurements

y=f(a,b,c..h)

Determination of the density of a homogeneous body by its mass and geometric dimensions.

There are 2 methods of measurement: the method of direct evaluation and the method of comparison with the measure.

Direct evaluation method- the value of the quantity is determined directly by the reading device of the measuring device.

To do this, it is necessary that the range of the scale readings be more value measured value.

With the method of direct assessment (NO), the instrument is set to zero using the base surface of the instrument. Under the influence of various factors (changes in temperature, humidity, vibrations, etc.), zero mixing can occur. Therefore, it is necessary to periodically check and adjust accordingly.

Comparison Method– the measured value is compared with the value reproduced by the measure. When measuring by comparison with a measure result of observation is the deviation of the measured quantity from the value of the measure. The value of the measured quantity from the value of the measure. The value of the measured quantity is obtained by algebraic summation of the value of the measure and the deviation from this measure, determined by the indication of the instrument.

L=M+P

Direct assessment method Comparison method

DP>L DP>L-M

The choice of measurement method is determined by the ratio between the range of indications of the measuring instrument and the value of the measured quantity.

If the range is less than the measured value, then the comparison method is used.

The comparison method is used when measuring, controlling parts in mass and serial production, that is, when there are no frequent readjustments of the measuring device.

For linear measurements, the difference between the two methods is: - relative, since measurement is always essentially a comparison with the unit, which is somehow embedded in the measuring instrument.

1. Characteristics of the system of tolerances and fits of smooth cylindrical joints: normal temperature, tolerance unit, qualifications, tolerance formula, diameter intervals and tolerance series.

2. Roughness parameters Ra, Rz, Rmax. Rationing and examples of designation in the drawing of surface roughness using these parameters.

3. Reduced external thread diameter. The total tolerance of the average thread diameter. Validity condition of external thread on the average diameter. An example of designating the accuracy of a bolt thread in a drawing.

1. Characteristics of the system of tolerances and fits of smooth cylindrical joints: the main deviations of shafts and holes and layouts, the tolerance field and its designation, preferred tolerance fields and their layouts.

2. Roughness parameters, S and Sm. Rationing and examples of designation in the drawing of surface roughness using these parameters.

3. Classification of gears according to their functional purpose. Examples of marking the accuracy of gears.

1. Three types of landings, the layout of the tolerance fields and the characteristics of these landings. Examples of designations of landings in the drawings.

2. Roughness parameter tp. Rationing and examples of designation in the drawing of surface roughness using this parameter.

3. Measurement errors. Classification of the components of the measurement error according to the reasons for their occurrence.

1. Three types of landings in the hole system. Schemes for the location of tolerance fields and examples of the designation of landings in the hole system in the drawing.

2. Deviations of the shape of cylindrical surfaces, their normalization and examples of designation on the drawings of the tolerances of the shape of cylindrical surfaces.

3. Reduced average diameter internal thread. The total tolerance of the average thread diameter. The condition of the validity of the internal thread on the average diameter. An example of designating the accuracy of a nut in a drawing.

1. Three types of landings in the shaft system. Schemes for the location of tolerance fields and examples of the designation of landings in the shaft system in the drawing.

2. Deviations of the shape of flat surfaces. Their rationing and examples of designation in the drawing of the tolerances of the shape of flat surfaces.

3. Rationing the accuracy of gears and gears. The principle of combining nom accuracy. Examples of marking the accuracy of gears.

1. Landing with a gap. The layout of the tolerance fields in the hole system and the shaft system. The use of landings with a gap and examples of designation in the drawings.

2. Principles of standardization of form deviations and designation of form tolerances in the drawings. Surface shape deviations, basic definitions.

3. Random measurement errors and their evaluation.

1. Interference landings. Schemes for the location of tolerance fields in the hole and shaft system. The use of interference fits and examples of designation in the drawings.

2. height parameters of surface roughness. Rationing and examples of designation on the drawings of surface roughness using height parameters.

3. Rationing of accuracy metric thread. Examples of designation in the drawings of landings of threaded connections with a gap.

1. Transitional landings. Schemes for the location of tolerance fields in the shaft and hole system. The use of transitional landings and examples of designation in the drawing.

2. Step parameters of surface roughness. Rationing and examples of designation on the drawing of surface roughness using step parameters.

3. Kinematic accuracy of gears and gears, its rationing. An example of gear accuracy designation for reference gears.

2. Roughness shape parameter. Rationing and examples of designation in the drawings of surface roughness using a shape parameter.

3. Systematic measurement errors, methods for their detection and elimination.

2. Designation on the drawings of surface roughness. Examples of designation of surface roughness, type of processing that is not set by the designer; processed with the removal of a layer of material; kept in the state of delivery; processed without removing a layer of material.

3. The main deviations of thread diameters for landings with a gap and their layout. Examples of the designation of landings of metric threads in the drawings.

1. Landing with a gap. The layout of the landing tolerance fields with a gap in the hole system. Show how Smax, Smin, Sm, Ts will change when the tolerances of the parts to be joined are changed by one quality. Examples of designations in the drawings of landings with a gap in the hole system.

2. Deviations in the location of surfaces, their normalization and examples of designation in the drawings of tolerances for the location of surfaces.

3. Contact of teeth in gear and its rationing. An example of gear accuracy designation for a power train.

1. Interference fits, layouts of tolerance fields for interference fits in the hole system. Show how Nmax, Nmin, Nm, TN will change when the tolerances of the parts to be joined are changed by one quality. Examples of designation in the drawings of interference fits in the hole system.

2. Surface roughness, its causes. Normalization of surface roughness and examples of designations in the drawings.

3. Choice of measuring instruments.

1. Transitional landings, layouts of tolerance fields for transitional landings in the hole system. Show how Smax, Smin, Sm(Nm), TSN will change when the tolerances of the parts to be joined change by one quality. Examples of designation on the drawings of transitional landings in the hole system.

2. Deviations from alignment and intersection of axes, their normalization and examples of designation in the drawings.

3. Rationing and designation on the drawings of the accuracy of the external thread.

1. Landing with a gap. The layout of the tolerance fields of landings with a gap in the shaft system. Show how Smax, Smin, Sm, Ts will change when the tolerances of the parts to be joined are changed by one quality. Examples of designation in the drawings of landings with a gap in the shaft system.

2. Deviation from symmetry and positional deviation, their normalization and examples of designation in the drawings.

3. Smooth operation of gears and gears, its rationing. An example of gear accuracy designation for a high speed transmission.

1. Interference fits, layouts of tolerance fields for interference fits in the shaft system. Show how Nmax, Nmin, Nm, TN will change when the tolerances of the parts to be joined are changed by one quality. Examples of designation on the drawings of interference fits in the shaft system.

2. Radial and end runouts, their normalization and examples of designation in the drawing.

3. Mathematical processing of observation results. The form of presentation of the measurement result.

1. Transitional landings, layouts of tolerance fields for transitional landings in the shaft system. Show how Smax, Smin, Sm(Nm), TSN will change when the tolerances of the parts to be joined change by one quality. Examples of designation on the drawings of transitional landings in the shaft system.

2. Roughness parameters Ra, Rz, Rmax. Examples of using these parameters to normalize surface roughness.

3. Principles for ensuring the interchangeability of threaded connections. Examples of marking the accuracy of threaded connections in the drawings.

1. Landing with a gap and their calculation (selection). Designation of landings with a gap in the drawings. Application examples of preferred clearance fits.

2. Surface roughness parameters Sm and S. Examples of using these parameters to normalize surface roughness.

3. Measurement error and its components. Summation of errors in direct and indirect measurements.

1. Interference fits and their calculation (selection). Designation of landings with an interference fit in the drawings. Application examples of preferred interference fits.

2. Roughness parameter tp and examples of its application for normalization of surface roughness.

3. Types of gear teeth mates in the transmission. Examples of marking the accuracy of gears.

1. Transitional landings and their calculation (selection). Designation of transitional landings in the drawings. Examples of the use of preferred transitional landings.

2. The principle of preference, series of preferred numbers.

3. The concept of control, control by limiting gauges. Schemes of location of tolerance fields of calibers for hole control. Calculation and designation on the drawings of the executive dimensions of plug gauges.

1. Fittings of rolling bearings in the joints with the housing and shaft and layout of tolerance fields. Examples of designation of landings of rolling bearings in the drawing.

2. The concept of interchangeability and its types.

3. Rationing and designation on the drawings of the accuracy of the internal thread.

1. The choice of landings of rolling bearings, depending on the type of loading of the rings and the accuracy class of the bearing. Examples of designation of landings of rolling bearings in the drawings.

3. The concept of control, control by limiting gauges. Schemes of location of tolerance fields of calibers for shaft control. Calculation and designation on the drawings of the executive dimensions of the gauges-brackets.

1. Schemes of the location of tolerance fields in the joints of rolling bearings with the shaft and housing. Examples of designation of landings of rolling bearings in the drawings.

2. Scientific and technical principles of standardization. The role of standardization in ensuring product quality.

3. Lateral clearance in gears and its regulation. Examples of marking the accuracy of gears.

1. Hole system. The layout of the tolerance fields of three types of landings in the hole system. Examples of the designation of landings in the hole system in the drawing.

2. Unification, simplification, typification and aggregation and their role in improving the quality of machines and devices.

3. Diametrical compensation of errors in the pitch and angle of the thread profile. An example of designating the accuracy of a bolt thread with a make-up length that differs from normal.

1.Shaft system. The layout of the tolerance fields of three types of landings in the shaft system. Examples of designation of landings in the shaft system in the drawings.

2. Product quality and its main indicators. Product quality certification.

3. Tolerance field of external thread and its designation. Limit contours of the external thread and the condition of validity.

In this case, in the designations of the parameters of the holes, capital letters of the Latin alphabet are used ( D, E, S), and shafts - lowercase ( d, e,s).

The mating surfaces are characterized by a common size called nominal connection size (D, d).

Valid part size is the size obtained during manufacture and measurement with an allowable error.

TD(Td)=D max (d max ) – D min (d min ).

The size tolerance determines the specified boundaries (limit deviations) of the actual size of the good part.

Hole tolerances TD and shaft Td can be defined as the algebraic difference between the upper and lower limit deviations:

TD(Td) = ES(es) – EI(ei).

The amount of tolerance depends on the size and the required level of precision in the manufacture of the part, which is determined by quality (degree of accuracy).

quality is a set of tolerances corresponding to the same degree of accuracy.

The cost of manufacturing parts and the quality of the joint work depend on the correct appointment of the quality. The following are recommended areas for applying qualifications:

- from 01 to 5 - for standards, gauge blocks and gauges;

- from 6 to 8 - for the formation of landings of critical parts, widely used in mechanical engineering;

- from 9 to 11 - to create landings of irresponsible nodes operating at low speeds and loads;

- from 12 to 14 - for tolerances on free dimensions;

- from 15 to 18 - for tolerances on workpieces.

On the working drawings of parts, tolerances are affixed next to the nominal size. In this case, the letter specifies the main deviation, and the number specifies the degree of accuracy. For example:

 25d6;  25 H7;  30 h8 ;  30 F8 .

7.2. The concept of landings and landing systems

1. With guaranteed clearance S given that: D min ≥ d max :

- maximum clearance S max = D max – d min ;

- minimum clearance S min = D min – d max .

2. With guaranteed tension N given that: D max d min :

- maximum tension N max = d max – D min ;

- minimum tension N min = d min – D max .

Interference fits provide the formation of permanent connections more often without the use of additional fastening.

3. transitional landings , at which it is possible to obtain both a gap and an interference fit in the joint:

- maximum clearance S max = D max – d min ;

- maximum tension N max = d max – D min .

Transition fits are designed for fixed detachable connections. Provide high centering accuracy. Require additional fastening with screws, dowels, etc.

ESDP provides landings in the hole system and in the shaft system.

30 or 30

.

Metrological practice has established that it is impossible to make absolutely exact dimensions of a part, and there is no need to always have a very accurate value for the size of the machined part.

It must be remembered that the more precisely the size must be processed, the more expensive the production. Apparently, it is not necessary to explain in particular that in various mechanisms and machines there are parts that must be processed with particular care, and there are parts for which careful manufacture is not required. Therefore, there is a need to talk about dimensional accuracy.

As in every case, with regard to dimensional accuracy, there are a number of concepts and definitions that are necessary in order to speak the same language and express your thoughts in a shorter way.

Consider a number of practically used definitions and concepts of dimensions and their deviations.

Size - the numerical value of a physical quantity obtained as a result of measuring a characteristic or parameter of an object (process) in the selected units of measurement. In most cases, it is the difference between the states of an object or process in terms of a selected parameter, characteristic, indicator over time compared to a measure, a standard, a true or actual value of a physical quantity.

Actual size - the size established by the measurement with an allowable error. The size is only then called valid when it is measured with an error that can be allowed by any regulatory document. This term refers to the case where a measurement is made in order to determine the suitability of the dimensions of an object or process for certain requirements. When such requirements are not established and measurements are not made for the purpose of product acceptance, the term measured size is sometimes used, i.e. the size obtained from the results of the measurement, instead of the term "actual size". In this case, the measurement accuracy is selected depending on the goal set before the measurement.

The true size is the size obtained as a result of processing, manufacturing, the value of which is unknown to us, although it exists, since it is impossible to measure completely without error. Therefore, the concept of "true size" is replaced by the concept of "actual size", which is close to the true one under the conditions of the goal.

Limit sizes are the maximum allowable sizes between which the actual size must be or which can be equal. From this definition, it can be seen that when it is necessary to manufacture a part, then its size should be given by two values, i.e. valid values. And these two values \u200b\u200bare called the largest limit size - the larger of the two limit sizes and the smallest limit size - the smaller of the two limit sizes. A suitable part must have a size between these limit sizes. However, specifying the requirements for manufacturing accuracy with two dimensions is very inconvenient when drawing up drawings, although in the USA this is how the size is specified. Therefore, in most countries of the world, the concepts of "nominal size", "deviations" and "tolerance" are used.

Nominal size - the size with respect to which the limit sizes are determined and which serves as the starting point for deviations. The size indicated on the drawing is nominal. The nominal size is determined by the designer as a result of calculations overall dimensions or for strength, or for rigidity, or taking into account design and technological considerations.

However, it is impossible to take for the nominal any size that turned out during the calculation.

It must be remembered that the economic efficiency of metrological support is achieved when it is possible to get by with a small range of sizes without compromising quality. So, if you imagine that the designer will put on the drawing any nominal size, for example, the size of the holes, then it will be practically impossible to produce drills centrally in tool factories, since there will be an infinite number of drill sizes.

In this regard, the concepts of preferred numbers and series of preferred numbers are used in industry, i.e. values to which calculated values should be rounded. Usually rounded up to the nearest higher. This approach makes it possible to reduce the number of standard sizes of parts and assemblies, the number cutting tool and other technological and control equipment.

Rows of preferred numbers throughout the world are accepted the same and are geometric progressions with denominators W; “VWVW 4 VlO, which are approximately equal to 1.6; 1.25; 1.12; 1.06 (a geometric progression is a series of numbers in which each subsequent number is obtained by multiplying the previous one by the same number - the denominator of the progression). These series are provisionally named R5; RIO; R20; R40.

Preferred numbers are widely used in standardization when it is necessary to set a number of values of normalized parameters or properties within certain ranges. The nominal values of linear dimensions in existing standards are also taken from the indicated series of preferred numbers with a certain rounding. For example, according to R5 (denominator 1.6), values 10 are taken; sixteen; 25; 40; 63; 100; 160; 250; 400; 630 etc.

Deviation - the algebraic difference between the limit and the real, i.e. measured sizes. Therefore, the deviation should be understood as how much the size differs from the allowable value when normalizing the requirements or according to the results of the measurement.

Since, when normalizing according to permissible deviations, there are two limiting sizes - the largest and smallest, then the terms upper and lower deviations are accepted when normalizing tolerances, i.e. indications of requirements within the size tolerance. The upper deviation is the algebraic difference between the largest limit and nominal sizes. The lower deviation is the algebraic difference between the actual and the smallest limit dimensions when normalized by the tolerance value.

The peculiarity of deviations is that they always have a sign, either plus or minus. An indication in the definition of an algebraic difference shows that both deviations, i.e. both upper and lower can have positive values, i.e. the largest and smallest limit sizes will be greater than the nominal, or minus values (both less than the nominal), or the upper deviation may have a plus, and the lower - a minus deviation.

At the same time, there may be cases when the upper deviation is greater than the nominal, then the deviation will take a plus sign, and the lower deviation is less than the nominal, then it has a minus sign.

The upper deviation is indicated by ES at the holes and es at the shafts, and sometimes - BO.

The lower deviation is indicated by EI at the holes, ei at the shafts, or - BUT.

Tolerance (usually denoted T) - the difference between the largest and smallest limit sizes, or the absolute value of the algebraic difference between the upper and lower deviations. A feature of the tolerance is that it does not have a sign. This is, as it were, a zone of size values, between which the actual size must be, i.e. good part size.

Synonyms for this term can be as follows: "allowable value", "dimensions", "characteristic", "parameters".

If we are talking about a tolerance of 10 microns, then this means that in a batch of suitable parts there may be parts whose dimensions in the limiting case differ from each other by no more than 10 microns.

The concept of tolerance is very important and is used as a criterion for the accuracy of manufacturing parts. The smaller the tolerance, the more accurate the part will be made. The larger the tolerance, the coarser the detail. But at the same time, the smaller the tolerance, the more difficult, more complicated and hence the more expensive the manufacture of parts; the larger the tolerances, the easier and cheaper it is to manufacture the part. So there is a certain contradiction between developers and manufacturers. Designers want tolerances to be small (more accurate product) and manufacturers want tolerances to be large (easier to manufacture).

Therefore, the choice of tolerance must be justified. In all cases, where possible, large tolerances should be used, as this is economically beneficial for production, provided that the quality of the output product does not deteriorate.

Very often, along with the term "tolerance" and instead of it (not quite right), the term "tolerance field" is used, since, as mentioned above, tolerance is a zone (field) within which the dimensions of a good part are located.

The tolerance field, or the field of the permissible value, is a field limited by the upper and lower deviations. The tolerance field is determined by the tolerance value and its position relative to the nominal size.

Basic concepts of tolerances and landings

The mechanisms of machines and devices consist of parts that perform certain relative movements in the process of work or are connected motionlessly. Details that interact to some extent in a mechanism are called conjugated.
Absolutely accurate manufacture of any part is impossible, just as it is impossible to measure its absolute size, since the accuracy of any measurement is limited by the capabilities of measuring instruments on this stage scientific and technological progress, while the limit of this accuracy does not exist. However, the execution of mechanism parts with the highest accuracy is often impractical, primarily from an economic point of view, since high-precision products are much more expensive to manufacture, and for normal functioning in a mechanism, it is quite enough to make a part with less accuracy, i.e., cheaper.

Production experience has shown that the problem of choosing the optimal accuracy can be solved by setting for each part size (especially for its mating sizes) the limits within which its actual size can fluctuate; at the same time, it is assumed that the assembly, which includes the part, must correspond to its purpose and not lose its operability under the required operating conditions with the necessary resource.

Recommendations for the selection of maximum deviations in the dimensions of parts are developed on the basis of many years of experience in the manufacture and operation of various mechanisms and devices and scientific research, and are set out in a unified system of tolerances and landings (ESDP CMEA). Tolerances and landings established ESDP CMEA
Consider the basic concepts of this system.

The nominal size is called the main size, obtained from the calculation of strength, rigidity, or selected structurally and affixed to the drawing. Simply put, the nominal size of the part is obtained by designers and developers by calculation. (based on the requirements of strength, rigidity, etc.) and is indicated on the detail drawing as the main dimension.
The nominal connection size is common to the hole and shaft that make up the connection. According to nominal dimensions, drawings of parts, assembly units and devices are performed on one scale or another.

For unification and standardization, series of nominal sizes are established (GOST 8032-84 "Preferred numbers and series of preferred numbers"). The calculated or selected size should be rounded to the nearest value from the standard range. This especially applies to the dimensions of parts obtained with a standard or normalized tool, or connecting in relation to other standard parts or assemblies.
To reduce the range of cutting and measuring tools used in production, it is first of all recommended to use sizes ending in 0 and 5 and then on 0; 2; 5 and 8 .

The size obtained as a result of measuring the part with the greatest possible accuracy is called the actual one.
Do not confuse the actual size of a part with its absolute size.
Absolute size - the real (actual) size of the part; it cannot be measured by any ultra-precise measuring instruments, since there will always be an error, primarily due to the level of development of science, engineering and technology. In addition, any material body at a temperature above absolute zero "breathes" - microparticles, molecules and atoms are constantly moving on its surface, breaking away from the body and returning back. Therefore, even with ultra-precise measuring instruments at our disposal, it is impossible to determine the absolute size of the part; one can only talk about the real size in an infinitely small segment (moment) of time.
The conclusion is obvious - the absolute size of the part (as well as any body) is an abstract concept.

The dimensions between which the actual size of the manufactured part can be located are called limiting, while the largest and smallest limit sizes are distinguished.
A part made in the interval between the limiting dimensions is considered suitable. If its size goes beyond the limit - it is considered a marriage.
According to the limiting dimensions, the type of connection of parts and the permissible inaccuracy of their manufacture are established.
For convenience, the drawings indicate the nominal size of the part, and each of the two limiting sizes is determined by its deviation from this size. The value and sign of the deviation is obtained by subtracting the nominal size from the corresponding limit size.

The difference between the largest limit and nominal dimensions is called the upper deviation (denoted es or ES), the difference between the smallest limit and nominal - the lower deviation (denoted ei or EI).
The upper deviation corresponds to the largest limit size, and the lower one to the smallest.

All mating (interacting) in the mechanism, parts are divided into two groups - shafts and holes.
The shaft denotes the outer (male) element of the part. In this case, the shaft does not have to have a round shape: the concept of “shaft” includes, for example, a key, and the keyway in this case is called a “hole”. The main shaft is called, the upper deviation of which is equal to zero.
The dimensions of the shaft in the diagrams and in the calculations are indicated by lowercase (small) letters: d, dmax, dmin, es, ei, etc.

A hole designates an inner (female) feature of a part. As in the case of the shaft, the hole does not have to be round - its shape can be any. The main hole is called the hole, the lower deviation of which is zero.
The dimensions of the hole in the diagrams and in the calculations are indicated in capital (capital) letters: D, Dmax, Dmin, ES, EI, etc.

Tolerance (T) is the difference between the largest and smallest limit dimensions of the part. That is, tolerance is the interval between the maximum dimensions, within which the part is not considered a marriage.
Shaft size tolerance is denoted Td, holes - TD. Obviously, the larger the dimensional tolerance, the easier it is to manufacture the part.
The dimensional tolerance of a part can be defined as the difference between the limit sizes or as the sum of the limit deviations:

TD(d) = D(d)max – D(d)min = ES(es) + EI(ei) ,

in this case, the signs of limit deviations should be taken into account, since the tolerance on the size of the part is always positive (cannot be less than zero).

Landings

The nature of the connection, determined by the difference between the female and male dimensions, is called fit.
The positive difference between the diameters of the hole and the shaft is called clearance. (denoted by the letter S), and negative - interference (denoted by the letter N).
In other words, if the shaft diameter is less than the hole diameter, there is a gap, but if the shaft diameter exceeds the hole diameter, there is interference in the interface.
The gap determines the nature of the mutual mobility of the mating parts, and the tightness determines the nature of their fixed connection.

Depending on the ratio of the actual dimensions of the shaft and the hole, mobile landings are distinguished - with a gap, fixed landings - with an interference fit and transitional landings, i.e., landings in which both a gap and an interference may be present (depending on what deviations have the actual dimensions of the mating parts from the nominal dimensions).
Landings in which a gap is necessarily present are called landings with a guaranteed gap, and landings in which an interference is required - with a guaranteed interference.
In the first case, the limiting dimensions of the hole and the shaft are chosen in such a way that there is a guaranteed gap in the interface.
The difference between the largest hole size limit (Dmax) and the smallest shaft size limit (dmin) determines the largest clearance (Smax) :

Smax \u003d Dmax - dmin.

The difference between the smallest hole size limit (Dmin) and the largest shaft size limit (dmax) - the smallest gap (Smin) :

Smin \u003d Dmin - dmax.

The actual gap will be between the specified limits, i.e. between the maximum and minimum gap. The gap is necessary to allow movement of the connection and the placement of grease. The higher the number of revolutions and the higher the viscosity of the lubricant, the larger the gap should be.

In interference fits, the limiting dimensions of the shaft and hole are chosen in such a way that there is a guaranteed interference in the interface, limited by the minimum and maximum values \u200b\u200b- Nmax and Nmin:

Nmax = dmax – Dmin , Nmin = dmin – Dmax .

Transitional fit and may give a small amount of clearance or interference. Before the parts are made, it is impossible to say what will be in conjugation. It only becomes clear when assembling. The clearance should not exceed the value of the largest clearance, and the preload - the value of the maximum preload. Transition fits are used when it is necessary to ensure the exact centering of the hole and shaft.
Total in ESDP CMEA provided 28 types of basic deviations for shafts and the same number for holes. Each of them is indicated by a lowercase Latin letter (GOST 2.304 - 81) if the deviation refers to the shaft, or an uppercase letter if the deviation refers to the hole.
The letter designations of the main deviations are taken in alphabetical order, starting from the deviations that provide the largest gaps in the joint. A combination of various deviations of the shaft and the hole can be used to obtain landings of a different nature. (clearance, tightness or transitional).

Fits in hole system and shaft system

Landings set ESDP CMEA, can be implemented by hole or shaft systems.

The hole system is characterized by the fact that in it for all landings the limiting dimensions of the hole remain constant, and the landings are carried out by a corresponding change in the limiting dimensions of the shaft (i.e. the shaft is fitted to the bore). The size of the hole is called the main, and the size of the shaft is called the landing.

The shaft system is characterized by the fact that in it for all landings the limiting dimensions of the shaft remain constant, and the landings are carried out by changing the hole (i.e. the hole is adjusted to fit the shaft). The size of the shaft is called the main one, and the holes are called the landing.

On the industrial enterprises the hole system is mainly used, since it requires fewer cutting and measuring tools, i.e., it is more economical. In addition, it is technologically more convenient to fit the shaft to the hole, and not vice versa, since it is more convenient to process and control measurements of the outer surface, rather than the inner one.
The shaft system is usually used for the outer rings of ball bearings and in cases where several parts with different fits are mounted on a smooth shaft.

In mechanical engineering, the most common landings are arranged in descending order of tightness and increasing clearance: press (Pr), lightly pressed (Pl), deaf (G), tight (T), tense (N), dense (P), slip (S), movement (D), running (X), easy running (L), wide running (W).
Press fits give a guaranteed tight fit. Deaf, tight, tense and tight landings are transitional, and the rest have a guaranteed gap.
For a slip fit, the guaranteed clearance is zero.

To assess the accuracy of connections (landings), they use the concept of landing tolerance, which is understood as the difference between the largest and smallest gaps (in landings with a gap) or the largest and smallest tightness (in tight landings). In transitional landings, the landing tolerance is equal to the difference between the largest and smallest interferences or the sum of the largest interference and the largest clearance.
The fit tolerance is also equal to the sum of the tolerances of the hole and the shaft.

qualifications

The set of tolerances corresponding to the same degree of accuracy for all nominal sizes is called quality (I). In other words, quality is the degree of accuracy with which a part is made, while taking into account the size of this part.
Obviously, if a very large and a very small part are made with the same tolerance, then the relative accuracy of manufacturing a large part will be higher. Therefore, the system of qualifications takes into account the fact that (with the same tolerances) the ratio of the tolerance to the nominal size of a large part will be less than the ratio of the tolerance to the nominal size of a small part (Fig. 2), i.e., a conditionally large part is made more accurately with respect to their sizes. If, for example, for a shaft with a nominal diameter of 3 meters, a millimeter deviation from the size can be considered insignificant, then for a shaft with a diameter of 10 mm, such a deviation will be very noticeable.
The introduction of a system of qualifications avoids such confusion, since the accuracy of manufacturing parts is tied to their dimensions.

By ESDP CMEA qualifications are standardized in the form 19 rows. Each qualification is indicated by a serial number 01; 0; 1; 2; 3;...; 17 , increasing with increasing tolerance.
The two most accurate qualifications - 01 and 0 .
Link to qualifications ESDP CMEA may be abbreviated with the letters IT "International Approval" followed by the qualification number.
For example, IT7 means tolerance for 7 -th qualification.

In the CMEA system, the following symbols are used to designate tolerances with an indication of qualifications:

The letters of the Latin alphabet are used, while the holes are defined in uppercase letters, and the shafts in lowercase.
Hole in hole system (main hole) denoted by the letter H and numbers - the number of the qualification. For example, H6, H11 etc.
The shaft in the hole system is indicated by the landing symbol and numbers - the quality number. For example, g6, d11 etc.
The conjugation of the hole and the shaft in the hole system is indicated fractionally: in the numerator - the hole tolerance, in the denominator - the shaft tolerance.

Graphic representation of tolerances and landings

For clarity, they often use a graphical representation of tolerances and landings using the so-called tolerance fields (see Fig. 3).

The construction is carried out as follows.
From the horizontal line, conditionally depicting the surface of the part at its nominal size, limit deviations are plotted on an arbitrarily chosen scale. Usually, on the diagrams, the deviations are indicated in microns, but tolerance fields can also be built in millimeters if the deviations are large enough.

The line, which, when constructing schemes of tolerance fields, corresponds to the nominal size and serves as the starting point for dimensional deviations, is called zero (0-0) .
Tolerance field - a field limited by upper and lower deviations, that is, with a graphical representation of the tolerance field, zones are shown that are limited by two lines drawn at distances corresponding to the upper and lower deviations on the selected scale.
Obviously, the tolerance field is determined by the tolerance value and its position relative to the nominal size.
On the diagrams, the tolerance fields have the form of rectangles, the upper and lower sides of which are parallel to the zero line and display the maximum deviations, and the sides in the selected scale correspond to the size tolerance.

The diagrams indicate the nominal D and limit (Dmax, Dmin, dmax, dmin) dimensions, limit deviations (ES, EI, es, ei) tolerance fields and other parameters.

The maximum deviation, which is closer to the zero line, is called the main (top or bottom). It defines the position of the tolerance field relative to the zero line. For tolerance fields located below the zero line, the upper deviation is the main one.
For tolerance fields located above the zero line, the main one is the lower deviation.

The principle of formation of tolerance fields, adopted in ESDP, allows a combination of any major deviations with any qualifications. For example, you can create tolerance fields a11, u14, c15 and others not specified in the standard. The exception is the main deviations J and j , which are replaced by the main deviations Js , and js .

The use of all major deviations and qualifications allows you to get 490 tolerance fields for shafts and 489 for holes. Such wide possibilities for the formation of tolerance fields allow the use of ESDP in various special cases. This is its essential merit. However, in practice, the use of all tolerance fields is uneconomical, as it will cause an excessive variety of landings and special technological equipment.

When developing national systems of tolerances and landings based on systems ISO from the whole variety of tolerance fields, only those fields are selected that provide the needs of the country's industry and its foreign economic relations.

h and H - the upper and lower deviations of the shaft and the hole, equal to zero (tolerances with basic deviations h and H are taken for the main shafts and holes).
a - h (A - H) - deviations that form tolerance fields for landings with gaps.
js - n (Js - N) - deviations that form the tolerance fields of transitional landings.
p - zc (P - ZC) - deviations forming tolerance fields for interference fits.

Schematically, the main deviations are shown in Fig. 4 .

The tolerance field in the ESDP CMEA is formed by a combination of one of the main deviations with a tolerance for one of the qualifications. In accordance with this, the tolerance field is indicated by the letter of the main deviation and the quality number, for example 65f6; 65e11- for the shaft; 65P6; 65H7- for the hole.
The main deviations depend on the nominal dimensions of the parts and remain constant for all qualifications. The exception is the main deviations of the holes J, K, M, N and shafts j and k, which, with the same nominal sizes, in different qualifications have different values. Therefore, on the diagrams of the tolerance field with deviations J, K, M, N, j, k, usually divided into parts and shown as stepped.

Type specific tolerance fields js6, js8, js9 etc. They actually do not have a main deviation, since they are located symmetrically with respect to the zero line. By definition, the main deviation is the deviation closest to the zero line. This means that both deviations of such specific tolerance fields can be recognized as basic, which is unacceptable.

Of particular importance are the main deviations H and h, which are equal to zero (figure). Tolerance fields with such basic deviations are located from the face value "into the body" of the part; they are called the tolerance fields of the main hole and the main shaft.
Landing designations are constructed as fractions, and in the numerator there is always the designation of the tolerance field of the female surface (hole), and in the denominator - the tolerance field of the covered (shaft).

When choosing the quality of the connection and the type of fit, the designer should take into account the nature of the interface, operating conditions, the presence of vibration, service life, temperature fluctuations and manufacturing costs.
It is recommended to choose the quality and type of landing by analogy with those parts and assemblies whose work is well known, or be guided by the recommendations of reference literature and regulatory documents (OSTs).
In accordance with the quality of fit, the surface finish of the mating parts is selected.

Tolerances and fits are established for four ranges of nominal sizes:

small - before 1 mm;
medium - from 1 before 500 mm;
big - from 500 before 3150 mm;
very large - from 3150 before 10 000 mm.

The middle range is the most important because it is used much more frequently.

Designation of tolerances in the drawings

Indications and designations on the drawings of the maximum deviations of the shape and location of surfaces are regulated by GOST 2.308-79, which provides for these purposes special signs and symbols.
The main provisions of this standard, the signs and symbols used to indicate limit deviations, can be found in this document ( WORD format, 400 kB).

It is more convenient to consider the basic concepts of interchangeability in terms of geometric parameters using the example of shafts and holes and their connections.

Shaft - a term conventionally used to refer to the outer elements of parts, including non-cylindrical elements.

Hole - a term conventionally used to refer to the internal elements of parts, including non-cylindrical elements.

Quantitatively, the geometric parameters of parts are evaluated by means of dimensions.

Size - the numerical value of a linear quantity (diameter, length, etc.) in the selected units of measurement.

Dimensions are divided into nominal, actual and limit.

Definitions are given in accordance with GOST 25346-89 "Unified system of tolerances and landings. General provisions, series of tolerances and basic deviations".

The nominal size is the size against which deviations are determined.

The nominal size is obtained as a result of calculations (strength, dynamic, kinematic, etc.) or is selected from some other considerations (aesthetic, structural, technological, etc.). The size obtained in this way should be rounded to the nearest value from a series of normal sizes (see section "Standardization"). The main share of the numerical characteristics used in technology is linear dimensions. Due to the large proportion of linear dimensions and their role in ensuring interchangeability, series of normal linear dimensions have been established. Rows of normal linear dimensions are regulated in the entire range, which is widely used.

The basis for normal linear dimensions are the preferred numbers, and in some cases their rounded values.

The actual size is the element size set by the measurement. This term refers to the case when a measurement is made to determine the suitability of the dimensions of a part to specified requirements. Measurement is understood as the process of finding the values of a physical quantity empirically using special technical means, and under the measurement error - the deviation of the measurement result from the true value of the measured quantity. True size - the size obtained as a result of processing the part. The value of the true size is unknown, since it is impossible to perform a measurement without error. In this regard, the concept of "true size" is replaced by the concept of "actual size".

Limit sizes - two maximum allowable sizes of the element, between which the actual size must be (or which may be equal to). For the limit size, which corresponds to the largest volume of material, i.e., the largest limit size of the shaft or the smallest limit size of the hole, the term maximum material limit is provided; for the limit size, which corresponds to the smallest volume of material, i.e., the smallest limit size of the shaft or the largest limit size of the hole, the limit of the minimum material.

Largest size limit - the largest allowable element size (Fig. 5.1)

Smallest size limit - the smallest allowable size of an element.

From these definitions it follows that when it is necessary to manufacture a part, its size must be given by two allowable values - the largest and the smallest. A suitable part must have a size between these limit values.

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

The actual deviation is the algebraic difference between the actual and the corresponding nominal dimensions.

Limit deviation - the algebraic difference between the limit and nominal sizes.

Deviations are divided into upper and lower. The upper deviation E8, ea (Fig. 5.2) is the algebraic difference between the largest limit and nominal sizes. (ER is the upper deviation of the hole, er is the upper deviation of the shaft).

The lower deviation E1, e (Fig. 5.2) is the algebraic difference between the smallest limit and nominal sizes. (E1 - bottom deviation of the hole, e - bottom deviation of the shaft).

Tolerance T is the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations (Fig. 5.2).

Standard tolerance P - any of the tolerances established by this system of tolerances and landings.

Tolerance characterizes the accuracy of the size.

Tolerance field - a field limited by the largest and smallest limit sizes and determined by the tolerance value and its position relative to the nominal size. With a graphical representation, the tolerance field is enclosed between two lines corresponding to the upper and lower deviations relative to the zero line (Fig. 5.2).

It is almost impossible to depict deviations and tolerances on the same scale with the dimensions of the part.

The so-called zero line is used to indicate the nominal size.

Zero line - a line corresponding to the nominal size, from which size deviations are plotted in the graphic representation of tolerance and fit fields. If the zero line is located horizontally, then positive deviations are plotted upwards from it, and negative deviations downwards (Fig. 5.2).

Using the above definitions, the following characteristics of shafts and holes can be calculated.

Schematic designation of tolerance fields

For clarity, it is convenient to present all the considered concepts graphically (Fig. 5.3).

In the drawings, instead of limiting dimensions, limit deviations from the nominal size are affixed. Considering that deviations can

can be positive (+), negative (-) and one of them can be equal to zero, then there are five possible cases of the position of the tolerance field in a graphic image:

1) upper and lower deviations are positive;
2) the upper deviation is positive, and the lower one is zero;
3) the upper deviation is positive and the lower deviation is zero;
4) the upper deviation is zero, and the lower deviation is negative;
5) upper and lower deviations are negative.

On fig. 5.4, but the listed cases for the hole are given, and in fig. 5.4, b - for the shaft.

For the convenience of normalization, one deviation is distinguished, which characterizes the position of the tolerance field relative to the nominal size. This deviation is called the main one.

The main deviation is one of two limit deviations (upper or lower), which determines the position of the tolerance field relative to the zero line. In this system of tolerances and landings, the main deviation is the closest to the zero line.

From formulas (5.1) - (5.8) it follows that the requirements for dimensional accuracy can be normalized in several ways. You can set two limit sizes, between which there must be

a - holes; b- shaft

measures of fit parts; you can set the nominal size and two maximum deviations from it (upper and lower); you can set the nominal size, one of the limit deviations (upper or lower) and the size tolerance.

Dimensional numbers, in the drawing, serve as the basis for determining the dimensions of the depicted product (detail). On the working drawings, the nominal dimensions are affixed. These are the dimensions calculated during design.

The size obtained as a result of measuring the finished part is called the actual size. The largest and smallest limit sizes are the established largest and smallest valid dimensions. admission size is the difference between the largest and smallest limit sizes. The difference between the measurement result and the nominal size is called the size deviation - positive if the size is greater than the nominal, and negative if the size is less than the nominal.

The difference between the largest size limit and the nominal size is called upper limit deviation, and the difference between the smallest limit size and the nominal - lower limit deviation. Deviations are indicated in the drawing by a sign (+) or (-), respectively. Deviations are written after the nominal size in smaller numbers one below the other, for example, where 100 is the nominal size; +0.023 is the upper and -0.012 is the lower deviation.

The tolerance field is the zone between the lower and upper limit deviations. Both deviations can be negative or positive. If one deviation is equal to zero, then it is not marked on the drawing. If the tolerance field is located symmetrically, then the deviation value is applied with a “+-” sign next to the dimension number with figures of the same size, for example:

Deviations of angle sizes are indicated in degrees, minutes and seconds, which should be expressed as integers, for example 38 degrees 43`+-24``

When assembling two parts that are included one into the other, they distinguish covering and covered surface. The female surface is collectively called the hole, and the covered one is the shaft. The size common to one and the other part of the connection is called nominal. It serves as the starting point for deviations. When establishing nominal dimensions for shafts and holes, it is necessary to round off the calculated dimensions, selecting the nearest dimensions from a number of nominal linear dimensions in accordance with GOST 6636-60.

Various connections machine parts have their own purpose. All these connections can be imagined as embracing one part by another, or as fitting one part into another, and some connections can be assembled and separated, while others are assembled and separated with difficulty.

Designations of maximum deviations of dimensions on the working drawings of parts and assembly drawings must comply with the requirements of GOST 2.109-73 and GOST 2.307-68.

When designating the maximum deviations of dimensions, it is necessary to follow the basic rules:
- linear dimensions and their maximum deviations in the drawings Indicated in millimeters without indicating the unit of measurement;
- on the working drawings, the maximum deviations are given for all sizes, except for reference ones; dimensions that determine the zones of roughness, heat treatment, coating, and for the dimensions of parts specified with an allowance, for which it is allowed not to indicate maximum deviations;
- on the assembly drawings, I put down the maximum deviations for the parameters that must be performed and controlled according to this assembly drawing, as well as for the dimensions of the parts shown on the assembly drawing, for which working drawings are not issued.

Examples of designation of limit deviations

Examples of designation of tolerances and landings in the drawings

7.Basic deviation- one of two limit deviations (upper or lower), which determines the position of the tolerance field relative to the zero line. In this system of tolerances and landings, the main deviation is the closest to the zero line. The main deviations are indicated by Latin letters, uppercase for holes (A...ZC) and lowercase for shafts (a...zc)

Upper deviation ES, es - algebraic difference between the largest limit and the corresponding nominal dimensions

Lower deviation EI, ei - algebraic difference between the smallest limit and the corresponding nominal size

The shaded area is called the size tolerance field. This area in the form of a rectangle is located between the limiting dimensions dmax and dmin and determines the range of dispersion of the actual dimensions of suitable parts. The nominal value d of the shaft size is taken as the zero line. The tolerance field is determined by the numerical value of the tolerance Td and the location relative to the zero line, i.e. two options.

The values of the tolerance fields are denoted by the letters IT and the number of the ordinal number of the qualification. For example: IT5, IT7. Conditional designation of tolerances. The size for which the tolerance field is indicated is indicated by a number (mm), followed by a symbol consisting of a letter / letters and a number / numbers - indicating the qualification number, for example 20g6, 20H8, 30h11, etc. It should be noted that the deviations are affixed with certain signs, while the tolerances of the value are always positive and the sign is not indicated.

The size tolerance determines the accuracy of the manufacturing of the part and affects the quality indicators of the products. With a decrease in the tolerance of parts whose performance is determined by wear (piston, cylinder of an internal combustion engine), such an important operational indicator as the service life increases. On the other hand, decreasing tolerances increases manufacturing costs.

To determine the numerical values of the product tolerance fields, the standards of the ISO system (in Russia, the ESDP system - a unified system of tolerances and landings) established 20 qualifications.

The qualifications are indicated by numbers: 01,0,1,2,3,……….18, in order of decreasing accuracy and increasing tolerances. The designation IT8 means that the size tolerance is set according to the 8th grade of accuracy.

Approximate areas of application of accuracy qualifications in mechanical engineering are as follows:

IT01 to IT3 for high-precision measuring instruments, gauges, templates; as a rule, such accuracy is not assigned for machine-building parts;

IT 4 to IT5 for precision engineering parts.

IT 6 to IT7 precision engineering parts, applied very widely;

IT 8 to IT9 average precision of machine building parts;

IT 10 to IT12 reduced part accuracy. All of the above qualifications form the landing of compounds;

Qualities coarser than the 12th are assigned to standardize the accuracy of free, non-contiguous surfaces of parts, the accuracy of the dimensions of workpieces.

The tolerance unit is the dependence of the tolerance on the nominal size, which is a measure of accuracy that reflects the influence of technological, design and metrological factors. The tolerance units in the systems of tolerances and fits are established on the basis of studies of the accuracy of machining parts. The tolerance value can be calculated by the formula T \u003d a i, where a is the number of tolerance units, depending on the level of accuracy (quality or degree of accuracy); i - tolerance unit.

Tolerance - the difference between the largest and smallest limit values of parameters, is set for the geometric dimensions of parts, mechanical, physical and Chemical properties. Assigned (selected) based on technological accuracy or requirements for the product (product)

To normalize the levels of accuracy in the ISO and CMEA systems, qualifications are introduced.

The quality is understood as a set of tolerances that vary depending on the nominal size and correspond to the same degree of accuracy, determined by the number of tolerance units a.

In the range up to 500mm - 19 qualifications: 0.1; 0; one; 2; …; 17.

In the range of 500-3150mm - 18 qualifications.

Gap landings.

Landing is the nature of the connection of parts, determined by the magnitude of the gaps or interferences resulting in it. Landing characterizes the freedom of relative movement of the connected parts or the degree of resistance to their mutual displacement.

Gap landings. A clearance fit is a fit that provides a clearance in the joint (the hole tolerance field is located above the shaft tolerance field). Clearance S is the positive difference between the dimensions of the hole and the shaft. The gap allows the relative movement of the mating parts.

Landing with a gap - provides a gap in the connection, and is characterized by the values of the largest and smallest gaps, with a graphic image, the hole tolerance field is located above the shaft tolerance field.

In cases where one part must move relative to another without pitching, a very small gap should be provided: in order for one part to rotate freely in another (for example, a shaft in a hole), the gap must be larger.

The nature and working conditions of mobile joints are diverse.

Landings of the H / h group are characterized by the fact that the minimum clearance in them is zero. They are used for pairs with high requirements for the centering of the hole and the shaft, if the mutual movement of the shaft and the hole is provided for during regulation, as well as at low speeds and loads.

The H5/h4 fit is used for joints with high requirements for centering accuracy and direction, in which rotation and longitudinal movement of parts are allowed during adjustment. These landings are used instead of transitional ones (including for interchangeable parts). For rotating parts, they are used only at low loads and speeds.

Landing H6 / h5 is prescribed for high requirements for centering accuracy (for example, tailstock quills lathe, measuring gears when they are installed on the spindles of gear measuring instruments).

Fit H7/h6 (preferred) is used with less stringent requirements for centering accuracy (for example, replaceable gears in machine tools, housings for rolling bearings in machine tools, cars and other machines).

Fit H8/h7 (preferred) is assigned to centering surfaces if manufacturing tolerances can be extended with slightly reduced alignment requirements.

ESDP allows the use of landings of the H / h group, formed from tolerance fields of qualifications 9 ... 12, for connections with low requirements for centering accuracy (for example, for landing gear pulleys, couplings and other parts on a shaft with a key for torque transmission , with low requirements for the accuracy of the mechanism as a whole and small loads).

H/g group fits (H5/g4; H6/g5 and H7/g6 preferred) have the smallest guaranteed gap of all gap fits. They are used for precise moving joints that require a guaranteed but small gap to ensure accurate centering, for example, a spool in pneumatic devices, a spindle in dividing head supports, in plunger pairs, etc.

Of all the moving landings, the most common are landings of the H / f group (H7 / f7 - preferred, H8 / f8, etc., formed from tolerance fields of qualifications 6, 8 and 9). For example, fit H7/f7 is used in plain bearings of electric motors of small and medium power, reciprocating compressors, in gearboxes of machine tools, centrifugal pumps, in internal combustion engines, etc.

Landings of the H / e group (H7 / e8, H8 / e8 - preferred, H7 / e7 and landings similar to them, formed from tolerance fields of qualifications 8 and 9) provide an easily movable connection during fluid friction. They are used for fast rotating shafts of large machines. For example, the first two landings are used for shafts of turbogenerators and electric motors operating with large loads. Landings H9 / e9 and H8 / e8 are used for large bearings in heavy engineering, freely rotating on gear shafts, and for other parts switched on by clutches, for centering cylinder covers.

Landings of the H / d group (H8 / d9, H9 / d9 - preferred and similar landings formed from tolerance fields of qualifications 7, 10 and 11) are used relatively rarely. For example, the H7/d8 fit is used at high speed and relatively low pressure in large bearings, as well as in the piston-cylinder interface in compressors, and the H9/d9 fit is used when the mechanisms are not very accurate.

Landing group H / s (H7 / s8 and H8 / s9) are characterized by significant guaranteed gaps, and they are used for connections with low requirements for centering accuracy. Most often, these landings are prescribed for plain bearings (with different temperature coefficients of linear expansion of the shaft and bushing) operating at elevated temperatures (in steam turbines, engines, turbochargers, and other machines in which the clearances are significantly reduced during operation due to the fact that the shaft heats up and expands more than the bearing shell). When choosing moving fits, the following considerations should be taken into account: the greater the speed of rotation of the part, the greater the gap should be.

Transition landings.

Transitional landings are provided only in exact qualifications. Transition fits provide good centering of the parts to be joined and are used in fixed detachable joints, which during operation are subjected to more or less frequent disassembly and assembly for inspection or replacement of replaceable parts. High accuracy centering and the relative ease of disassembly and assembly of the connection are provided by hell due to small gaps and tightness. Small gaps limit the mutual radial mixing of parts in the joints, and small interferences contribute to their coaxiality during assembly.

· They are characterized by a moderate guaranteed clearance sufficient to ensure free rotation in plain bearings with grease and liquid lubrication in light and medium operating conditions (moderate speeds - up to 150 rad / s, loads, small temperature deformations).

· H/js landings; js/h- "dense". Probability of getting a pull P(N) ≈ 0.5 ... 5%, and, consequently, gaps are predominantly formed in the conjugation. Provides easy assembly.

· Landing H7/js6 used to mate bearing cups with housings, small pulleys and handwheels with shafts.

· Landing H/k; K/h- "tense". Probability of getting a pull P(N) ≈ 24...68%. However, due to the influence of form deviations, especially with long connection lengths, gaps are not felt in most cases. Provide good centering. Assembly and disassembly is carried out without significant effort, for example, using hand hammers.

· Landing H7/k6 widely used for mating gears, pulleys, flywheels, couplings with shafts.

· Landing H/m; m/h- "tight". Probability of getting a pull P(N) ≈ 60...99.98%. They have a high degree of centering. Assembly and disassembly is carried out with considerable effort. They are usually dismantled only during repairs.

· Landing H7/m6 used for mating gears, pulleys, flywheels, couplings with shafts; for installing thin-walled bushings in housings, cams on a camshaft.

· Landings H/n ; N/h- "deaf". Probability of getting a pull P(N) ≈ 88...100%. They have a high degree of centering. Assembly and disassembly is carried out with considerable effort: presses are used. They are usually dismantled only during major repairs.

· Landing H7/n6 it is used for pairing heavily loaded gears, couplings, cranks with shafts, for installing permanent conductor bushings in conductor housings, pins, etc.

Examples of assigning transitional landings (a - connection "shaft - gear"; b - connection "piston - piston pin- connecting rod head; in- connection "shaft - flywheel"; G - connection "sleeve - body").

Landings with interference.

Landings with a guaranteed tightness are used to obtain fixed one-piece connections, and the relative immobility of the mating parts is ensured due to the elastic deformations that occur when the shaft is connected to the hole. In this case, the maximum dimensions of the shaft are greater than the maximum dimensions of the hole. In some cases, to increase the reliability of the connection, pins or other means of fastening are additionally used, while the torque is transmitted by the pin, and the tightness keeps the part from axial movement.

Examples of the use of interference fit. The frequency of application of preferred interference fits corresponds to the order of increasing guaranteed interference.

For connections of thin-walled parts, as well as parts with thicker walls that experience small loads, fit will be preferable H7/r6. For connections of conductor bushings with the conductor body, locking bushings with additional fastening, landings will be preferable H7/r6, h7/s6. Landing H7/u7 it is used for such connections as plain bearing bushings in heavy engineering, worm wheel rims, flywheels. Landings characterized by the largest values of guaranteed tightness - H8/x8, H8/z8, are used for heavily loaded connections that perceive large torques and axial forces.

Interference fits are designed to obtain fixed, one-piece connections of parts without their additional fastening.

It is more convenient to consider the basic concepts of interchangeability in terms of geometric parameters using the example of shafts and holes and their connections.

Shaft - a term conventionally used to refer to the outer elements of parts, including non-cylindrical elements.

Hole - a term conventionally used to refer to the internal elements of parts, including non-cylindrical elements.

Quantitatively, the geometric parameters of parts are evaluated by means of dimensions.

Size - the numerical value of a linear quantity (diameter, length, etc.) in the selected units of measurement.

Dimensions are divided into nominal, actual and limit.

Definitions are given in accordance with GOST 25346-89 "Unified system of tolerances and landings. General provisions, series of tolerances and basic deviations."

The nominal size is the size against which deviations are determined.

The nominal size is obtained as a result of calculations (strength, dynamic, kinematic, etc.) or is selected from some other considerations (aesthetic, structural, technological, etc.). The size thus obtained should be rounded to the nearest value from a range of normal sizes. The main share of the numerical characteristics used in technology is linear dimensions. Due to the large proportion of linear dimensions and their role in ensuring interchangeability, series of normal linear dimensions have been established. Rows of normal linear dimensions are regulated in the entire range, which is widely used.

The basis for normal linear dimensions are the preferred numbers, and in some cases their rounded values.

The actual size is the element size set by the measurement. This term refers to the case when a measurement is made to determine the suitability of the dimensions of a part to specified requirements. Measurement is the process of finding the values of a physical quantity empirically using special technical means, and measurement error is the deviation of the measurement result from the true value of the measured quantity. True size - the size obtained as a result of processing the part. The value of the true size is unknown, since it is impossible to perform a measurement without error. In this regard, the concept of "true size" is replaced by the concept of "actual size".

Largest size limit - the largest allowable size of an element.

Smallest size limit - the smallest allowable size of an element.

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

The actual deviation is the algebraic difference between the actual and the corresponding nominal dimensions.

Limit deviation - the algebraic difference between the limit and nominal sizes.

Deviations are divided into upper and lower. The upper deviation E8, ea is the algebraic difference between the largest limit and nominal sizes. (ER is the upper deviation of the hole, er is the upper deviation of the shaft).

The lower deviation E1, e is the algebraic difference between the smallest limit and nominal sizes. (E1 - bottom deviation of the hole, e - bottom deviation of the shaft).

Tolerance T is the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations.

Standard tolerance P - any of the tolerances established by this system of tolerances and landings.

Tolerance characterizes the accuracy of the size.

It is almost impossible to depict deviations and tolerances on the same scale with the dimensions of the part.

The so-called zero line is used to indicate the nominal size.

Landing - the nature of the connection of two parts, determined by the difference in their sizes before assembly.