RU2745990C1 - Assembly method for single size groups of equal number of parts of one size group - Google Patents

Abstract

FIELD: mechanical engineering.

SUBSTANCE: invention relates to mechanical engineering and namely to measuring equipment. The invention can be used to measure and control parts including those in the tested batches when batching and selecting parts by sorting them into an equal number of size groups with subsequent assembly according to the same-name size groups. The method includes an initial reduction in the tolerances of the actual dimensions with respect to the no-pass limit by twice the probabilistic limit value of the size output (c) for each tolerance limit for incorrectly accepted defective parts with known accuracy of the technological process or by the value of the permissible measurement error (δ_chg) with unknown accuracy of the technological process to exclude the displacement of the grouping center

of tolerances of actual dimensions. When batching and selecting parts by sorting them into an equal number of size groups followed by assembly according to the same size groups excluding displacement of the grouping centers

of tolerances of intermediate and extreme size groups in relation to the middle of the tolerance of actual dimensions Ес(IТ), the tolerances of actual dimensions are divided into an equal number of size groups and completing and selecting parts by sorting them into an equal number of size groups with subsequent assembly according to the same size groups of an equal number of parts of one size group is carried out in such a way so that the largest group gaps and tightness decrease with a decrease in real gaps and tightness in matching joints by narrowing the tolerances of the actual dimensions to the shape tolerance of real surfaces TCEd=Т_sd(2Δ_sd), TCED=Т_sD(2Δ_sD) in diametrical terms because the deviations of the shape of the real surface (ECE) limited by the size tolerance are counted from the base surface of the shape and, depending on the type of surface, are estimated by complex and elementary parameters of the geometric accuracy of the shape, reducing the tolerances of the actual dimensions to the shape tolerance of real surfaces, which limits the shape deviations in diametrical terms to the area in space or on a plane, inside which there are points of a real surface or a profile set according to a two-contact scheme by a universal instrument measuring shape errors of real surfaces with a limited tolerance of the size Td, TD in a symmetric relation to the average diameter

by random scattering of its actual dimensions or shape tolerance TCEd=Т_sd(2Δ_sd), TCED=Т_sD(2Δ_sD) symmetrically from the middle radius

by the probability distribution of deviations of its shape, provided that the straight line r=a⋅x+b is located along the shortest distance relative to at least one of the enveloping lines of the family of radii of the real profile {r₁,r₂,…r_n} of the cylindrical part.

EFFECT: method makes it possible to ensure that an equal number of parts of the same size group are supplied to the assembly within the same size groups in the tested batches of parts during the assembly and selection by sorting them into an equal number of size groups, for example, when assembling parts such as cylinder liners, pistons, piston pins, a bearing bush located in the upper head of the connecting rods, the main and connecting rod journals of the crankshaft and their liners, the cylinders of the hydraulic vacuum amplifier and the control valve and their pistons, the front axle beam and the kingpin of the pivot pin, the main brake cylinder and its piston, the sleeve of the steering gear housing and the steering bipod shaft , cross studs, bearing bushings of satellites and differential box cups, rolling elements when installed in rolling bearings.

1 cl, 5 dwg

Description

The invention relates to mechanical engineering, in particular to measuring equipment and can be used to measure and control parts, including in the tested batches of parts when completing and selecting by sorting them into an equal number of size groups with subsequent assembly according to the same size groups.

It is known that ensuring the specified accuracy in the absence of precise processing of parts is achieved by using selective assembly [A.I. Yakushev Interchangeability, standardization and technical measurements - M .: Mashinostroenie, 1979, S. 211] by completing and selecting parts made with relatively wider tolerances of actual sizes by sorting them into an equal number of size groups with narrower group tolerances with subsequent assembly by the same size groups so that the largest group gaps and tightness decrease, and the smallest ones increase, approaching with an increase in the number of sorting groups to the average gap or tightness that corresponds to the midpoints of the tolerances of the actual dimensions.

допусков действительных размеров, а при комплектовании и подборе деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам - неучтенные смещения центров группирования

допусков промежуточных и крайних размерных групп по отношению к середине Ес(IT) допуска действительных размеров, что создает условия для так называемого незавершенного производства, когда становится невозможным использовать все поступающие на сборку детали.The known method does not make it possible to ensure that an equal number of parts of the same size group in the tested batches of parts are supplied to the assembly by the same size groups in the checked batches of parts during picking and selection by sorting them into an equal number of size groups, since due to the influence of deviations in the shape of real surfaces, a displacement of the grouping center occurs

tolerances of actual dimensions, and when completing and selecting parts by sorting them into an equal number of size groups with subsequent assembly by size groups of the same name, unaccounted displacements of the grouping centers

tolerances of intermediate and extreme size groups in relation to the middle of the EC (IT) tolerance of actual dimensions, which creates conditions for the so-called work-in-progress, when it becomes impossible to use all the parts arriving for assembly.

при неизвестной точности технологического процесса Т_пр=IT-δ_изм.It is known that the accuracy of manufacturing and processing of parts is checked by finding, for each part, the largest and smallest dimensions when they are further considered as the limits of the maximum and minimum material used in the control of parts with limiting calibers by setting the production tolerance T _pr [Yu.V. Dimov Metrology, standardization and certification - St. Petersburg: Peter, 2004, p. 245] by combining the acceptance limits (PGmax, PGmin) with the limiting dimensions, according to which, with the established influence of the permissible measurement error (δ _meas ) on the grading result, acceptance control of suitable parts, either by displacement inwardly of the acceptance limits established by the IT size tolerance by the probabilistic limit value (s) of the size output beyond each tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process T _pr = IT-2⋅s, or by the value of half of the permissible measurement error

with unknown accuracy of the technological process T _pr = IT-δ _meas .

но не должны выходить за пределы арбитражного допуска

увеличенного на смещение приемочных границ относительно предельных отклонений допуска размера или назначение допускаемой погрешности измерений (δ_изм) при совмещении приемочных границ с предельными размерами, что из-за наличия погрешности измерений влияет на достоверность результатов измерений и контроля деталей, в том числе в проверяемых партиях деталей при комплектовании и подборе сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам и может привести к появлению областей вероятностных ошибок первого и второго рода в случае ошибочного принятия некоторых бракованных деталей годными (α₁), а некоторых годных - бракованными (β₁), смещению центра группирования

допусков действительных размеров, а при комплектовании и подборе деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам - к неучтенным смещениям центров группирования

допусков промежуточных и крайних размерных групп по отношению к середине Ес(IT) допуска действительных размеров.The known method of controlling the suitability of parts does not allow for the receipt of an equal number of parts of the same size group in the checked batches of parts in the assembly and selection by sorting them into an equal number of size groups for the same size groups, since the actual dimensions of the parts recognized as suitable may go beyond the production admission

but must not go beyond the arbitration tolerance

increased by the displacement of the acceptance limits relative to the maximum deviations of the size tolerance or the assignment of the permissible measurement error (δ _meas ) when aligning the acceptance boundaries with the maximum dimensions, which, due to the presence of measurement errors, affects the reliability of the measurement results and control of parts, including in the tested batches of parts when completing and selecting by sorting them into an equal number of size groups with subsequent assembly according to the same size groups and can lead to the appearance of areas of probabilistic errors of the first and second kind in the case of erroneous acceptance of some defective parts as good (α ₁ ), and some good ones - defective (β ₁ ), displacement of the grouping center

tolerances of actual dimensions, and when assembling and selecting parts by sorting them into an equal number of size groups with subsequent assembly by size groups of the same name - to unaccounted for displacements of the grouping centers

tolerances of intermediate and extreme dimension groups in relation to the middle of the EC (IT) tolerance of the actual dimensions.

The technical result of the invention is to ensure that an equal number of parts of the same size group in the checked batches of parts are received for assembly according to the same size groups in the checked batches of parts during the assembly and selection by sorting them into an equal number of size groups.

The specified technical result is achieved by the fact that in the assembly method according to the same size groups of an equal number of parts of the same size group, including splitting the tolerances of the actual dimensions into an equal number of size groups, completing and selecting parts by sorting them into an equal number of size groups with subsequent assembly by the same size groups so that the largest group gaps and tightness decrease, and the smallest increase, approaching with an increase in the number of sorting groups to the average gap or tightness that corresponds to the midpoints of the tolerances of the actual dimensions, initially reduce the tolerances of the actual dimensions relative to the no-pass limit by twice the probability limit value of the size output c) for each tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process, or for the value of the permissible measurement error (δ _meas ) with an unknown accuracy of the technological process, which affects reduction of real gaps and tightness in mates by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression

where S _f , N _f - real clearances and tightness in the mates, reduced by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

D _mmc , D _lmc - the limit of the maximum and minimum of the material, limiting the relative non-passable limit affecting the narrowing of the tolerances of the actual dimensions of the cylindrical internal elements, the form tolerance of the real surfaces TCED = T _f D (2∆ _f D) in diametrical terms;

d _MMC , d _LMC - the limit of the maximum and the minimum of the material, limiting relative to the no-passage limit influencing the narrowing of the tolerances of the actual dimensions of the cylindrical external elements, the tolerance of the shape of the real surfaces TCEd = T _f d (2Δ _f d) in diametrical terms

- задаваемый для цилиндрического внутреннего элемента абсолютной алгебраической разностью между пределом максимума и минимума материала допуск формы реальных поверхностей в диаметральном выражении;

- given for a cylindrical inner element by the absolute algebraic difference between the maximum and minimum material limit, the tolerance of the shape of real surfaces in diametrical terms;

TCEd (2ECEd) = T _f d (2∆ _f d) = d _MMC -d _LMC - the tolerance of the shape of real surfaces in diametrical terms set for the cylindrical outer element by the algebraic difference between the maximum and minimum material limit;

TD = D _MMC -D _min , Td = d _max -d _MMC - actual dimensions tolerances set with the tolerance of the shape of real surfaces initially excluded relative to the no-pass limit TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression for a cylindrical inner element, the algebraic difference between the maximum material limit D _MMC and the lower limit hole size D _min , and for a cylindrical outer element, the algebraic difference between the upper limit shaft size d _max and the maximum material limit d _MMC ;

- вероятностный допуск посадки, задаваемый среднеквадратическим сложением допусков действительных размеров с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=T_фD(2Δ_фD) в диаметральном выражении;

- the probabilistic tolerance of landing, specified by the root-mean-square addition of the tolerances of the actual dimensions with the tolerance of the shape of real surfaces initially excluded relative to the no-pass limit, TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression;

- задаваемые полусуммой предельных отклонений координаты середины допусков действительных размеров цилиндрического внутреннего и наружного элементов с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении;

- given by the half-sum of the maximum deviations, the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded shape tolerance of the real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametrical terms;

S _c = E _c- e _c - the average gap, specified by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), tced = T _f D (2∆ _f D) in diametrical terms;

допусков действительных размеров, а при комплектовании и подборе деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам исключаются смещения центров группирования

допусков промежуточных и крайних размерных групп по отношению к середине допуска Ес(IT) действительных размеров, что позволяет обеспечить постоянство групповых зазоров и натягов в сопряжениях при переходе от одной размерной группы к другойN _c = e _c -E _c is the average tightness set by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical outer and inner elements with the initially excluded shape tolerance of the real surfaces TCEd = T _f d (2Δ _f d), tced = T _φ D (2Δ _φ D), in diametric expression, which excludes the displacement of the center of the grouping

tolerances of actual dimensions, and when assembling and selecting parts by sorting them into an equal number of size groups with subsequent assembly by size groups of the same name, displacements of the grouping centers are excluded

tolerances of intermediate and extreme size groups in relation to the middle of the tolerance EC (IT) of the actual dimensions, which makes it possible to ensure the constancy of the group gaps and tightness in the mates when moving from one size group to another

where S _fk , N _fk are the group gaps and tightness in the mates, specified with constancy when passing from one size group to another when dividing the tolerances of the actual dimensions into an equal number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametrical expression;

- групповые допуски одноименных размерных групп цилиндрического внутреннего и наружного элементов, задаваемые при разбиении допусков действительных размеров на равное к число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении;

- group tolerances of the same dimensional groups of cylindrical inner and outer elements, set when dividing the tolerances of actual dimensions into an equal number of size groups with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), tced = T _f D (2Δ _f D) in diametrical terms;

- задаваемое при разбиении допусков действительных размеров число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении;

- the number of size groups specified when dividing the tolerances of actual dimensions with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametric terms;

- вероятностный групповой допуск посадки, задаваемый среднеквадратическим сложением k-ых групповых допусков одноименных размерных групп цилиндрического внутреннего и наружного элементов при разбиении допусков действительных размеров на равное к число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении;

is the probabilistic group tolerance of landing, specified by the root-mean-square addition of the k-th group tolerances of the same dimensional groups of the cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into an equal number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2Δ _f d), tced = T _f D (2∆ _f D) in diametrical expression;

S = E-e _ck - the average group gap, set with constancy in the transition from one dimensional group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same dimensional groups of the cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into an equal number of dimensional groups with initially excluded with respect to the non-passable limit of the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametrical expression;

N = е _ck -Е _ck - the average group interference, set with constancy in the transition from one size group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same size groups of the cylindrical outer and inner elements when dividing the tolerances of the actual dimensions into an equal number size groups with initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametrical expression;

- задаваемые полусуммой предельных отклонений координаты середины k-ых групповых допусков одноименных размерных групп цилиндрического внутреннего и наружного элементов при разбиении допусков действительных размеров на равное k число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении, с расширением допусков действительных размеров лишь за счет уменьшения допуска формы реальных поверхностей TCEd=T_фd(2Δ_фd), tced=T_фD(2Δ_фD) в диаметральном выражении, потому как ограниченные допуском размера отклонения формы реальной поверхности (ЕСЕ) отсчитываются от базовой поверхности формы и в зависимости от вида поверхности оцениваются комплексными и элементными параметрами геометрической точности формы, уменьшая допуски действительных размеров на допуск формы реальных поверхностей, ограничивающий в диаметральном выражении отклонения формы областью в пространстве или на плоскости, внутри которой находится точки реальной поверхности или профиля так, что за наибольший допустимый размер вала d_Дmax принимается диаметр описанного прилегающего цилиндра вращения наименьшего возможного радиуса, который бы касался наиболее выступающих точек реальной наружной цилиндрической поверхности вращения и был не больше предела максимума материала d_Дmax≤d_MMC, d_MMC≥d_min+2Δ_фd и верхнего предельного размера вала d_Дmax≤d_max, а наименьший действительный размер вала d_Дmin оценивается отклонениями формы, ограниченными допуском формы реальной наружной цилиндрической поверхности вращения d_Дmin=d_Дmax-2Δ_фd, принимая за наименьший допустимый размер вала d_Дmin размер, измеренный по двухконтактной схеме универсальным средством измерений, который должен быть не меньше предела минимума материала d_Дmin≥d_LMC или нижнего предельного размера вала d_Дmin≥d_min при условии, что за наименьший допустимый размер отверстия D_Дmin принимается диаметр вписанного прилегающего цилиндра вращения наибольшего возможного радиуса, который бы касался наиболее выступающих точек реальной внутренней цилиндрической поверхности вращения и был не меньше предела максимума материала D_Дmin≥D_MMC, D_MMC≤D_max-2Δ_фD и нижнего предельного размера отверстия D_Дmin≥D_min, а наибольший действительный размер отверстия D_Дmax оценивается отклонениями формы, ограниченными допуском формы реальной внутренней цилиндрической поверхности вращения D_Дmax=D_Дmin+2Δ_фD, принимая за наибольший допустимый размер отверстия D_Дmax размер, измеренный по двухконтактной схеме универсальным средством измерений, который должен быть не больше предела минимума материала D_Дmax≤D_LMC или верхнего предельного размера отверстия D_Дmax≤D_max

- the coordinates of the midpoint of the k-th group tolerances of the same size groups of cylindrical inner and outer elements specified by the half-sum of the maximum deviations when dividing the tolerances of the actual dimensions into an equal number of size groups with the initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2Δ _f d ), tced = T _f D (2∆ _f D) in diametrical expression, with the expansion of the tolerances of the actual dimensions only by reducing the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), tced = T _f D (2∆ _f D) in diametrical terms, because the deviations of the shape of the real surface (ECE) limited by the size tolerance are measured from the base surface of the shape and, depending on the type of surface, are estimated by complex and elementary parameters of the geometric accuracy of the shape, reducing the tolerances of the actual dimensions to the shape tolerance of real surfaces, limiting in diametric terms deviations of the shape by an area in space or by n flap, inside which there are points of a real surface or profile so that the largest allowable shaft size d _{Dmax is} taken to be the diameter of the described adjacent cylinder of rotation of the smallest possible radius that would touch the most protruding points of the real outer cylindrical surface of rotation and was not more than the maximum material limit d _{Dmax ≤} d _MMC , d _MMC≥ d _min + 2Δ _ф d and the upper limiting shaft size d _Дmax ≤d _max , and the smallest actual size of the shaft d _Дmin is estimated by form deviations limited by the shape tolerance of the real outer cylindrical surface of rotation d _Дmin = d _Дmax -2Δ _f d, taking for the smallest allowable shaft size d _{Dmin the} size measured by a two-contact scheme with a universal measuring instrument, which must be not less than the minimum material limit d _Dmin ≥d _LMC or the lower limit shaft size d _Dmin ≥d _min , provided that for the smallest allowable hole size D _{Dmin is} assumed to be the diameter of the inscribed adjacent of rotation of the cylinder the largest possible radius of which would touch the outermost points of the actual inner cylindrical surface of revolution and is not less than the maximum limit of the material _Dmin D ≥D _MMC, D _MMC ≤D _max -2Δ _f D and the lower limit _Dmin aperture size D ≥D _min , and the largest actual hole size D _Dmax is estimated by shape deviations limited by the shape tolerance of the real inner cylindrical surface of rotation D _Dmax = D _Dmin + 2Δ _f D, taking for the largest allowable hole size D _{Dmax the} size measured according to a two-contact scheme by a universal measuring instrument, which should be not more than the limit of the minimum material D _Dmax ≤D _LMC or the upper limit hole size D _Dmax ≤D _max

d _MMC ≥d _min + 2∆ _f d, d _LMC ≤d _Dmax -2∆ _f d, d _Dmin ≥d _min , d _Dmax ≤d _max ,

D _MMC ≤D _max -2∆ _f D, D _LMC ≥D _Dmin + 2∆ _f D, D _Dmin ≥D _min , D _Dmax ≤D _max .

The essence of the technical solution is illustrated by drawings, where

- in Fig. 1 shows a diagram of finding the error in the shape of the real surface of revolution in diametrical and radius expressions, provided that the straight line r = a⋅x + b is located along the shortest distance relative to at least one of the enveloping lines of the family of radii of the real profile {r ₁ , r ₂ , ... r _n } cylindrical part;

действительного поля рассеивания распределенной по нормальному закону плотности вероятности совокупности средней

в пределах возникающей за интервалами

допусков действительных размеров вероятностной ошибки первого рода в случае ошибочного принятия некоторых бракованных деталей годными (α₁);- in Fig. 2 shows a diagram of an unaccounted displacement of the grouping center

of the real scattering field of the normally distributed probability density of the aggregate average

within the arising at intervals

tolerances of the actual sizes of the probabilistic error of the first kind in the case of erroneous acceptance of some defective parts as suitable (α ₁ );

- in Fig. 3 shows a scheme for dividing the tolerances of actual dimensions into an equal number of size groups, which, due to the influence of deviations in the shape of real surfaces, leads to assembly for the same size groups of a different number of parts of the same size group in the tested batches of parts when completing and selecting by sorting them into an equal number of dimensional groups;

- in Fig. 4 shows a scheme for dividing the tolerances of actual dimensions into an equal number of size groups with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms for admission to the assembly according to the same size groups of an equal number of parts of the same size group in the checked batches of parts during picking and selection by sorting them into an equal number of size groups;

- in Fig. 5 shows a diagram of reducing real gaps and tightness in mates by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms.

допусков действительных размеров (фиг. 2), а при комплектовании и подборе деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам исключения смещения центров группирования

допусков промежуточных и крайних размерных групп по отношению к середине допуска Ее(IT) действительных размеров (фиг. 3), разбиение допусков действительных размеров на равное число размерных групп (фиг. 4), комплектование и подбор деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерных группам равного количества деталей одной размерной группы так, что с уменьшением реальных зазоров и натягов в сопряжениях посредством сужения допусков действительных размеров на допуск формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении наибольшие групповые зазоры и натяги уменьшаются, а наименьшие увеличиваются, приближаясь с ростом числа групп сортировки с постоянством групповых зазоров и натягов в сопряжениях при переходе от одной размерной группы к другой к тому среднему зазору или натягу, что соответствует серединам допусков действительных размеров (фиг. 4). Расширение допусков действительных размеров проводится лишь за счет уменьшения допуска формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении (фиг. 5), потому как ограниченные допуском размера отклонения формы реальной поверхности (ЕСЕ) отсчитываются от базовой поверхности формы и в зависимости от вида поверхности оцениваются комплексными и элементными параметрами геометрической точности формы, уменьшая допуски действительных размеров на допуск формы реальных поверхностей, ограничивающий в диаметральном выражении отклонения формы областью в пространстве или на плоскости, внутри которой находится точки реальной поверхности или профиля установленной по двухконтактной схеме универсальным средством измерений погрешности формы реальных поверхностей ограниченным допуском размера Td, TD в симметричном отношении от среднего диаметра

случайным рассеиванием ее действительных размеров или допуском формы TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в симметричном отношении от среднего радиуса

вероятностным распределением отклонений ее формы (фиг. 1) при условии размещения прямой r=a⋅x+b по кратчайшему расстоянию относительно хотя бы одной из огибающих линий семейства радиусов реального профиля {r₁,r₂,…r_n} цилиндрической детали.The method includes an initial reduction in the tolerances of the actual dimensions with respect to the no-pass limit by twice the probabilistic limit value of the size output (c) for each tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process, or by the value of the permissible measurement error (δ _meas ) with an unknown accuracy of the technological process to avoid displacement of the grouping center

tolerances of actual dimensions (Fig. 2), and when completing and selecting parts by sorting them into an equal number of size groups, followed by assembly according to the same size groups, excluding displacement of the grouping centers

tolerances of intermediate and extreme size groups in relation to the middle of the tolerance Ee (IT) of the actual dimensions (Fig. 3), splitting the tolerances of the actual dimensions into an equal number of size groups (Fig. 4), completing and selecting parts by sorting them into an equal number of size groups with subsequent assembly according to the same size groups of an equal number of parts of the same size group so that with a decrease in real gaps and tightness in mates by narrowing the tolerances of the actual dimensions to the shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D ( 2Δ _f D) in diametrical terms, the largest group gaps and tightness decrease, and the smallest ones increase, approaching with an increase in the number of sorting groups with the constancy of group gaps and tightness in the mates when moving from one size group to another to that average gap or tightness, which corresponds to the midpoints tolerances of actual dimensions (Fig. 4). The expansion of the tolerances of the actual dimensions is carried out only by reducing the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms (Fig. 5), because the shape deviations limited by the size tolerance real surfaces (ECE) are measured from the base surface of the form and, depending on the type of surface, are estimated by complex and elemental parameters of the geometric accuracy of the shape, reducing the tolerances of the actual dimensions to the shape tolerance of real surfaces, limiting the deviations of the shape in diametrical terms to an area in space or on a plane inside is a point of a real surface or a profile set according to a two-contact scheme with a universal measuring instrument of the shape error of real surfaces with a limited tolerance of the size Td, TD in a symmetrical relation to the average diameter

random scattering of its actual dimensions or the tolerance of the form TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in a symmetric ratio from the average radius

the probability distribution of deviations of its shape (Fig. 1) provided that the straight line r = a⋅x + b is located along the shortest distance relative to at least one of the enveloping lines of the family of radii of the real profile {r ₁ , r ₂ , ... r _n } of the cylindrical part.

The assembly method for the same size groups of an equal number of parts of the same size group is carried out as follows.

случайным рассеиванием ее действительных размеров или допуском формы TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в симметричном отношении от среднего радиуса

вероятностным распределением отклонений ее формыThe suitability of a part cannot be assessed by one size, as well as from the entire set of sizes it is possible to indicate one by which it is possible to carry out a quantitative and qualitative assessment of the accuracy of manufacturing and processing of a part, since for this purpose it is required to find the largest, smallest and average dimensions. The error in the shape of the real surface allows you to give a visual representation of the approximation of the actual dimensions to those specified in the drawing, but does not give a judgment about the suitability of the part and the location of all its dimensions within the tolerance, since the dimensions of the cylindrical part in various sections and points take on different values from each other (Fig. . 1), and the variability of the current radius in a given section is set by the position of the axial and angular coordinates. From which it follows that the accuracy of manufacturing and processing of an individual part is reduced to finding, according to a two-contact scheme, a universal means of measuring the error of the shape of a real surface with a limited tolerance of the size Td, TD in a symmetrical ratio of the average diameter

random scattering of its actual dimensions or the tolerance of the form TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in a symmetric ratio from the average radius

the probability distribution of deviations of its shape

where t is the coefficient of the Laplace function;

n ₁ n ₂ - the volume of samples according to the results of measurements of the largest and smallest dimensions of a dimensional element in a batch of parts N;

- средний диаметр и средний радиус цилиндрического наружного элемента;

- average diameter and average radius of the cylindrical outer element;

- средний диаметр и средний радиус цилиндрического внутреннего элемента;

- average diameter and average radius of the cylindrical inner element;

- допуск формы реальной поверхности в диаметральном выражении, задаваемый для цилиндрического внутреннего элемента абсолютной алгебраической разностью между пределом максимума и минимума материала;

- the tolerance of the shape of the real surface in diametrical expression, specified for the cylindrical inner element by the absolute algebraic difference between the maximum and minimum material limits;

TCEd (2ECEd) = T _f d (2∆ _f d) = d _MMC -d _LMC is the tolerance of the shape of a real surface in diametrical expression, specified for a cylindrical outer element by the algebraic difference between the maximum and minimum material limit.

был положительно определенным.This statement is true if the straight line r = a⋅x + b is located along the shortest distance relative to at least one of the enveloping lines of the family of radii of the real profile {r ₁ , r ₂ ,… r _n } of the cylindrical part. For this condition to be satisfied, it is necessary and sufficient that the determinant of the second-order differential for the function

was positively definite.

Differential of the second order for the function

Based on the fact that the partial derivatives of equation (1) of the second-order differential for the function

примет видthen equation (1) of the second-order differential for the function

will take the form

был положительно определеннымIn order for the determinant of the second-order differential for the function

was positively definite

it is necessary and sufficient that the corner minors are also positive.

поскольку радиусы {r₁,r₂,…r_n} задаются в различных сечениях относительно одной из огибающих линий реального профиля цилиндрической детали и принимают отличные друг от друга значения.First-order corner minor is positive

since the radii {r ₁ , r ₂ , ... r _n } are set in different sections relative to one of the enveloping lines of the real profile of the cylindrical part and take different values from each other.

The second-order corner minor is also positive

для n+1based on the inequality

for n + 1

since the expressions in brackets are positive and represent the squares of the difference between the abscissas of different radii, set in different sections relative to one of the enveloping lines of the family of radii of the real profile {r ₁ , r ₂ , ... r _n } of the cylindrical part.

случайным рассеиванием ее действительных размеров или допуском формы TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в симметричном отношении от среднего радиуса

, вероятностным распределением отклонений ее формы.From which it follows that with the fulfillment of the condition for placing the straight line r = a⋅x + b along the shortest distance relative to at least one of the enveloping lines of the family of radii of the real profile {r ₁ , r ₂ , ... r _n } of a cylindrical part, installed according to a two-contact scheme universal measuring instrument, the error of the shape of the real surface is set by the limited tolerance of the size Td, TD in a symmetrical relation to the average diameter

random scattering of its actual dimensions or the tolerance of the form TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in a symmetric ratio from the average radius

, the probability distribution of deviations of its shape.

не принимает значений, которые бы отличались по абсолютной величине более чем 3⋅σ от среднего арифметического

в пределах границ доверительного интервала

В связи с чем, надежность а распределенной по закону Гаусса плотности вероятности совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N при заданной точности εRandom value

does not take values that differ in absolute value by more than 3⋅σ from the arithmetic mean

within the confines of the confidence interval

In this connection, the reliability and the probability density distributed according to the Gaussian law of the population of the mean

obtained by combining compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N for a given accuracy ε

- эмпирическая дисперсия разности

средних арифметических

однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N;Where

- empirical variance of the difference

arithmetic means

homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N;

- эмпирическая дисперсия генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N;

is the empirical variance of the general population of the average

obtained by combining compositions of homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N;

- средние арифметические однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N.

- arithmetic means of homogeneous sample populations

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N.

в сравнении со средним арифметическим

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

(фиг. 2), полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N, средних арифметических

распределенных по нормальному закону однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента со средними квадратическими отклонениями

и совпадающими с приемочными границами

результатов измерений наибольшего и наименьшего размеров размерного элемента мгновенными центрами рассеивания

The observed discrepancy of the differences

versus arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

(Fig. 2) obtained by combining the compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N, arithmetic means

normally distributed homogeneous sample sets

measurement results of the largest and smallest dimensions of a dimensional element with standard deviations

and coinciding with the acceptance limits

results of measurements of the largest and smallest dimensions of a dimensional element by instantaneous scattering centers

- эмпирическая дисперсия разности

средних арифметических

однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N и наблюдаемого расхождения разности

в сравнении со средним арифметическим

однородной выборочной совокупности

результатов измерений наибольшего размера размерного элемента со средним квадратическим отклонением

и совпадающим с верхней приемочной границей

результатов измерений наибольшего размера размерного элемента мгновенным центром рассеивания

среднего арифметического

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N;Where

- empirical variance of the difference

arithmetic means

homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample size n ₁ , n ₂ in a batch of parts N and the observed discrepancy of the difference

versus arithmetic mean

homogeneous sample

results of measurements of the largest dimension of a dimensional element with a standard deviation

and coinciding with the upper acceptance limit

the results of measurements of the largest dimension of the dimensional element by the instantaneous scattering center

arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N;

- эмпирическая дисперсия разности

средних арифметических

однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N и наблюдаемого расхождения разности

в сравнении со средним арифметическим

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N, среднего арифметического

однородной выборочной совокупности

результатов измерений наименьшего размера размерного элемента со средним квадратическим отклонением

и совпадающим с нижней приемочной границей

результатов измерений наименьшего размера размерного элемента мгновенным центром рассеивания

- empirical variance of the difference

arithmetic means

homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample size n ₁ , n ₂ in a batch of parts N and the observed discrepancy of the difference

versus arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N, arithmetic mean

homogeneous sample

measurement results of the smallest dimension element with standard deviation

and coinciding with the lower acceptance limit

measurement results of the smallest dimension element by the instantaneous scattering center

- задаваемое функций Лапласа наблюдаемое расхождение разности

в сравнении со средним арифметическим

однородной выборочной совокупности

результатов измерений наибольшего размера размерного элемента со средним квадратическим отклонением

и совпадающим с верхней приемочной границей

результатов измерений наибольшего размера размерного элемента мгновенным центром рассеивания

среднего арифметического

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N;

is the observed discrepancy of the difference given by the Laplace function

versus arithmetic mean

homogeneous sample

results of measurements of the largest dimension of a dimensional element with a standard deviation

and coinciding with the upper acceptance limit

the results of measurements of the largest dimension of the dimensional element by the instantaneous scattering center

arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N;

- задаваемое функций Лапласа наблюдаемое расхождение разности

в сравнении со средним арифметическим

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N, среднего арифметического

однородной выборочной совокупности

результатов измерений наименьшего размера размерного элемента со средним квадратическим отклонением

и совпадающим с нижней приемочной границей

результатов измерений наименьшего размера размерного элемента мгновенным центром рассеивания

is the observed discrepancy of the difference given by the Laplace function

versus arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N, arithmetic mean

homogeneous sample

measurement results of the smallest dimension element with standard deviation

and coinciding with the lower acceptance limit

measurement results of the smallest dimension element by the instantaneous scattering center

в сравнении со средним арифметическим

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N, средних арифметических

однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента со средними квадратическими отклонениями

и совпадающими с приемочными границами

результатов измерений наибольшего и наименьшего размеров размерного элемента мгновенными центрами рассеивания

влияет на появление в пределах возникающих на интервалах

допусков действительных размеров вероятностных ошибок первого и второго рода в случае ошибочного принятия некоторых бракованными деталей годными (α₁) и некоторых годных деталей бракованными (β₁) смещения мгновенного центра рассеивания

распределенной по закону Гаусса плотности вероятности совокупности средней

задаваемого в виде замыкающего звена размерной цепи (фиг. 2) абсолютной алгебраической разностью между координатой центра группирования действительного поля рассеивания

плотности вероятности совокупности средней

и координатой середины допуска Ec(IT) действительных размеровThe observed discrepancy of the differences

versus arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N, arithmetic means

homogeneous samples

measurement results of the largest and smallest dimensions of a dimensional element with standard deviations

and coinciding with the acceptance limits

results of measurements of the largest and smallest dimensions of a dimensional element by instantaneous scattering centers

affects the appearance within arising intervals

tolerances of the actual sizes of probabilistic errors of the first and second kind in the case of erroneous acceptance of some defective parts as good (α ₁ ) and some good parts as defective (β ₁ ) displacements of the instantaneous center of scattering

the Gaussian distribution of the probability density of the population of the mean

given in the form of a closing link of the dimensional chain (Fig. 2) by the absolute algebraic difference between the coordinate of the center of grouping of the real scattering field

the probability density of the population mean

and the coordinate of the middle of the tolerance Ec (IT) of the actual dimensions

- вероятностные ошибки первого и второго рода в случае ошибочного принятия некоторых бракованными деталей годными (α₁) и некоторых годных деталей бракованными (β₁), возникающие на интервалах

допусков действительных размеров от наблюдаемого расхождения разностей

в сравнении со средним арифметическим

распределенной по закону Гаусса плотности вероятности генеральной совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N, средних арифметических

однородных выборочных совокупностей

результатов измерений, задающих размещение приемочных границ

по отношению к середине допуска Ec(IT) действительных размеров.Where

- probabilistic errors of the first and second kind in the case of erroneous acceptance of some defective parts as suitable (α ₁ ) and some suitable parts as defective (β ₁ ), arising at intervals

tolerances of actual dimensions from the observed discrepancy of the differences

versus arithmetic mean

the Gaussian distribution of the probability density of the general population of the mean

obtained by combining compositions of homogeneous samples

results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N, arithmetic means

homogeneous samples

measurement results defining the placement of acceptance boundaries

relative to the center of the Ec (IT) tolerance of the actual dimensions.

действительного поля рассеивания распределенной по нормальному закону плотности вероятности совокупности средней

полученной посредством объединения композиций однородных выборочных совокупностей

результатов измерений наибольшего и наименьшего размеров размерного элемента с объемом выборок n₁, n₂ в партии деталей N (фиг. 2), реальные зазоры и натяги в сопряжениях необходимо уменьшать посредством сужения допусков действительных размеров относительно непроходного предела на соответствующий сумме вероятностных ошибок первого и второго рода в случае ошибочного принятия некоторых бракованными деталей годными (α₁) и некоторых годных деталей бракованными (β₁) допуск формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении, задаваемый удвоенным вероятностным предельным значением выхода размера (с) за каждую границу допуска у неправильно принятых бракованных деталей при известной точности технологического процесса, либо значением допускаемой погрешности измерений (δ_изм) при неизвестной точности технологического процесса.From which it follows that to eliminate the displacement of the grouping center arising from the influence of deviations in the shape of real surfaces

of the real scattering field of the normally distributed probability density of the aggregate average

obtained by combining compositions of homogeneous samples

the results of measurements of the largest and smallest dimensions of a dimensional element with a sample volume n ₁ , n ₂ in a batch of parts N (Fig. 2), the real clearances and tightness in the mates must be reduced by narrowing the tolerances of the actual dimensions relative to the no-pass limit by the sum of the probabilistic errors of the first and second kind in the case of erroneous acceptance of some defective parts as suitable (α ₁ ) and some suitable parts as defective (β ₁ ) the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression , set by the doubled probabilistic limit value of the size output (c) for each tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process, or by the value of the permissible measurement error (δ _meas ) with an unknown accuracy of the technological process.

Proceeding from subordination to the normal law of distribution of random scattering of sizes, the average size, as a systematic component of the measured value, determines the position of the coordinate of the middle of the tolerance of the actual dimensions Ec (IT), from which, in turn, random scattering of the actual dimensions is set in a symmetric relation (Fig. 2). Then, with the algebraic summation of the systematic parts of the quantities and the mean square - random, the elimination of the receipt for the assembly for the same size groups of different numbers of parts of the same size group in the tested batches of parts during the picking and selection by sorting them into an equal number of size groups is achieved by reducing the tolerances of the actual dimensions relative to the no-pass limit by doubled the probabilistic limiting value of the size output (c) for each tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process, or for the value of the permissible measurement error (δ _meas ) with an unknown accuracy of the technological process, which affects the decrease in real clearances and tightness in the mates by narrowing the tolerances of actual dimensions to the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression (Fig. 5)

where S _f , N _f - real clearances and tightness in the mates, reduced by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

D _MMC , D _LMC - the limit of the maximum and minimum of the material, limiting relative to the no-pass limit affecting the narrowing of the tolerances of the actual dimensions of the cylindrical internal elements, the tolerance of the shape of the real surfaces TCED = T _f D (2∆ _f D) in diametrical terms;

d _MMC , d _LMC - the limit of the maximum and the minimum of the material, limiting relative to the no-passage limit influencing the narrowing of the tolerances of the actual dimensions of the cylindrical external elements, the tolerance of the shape of the real surfaces TCEd = T _f d (2Δ _f d) in diametrical terms

- задаваемый для цилиндрического внутреннего элемента абсолютной алгебраической разностью между пределом максимума и минимума материала допуск формы реальных поверхностей в диаметральном выражении;

- given for a cylindrical inner element by the absolute algebraic difference between the maximum and minimum material limit, the tolerance of the shape of real surfaces in diametrical terms;

TCEd = (2ECEd) = T _f d (2∆ _f d) = d _MMC -d _LMC - specified for a cylindrical outer element by the algebraic difference between the maximum and minimum material limit, the shape tolerance of real surfaces in diametrical terms;

TD = D _MMC -D _min , Td = d _max -d _MMC - actual dimensions tolerances set with the tolerance of the shape of real surfaces initially excluded relative to the no-pass limit TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression for a cylindrical inner element, the algebraic difference between the maximum material limit D _MMC and the lower limit hole size D _min , and for a cylindrical outer element, the algebraic difference between the upper limit shaft size d _max and the maximum material limit d _MMC ;

- вероятностный допуск посадки, задаваемый среднеквадратическим сложением допусков действительных размеров с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении;

- the probabilistic tolerance of landing, specified by the root-mean-square addition of the tolerances of the actual dimensions with the tolerance of the shape of real surfaces that was initially excluded relative to the no-pass limit, TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression;

- задаваемые полусуммой предельных отклонений координаты середины допусков действительных размеров цилиндрического внутреннего и наружного элементов с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении;

- given by the half-sum of the maximum deviations, the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametric terms;

S _c = Е _с -е _с - the average gap, set by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

допусков действительных размеров (фиг. 2), а при комплектовании и подборе деталей сортировкой их на равное число размерных групп с последующей сборкой по одноименным размерным группам исключаются смещения центров группирования

допусков промежуточных и крайних размерных групп по отношению к середине допуска Ес(IT) действительных размеров (фиг. 3), что позволяет обеспечить постоянство групповых зазоров и натягов в сопряжениях при переходе от одной размерной группы к другой (фиг. 4)N _c = e _c -E _c is the average tightness specified by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical outer and inner elements with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _φ D (2Δ _φ D) in diametrical expression, which excludes the displacement of the grouping center

tolerances of actual dimensions (Fig. 2), and when assembling and selecting parts by sorting them into an equal number of size groups, followed by assembly according to the same size groups, displacements of the grouping centers are excluded

tolerances of intermediate and extreme size groups in relation to the middle of the tolerance Ec (IT) of the actual dimensions (Fig. 3), which makes it possible to ensure the constancy of the group gaps and tightness in the mates when moving from one size group to another (Fig. 4)

where S _fk , N _fk - group gaps and tightness in the mates, set with constancy in the transition from one size group to another when dividing the tolerances of the actual dimensions into an equal number of size groups with the initially excluded relative to the non-passable limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametric terms;

- групповые допуски одноименных размерных групп цилиндрического внутреннего и наружного элементов, задаваемые при разбиении допусков действительных размеров на равное к число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении;

- group tolerances of the same dimensional groups of cylindrical inner and outer elements, set when dividing the tolerances of actual dimensions into an equal number of size groups with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2Δ _f D) in diametrical terms;

- задаваемое при разбиении допусков действительных размеров число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении;

- the number of size groups specified when dividing the tolerances of actual dimensions with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametric terms;

- вероятностный групповой допуск посадки, задаваемый среднеквадратическим сложением k-ых групповых допусков одноименных размерных групп цилиндрического внутреннего и наружного элементов при разбиении допусков действительных размеров на равное к число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении;

- the probabilistic group tolerance of landing, specified by the root-mean-square addition of the k-th group tolerances of the same size groups of the cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into an equal number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

S _ck = Е _{cк-е ck} - the average group gap, set with constancy in the transition from one dimensional group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same dimensional groups of the cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into equal k the number of size groups with the initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

N _ck = е _ck -Е _ck - the average group interference, set with constancy during the transition from one dimensional group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same dimensional groups of the cylindrical outer and inner elements when dividing the tolerances of the actual dimensions into equal k the number of size groups with the initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms;

- задаваемые полусуммой предельных отклонений координаты середины k-ых групповых допусков одноименных размерных групп цилиндрического внутреннего и наружного элементов при разбиении допусков действительных размеров на равное k число размерных групп с изначально исключенным относительно непроходного предела допуском формы реальных поверхностей TCEd=Т_фd(2Δ_фd), TCED=Т_фD(2Δ_фD) в диаметральном выражении.

- the coordinates of the midpoint of the k-th group tolerances of the same size groups of cylindrical inner and outer elements specified by the half-sum of the maximum deviations when dividing the tolerances of the actual dimensions into an equal k number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2Δ _f d ), TCED = T _f D (2∆ _f D) in diametrical expression.

The expansion of the tolerances of the actual dimensions is carried out only by reducing the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms (Fig. 5), because the shape deviations limited by the size tolerance real surfaces (ECE) are measured from the base surface of the form and, depending on the type of surface, are estimated by complex and elemental parameters of the geometric accuracy of the shape, reducing the tolerances of the actual dimensions to the shape tolerance of real surfaces, limiting the deviations of the shape in diametrical terms to an area in space or on a plane inside which a point of a real surface or profile is found so that the diameter of the described adjacent cylinder of rotation of the smallest possible radius that touches the most protruding points of the real outer cylindrical surface of rotation and is not more than the maximum material limit d _Dmax ≤d _{MMC is taken as the largest allowable shaft size dd max} , d _MMC ≥d _min + 2Δ _f d and the upper limiting shaft size d _Dmax ≤d _max , and the smallest actual size of the shaft d _Dmin is estimated by form deviations limited by the shape tolerance of the real outer cylindrical surface of rotation d _Dmin = d _Dmax -2Δ _f d, taking as the smallest allowable shaft size d _Дmin size, measured according to a two-contact scheme by a universal measuring instrument, which must not be less than the minimum material limit d _Дmin ≥d _LMC or the lower limit shaft size d _Дmin ≥d _min , provided that the diameter of the inscribed cylinder is taken as the smallest permissible hole size D _Дmin rotation of the largest possible radius that would touch the most protruding points of the real inner cylindrical surface of revolution and was not less than the maximum material limit D _Dmin ≥D _MMC , D _MMC ≤D _max -2Δ _f D and the lower limit hole size D _Dmin ≥D _min , the largest the actual size of the hole Dd _max is estimated by the deviations of the shape, limited by the shape tolerance of the real internal cylindrical surface of revolution Dd _max = D _Dmin + 2Δ _f D, taking for the largest permissible hole size Dd _{max the} size measured by a two-contact scheme with a universal measuring instrument, which should not exceed the minimum material limit Dd _max ≤D _LMC or the upper limit size holes Dd _max <D _max

d _MMC ≥ d _min + 2∆ _f d, d _LMC ≤d _Dmax -2∆ _f d, d _Dmin ≥d _min, d _Dmax ≤d _max ,

D _MMC ≤D _max -2∆ _f D, D _LMC ≥D _Dmin + 2∆ _f D, D _Dmin ≥D _min , D _Dmax ≤D _max

Thus, the proposed method makes it possible to ensure that an equal number of parts of the same size group in the checked batches of parts in the checked batches of parts in the assembly and selection by sorting them into an equal number of size groups, for example, when assembling parts such as cylinder liners, pistons, piston pins , a bearing sleeve located in the upper head of the connecting rods, the main and connecting rod journals of the crankshaft and their liners, the cylinders of the hydraulic vacuum amplifier and the control valve and their pistons, the front axle beam and the kingpin of the pivot pin, the main brake cylinder and its piston, the steering gear housing bush and steering arm shaft, cross studs, bearing sleeve of satellites and differential box cups, rolling elements when installed in rolling bearings.

Claims (22)

The method of assembly according to the same size groups of an equal number of parts of the same size group, including splitting the tolerances of the actual dimensions into an equal number of size groups, completing and selecting parts by sorting them into an equal number of size groups, followed by assembly according to the same size groups so that the largest group gaps and tightness decrease, and the smallest increase, approaching with an increase in the number of sorting groups to the average gap or interference, which corresponds to the midpoints of the tolerances of the actual dimensions, characterized in that they initially reduce the tolerances of the actual dimensions relative to the no-pass limit by twice the probabilistic limit value of the size output (c) for each the tolerance limit for incorrectly accepted defective parts with a known accuracy of the technological process or on the value of the permissible measurement error (δ _meas ) with an unknown accuracy of the technological process, which affects a decrease in real clearances and tension gov in mates by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression

where S _f , N _f - real clearances and tightness in the mates, reduced by narrowing the tolerances of the actual dimensions to the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms; D _MMC , D _LMC - the limit of the maximum and minimum of the material, limiting relative to the no-pass limit affecting the narrowing of the tolerances of the actual dimensions of the cylindrical internal elements, the tolerance of the shape of the real surfaces TCED = T _f D (2∆ _f D) in diametrical terms; d _MMC , d _LMC - the limit of the maximum and the minimum of the material, limiting relative to the no-pass limit affecting the narrowing of the tolerances of the actual dimensions of the cylindrical external elements, the tolerance of the shape of the real surfaces TCEd = T _f d (2∆ _f d), in diametrical terms;

- given for a cylindrical inner element by the absolute algebraic difference between the maximum and minimum material limit, the tolerance of the shape of real surfaces in diametrical terms; TCEd (2ECEd) = T _f d (2∆ _f d) = d _MMC -d _LMC - the tolerance of the shape of real surfaces in diametrical terms set for the cylindrical outer element by the algebraic difference between the maximum and minimum material limit; TD = D _MMC -D _min , Td = d _max -d _MMC - actual dimensions tolerances set with the tolerance of the shape of real surfaces initially excluded relative to the no-pass limit TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression for a cylindrical inner element, the algebraic difference between the maximum material limit D _MMC and the lower limit hole size D _min , and for a cylindrical outer element, the algebraic difference between the upper limit shaft size d _max and the maximum material limit d _MMC ;

- the probabilistic tolerance of landing, specified by the root-mean-square addition of the tolerances of the actual dimensions with the tolerance of the shape of real surfaces that was initially excluded relative to the no-pass limit, TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression;

- given by the half-sum of the maximum deviations, the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametric terms; S _c = Е _с -е _с - the average gap, set by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical inner and outer elements with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2∆ _f D) in diametrical terms; N _c = e _c -E _c is the average tightness specified by the algebraic difference between the coordinates of the middle of the tolerances of the actual dimensions of the cylindrical outer and inner elements with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _φ D (2Δ _φ D) in diametrical expression, which excludes the displacement of the grouping center

tolerances of actual dimensions, and when assembling and selecting parts by sorting them into an equal number of size groups with subsequent assembly by size groups of the same name, displacements of the grouping centers are excluded

tolerances of intermediate and extreme size groups in relation to the middle of the tolerance Ee (IT) of the actual dimensions, which makes it possible to ensure the constancy of the group gaps and tightness in the mates when moving from one size group to another

where S _fk , N _fk - group gaps and tightness in the mates, set with constancy when passing from one size group to another when dividing the tolerances of the actual dimensions into an equal number of size groups with the initially excluded relative to the non-passable limit of the shape tolerance of the real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2Δ _f D) in diametric terms;

- group tolerances of the same dimensional groups of cylindrical inner and outer elements, set when dividing the tolerances of actual dimensions into an equal number of size groups with the initially excluded shape tolerance of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2Δ _f D) in diametrical terms;

- the number of size groups specified when dividing the tolerances of actual dimensions with the initially excluded tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametric terms;

- the probabilistic group tolerance of landing, specified by the root-mean-square addition of the k-th group tolerances of the same dimensional groups of the cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into an equal number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2Δ _f d), TCED = T _f D (2∆ _f D) in diametrical terms; S = E _ck- e _sk - the average group gap, set with constancy in the transition from one dimensional group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same dimensional groups of cylindrical inner and outer elements when dividing the tolerances of the actual dimensions into an equal number size groups with initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression; N = е _ck -Е _ck - the average group interference, set with constancy in the transition from one size group to another by the algebraic difference between the coordinates of the middle of the k-th group tolerances of the same size groups of the cylindrical outer and inner elements when dividing the tolerances of the actual dimensions into an equal number size groups with initially excluded relative to the no-pass limit of the shape tolerance of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical expression;

- the coordinates of the middle of the k-th group tolerances of the same size groups of cylindrical inner and outer elements specified by the half-sum of the maximum deviations when dividing the tolerances of the actual dimensions into an equal number of size groups with the tolerance of the shape of real surfaces TCEd = T _f d (2Δ _f d ), TCED = T _f D (2∆ _f D) in diametrical expression, with the expansion of the tolerances of the actual dimensions only by reducing the tolerance of the shape of real surfaces TCEd = T _f d (2∆ _f d), TCED = T _f D (2∆ _f D) in diametrical terms, because the deviations of the shape of the real surface (ECE) limited by the size tolerance are measured from the base surface of the form and, depending on the type of surface, are estimated by the complex and elemental parameters of the geometric accuracy of the form, reducing the tolerances of the actual dimensions to the form tolerance of real surfaces, limiting the deviations of the form in diametrically by an area in space or on a plane inside which points of the real surface are profile so that the diameter of the described adjacent cylinder of rotation of the smallest possible radius that touches the most protruding points of the real outer cylindrical surface of rotation and is not more than the maximum material limit d _Dmax ≤d _MMC , d _MMC ≥d _{min is} taken as the largest allowable shaft size d _Dmax + 2Δ _f d and upper limiting the size of the shaft d _Dmax ≤d _max, the actual size and the smallest measured deviations shaft shape, limited admission forms actual outer cylindrical surface of rotation d _{Dmin Dmax} = d _f d -2Δ, taking as a smallest allowed size d _Dmin shaft size, measured by double contact scheme with a universal measuring instrument, which must be not less than the limit of the minimum material d _Dmin ≥ d _LMC or the lower limiting shaft size d _Dmin > d _min , provided that the smallest permissible hole size D _{Dmin is} taken to be the diameter of the inscribed adjacent cylinder of rotation of the largest possible radius, which would touch the most protruding points of the real inner cylindrical surface of revolution and was not less than the limit of the maximum material D _Dmin ≥ D _MMC , D _MMC ≤D _max -2Δ _f D and the lower limit hole size D _Dmin ≥D _min , and the largest actual size of the hole Dd _max is estimated by deviations of the form, limited by the form tolerance of the real ext of the morning cylindrical surface of rotation D _Dmax = D _Dmin + 2∆ _f D, taking for the largest allowable hole size Dd _{max the} size measured by a two-contact scheme with a universal measuring instrument, which should not be more than the minimum material limit D _Dmax ≤D _LMC or the upper limiting hole size Dd _max ≤D _max

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