Calculation of dependent dimensional tolerances that determine the location of the axes of the holes. Dependent location and shape tolerances Regardless of its view size

Rectangular coordinate system

Continuation of the table. 2.15

Polar coordinate system

Diameter
fixing
details d

It is recommended to selectively control deviations in the form and arrangement of elements with general tolerances to ensure that the usual manufacturing accuracy does not deviate from the originally established one. The deviation of the form and location of the element beyond the general tolerance should not lead to automatic rejection of the part, if the ability of the part to function is not violated.

The location or shape tolerances set for shafts or holes can be dependent and independent.

addicted is called the tolerance of the shape or location, the minimum value of which is indicated in the drawings or technical requirements and which can be exceeded by an amount corresponding to the deviation of the actual size of the part from the passage limit (the largest limit size of the shaft or the smallest limit size of the hole):

T head \u003d T min + T additional,

where T min is the minimum part of the tolerance associated with the allowable clearance in the calculation; T add - an additional part of the tolerance, depending on the actual dimensions of the surfaces under consideration.

Dependent location tolerances are set for parts that are mated with counter-parts simultaneously on two or more surfaces and for which interchangeability requirements are reduced to ensuring assembly, i.e. the possibility of connecting parts on all mating surfaces. Dependent tolerances are associated with gaps between mating surfaces, and their maximum deviations must be in accordance with the smallest limit size of the enclosing surface (holes) and the largest limit size of the covered surface (shafts). Dependent tolerances are usually controlled by complex gauges, which are prototypes of mating parts. These calibers are always through, which guarantees a fit-free assembly of products.

Example. Figure 24 shows a part with holes different sizesÆ20 +0.1 and Æ30 +0.2 with alignment tolerance T min = 0.1 mm. The additional part of the tolerance is determined by the expression T add \u003d D1 action - D1 min + D2 action - D2 min.

At the largest values ​​of the actual dimensions of the holes T add max \u003d 30.2–30 + 20.1 -20 \u003d 0.3. In this case, T head max \u003d 0.1 + 0.3 \u003d 0.4.

Figure 24 - Dependent hole alignment tolerance

Independent called the tolerance of the location (shape), the numerical value of which is constant for the entire set of parts manufactured according to this drawing, and does not depend on the surfaces. For example, when it is necessary to maintain the alignment of the seats for rolling bearings, to limit the fluctuation of the center distances in the gearbox housings, etc., the actual location of the axes of the surfaces should be controlled.

End of work -

This topic belongs to:

Metrology

The concept of metrology as a science metrology is the science of measurements, methods and .. basic concepts related to measurement objects ..

If you need additional material on this topic, or you did not find what you were looking for, we recommend using the search in our database of works:

What will we do with the received material:

If this material turned out to be useful for you, you can save it to your page on social networks:

All topics in this section:

The concept of metrology as a science
Metrology is the science of measurements, methods and means of ensuring their unity and ways to achieve the required accuracy. In practical life, a person

The concept of measuring instruments
A measuring instrument (MI) is a technical tool (or a set of technical means) intended for measurement, having a normalized metrological character

Metrological characteristics of measuring instruments
Metrological characteristics of measuring instruments are characteristics of properties that affect the results and measurement errors. Appointment information meter

Factors affecting measurement results
In metrological practice, when carrying out measurements, it is necessary to take into account a number of factors that affect the measurement results. This is the object and subject of measurement, the method of measurement, cf.

Methods for measuring physical quantities
Measurement methods are determined by the type of measured quantities, their dimensions, the required accuracy of the result, the required speed of the measurement process, and other data. There is m

Formation of the measurement result. Measurement errors
The measurement procedure consists of the following main stages: 1) acceptance of the object measurement model; 2) choice of measurement method; 3) choice of measuring instruments;

Presentation of measurement results
There is a rule: measurement results are rounded up to the nearest "error". In practical metrology, rules for rounding off results and measurement errors have been developed. os

Causes of measurement errors
There are a number of error terms that dominate the total measurement error. These include: 1) Errors depending on the means of measurement. But

Handling multiple measurements
We assume that the measurements are equal, i.e. performed by one experimenter, under the same conditions, with one device. The technique boils down to the following: n observations are made (one

Student's distribution (t-test)
n/α 0.40 0.25 0.10 0.05 0.025 0.01 0.005 0.0005

Measurement techniques
The main loss of accuracy in measurements occurs not due to a possible metrological malfunction of the measuring instruments used, but primarily due to the imperfection of the method.

The concept of metrological support
Metrological support (MO) is understood as the establishment and application of scientific and organizational foundations, technical means, rules and norms, necessary

System approach in the development of metrological support
When developing MO, it is necessary to use a systematic approach, the essence of which is to consider MO as a set of interrelated processes united by one goal - achieved

Basics of metrological support
Metrological support has four bases: scientific, organizational, regulatory and technical. Their content is shown in Figure 1. Individual aspects of MO are considered in the recommendation

Legislation of the Russian Federation on ensuring the uniformity of measurements
The regulatory framework for ensuring the uniformity of measurements is shown in Figure 2.

National system for ensuring the uniformity of measurements
The National System for Ensuring the Uniformity of Measurements (NSOEI) is a set of rules for performing work to ensure the uniformity of measurements, its participants and rules

The main types of metrological activities to ensure the uniformity of measurements
The unity of measurements is understood as such a state of measurements in which their results are expressed in legal units of quantities and errors (indefinitely

Conformity assessment of measuring instruments
When carrying out measurements related to the sphere of state regulation of ensuring the uniformity of measurements, on the territory of Russia, SI must be used that meet the requirements

Approval of the type of measuring instruments
Type approval (except for SOSSVM) is carried out on the basis of positive test results. Approval of the type of SOSSVM is carried out on the basis of positive results of the atte

Measurement procedures certification
A measurement technique is a set of operations and rules, the implementation of which ensures that a measurement result is obtained with a specified error.

Verification and calibration of measuring instruments
Verification of measuring instruments is a set of operations performed in order to confirm the conformity of the actual values ​​of the metrological characteristics

Structure and functions of the metrological service of an enterprise, organization, institution that is a legal entity
The metrological service of an enterprise, organization and institution enjoying the rights of a legal entity, regardless of the form of ownership (hereinafter - the enterprise) includes a department (service)

The concept of interchangeability
Interchangeability is the property of the same parts, components or assemblies of machines, etc., which allows you to install parts (assemblies, assemblies) during assembly or replacement

Qualities, main deviations, landings
The accuracy of a part is determined by the accuracy of dimensions, the roughness of surfaces, the accuracy of the shape of surfaces, the accuracy of location and the waviness of surfaces. To ensure

Designation of tolerance fields, limit deviations and landings in the drawings
Limit deviations of linear dimensions are indicated on the drawings by conditional (letter) designations of tolerance fields or numerical values ​​​​of limit deviations, as well as letter

Unspecified limit deviations of dimensions
Limit deviations that are not indicated directly after the nominal dimensions, but specified by a general entry in the technical requirements of the drawing, are called unspecified limit deviations.

Recommendations for the use of clearance fits
H5/h4 fit (Smin= 0 and Smax = Td +Td) is assigned to couples with precise centering and direction, in which rotation and longitudinal movement are allowed

Recommendations for the use of transitional landings
Transition fits H / js, H / k, H / m, H / n are used in fixed detachable joints for centering interchangeable parts or parts that, if necessary, can move in

Tips for Using Interference Fits
Landing N/r; Р/h - "lightly pressed" - are characterized by a minimum guaranteed tightness. Installed in the most accurate qualifications (shafts 4 - 6th, holes 5 - 7-

The concept of surface roughness
Surface roughness according to GOST 25142 - 82 is a set of surface irregularities with relatively small steps, selected using the base length. Bazova

Roughness parameters
According to GOST 2789 - 73, the surface roughness of products, regardless of the material and method of manufacture, can be evaluated by the following parameters (Figure 10):

General terms and definitions
The tolerances of the shape and location of the surfaces of machine parts and instruments, terms, definitions related to the main types of deviations are standardized by GOST 24642 ​​- 81. The basis

Form deviations and tolerances
Form deviations include deviations of straightness, flatness, roundness, profile of the longitudinal section and cylindricity. Deviations in the shape of flat surfaces

Deviations and location tolerances
The deviation of the location of the surface or profile is the deviation of the actual location of the surface (profile) from its nominal location. Quantitative location deviations about

Total deviations and tolerances of the shape and location of surfaces
The total deviation of the form and location is the deviation, which is the result of the joint manifestation of the deviation of the form and the deviation of the location of the element in question (according to

Numerical values ​​​​of tolerances of the shape and location of surfaces
According to GOST 24643 - 81, 16 degrees of accuracy are established for each type of tolerance of the shape and location of surfaces. The numerical values ​​​​of tolerances change from one degree to another

Designation in the drawings of shape and location tolerances
The type of tolerance of the shape and location according to GOST 2.308 - 79 should be indicated in the drawing with the signs (graphic symbols) given in table 4. I enter the sign and numerical value of the tolerance

Unspecified shape and location tolerances
Directly in the drawing, as a rule, the most critical tolerances for the shape and location of surfaces are indicated. According to GOST 25069 - 81, all indicators of form accuracy and location

Rules for defining bases
1) If the part has more than two elements for which the same unspecified location or runout tolerances are established, then these tolerances should be attributed to the same base;

Rules for determining the defining size tolerance
The defining tolerance of a size is understood as: 1) When determining an unspecified tolerance of perpendicularity or end runout, the tolerance of a size coordinating

Surface waviness
Surface waviness is understood as a set of periodically repeating irregularities, in which the distances between adjacent hills or depressions exceed the base length l.

Rolling bearing tolerances
The quality of bearings, other things being equal, is determined by: 1) accuracy connecting dimensions and the width of the rings, and for roller angular contact bearings e

Selection of rolling bearing fits
The fit of the rolling bearing on the shaft and in the housing is selected depending on the type and size of the bearing, its operating conditions, the value and nature of the loads acting on it and the type of loading of the rings

Solution
1) With a rotating shaft and a constant force Fr, the inner ring is loaded with circulation loads, and the outer ring with local loads. 2) Load intensity

Bearing symbols
System symbols ball and roller bearings, GOST 3189 - 89 is installed. The symbol of the bearing gives a complete picture of its overall dimensions, designs, manufacturing accuracy

Angular tolerances
Tolerances of angular dimensions are assigned according to GOST 8908 - 81. Tolerances of angles AT (from the English. Angle tolerance - angle tolerance) should be assigned depending on the nominal length L1 of the smaller side

System of tolerances and landings for conical connections
A conical connection has advantages over a cylindrical one: it is possible to adjust the amount of clearance or interference by relative displacement of parts along the axis; with a fixed connection

The main parameters of the metric fastening thread
Cylindrical thread parameters (Figure 36, a): average d2 (D2); outer d (D) and inner d1 (D1) diameters on

General principles of interchangeability of cylindrical threads
Tolerance and fit systems that ensure the interchangeability of metric, trapezoidal, thrust, pipe and other cylindrical threads are built on a single principle: they take into account the presence of mutual

Tolerances and fits of threads with clearance
Tolerances for metric threads with large and small pitches for diameters of 1 - 600 mm are regulated by GOST 16093 - 81. This standard sets the maximum deviations of thread diameters in

Tolerances of threads with interference and with transition fits
The landings in question serve mainly to connect the studs to the body parts, if screw or bolt-nut connections cannot be used. These landings are used in fasteners

Standard threads for general and special applications
Table 9 shows the names of standard general-purpose threads, the most widely used in machine and instrument making, and gives examples of their designation in the drawings. To the most

Kinematic transmission accuracy
To ensure kinematic accuracy, standards are provided that limit the kinematic error of the transmission and the kinematic error of the wheel. kinematic

Transmission smoothness
This transmission characteristic is determined by parameters, the errors of which repeatedly (cyclically) appear per revolution of the gear and also form part of the kinematic error

Gear contact
To increase the wear resistance and durability of gears, it is necessary that the completeness of contact of the mating side surfaces of the gear teeth be the greatest. With incomplete and unequal

Side clearance
To eliminate possible jamming when the transmission is heated, to ensure the conditions for the flow of lubricant and to limit the backlash when reversing the reference and dividing real gears

Designation of wheel and gear accuracy
The accuracy of the manufacture of gears and gears is set by the degree of accuracy, and the requirements for the side clearance are set by the type of conjugation according to the standards of the side clearance. Symbol examples:

The choice of the degree of accuracy and controlled parameters of gears
The degree of accuracy of the wheels and gears is set depending on the requirements for kinematic accuracy, smoothness, transmitted power, as well as peripheral speed of the wheels. When choosing the degree of accuracy

Tolerances for bevel and hypoid gears
The principles of building a tolerance system for bevel gears (GOST 1758 - 81) and hypoid gears (GOST 9368 - 81) are similar to the principles for building a system for spur gears

Tolerances of worm gears
For worm cylindrical gears, GOST 3675 - 81 establishes 12 degrees of accuracy: 1, 2,. . ., 12 (in descending order of accuracy). For worms, worm wheels and worm gears

Tolerances and Fits for Straight-Tooth Joints
According to GOST 1139 - 80, tolerances are established for connections with centering on the inner d and outer D diameters, as well as on the sides of the teeth b. Because the view is centered

Tolerances and fits of splines with involute tooth profile
Nominal dimensions of involute spline connections (Figure 58), nominal dimensions by rollers (Figure 59) and common normal lengths for individual measurements of splined shafts and bushings should

Accuracy control of splines
Spline connections are controlled by complex through gauges (Figure 61) and element-by-element non-through gauges.

A method for calculating dimensional chains that ensures complete interchangeability
To ensure complete interchangeability, dimensional chains are calculated using the maximum-minimum method, in which the tolerance of the closing size is determined by arithmetic addition of the tolerances.

Theoretical and probabilistic method for calculating dimensional chains
When calculating dimensional chains by the maximum-minimum method, it was assumed that during processing or assembly, a simultaneous combination of the largest increasing and smallest decreasing sizes is possible.

Group interchangeability method in selective assembly
The essence of the method of group interchangeability lies in the manufacture of parts with relatively wide technologically feasible tolerances, selected from the relevant standards, grade

Adjustment and fit method
Regulation method. The regulation method is understood as the calculation of dimensional chains, in which the required accuracy of the initial (closing) link is achieved by a deliberate change

Calculation of flat and spatial dimensional chains
Flat and spatial dimensional chains are calculated using the same methods as linear ones. It is only necessary to bring them to the form of linear dimensional chains. This is achieved by designing

Historical foundations for the development of standardization
Man has been engaged in standardization since ancient times. For example, writing is at least 6,000 years old and originated according to the latest finds in Sumer or Egypt.

Legal basis for standardization
The legal basis for standardization in the Russian Federation is established by The federal law"On technical regulation" of December 27, 2002. It is mandatory for all state

Principles of technical regulation
Currently installed following principles: 1) the application of uniform rules for establishing requirements for products or for related design processes (including surveys), production

Objectives of technical regulations
The Law on Technical Regulation establishes a new document – ​​the technical regulation. Technical regulation - a document that is adopted by an international treaty of Russia

Types of technical regulations
IN Russian Federation two types of technical regulations are applied: - general technical regulations; - special technical regulations. General technical regulations ra

The concept of standardization
The content of standardization terms has come a long evolutionary path. The clarification of this term took place in parallel with the development of standardization itself and reflected the level of its development on the p

Goals of standardization
Standardization is carried out in order to: 1) Increase the level of security: - life and health of citizens; - property of individuals and legal entities; - state

Object, aspect and area of ​​standardization. Levels of standardization
The object of standardization is a specific product, service, production process (work), or groups of homogeneous products, services, processes for which requirements are being developed.

Principles and functions of standardization
The main principles of standardization in the Russian Federation, which ensure the achievement of the goals and objectives of its development, are: 1) the voluntary application of documents in the field of standardization

International standardization
International standardization (IS) is an activity in which two or more sovereign states take part. MS has a prominent role in deepening world economic cooperation, in m

A set of standards of the national standardization system
For the implementation of the Federal Law "On Technical Regulation" since 2005, 9 national standards complex “Standardization of the Russian Federation”, which replaced the complex “ State system standardization". This

The structure of standardization bodies and services
The national body for standardization is the Federal Agency for Technical Regulation and Metrology (Rostekhregulirovanie), which replaced the State Standard. It obeys directly

Normative documents on standardization
Regulations on standardization (ND) - documents containing rules, general principles for the object of standardization and are available to a wide range of users. ND includes: 1)

Categories of standards. Standard designations
Standardization categories are distinguished by the level at which standards are accepted and approved. Four categories are established: 1) international; 2) intergo

Types of standards
Depending on the object and aspect of standardization, GOST R 1.0 establishes the following types of standards: 1) fundamental standards; 2) product standards;

State control over compliance with the requirements of technical regulations and standards
State control is exercised officials the state control body of the Russian Federation for compliance with the requirements of TR regarding the stage of product circulation. Bodies of state control of the region

Organization Standards (STO)
The organization and procedure for the development of SRT is contained in GOST R 1.4 - 2004. Organization - a group of employees and the necessary funds with the distribution of responsibilities of authority and mutual

The need for preferred numbers (P.N.)
The introduction of the IF is caused by the following considerations. The use of the inverter allows the best way to coordinate the parameters and dimensions of a single product with all related

Series based on arithmetic progression
Most often, the IF series are built on the basis of a geometric progression, less often on the basis of an arithmetic progression. In addition, there are varieties of rows built on the basis of the "golden"

Series based on geometric progression
The long practice of standardization has shown that the most convenient are the series built on the basis of a geometric progression, since this results in the same relative difference between

Properties of series of preferred numbers
IF series have the properties of a geometric progression. The IF series are not limited in both directions, while numbers less than 1.0 and more than 10 are obtained by dividing or multiplying by 10, 100, etc.

Limited, sample, composite and approximate series
Limited rows. If it is necessary to limit the main and additional series, their designations indicate the limit members, which are always included in the limited series. Example. R10(

The concept and types of unification
During unification, a minimum allowable but sufficient number of types, types, standard sizes, products, assembly units and parts with high quality indicators is established.

Unification level indicators
The level of unification of products is understood as their saturation with unified constituent elements; parts, modules, nodes. The main quantitative indicators of the level of product unification

Determination of the indicator of the level of unification
The assessment of the level of unification is based on the correction of the following formula:

History of certification development
"Certificate" in Latin means "done right". Although the term "certification" has become known in Everyday life and commercial practice

Terms and definitions in the field of conformity assessment
Conformity assessment - direct or indirect determination of compliance with the requirements for an object. A typical example of activity for assessing

Goals, principles and objects of conformity assessment
Conformity assessment is carried out in order to: - certify the conformity of products, design processes (including surveys), production, construction, installation

The role of certification in improving product quality
Radically improving the quality of products in modern conditions is one of the key economic and political tasks. That is why the set of the same

Product certification schemes for compliance with the requirements of technical regulations
Certification scheme - a certain set of actions, officially accepted as evidence of product compliance with specified requirements.

Schemes for declaring conformity for compliance with the requirements of technical regulations
Table 17 - Schemes for declaring conformity for compliance with the requirements of technical regulations Designation of the scheme Content of the scheme and its use

Service certification schemes
Table 18 - Service certification schemes Scheme No. Assessment of the quality of services provided Verification (testing) of the results of services

Compliance Schemes
Table 19 - Product certification schemes Scheme number Tests in accredited testing laboratories and other methods of proof

Mandatory confirmation of compliance
Mandatory confirmation of conformity can be carried out only in cases established by technical regulations and solely for compliance with their requirements. Wherein

Declaration of Conformity
The Federal Law "On Technical Regulation" sets out the conditions under which a declaration of conformity can be adopted. First of all, this form of confirmation of conformity d

Mandatory certification
Mandatory certification in accordance with the Federal Law "On Technical Regulation" is carried out by an accredited certification body on the basis of an agreement with the applicant.

Voluntary confirmation of compliance
Voluntary confirmation of conformity should be carried out only in the form of voluntary certification. Voluntary certification is carried out at the initiative of the applicant on the basis of an agreement

Certification systems
A certification system is understood as a set of certification participants operating in a certain area according to the rules defined in the system. The concept of "certification system" in

Certification procedure
Certification of products passes through the following main stages: 1) Submission of an application for certification; 2) Consideration and adoption of a decision on the application; 3) Selection, id

Certification Bodies
Certification Body - entity or individual entrepreneur accredited in in due course to carry out certification work.

Test laboratories
Testing laboratory - a laboratory that conducts tests ( certain types tests) of certain products. During the ser

Accreditation of certification bodies and testing laboratories
According to the definition given in the Federal Law "On Technical Regulation", accreditation is "the official recognition by the accreditation body of the competence of a physical

Service certification
Certification is carried out by accredited service certification bodies within their scope of accreditation. Certification examines the characteristics of services and uses methods

Quality systems certification
IN last years There is a rapidly growing number of companies worldwide that have certified their quality systems to the ISO 9000 series of standards.

Deviations in the arrangement of surfaces and coordinating dimensions, as well as deviations in dimensions (diameters, widths, etc.) can appear both jointly and independently of each other. Their mutual influence is possible both in the manufacturing process and in the control process. Therefore, it is customary to consider independent and dependent tolerances for the location of surfaces and coordinating dimensions.

independent admission- the tolerance of the relative position or shape, the numerical value of which is constant and does not depend on the actual dimensions of the surfaces or profiles under consideration.

Dependent location or shape tolerance- this is a variable tolerance, the minimum value of which is indicated in the drawing or technical requirements and which can be exceeded by an amount corresponding to the deviation of the actual size of the surface of the part from the maximum material limit (the largest shaft size limit or the smallest hole size limit). To indicate the dependent tolerance, after its numerical value in the frame, write the letter M in a circle à.

According to GOST R 50056-92, the concepts are established - the minimum and maximum value of the dependent tolerance.

Minimum Dependent Tolerance- the numerical value of the dependent tolerance, when the considered (normalized) element and (or) the base have dimensions, equal to the limit material maximum.

The minimum dependent tolerance value can be zero. In this case, location deviations are allowed within the element size tolerance field. With a dependent position tolerance of zero, the size tolerance is the sum of the size and position tolerances.

Maximum Dependent Tolerance- the numerical value of the dependent tolerance, when the considered element and (or) the base have dimensions equal to the limit of the minimum material.

Dependent tolerances are assigned only to elements (their axes or symmetry planes) that are holes or shafts.

The following dependent shape tolerances exist:

- tolerance of straightness of the axis of the cylindrical surface;

– flatness tolerance of the surface of symmetry of flat elements.

Dependent tolerances of relative position:

- tolerance of perpendicularity of the axis or plane of symmetry relative to the plane or axis;

– tolerance of the inclination of the axis or plane of symmetry relative to the plane or axis;

- alignment tolerance;

– symmetry tolerance;

- tolerance of the intersection of the axes;

- positional tolerance of the axis or plane of symmetry.

Dependent tolerances of coordinating dimensions:

- tolerance of the distance between the plane and the axis or the plane of symmetry;

- distance tolerance between the axes (planes of symmetry) of two elements.

Dependent location tolerances are assigned mainly in cases where it is necessary to ensure the assembly of parts mating simultaneously on several surfaces with specified gaps or interferences. The use of dependent shape and location tolerances reduces the cost of manufacturing and simplifies product acceptance.

The numerical value of the dependent tolerance can be related to:

1) with the actual dimensions of the element in question;

2) with the actual dimensions of the base element;

3) with the actual dimensions of both the base and the considered elements.

When designating a dependent tolerance in the drawings in accordance with GOST 2.308-79, the icon à is used.

If the dependent tolerance is related to the actual size of the element in question, symbol is indicated after the numerical value of the tolerance.

If the dependent tolerance is related to the actual size of the base element, the symbol is indicated after letter designation bases.

If the dependent tolerance is related to the actual size of the element under consideration and the dimensions of the base element, then the à sign is indicated twice after the numerical value of the tolerance and after the letter designation of the base.

Dependent tolerances are usually controlled by complex gauges, which are prototypes of mating parts. These calibers are only pass-through and guarantee a fit-free assembly of products. Complex calibers are quite complex and expensive to manufacture, so the use of a dependent tolerance is advisable only in serial and mass production.

The standards establish two types of location tolerances: dependent and independent.

dependent tolerance has a variable value and depends on the actual dimensions of the base and considered elements. Dependent tolerance is more technologically advanced.

Dependent may be the following tolerances for the location of surfaces: positional tolerances, tolerances for coaxiality, symmetry, perpendicularity, intersection of axes.

Shape tolerances can be dependent: axis straightness tolerance and flatness tolerance for the symmetry plane.

Dependent tolerances must be indicated by a symbol or specified in text in the technical requirements.

independent admission has a constant numerical value for all parts and does not depend on their actual dimensions.

The tolerance of parallelism and inclination can only be independent.

If there are no special symbols on the drawing, the tolerances are understood as independent. For independent tolerances, a symbol may be used, although it is not required.

Independent tolerances are used for critical connections when their value is determined by the functional purpose of the part.

Independent tolerances are also used in small-scale and single-piece production, and their control is carried out by universal measuring instruments (see table 3.13).

Dependent tolerances are set for parts that are mated simultaneously on two or more surfaces, for which interchangeability is reduced to ensuring assembly on all mating surfaces (connection of flanges with bolts).

Dependent tolerances are used in connections with a guaranteed clearance in large-scale and mass production, their control is carried out by location gauges. The drawing indicates the minimum tolerance value (Tr min), which corresponds to the passage limit (the smallest hole size limit or the largest shaft size limit). The actual value of the dependent location tolerance is determined by the actual dimensions of the parts to be joined, i.e., it may be different in different assemblies. For sliding fit connections, Tp min = 0. The total value of the dependent tolerance is determined by adding an additional value to Tr min T add, depending on the actual dimensions of this part (GOST R 50056):

Tp head \u003d Tr min + T add.

Examples of calculating the tolerance expansion value for typical cases are given in Table 3.14. This table also gives formulas for converting location tolerances to positional tolerances when designing location gauges (GOST 16085).

The location of the axes of holes for fasteners (bolts, screws, studs, rivets) can be specified in two ways:

Coordinate, when limit deviations ± δL of coordinating dimensions are given;

Positional, when positional tolerances are set in diametric terms - Tr.

Table 3.13 - Conditions for choosing a dependent location tolerance

Recalculation of tolerances from one method to another is carried out according to the formulas of Table 3.15 for a system of rectangular and polar coordinates.

The coordinate method is used in single, small-scale production, for unspecified location tolerances, and also in cases where fitting of parts is required, if different tolerance values ​​\u200b\u200bare given in coordinate directions, if the number of elements in one group is less than three.

The positional method is more technologically advanced and is used in large-scale and mass production. Positional tolerances are most commonly used to specify the location of the axes of holes for fasteners. In this case, the coordinating dimensions are indicated only nominal values ​​in square frames, since the concept of "general tolerance" does not apply to these dimensions.

The numerical values ​​of positional tolerances do not have degrees of accuracy and are determined from the base series of numerical values ​​according to GOST 24643. The base series consists of the following numbers: 0.1; 0.12; 0.16; 0.2; 0.25; 0.4; 0.5; 0.6; 0.8 µm, these values ​​can be increased by 10 ÷ 10 5 times.

The numerical value of the positional tolerance depends on the type of connection BUT(bolted, two through holes in the flanges) or IN(connection with studs, i.e., a gap in one part). According to the known diameter of the fastener, a row of holes is determined from table 3.16, their diameter ( D) and minimum clearance ( S min).

Table 3.14 - Recalculation of surface location tolerances for positional tolerances

Surface Location Tolerance	Sketch	Formulas for determining positional tolerance	Maximum tolerance expansion Tdop
Tolerance of coaxiality (symmetry) relative to the axis of the base surface		For the base T P = 0 For con T rollable surface T And T P = T FROM	T add = Td 1 T add = Td 2
Tolerance of alignment (symmetry) relative to a common axis		T P1 = T C1 T P2 = T C2	T add = Td 1 + Td 2
Tolerance of coaxiality (symmetry) of two surfaces Base not specified		T P1 = T P2 =	T add = TD 1 + TD 2
Tolerance of perpendicularity of the surface axis relative to the plane		T P = T	T add = TD

On the drawing of the part, the value of the positional tolerance is indicated (see table 3.7), resolving the issue of its dependence. For through holes, the tolerance is assigned dependent, and for threaded holes, it is independent, so it expands.

For connection type (A) T pos = S p , for connections of type ( IN) for through holes T pos = 0.4 S p , and for threaded T pos =(0.5÷0.6) S p (Figure 3.4).

1, 2 - connected parts

Figure 3.4 - Types of connection of parts using fasteners:

but- type A, with bolts; b– type B, studs, pins

Estimated gap S p, necessary to compensate for the error in the location of the holes, is determined by the formula:

S p= S min ,

where coefficient TO using a gap to compensate for deviations in the location of the axes of holes and bolts. It can take the following values:

K = 1 - in joints without adjustment under normal assembly conditions;

K = 0.8 - in connections with adjustment, as well as in connections without adjustment, but with recessed and countersunk screw heads;

K = 0.6 - in joints with adjustment of the arrangement of parts during assembly;

K = 0 - for the basic element, made on a sliding fit (H / h), when the nominal positional tolerance of this element is zero.

If a positional tolerance is negotiated at a certain distance from the surface of the part, then it is specified as a protruding tolerance and is indicated by the symbol ( R). For example: the center of the drill, the end of the stud screwed into the body.

Table 3.15 - Recalculation of the maximum deviations of dimensions coordinating the axes of the holes for positional tolerances in accordance with GOST 14140

Location type	Sketch	Formulas for determining positional tolerance (in diametric terms)
Rectangular coordinate system
I	One hole specified from the assembly base	T p = 2δ L δ L= ±0.5 T R T add = TD
II	Two holes are coordinated with respect to each other (no assembly base)	T p = δ L δ L = ± T R T add = TD
III	Three or more holes arranged in one row (no assembly base)	T p = 1.4δ L δ L=± 0.7 T R T add = TD δ L y=±0.35 T p(δ L y - about T declension about T wear T reference axis) δ L forest = δ L∑∕2 (ladder) δ L cep = δ L∑ ∕(n–1) (chain) δ L∑ is the largest distance T oyanie between the axes of adjacent T vers T uy
IV	Two or more holes are arranged in one row (specified from the assembly base)	T add = TD T p = 2.8δ L 1 = 2.8 δ L 2 δ L 1 = δ L 2 = ± 0.35 T p(o T axis deviation T common plane T and - A or assembly base)
VVI	Holes arranged in two rows (no assembly base) Holes coordinated with respect to two assembly bases	T p 1.4δ L 1 1.4 δ L 2 δ L 1 = δ L 2 = ± 0.7 T R T p = δ L d δ L d = ± T T add = TD δ L 1 = δ L 2 = δ L T p 2.8 δ L δ L= ± 0.35 T R
VII	Holes arranged in several rows (no assembly base)	δ L 1 = δ L 2 = … δ L T p 2.8 δ L δ L= ± 0.35 T R T p = δ L d δ L d = ± T p (size is set to the diagonal) T add = TD
Polar coordinate system
VIII	Two holes coordinated with respect to the axis of the central element	T p = 2.8 δR δR = ± 0.35 T T s) T add = TD
IX X	Three or more holes arranged in a circle (no assembly base) Three or more holes are arranged in a circle, the central element is the assembly base	T add = TD T p = 1.4 δα δα = ± 0.7 Tр δα = ± 3400 (angular min T s) δα 1 = δα 2 = T add = TD + TD bases

Table 3.16 - Diameters of through holes for fasteners and their corresponding guaranteed clearances in accordance with GOST 11284, mm

3.4 General tolerances for shape and surface arrangement

From 01/01/2004, unspecified tolerances for the shape and location of surfaces must be specified in accordance with GOST 30893.2-02 “ONV. General tolerances. Shape tolerances and surface arrangement not specified individually. Previously, GOST 25069 was in effect, which has been cancelled.

The general roundness and cylindricity tolerances are equal to the diameter tolerance, but must not exceed the diameter tolerances and the total radial runout tolerance. For particular types of shape deviations (ovality, cone-shape, barrel-shape, saddle-shape), the general tolerances are considered equal to the radius tolerance, i.e. 0.5 Td (TD).

The general tolerances for parallelism, perpendicularity, inclination are equal to the total tolerance for flatness or straightness. The base surface is treated as contiguous and its shape error is not taken into account.

Unspecified tolerances for the location of surfaces refer to non-critical surfaces of machine parts and are not specifically specified in the drawings, but must be provided technologically (processing from one installation, from one base, one tool, etc.).

Unspecified location tolerances can be conditionally divided into three groups:

The first is indicators, deviations of which are allowed within the entire tolerance field of the size of the element under consideration or the size between the elements (see table 3.17);

Table 3.17 - Calculation of the location tolerance, limited by the size tolerance field

Location tolerance type	Sketch	Size tolerance	Location tolerance
Tolerance of parallelism of planes, axes and plane		T h T h = h max- h min T h1 on L M T h2 on L B L M - shorter length L B - long length	T h = T r full length L TT p = T h1 + T h2
Tolerance of parallelism of the axes of the holes at equal length		L M= L B T h1 = T h2 T h3	T p = T h1 + T h2 T p = T h3
Alignment tolerance (size tolerance is set in one coordinate plane)		T h Remote location T h - for a common axis. Adjacent location	T p = T p = T h
Alignment tolerance when the axis location is given in two coordinate directions		T hx and T hu T hx and T hu	T p = × × T p=
Symmetry tolerance relative to a common plane of symmetry		T h	T p = For two elements T ov T p = T h For one element
Tolerance of symmetry of one element relative to another		T h	T p = T h
Tolerance of intersection of axes in one plane		T h	T p = T h

The second - indicators, the deviations of which are not limited by the size tolerance field and are not part of it, they were covered by the GOST 25069 tables, and now GOST 30893.2-2002;

Third - the indicators of these parameters are indirectly limited by tolerances of other sizes (limiting deviations of center distances with a positional system for setting the axes of the holes, tilt tolerance and angle tolerance in linear terms).

The choice of the type of tolerance is determined by the structural shape of the part. The choice of the base surface is made as follows:

Unspecified tolerances must be determined from previously selected bases for the specified location or runout tolerances of the same name;

If the base is not previously selected, then the longest surface is taken as the base surface, which ensures reliable installation of the part during measurement (for example, for alignment tolerance, the base will be a shaft step of a greater length, and with the same lengths and qualifications - a surface of large diameter).

The values ​​​​of the general tolerances of the shape and location (orientation) are set for three classes of accuracy, which characterize various conditions for normal production accuracy, achieved without the use of additional processing of increased accuracy (table 3.18).

The class designations for general location tolerances have been established by the standard as follows: H - exact, K - medium, L - rough. The choice of accuracy class is carried out taking into account the functional requirements for the part and the possibilities of production.

Table 3.18 - General tolerances for the shape and location of surfaces in accordance with GOST 30893.2

GOST 30893.2 - K;

General tolerances GOST 30893.2 - mK;

GOST 30893.2 - mK.

In the last two examples, the general tolerance of the average accuracy class t for linear and angular dimensions according to GOST 30893.1, as well as the average class for general tolerances of shape and location - K.

It is recommended to selectively control deviations in the form and arrangement of elements with general tolerances to ensure that the usual manufacturing accuracy does not deviate from the originally established one. The deviation of the form and location of the element beyond the general tolerance should not lead to automatic rejection of the part, if the ability of the part to function is not violated.

4 Rationing the accuracy of keyed and splined connections

4.1 Keyed connections

4.1.1 Purpose of keyed connections and their design

Keyed connections are designed to obtain detachable connections that transmit torques. They ensure the rotation of gears, pulleys and other parts mounted on shafts along transitional fits, in which, along with interference, there may be gaps. Keyway sizes are standardized.

There are key connections with prismatic (GOST 23360), segmented (GOST 24071), wedge (GOST 24068) and tangential (GOST 24069) keys. Key connections (Figures 4.1 and 4.2) with feather keys are used in lightly loaded low-speed gears (kinematic feed chains of machine tools), in large-sized products (forging and pressing equipment, flywheels of internal combustion engines, centrifuges, etc.). V-keys and tangential keys take axial loads when reversing in heavily loaded joints. The most widely used are feather keys.

Figure 4.1 - Keyed connection

Parallel keys have three versions (figure 4.3). The type of key design determines the shape of the groove on the shaft (Figure 4.4). Execution 1 - for a closed groove, for normal connection in the conditions of serial and mass types of production; execution 2 - for an open groove with control keys, when the sleeve moves along the shaft when free connection; execution 3 - for a semi-open groove with keys mounted on the end of the shaft with tight connection, pressed bushing on the shaft, in single and small-scale production types. The key size depends on the nominal size of the shaft diameter and is determined according to GOST 23360 (see table 4.1).

Figure 4.2 - Cross section of the key and grooves:

but - key section; b– section of grooves ( r- corresponds to maximum value)

a B C)

Figure 4.3 - Types of keys:

but– execution 1; b– execution 2; in– version 3

a B C)

Figure 4.4 - Forms of grooves on the shafts:

but- closed; b– open; in– semi-open

Table 4.1 - Dimensions of connections with parallel keys according to GOST 23360 (limited), mm

Examples of key symbols:

1) Key 16 × 10 × 50 GOST 23360 (prismatic key, version 1; b× h = 16 × 10, key length l = 50).

2) Key 2 (3) 18 × 11 × 100 GOST 23360 (prismatic key,
version 2 (or 3), b × h = 18 × 11, key length l = 100).

Key seat size is key width b. According to this size, the key mates with two grooves: a groove on the shaft and a groove in the sleeve.

The keys are usually connected to the grooves of the shafts motionlessly, but with the grooves; bushing - with a gap. Preload is necessary so that the keys do not move during operation, and the gap is necessary to compensate for inaccuracies in the dimensions and relative position of the grooves. Keys, regardless of fit, are made in size b with tolerance h 9, which makes it possible to manufacture them centrally. Other dimensions are less important: key height h- on h 11, key length l- on h 14, the length of the groove for the key L - according to H 15.

The layouts of tolerance fields for connections with parallel and segmented keys are shown in Figure 4.5.

a B C)

Figure 4.5 - Schemes of the location of the tolerance fields for the size b of the key connection:

but- free; b– normal; in- dense; - key tolerance; - shaft groove tolerance; – bushing slot tolerance

The key landings are carried out according to the shaft system ( CH). The standard allows various combinations of tolerance fields for grooves on the shaft and in the sleeve with a key width tolerance field.

The most common is the normal connection, when the sleeve (gear) is located in the middle of the shaft.

Loose coupling is used for guide keys (the gear wheel moves along the shaft).

A tight connection is used in the case of reverse rotation of the shaft or when the key is located on the end of the shaft.

4.1.3. Requirements for the design of keyed connections

Limit deviations of dimensions for the selected tolerance fields should be determined according to the tables of GOST 25347 or according to tables 1.1, 1.2 and 1.3 of this manual. Examples of the design of the key connection on the assembly drawing, the cross sections of the shaft and bushing involved in the connection with the feather key are shown in Figures 4.6 and 4.7.

1 - bushing; 2 - key; 3 - shaft

Figure 4.6 - Making a keyed connection:

but– complete cross-section; b- section of the key

When performing a cross section of a keyed connection, it is necessary to indicate the fit, and for the key, the tolerance fields for dimensions b And h dowels in mixed form and surface roughness. On the drawings of the cross sections of the shaft and bushing, it is necessary to indicate the surface roughness, the tolerance fields for dimensions b, d and D in mixed form, and the dimensions of the depth of the grooves should also be normalized: on the shaft t 1 - the preferred option or (d - t 1) with a negative deviation and in the sleeve (d + t 2) - the preferred option or b with a positive deviation. In both cases, the deviations are selected depending on the height of the key h(see table 4.1). In addition, in the drawings of the cross sections of the shaft and bushing, it is necessary to limit the accuracy of the shape and relative position of the surfaces with tolerances. Requirements are made for tolerances from the symmetry of the keyways and the parallelism of the plane of symmetry of the groove relative to the axis of the part (base). Parallelism tolerance should be taken equal to 0.5 IT 9, symmetry tolerance in the presence of one key in the connection - 2 IT 9, and with two keys located diametrically, - 0.5 IT 9 from the nominal size b of the key. Symmetry tolerances can be dependent in high-volume and mass production.

Figure 4.7 - Cross sections:

but- shaft, keyway execution 2; b- bushings

4.2 Spline connections

4.2.1 Purpose, brief description and classification of spline connections

Spline joints are designed to transmit high torques, they have high fatigue strength, high centering and guiding accuracy. This is achieved high precision the size of the shape and arrangement of the teeth (splines) around the circumference.

Depending on the profile of the teeth, splines are divided into straight-sided, involute and triangular. The most widely used are spline joints with a straight-sided tooth profile (Figure 4.8), which have even number teeth (6, 8, 10, 16, 20). Straight-sided spline connections are made in accordance with GOST 1139, which sets three gradations of the height of the number of teeth for the same diameter. In accordance with this, the compounds are divided into light, medium and heavy series (table 4.3). The choice of series depends on the magnitude of the transmitted load.

Figure 4.8 - The main elements of a spline connection with a straight-sided tooth profile: a - section of the sleeve; b - shaft section

Spline joints with involute tooth profile (GOST 6033) are standardized for modules m = 0.5...10 mm, for diameters 4...500 mm and number of teeth z= 6.. .82. Tooth profile angle α =30°.

Spline joints with an involute tooth profile, compared to straight-sided ones, transmit high torques, have a lower (by 10...40%) stress concentration at the base of the teeth, increased cyclic strength and durability, provide better centering and guidance of parts, are easy to manufacture, so how they can be milled by running. Spline connections with an involute tooth profile are widely used in the automotive industry. Designation example when centering on the sides of the teeth: 50×2×9 H/9g GOST 6033 indicates that the nominal diameter is 50 mm, module m = 2 mm, fit on the sides of the teeth 9 H/9g.

V-profile splines are not standardized, they have fine teeth. The profile angle is characterized by the angle of the cavity on the shaft 2β. The main parameters of connections of this type are: t = 0.3 ... 0.8 mm; z = 15...70; 2β = 90° or 72°.

V-profile splines are most often used in place of interference fits when the latter are undesirable, as well as for thin-walled bushings for low torque transmission.

Table 4.3 - Main dimensions according to GOST 1139 of straight-sided splines, mm

Recommended related articles

Construction on the site

Gymnema Sylvestra: useful properties, use in the treatment and prevention of Gymnema vulgaris

Family: Asclepiadaceae, swivels. Latin name: Gymnema sylvestre. English name: Periploca of the woods, Gudmar, Ram's...

decorative trees

The age factor in powerlifting

Of course, different sports should be practiced at the right time. For the first time, he comprehensively studied the issue of age in powerlifting and weightlifting.