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

Shaft is a term conventionally used to designate the external elements of parts, including non-cylindrical elements.

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

The geometric parameters of parts are quantified using 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 limiting.

Definitions are given according to GOST 25346-89 " Unified system tolerances and landings. General provisions, series of tolerances and main deviations."

The nominal size is the size relative to which deviations are determined.

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

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

Actual size is the size of the element as determined by the measurement. This term refers to the case where a measurement is made to determine the suitability of the dimensions of a part to specified requirements. Measurement refers to the process of finding values physical quantity experimentally with the help of special technical means, and under measurement error - the deviation of the measurement result from the true value of the measured value. True size is the size obtained as a result of processing the part. The true size is unknown because it is impossible to measure without error. In this regard, the concept of “true size” is replaced by the concept of “actual size”.

Limit dimensions - two maximum permissible dimensions of an element, between which the actual size must be (or can be equal to). For the limit size to which the largest volume of material corresponds, 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 to which the smallest volume of material corresponds, i.e. the smallest limit size of the shaft or the largest limit size of the hole, the minimum material limit.

The largest limit size is the largest allowable size of an element.

The smallest size limit is the smallest allowable element size.

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

Deviation is the algebraic difference between the size (actual or maximum size) and the nominal size.

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

The maximum deviation is the algebraic difference between the maximum 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. (EA is the upper deviation of the hole, EG is the upper deviation of the shaft).

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

Tolerance field - a field limited by the largest and smallest maximum sizes and determined by the value of the tolerance and its position relative to the nominal size. In a graphical representation, the tolerance field is enclosed between two lines corresponding to the upper and lower deviations relative to the zero line.

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

To indicate the nominal size, the so-called zero line is used.

Zero line - a line corresponding to the nominal size, from which dimensional deviations are plotted when graphically depicting tolerance and fit fields. If the zero line is located horizontally, then positive deviations are laid up from it, and negative deviations are laid down.

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

Interchangeability Basics

Interchangeability is a property of the same parts, components or assemblies of machines, etc., which allows you to install parts (assemblies, assemblies) during the assembly process or replace them without preliminary adjustment while maintaining all the requirements for the operation of the component, assembly and structure as a whole . The specified properties of products arise as a result of the implementation of scientific and technical activities, united by the concept " principle of interchangeability".

Most widely used full interchangeability, which provides the possibility of non-fitting assembly (or replacement during repair) of any parts of the same type independently manufactured with a given accuracy into assembly units, and the latter into products, subject to the requirements for them (assembly units or products) technical requirements in all quality parameters. Meeting the requirements for the accuracy of parts and assembly units of products is the most important initial condition for ensuring interchangeability. In addition, to ensure interchangeability, it is necessary to fulfill other conditions: establish optimal nominal values ​​of the parameters of parts and assembly units, fulfill the requirements for the material of parts, technology for their manufacture and control, etc. Parts, assembly units and products as a whole can be interchangeable. First of all, these should be parts and assembly units, on which the reliability and other performance indicators of products depend. This requirement naturally also applies to spare parts.

With complete interchangeability:

the assembly process is simplified - it comes down to simply connecting parts by mostly low-skilled workers;

it becomes possible to accurately normalize the assembly process in time, set the required pace of work and apply the in-line method;

conditions are created for the automation of the processes of manufacturing and assembly of products, as well as broad specialization and cooperation of factories (in which the supplier plant produces standardized products, assembly units and parts of a limited range and supplies them to the plant that produces the main products);

the repair of products is simplified, since any worn or broken part or assembly unit can be replaced with a new one (spare).

Sometimes, in order to meet operational requirements, it is necessary to manufacture parts and assembly units with small tolerances that are economically unacceptable or technologically difficult to meet. In these cases, to obtain the required assembly accuracy, group selection of parts (selective assembly), compensators, adjustment of the position of certain parts of machines and devices, fitting and other additional technological measures are used, while the requirements for the quality of assembly units and products must be met. like this interchangeability is called incomplete (limited). It can be carried out not for all, but only for individual geometric or other parameters.

External interchangeability - This is the interchangeability of purchased and cooperative products (mounted into other more complex products) and assembly units in terms of performance indicators, as well as in the size and shape of connecting surfaces. For example, in electric motors, external interchangeability is ensured by shaft speed and power, as well as by the dimensions of the connecting surfaces; in rolling bearings - by the outer diameter of the outer ring and the inner diameter of the inner ring, as well as by rotation accuracy.

Internal interchangeability applies to parts, assembly units and mechanisms included in the product. For example, in a rolling bearing, the rolling elements and rings have internal group interchangeability.

Level of production interchangeability can be characterized by the interchangeability coefficient K in, equal to the ratio of the labor intensity of manufacturing interchangeable parts and assembly units to the total labor intensity of manufacturing the product. The value of this coefficient may vary, but the degree to which it approaches unity is an objective indicator of the technical level of production.

Compatibility -this is the property of objects to take their place in a complex finished product and perform the required functions during joint or sequential operation of these objects and a complex product under given operating conditions.

Interchangeability, which ensures the performance of products with optimal and stable (within specified limits) performance indicators over time or with optimal performance quality of functioning for assembly units and their interchangeability according to these indicators are called functional.

Functional are geometric, electrical, mechanical and other parameters that affect the performance of machines and other products or the service functions of assembly units. For example, the engine power (operational parameter) depends on the gap between the piston and the cylinder (functional parameter).

Classification of sizes according to purpose and type of parts being connected.

During design, linear and angular dimensions details characterizing its size and shape. They are assigned based on the results of calculations of parts for strength and rigidity, as well as on the basis of ensuring the manufacturability of the design and other indicators in accordance with the functional purpose of the part. The drawing must contain all the dimensions necessary for the manufacture of the part and its control.

Dimensions that directly or indirectly affect the performance of a machine or the service functions of components and parts are called functional. They can be on both mating (for example, at the shaft and hole) and non-mating surfaces (for example, the size of the turbine blade blade, the dimensions of the carburetor jet channels, etc.)

Parameter -This is an independent or interrelated quantity that characterizes any product or phenomenon (process) as a whole or their individual properties. Parameters define technical characteristics product or process primarily in terms of performance, basic dimensions, design.

Size -this is the numerical value of a linear quantity (diameter, length, etc.) in the selected units of measurement. Dimensions are divided into nominal, actual and limiting.

Nominal- this is the size relative to which the maximum dimensions are determined and which also serves as the starting point for measuring deviations. The nominal size is the main size obtained on the basis of kinematic, dynamic and strength calculations or selected from structural, technological, operational, aesthetic and other considerations.

Valid - This is the size established by measurement with permissible error.

Limit -these are two maximum permissible sizes, between which the actual size must be or can be equal to.

Limit dimensions at prescribed length shall be interpreted as follows:

for holes the diameter of the largest regular imaginary cylinder that can be inscribed in the hole so as to be in close contact with the most protruding points of the surface (the size of the mating part of an ideal geometric shape adjacent to the hole without clearance) must not be less than the through size limit. Additionally largest diameter at any point in the opening shall not exceed the no-pass size limit;

for shafts -The diameter of the smallest regular imaginary cylinder that can be circumscribed around the shaft so as to make close contact with the most prominent points of the surface (the size of the mating part of an ideal geometric shape adjacent to the shaft without clearance) should not be greater than the through size limit. Additionally, the minimum diameter at any location on the shaft must not be less than the no-go size limit.

Largest size limit - is the larger of the two extremes, least- this is the smaller of the two maximum sizes (Fig. 2.1).GOST 25346-89 establishes new terms associated with maximum sizes - “pass” and “non-pass” limits.

The term " passing limit" apply to whichever of the two limit sizes corresponds to maximum number material, namely the upper limit for the shaft, the lower limit for the hole. In the case of the use of limit gauges, we are talking about the maximum size checked by a pass gauge.

The term " impassable limit"applies to the one of the two limit sizes that corresponds to the minimum amount of material, namely the lower limit for the shaft, the upper limit for the hole. In the case of using limit gauges, we are talking about the limit size checked by a no-go gauge.

Dimensional deviations and tolerances.

Deviation -it is the algebraic difference between the size (real, limit, etc.) and the corresponding nominal size.

Actual deviation - is the algebraic difference between the real and nominal sizes.

Maximum deviation - this is the algebraic difference between the maximum and nominal sizes.

It is advisable to consider the classification of deviations according to geometric parameters using the example of a connection between a shaft and a hole. The term "shaft" is used to designate the external (male) elements of parts, the term "hole" is used to designate internal (male) elements of parts. The terms “shaft” and “hole” refer not only to cylindrical parts with a circular cross-section, but also to elements of parts of other shapes (for example, limited by two parallel planes - a keyed connection).

Limit deviations are divided into upper and lower. Upper - is the algebraic difference between the largest limit and nominal sizes, lower deviation - this is the algebraic difference between the smallest limit and nominal sizes.

Rice. 2.1. Tolerance fields of the hole and shaft when landing with a gap (hole deviations are positive, shaft deviations are negative)

GOST 25346-89 adopted symbols: upper hole deviation ES, shaft - es, lower hole deviation EI, shaft - ei. In the tables of standards, the upper and lower deviations are indicated in micrometers (µm), in the drawings - in millimeters (mm). Deviations equal to zero are not indicated. In Fig. 2.1 provides examples of placing deviations in drawings of parts and connections.

Tolerance- this is the difference between the largest and smallest limit sizes or the absolute value of the algebraic difference between the upper and lower deviations (see Fig. 2.1). According to GOST 25346-89, the concept " system approval" - this is a standard tolerance (any of the tolerances) established by this system of tolerances and fits.

Zero line -this is a line corresponding to the nominal size, from which dimensional deviations are plotted when graphically depicting tolerances and fits. When the zero line is horizontal, positive deviations are laid up from it, and negative deviations are laid down (see Fig. 2.1).

Tolerance field -This is a field limited by the upper and lower deviations. The tolerance field is determined by the size of the tolerance and its position relative to the nominal size. In a graphical representation, the tolerance field is enclosed between two lines corresponding to the upper and lower deviations relative to the zero line (see Fig. 2.1).

To simplify tolerances, you can depict graphically in the form of tolerance fields(Fig. 2.1, b ). In this case, the axis of the product (in Fig. 2.1, b not shown) is always located under the diagram.

Security questions

1. What is interchangeability?
2. What is the size?
3. What sizes are there according to purpose?
4. Nominal, actual and limiting sizes.
5. What deviations are there for sizes?
6. What is a permit?

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

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

True Size– a certain absolute value to which we strive to improve the quality of products.
Actual size– element size established by measurements with permissible error.

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

Nominal size– the size relative to which the maximum dimensions are determined and which also serves as the starting point for measuring deviations. For mating parts, the nominal size is common. It is determined by calculations of strength, stiffness, etc., rounded to highest value taking into account “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, range of measuring, cutting and measuring tools, etc.).

Rows of normal linear dimensions are geometric progressions with a denominator. There are five values ​​in a row. These relationships are preserved 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 subsequent 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 dimensions: two maximum permissible dimensions of an element, between which it must lie, or to which the actual size can be equal.

Largest limit size: the largest allowable size of an element, the nominal is the opposite.

Dmax, Dmin, dmax, dmin

In order to simplify the designation of maximum dimensions, maximum deviations from the nominal size have been introduced in the drawings.

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

Actual deviation is called the algebraic difference between the real and nominal sizes.

Deviation values ​​can be a positive or negative number.

On mechanical engineering drawings, linear, nominal, maximum dimensions, as well as deviations are indicated in millimeters.

Angular dimensions and their maximum deviations are indicated in degrees, minutes, seconds with units indicated.

If the absolute values ​​of the deviations are equal, 42 + 0.2; 120 + 2

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

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

Tolerance is 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 parts in a batch that are considered suitable, i.e., it determines the specified manufacturing accuracy.

Rational tolerance assignment is an important task that combines economic and quality production requirements.

As the tolerance increases, the quality of products, as a rule, deteriorates, but the cost of production falls.

The space on the diagram limited by the lines of upper and lower deviations is called tolerance zone.

A simplified representation of the tolerance fields, in which the hole and shaft patterns none.

Example: Construct a diagram of the location 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.

Indication of deviations in drawings.

dmax = d + es

Associated with the concept of interchangeability is the concept of the suitability of a part. Any real part will be suitable if:

dmin< dr < dmax

ei< er < es

For example: shafts

dr1 = 20.03 – valid

dr2 = 20.05 – correctable defect

dr3 = 20.0 – uncorrectable defect

The concept of planting.

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

Gap is the difference between the sizes of the hole and the shaft, if the hole size larger size shaft

Movable joints are characterized by the presence of gaps.

Preference is 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 connections are usually characterized by the presence of interference.

There are three types of fits: with clearance, interference and temporary.

Transitional landings.

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

Fixed connections.

Transitional landings are calculated at 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.

Surface location deviations.

Deviation of the actual surface location from its smallest location.

Types of location deviations.

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

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

Deviation from alignment – greatest distance(Δ1, Δ2) between the axis of the surface of rotation under consideration and the common axis of rotation.

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

To control alignment, special devices are used.

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

To control alignment, special devices are used:

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

3. Measurement methods and their differences.

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

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

Indirect measurement– the desired value is found from the known relationship between the desired value and quantities determined 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 measurement methods: the method of direct assessment and the method of comparison with a measure.

Direct assessment method– the value of the quantity is determined directly from the reading device of the measuring device.

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

With the direct assessment method (DO), the device is adjusted to zero using the base surface of the device. Under the influence of various factors (changes in temperature, humidity, vibrations, etc.), a shift in zero may 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 from the reading of the device.

L=M+P

Direct assessment method Comparison method

DP>L DP>L-M

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

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

The comparison method is used when measuring and controlling parts in mass and serial production, i.e. 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 a unit, which is somehow embedded in the measuring instrument.

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

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

3. Reduced diameter external thread. Total tolerance of the average thread diameter. Suitability conditions for external threads along the average diameter. An example of indicating the accuracy of a bolt thread in a drawing.

1. Characteristics of the system of tolerances and fits for smooth cylindrical joints: main deviations of shafts and holes and layout diagrams, tolerance range and its designation, preferred tolerance ranges and their location diagrams.

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

3. Classification of gears by functional purpose. Examples of gear accuracy designations.

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

2. Roughness parameter tp. Normalization and examples of designation of surface roughness in a drawing using this parameter.

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

1. Three types of landings in the hole system. Layout diagrams of tolerance fields and examples of designation of fits in the hole system in the drawing.

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

3. Given average internal thread diameter. Total tolerance of the average thread diameter. Suitability conditions for internal threads along the average diameter. An example of a nut's accuracy designation in a drawing.

1. Three types of fits in the shaft system. Layout diagrams of tolerance fields and examples of designation of fits in the shaft system in the drawing.

2. Deviations in the shape of flat surfaces. Their standardization and examples of designation on the drawing of tolerances for the shape of flat surfaces.

3. Standardization of the accuracy of gears and gears. The principle of combining precision levels. Examples of gear accuracy designations.

1. Landings with a gap. Schemes for the location of tolerance fields in the hole system and shaft system. Application of clearance landings and examples of designation in drawings.

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

3. Random measurement errors and their assessment.

1. Preference fit. Schemes for the location of tolerance fields in the hole and shaft system. Application of interference fits and examples of designation in the drawings.

2. height parameters of surface roughness. Standardization and examples of designation of surface roughness in drawings using height parameters.

3. Standardization of accuracy metric thread. Examples of designations on landing drawings threaded connections with a gap.

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

2. Step parameters of surface roughness. Standardization and examples of designation of surface roughness in a drawing using step parameters.

3. Kinematic accuracy of gears and gears, its standardization. An example of a gear precision designation for reference gears.

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

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

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

3. Main deviations of thread diameters for clearance fits and their arrangement diagrams. Examples of designation of metric thread fits in the drawings.

1. Landings with clearance. Schemes for the location of tolerance fields for landings with a gap in the hole system. Show how Smax, Smin, Sm, Ts will change when the tolerances of the parts being connected change by one grade. Examples of designation in drawings of landings with a gap in the hole system.

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

3. Contact of teeth in the gear and its normalization. An example of a gear precision designation for a power transmission.

1. Interference fits, layout diagrams of tolerance fields for interference fits in the hole system. Show how Nmax, Nmin, Nm, TN will change when the tolerances of the parts being connected change by one grade. Examples of designation in drawings of interference fits in a hole system.

2. Surface roughness, the reasons for its occurrence. Standardization of surface roughness and examples of designation in drawings.

3. Selection of measuring instruments.

1. Transitional fits, layout diagrams of tolerance fields for transitional fits in the hole system. Show how Smax, Smin, Sm(Nm), TSN will change when the tolerances of the parts being connected change by one grade. Examples of designation in drawings of transitional fits in a hole system.

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

3. Standardization and designation of external thread accuracy on drawings.

1. Landings with clearance. Layout of tolerance fields for clearance fits in the shaft system. Show how Smax, Smin, Sm, Ts will change when the tolerances of the parts being connected change by one grade. Examples of designation in 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 normalization. An example of the precision designation of a gear for high-speed transmission.

1. Interference fits, layout diagrams of tolerance fields for interference fits in the shaft system. Show how Nmax, Nmin, Nm, TN will change when the tolerances of the parts being connected change by one grade. Examples of designation in drawings of interference fits in the shaft system.

2. Radial and axial runout, their standardization and examples of designation in the drawing.

3. Mathematical processing of observation results. Form for presenting the measurement result.

1. Transitional fits, layout diagrams of tolerance fields for transitional fits in the shaft system. Show how Smax, Smin, Sm(Nm), TSN will change when the tolerances of the parts being connected change by one grade. Examples of designation in drawings of transitional fits 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. Landings 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 the use of these parameters to normalize surface roughness.

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

1. Preference fits and their calculation (selection). Designation of interference fits on the drawings. Application examples of preferred interference fits.

2. Roughness parameter tp and examples of its use for normalizing surface roughness.

3. Types of mating of wheel teeth in transmission. Examples of gear accuracy designations.

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 calibers. Layout of tolerance fields of gauges for hole inspection. Calculation and designation on the drawings of the executive dimensions of plug gauges.

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

2. The concept of interchangeability and its types.

3. Standardization and designation of internal thread accuracy on drawings.

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 rolling bearing landings in the drawings.

3. The concept of control, control by limiting calibers. Layout diagrams of tolerance fields of gauges for shaft inspection. Calculation and designation on the drawings of the as-built dimensions of staple gauges.

1. Layout diagrams of tolerance fields in connections of rolling bearings with the shaft and housing. Examples of designation of rolling bearing landings in the drawings.

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

3. Side clearance in gears and its rationing. Examples of gear accuracy designations.

1. Hole system. Layout of tolerance fields for three types of fits in the hole system. Examples of designation of fits in the hole system in the drawing.

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

3. Diametric compensation for pitch and thread profile angle errors. An example of designating the accuracy of a bolt thread with a make-up length different from normal.

1.Shaft system. Layout of tolerance fields for three types of fits in the shaft system. Examples of designation of fits in the shaft system in the drawings.

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

3. External thread tolerance field and its designation. Limit contours of external threads and validity conditions.

LECTURE No. 2

Methods for normalizing parameters during design.

Standardization stages:

–– selection of nominal value;

–– establishing limit values ​​or maximum deviations

Nominal values – selected based on the requirements for strength, rigidity, kinematic accuracy of the machine, etc.

Limit values – are prescribed to ensure the normal operation of interfaces of 2 or more parts (in dimensional chains).

Standardization methods:

–– research: ensures the correctness and quality of solutions for new problems; very expensive.

–– analogue method: used for trivial tasks. Provides time savings. Based on experience - calculation of fits with clearance, interference, rolling bearings, etc.

On the working drawing of machine parts, the designer puts nominal size - a common size for all connected parts, determined based on strength, rigidity or structural considerations. It serves as the starting point for deviations.

Can a designer make any size nominal?

In accordance with GOST 6636-69 “Normal linear dimensions” it must be rounded to those available in this GOST. Series of normal linear dimensions are geometric progressions. There are four of them, they are designated Ra5, Ra10, Ra20, Ra40.

Ra5	Ra10	Ra20	Ra40
1,6	1,25	1,12	1,06

Preference is given to sizes from the rows with the largest gradation - row 5 is the most preferable.

Reducing the number of sizes leads to a reduction in the standard sizes of cutting and measuring tools, dies, fixtures, and ensures the typification of technological processes.

Actual (true) size - the size that is obtained after manufacturing and measuring the part, part, size with permissible error.

d – nominal size;

d d is the actual size, for the suitability of the part it ranges from d max to d min:

These are the maximum dimensions.

Passing limit – limit size corresponding to the maximum amount of material (d max and D min)

Impassable limit – maximum size corresponding to the minimum amount of material (d min and D max)

Let's simplify the task. We will count the dimensions from one plane.

Limit contours have the shape of a nominal surface (contour) and correspond to the largest d max and smallest d min dimensions of the part.

Limit contour lines of the P.K part

This drawing can be further simplified, because the main task is to ensure the accuracy of the nominal size.

The figure shows that the largest permissible fluctuation in dimensions is characterized by tolerance.

Size tolerance – the difference between the largest and smallest limit sizes (T-Tolerance)

Hole tolerance

Shaft tolerance

The tolerance is always T>0. It determines the permissible size variation of suitable parts in a batch. (manufacturing tolerance)

Size deviation – the difference between the size and the corresponding nominal size (E,e-ecart)

Lower deviation – the difference between the smallest limit and nominal sizes (I,i – inferieur):

Hole shaft

Upper deviation – difference between the largest limit and nominal size (S,s – superieur):

Hole shaft

Lower and upper – maximum deviations.

Actual deviation – algebraic difference between real and nominal sizes:

Hole shaft

Limit dimensions = nominal dimensions + deviation.

Hole

Tolerance field – the zone between the largest and smallest limit sizes, depicted graphically.

Zero line – a line on the tolerance zone diagram corresponding to the nominal size or nominal contour.

We will plot the deviations along the y-axis. These will be the coordinates relative to the zero line of the limit contours. Deviations can have a “+” and “-” sign; the tolerance field relative to the zero line will be located differently. (Example for shaft)

The tolerance value can be determined through deviations:

Tolerance – algebraic difference between the upper and lower deviations (>0)

Deviations can be e>0, e<0, е=0

Schematic representation of tolerance fields.

Tolerance fields are plotted to scale. Tolerance fields are depicted as rectangles. Relative to the zero line, the rectangle is positioned so that the upper side determines the upper deviation, and the lower side determines the lower one. The deviation values ​​with signs are indicated at the vertices of the two right corners of the rectangles (µm). Graphically, the height of the rectangle represents the tolerance value. The length of the rectangle is arbitrary.

Zero line, defines the nominal size (in mm)

In reference books d, D – in mm; deviations es, ei, ES, EJ and tolerances TD, Td in µm, 1 µm = 10 -6 m = 10-3 mm.

Example. Construct a tolerance field and enter deviations, determine the maximum dimensions.

d = 40 mm; EJ = 0; TD = 39 µm (H8); es = -25 µm; Td = 25 µm

Hole

In modern construction, buildings and structures are assembled from individual elements and structures manufactured at the appropriate factories.

When manufacturing prefabricated elements, it is almost impossible to obtain absolutely precisely the dimensions specified for them by design or regulatory documentation, which, moreover, are not the same in different sections of the element and vary from product to product.

The occurrence of deviations from the specified dimensions and shape in the manufacture of steel structures is caused by inaccuracy of equipment, processing devices, as well as cutting tools, inaccuracy in the location of workpieces and their incorrect fastening, non-compliance with processing modes and conditions, and other reasons.

The accuracy of manufacturing reinforced concrete products largely depends on the state of the technological equipment, i.e. curvature of the sides of the molds, deflection of the pallets, wear of the locking hinges, displacement of the clamps of the embedded parts and many other technological factors.

When drawing up a drawing of a steel or reinforced concrete product, the designer establishes, based on working conditions, its geometric dimensions in selected units of measurement. There is a distinction between the actual size Xi and the nominal size Xnom.

The actual size is the size obtained as a result of measurement with an acceptable error.

The nominal size is the main design size, determined based on its functional purpose and serves as the starting point for deviations. Taking into account manufacturing and installation errors, in the drawings, in addition to the nominal (design) size Xnom, two maximum permissible sizes are indicated, the larger of which is called the largest Xmax, and the smaller - the smallest Xmin maximum dimensions. The actual size must be within the maximum permissible sizes, i.e. Xmax ?Xi ?Xmin.

For the successful assembly of buildings and structures, it is necessary that the manufactured steel and reinforced concrete products in size and configuration correspond to the functional purpose, i.e. meet production and operational requirements.

The main characteristics of the configuration of prefabricated elements are straightness, flatness, perpendicularity of adjacent surfaces, and equality of diagonals.

The dimensions, shape, and position of structures, characterized by linear and angular quantities, have received a general name - geometric parameters. The latter, like dimensions, are divided into actual and nominal.

The quality of installation of buildings and structures largely depends on the selected interface design and the achieved accuracy of manufacturing of structural elements. Since issues of precision in manufacturing products are of practical importance for prefabricated construction, it is necessary to manufacture prefabricated elements with such geometric accuracy that will ensure the designed nature of the connections and assembly of structures without additional adjustment of the elements. This assumes that the assembled elements will be interchangeable across product brands.

Under interchangeability in the system for ensuring geometric accuracy in construction, they understand the property of independently manufactured elements of the same type to ensure the possibility of using them one instead of another without additional processing. The interchangeability of elements of the same type is achieved by complying with uniform requirements for their geometric accuracy.

Interchangeable prefabricated elements can be manufactured strictly according to drawings independently of each other at different times and in different factories, but they must be the same (within tolerance) in size, shape and physical and mechanical properties.

The principle of interchangeability of elements predetermines the assembleability of structures, i.e. the property of independently manufactured elements to provide the ability to assemble from them structures of buildings and structures with geometric accuracy that meets the operational requirements for the structure.

Interchangeability in standard construction is the main and necessary condition for modern mass and serial production. The interchangeability of prefabricated elements is ensured by the accuracy of their parameters, in particular their dimensions.