Dependent tolerance. Eskd
Location tolerances can be dependent or independent.
Independent admission location is a tolerance, the value of which is constant for the entire set of elements of the part and does not depend on the actual dimensions of these elements. If there is no indication on the drawing, then the location tolerance is considered independent.
Independent tolerances are assigned if, in addition to assembly, it is required to ensure the proper functioning of the product (uniform gap, tightness).
Examples of independent tolerances:
1.tolerances of the location of the seats of the parts connected to the rolling bearings;
2. Tolerances of the location of the axes of the holes for the pins, installed on a transitional fit.
Parallelism and tilt tolerances are always independent. The rest of the location tolerances can be either dependent or independent.
Dependent tolerance Is a tolerance indicated in the drawing as a value that can be increased by a value depending on the deviation of the actual size of the element from the maximum material limit (- for a shaft; - for a hole).
Key features of dependent tolerances:
1. refer only to shafts and holes;
2. the drawing indicates the minimum value of the tolerance;
3. this minimum value refers to elements whose actual dimensions are equal to the maximum material limit;
4. it is allowed to increase this minimum value of the tolerance by the amount of deviation of the actual size of the element from the maximum material limit;
5. appointed only to ensure the collection of products;
6.the dependent tolerance indicated on the drawing may be is zero... This means that position deviation is only allowed for parts whose actual dimensions differ from the maximum material limit.
Dependent tolerance:
If the actual dimensions of the elements of the parts differ from the maximum material limit (;), then the parts will be assembled even with larger values of the deviation of the location than indicated in the drawing. To the extent that the manufacturing tolerance is used, the location tolerance can be increased to the same extent. Part of the manufacturing tolerance is given to compensate for location errors. Since the location tolerance determines the location of the two elements, the size of the dependent tolerance may depend on:
1. the actual size of the base element;
2. the actual size of the standardized element;
3. the actual dimensions of both elements.
If the dependent tolerance depends on the actual size of only one element (basic or standardized), then its value is determined by the formula:
where is the value of the dependent tolerance indicated in the drawing; , - deviations of the actual size of the element from the maximum material limit.
If the dependent tolerance depends on the actual dimensions of the two elements, then:
With full use of the tolerances for the manufacture of elements, when the actual dimensions are equal to the minimum material limit (,), the limiting value of the dependent tolerance is obtained:
, (4)
, (5)
Thus, the dependent tolerance can be represented as the sum of two components:
, (7)
where is the constant value of the dependent tolerance (the minimum value indicated in the drawing); - the variable part of the dependent tolerance (depends on the deviation of the actual size from the maximum material limit).
Location or shape tolerances can be dependent or independent.
Dependent tolerance- this is the tolerance of location or shape, indicated in the drawing as a value that is allowed to be exceeded by an amount depending on the deviation of the actual size of the element in question from the maximum of the material.
Dependent tolerance is a variable tolerance, its minimum value is indicated in the drawing and is allowed to be exceeded by changing the dimensions of the elements in question, but so that their linear dimensions do not go beyond the prescribed tolerances.
Dependent Tolerances locations, as a rule, are assigned in cases where it is necessary to ensure the collection of parts that are mated simultaneously on several surfaces.
In some cases, with dependent tolerances, it is possible to transfer a part from a scrap to a suitable way additional processing, for example by reaming the holes. As a rule, it is recommended that dependent tolerances be assigned to those elements of parts for which only collection requirements are imposed.
Constrained tolerances are usually controlled by complex gauges, which are prototypes of the mating parts. These gauges are straight through only, they guarantee a fit-free assembly of products.
An example of a dependent tolerance assignment is shown in Fig. 3.2. The letter "M" indicates that the tolerance is dependent, and the way of indicating that the value of the alignment tolerance can be exceeded by changing the dimensions of both holes.
Rice. 3.2. Dependent Tolerances
The figure shows that when making holes with minimum dimensions the maximum deviation from alignment can be no more than m \ n = 0.005 (Fig. 3.2, b). When making holes with the maximum permissible dimensions, the value of the maximum alignment deviation can be increased (Fig. 3.2, c). The largest maximum deviation is calculated by the formula.
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.
The following tolerances of the location of surfaces can be dependent: positional tolerances, tolerances of alignment, symmetry, perpendicularity, intersection of axes.
Shape tolerances can be dependent: axis straightness tolerance and flatness tolerance for the plane of symmetry.
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.
Parallelism and tilt tolerance can only be independent.
In the absence of special designations in the drawing, the tolerances are understood as independent. A symbol may be used for independent tolerances, although it is optional.
Independent tolerances are used for critical connections when their value is determined functional purpose details.
Independent tolerances are also used in small-scale and one-off production, and their control is carried out with universal measuring instruments (see table 3.13).
Dependent tolerances are established for parts that are mated simultaneously on two or more surfaces, for which interchangeability is reduced to ensuring collection across all mating surfaces (flange connection with bolts).
Dependent tolerances are used in joints with a guaranteed clearance in large-scale and mass production, they are controlled by position gauges. The drawing indicates the minimum tolerance value ( Tr min), which corresponds to the flow limit (smallest limit hole size or largest limit shaft size). The actual value of the dependent location tolerance is determined by the actual dimensions of the parts to be joined, that is, in different assemblies it may be different. Slip fit connections Tp min = 0. The full value of the dependent tolerance is determined by adding to Tr min additional value T additional, depending on the actual dimensions of this part (GOST R 50056):
Tp head = Tr min + T add.
Examples of calculating the value of the expansion of the tolerance for typical cases are given in table 3.14. This table also gives formulas for recalculating location tolerances to positional tolerances when designing location calibers (GOST 16085).
The location of the axes of holes for fasteners (bolts, screws, studs, rivets) can be specified in two ways:
Coordinate, when the limit deviations are set ± δ L coordinating sizes;
Positional, when positional tolerances are specified in diametric terms - Tr.
Table 3.13 - Conditions for choosing a dependent location tolerance
|
Connection working conditions |
Location tolerance type |
|
Selection conditions: Large-scale, mass production It is required to ensure only collection under the condition complete interchangeability Location gauge control Connection type: Irresponsible connections Through holes for fasteners |
Dependent |
|
Selection conditions: Single and small batch production Correct functioning of the connection is required (centering, tightness, balancing and other requirements) Control by universal means Connection type: Critical joints with interference or transitional landings Threaded stud holes or pin holes Bearing seats, holes for gear shafts |
Independent |
Recalculation of tolerances from one method to another is carried out according to the formulas of Table 3.15 for the system of rectangular and polar coordinates.
The coordinate method is used in one-off, small-scale production, for unspecified location tolerances, as well as in cases where fit of parts is required, if different values of tolerances in coordinate directions are set, if the number of elements in one group is less than three.
The positional method is more technological and is used in large-scale and mass production. Positional tolerances are most commonly used to specify the axis position of fastener holes. In this case, the coordinating dimensions are indicated only nominal values in square frames, since these dimensions are not covered by the concept of "general tolerance".
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 A(bolted, two through holes in the flanges) or V(stud connection, i.e. clearance in one piece). According to the known diameter of the fastener, a number of holes are determined according to table 3.16, their diameter ( D) and minimum clearance ( S min).
Table 3.14 - Recalculation of the tolerances of the location of surfaces to positional tolerances
|
Surface location tolerance |
Positional Tolerance Formulas |
Maximum extension of tolerance Tdop |
|
|
Coaxiality (symmetry) tolerance relative to the axis of the base surface |
|
For the base T P = 0 For con T rollable surface T and T P = T WITH |
T add = Td 1 T add = Td 2 |
|
Alignment (symmetry) tolerance relative to the common axis |
|
T P1 = T C1 T P2 = T C2 |
T add = Td 1 + Td 2 |
|
Coaxiality (symmetry) tolerance of two surfaces Base not specified |
|
T P1 = T P2 = |
T add = TD 1 + TD 2 |
|
Perpendicularity tolerance of the surface axis relative to the plane |
|
T P = T |
T add = TD |
On the drawing, the details indicate the value of the positional tolerance (see table 3.7), deciding on its dependence. For through holes the tolerance is assigned dependent, and for threaded - independent, therefore it expands.
For connection type (A) T pos = S p, for connections like ( V) 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 - parts to be connected
Figure 3.4 - Types of connection of parts using fasteners:
a- type A, bolted; b- type B, pins, pins
Design clearance S p, required to compensate for the error in the location of the holes, is determined by the formula:
S p = S min,
where the coefficient TO use of the gap to compensate for the deviation of the axis of the holes and bolts. It can take on the following values:
TO= 1 - in joints without adjustment under normal assembly conditions;
TO = 0.8 - in connections with adjustment, as well as in connections without adjustment, but with recessed and countersunk screw heads;
TO= 0.6 - in connections with adjustment of the arrangement of parts during assembly;
K = 0 - for a base element made on a sliding fit ( H/h), when the nominal positional tolerance of that element is zero.
If the 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 a stud screwed into the body.
Table 3.15 - Recalculation of maximum deviations of dimensions coordinating the axes of the holes to positional tolerances in accordance with GOST 14140
|
Location type |
Formulas for determining positional tolerance (in diametric terms) |
|
|
Rectangular coordinate system |
||
|
One hole is assigned from the assembly base
|
T p = 2δ L δ L= ± 0.5 T R T add = TD |
|
|
The two holes are coordinated relative to each other (no assembly base)
|
T p = δ L δ L = ± T R T add = TD |
|
|
Three or more holes 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 R (δ L y - about T leaning about T wear T(except for the base axis) δ L forest = δ L∑ ∕ 2 (ladder) δ L chain = δ L∑ ∕ (n – 1) (chain) δ L∑ - the largest race T friction between the axes of adjacent T vers T ui |
|
|
Two or more holes are located in one row (given 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 R (O T deviation of axes about T common plane T and - A or assembly base) |
|
|
The holes are arranged in two rows (no assembly base)
The holes are coordinated with respect to the two build bases |
T p1.4δ 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 R (the size is set to the diagonal) T add = TD δ L 1 = δ L 2 = δ L T p 2.8 δ L δ L= ± 0.35 T R |
|
|
The holes are 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 R (the size is set to the diagonal) T add = TD |
|
|
Polar coordinate system |
||
|
Two holes coordinated with respect to the axis of the central element
|
T p = 2.8 δR δR = ± 0.35 T R δα
= ± (corner mine T s) T add = TD |
|
|
Three or more holes are located in a circle (no assembly base)
Three or more holes are located in a circle, the central element is the assembly base |
T add = TD T p = 1.4 δα δα = ± 0.7 T R (corner mine T s) δα 1 = δα 2 = T add = TD + TD bases |
|
3400
Table 3.16 - Diameters of through holes for fasteners and the corresponding guaranteed clearances in accordance with GOST 11284, mm
|
Fastener diameter d | ||||||
|
Notes: 1 Row 1 is preferred and is used for connection types A and V(holes can be obtained by any method). 2 For connection types A and V it is recommended to use the 2nd row when making holes by marking, punching with a high-precision die, in investment casting or under pressure. 3 Type connections A can be performed on the 3rd row with an arrangement from 6th to 10th type, as well as connections of the type V when positioned from 1st to 5th view (any processing method, except riveted joints). |
||||||
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.
The following tolerances of the location of surfaces can be dependent: positional tolerances, tolerances of alignment, symmetry, perpendicularity, intersection of axes.
Shape tolerances can be dependent: axis straightness tolerance and flatness tolerance for the plane of symmetry.
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.
Parallelism and tilt tolerance can only be independent.
In the absence of special designations in the drawing, the tolerances are understood as independent. A symbol may be used for independent tolerances, although it is optional.
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 one-off production, and their control is carried out with universal measuring instruments (see table 3.13).
Dependent tolerances are established for parts that are mated simultaneously on two or more surfaces, for which interchangeability is reduced to ensuring collection across all mating surfaces (flange connection with bolts).
Dependent tolerances are used in joints with a guaranteed clearance in large-scale and mass production, they are controlled by position gauges. The drawing indicates the minimum value of the tolerance (Tr min), which corresponds to the flow limit (the smallest limit hole size or the largest limit shaft size). The actual value of the dependent location tolerance is determined by the actual dimensions of the parts to be joined, that is, in different assemblies it may be different. For sliding fit connections, Tp min = 0. Full value dependent tolerance is determined by adding an additional value to Tr min T additional, depending on the actual dimensions of this part (GOST R 50056):
Tp head = Tr min + T add.
Examples of calculating the value of the expansion of the tolerance for typical cases are given in table 3.14. This table also gives formulas for recalculating location tolerances to positional tolerances when designing location calibers (GOST 16085).
The location of the axes of holes for fasteners (bolts, screws, studs, rivets) can be specified in two ways:
Coordinate, when the maximum deviations ± δL of the coordinating dimensions are specified;
Positional, when positional tolerances are specified in diametric terms - Tr.
Table 3.13 - Conditions for choosing a dependent location tolerance
| Connection working conditions | Location tolerance type |
| Conditions for selection: Large-scale, mass production It is required to ensure only assembly under the condition of complete interchangeability Control by positioning gauges Type of connections: Irresponsible connections Through holes for fasteners | Dependent |
| Conditions for selection: Single and small-scale production It is required to ensure the correct functioning of the joint (centering, tightness, balancing and other requirements) Control by universal means Type of joints: Responsible joints with interference or transitional fits Threaded holes for studs or pin holes Bearing seats, holes for gear shafts | Independent |
Recalculation of tolerances from one method to another is carried out according to the formulas of Table 3.15 for the system of rectangular and polar coordinates.
The coordinate method is used in one-off, small-scale production, for unspecified location tolerances, as well as in cases where fit of parts is required, if different values of tolerances in coordinate directions are set, if the number of elements in one group is less than three.
The positional method is more technological and is used in large-scale and mass production. Positional tolerances are most commonly used to specify the axis position of fastener holes. In this case, the coordinating dimensions are indicated only nominal values in square frames, since these dimensions are not covered by the concept of "general tolerance".
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 A(bolted, two through holes in the flanges) or V(stud connection, i.e. clearance in one piece). According to the known diameter of the fastener, a number of holes are determined according to table 3.16, their diameter ( D) and minimum clearance ( S min).
Table 3.14 - Recalculation of the tolerances of the location of surfaces to positional tolerances
| Surface location tolerance | Sketch | Positional Tolerance Formulas | Maximum extension of tolerance Tdop |
| Coaxiality (symmetry) tolerance relative to the axis of the base surface |  | For the base T P = 0 For end T rollable surface T and T P = T WITH | T add = Td 1 T add = Td 2 |
| Alignment (symmetry) tolerance relative to the common axis |  | T P1 = T C1 T P2 = T C2 | T add = Td 1 + Td 2 |
| Coaxiality (symmetry) tolerance of two surfaces Base is not specified |  | T P1 = T P2 = | T add = TD 1 + TD 2 |
| Perpendicularity tolerance of the surface axis relative to the plane |  | T P = T | T add = TD |
On the drawing, the details indicate the value of the positional tolerance (see table 3.7), deciding on its dependence. For through holes, the tolerance is assigned dependent, and for threaded holes - independent, so it expands.
For connection type (A) T pos = S p, for connections like ( V) 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 - parts to be connected
Figure 3.4 - Types of connection of parts using fasteners:
a- type A, bolted; b- type B, pins, pins
Design clearance S p, required to compensate for the error in the location of the holes, is determined by the formula:
S p = S min,
where the coefficient TO use of the gap to compensate for the deviation of the axis of the holes and bolts. It can take on the following values:
K = 1 - in connections 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 a base element made on a sliding fit (H / h), when the nominal positional tolerance of this element is zero.
If the 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 a stud screwed into the body.
Table 3.15 - Recalculation of maximum deviations of dimensions coordinating the axes of the holes to positional tolerances in accordance with GOST 14140
| Location type | Sketch | Formulas for determining positional tolerance (in diametric terms) |
| Rectangular coordinate system | ||
| I | One hole is assigned from the assembly base  | T p = 2δ L δ L= ± 0.5 T R T add = TD |
| II | The two holes are coordinated relative to each other (no assembly base)  | T p = δ L δ L = ± T R T add = TD |
| III | Three or more holes 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 leaning about T wear T along the base axis) δ L forest = δ L∑ ∕ 2 (ladder) δ L chain = δ L∑ ∕ (n – 1) (chain) δ L∑ - the largest race T friction between the axes of adjacent T vers T ui |
| IV | Two or more holes are located in one row (given 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 deviation of axes about T common plane T and - A or assembly base) |
| V VI | The holes are arranged in two rows (no assembly base)  The holes are coordinated with respect to the two build 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 | The holes are 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 given before 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 are located in a circle (no assembly base)  Three or more holes are located in a circle, the central element is the assembly base | T add = TD T p = 1.4 δα δα = ± 0.7 T p δα = ± 3400 (angular mine T s) δα 1 = δα 2 = T add = TD + TD bases |
Table 3.16 - Diameters of through holes for fasteners and the corresponding guaranteed clearances in accordance with GOST 11284, mm
| Fastener diameter d | 1st row | 2nd row | 3rd row | |||
| DH12 | S min | DH 14 | S min | DH14 | S min | |
| 4,3 | 0,3 | 4,5 | 0,5 | 4,8 | 0,8 | |
| 5,3 | 0,3 | 5,5 | 0,5 | 5,8 | 0,8 | |
| 6,4 | 0,4 | 6,6 | 0,6 | |||
| 7,4 | 0,4 | 7,6 | 0,6 | |||
| 8,4 | 0,4 | |||||
| 10,5 | 0,5 | |||||
| Notes: 1 Row 1 is preferred and is used for connection types A and V(holes can be obtained by any method). 2 For connection types A and V it is recommended to use the 2nd row when making holes by marking, punching with a high-precision die, in investment casting or under pressure. 3 Type connections A can be performed on the 3rd row with an arrangement from 6th to 10th type, as well as connections of the type V when positioned from 1st to 5th view (any processing method, except riveted joints). |
3.4 General tolerances for the shape and location of surfaces
Since 01.01.2004, unspecified tolerances of the shape and location of surfaces must be specified in accordance with GOST 30893.2-02 “ONV. General tolerances. Shape tolerances and surface arrangements not specified individually. " Previously, GOST 25069 was in effect, which has been canceled.
General tolerances for roundness and cylindricity are the same as for diameter, but should not exceed the tolerances for diameter and general tolerance for radial runout. For particular types of shape deviations (ovality, taper, barrel-shaped, saddle-shaped), the general tolerances are considered equal to the radius tolerance, i.e. 0.5 Td (TD).
General tolerances for parallelism, perpendicularity, tilt are equal to the overall tolerance for flatness or straightness. The reference surface is considered to be adjacent, and its shape error is not considered.
Unspecified tolerances of the location of surfaces refer to irresponsible 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 the indicators, the deviations of which are allowed within the entire tolerance field of the size of the element in question 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 |
| Parallelism tolerance 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 p along the entire 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 |
| Coaxiality tolerance (dimension tolerance is specified in one coordinate plane) |  | T h Exploded layout T h - for a common axis. Adjacent location | T p = T p = T h |
| Coaxiality tolerance when the axis location is specified in two coordinate directions |  | T hx and T hу T hx and T hу | T p = × × T p = |
| Symmetry tolerance with respect to common plane symmetry |  | T h | T p = For two elements T ov T p = T h For one element |
| Symmetry tolerance 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 to the size tolerance field and are not its part of, they were covered by the tables GOST 25069, and now GOST 30893.2-2002;
Third, the indicators of these parameters are indirectly limited by the tolerances of other dimensions (maximum deviations of the center-to-center distances with the positional system for specifying the axes of the holes, the tilt tolerance and the angle tolerance in linear terms).
The choice of the type of tolerance is determined by the structural form of the part. The choice of the base surface is made as follows:
Unspecified tolerances should be determined from the previously selected bases for the indicated location or runout tolerances of the same name;
If the base has not been previously selected, then for base surface the surface of the greatest extent is taken, providing secure installation parts when measuring (for example, for the alignment tolerance, the base will be the shaft step longer length, and with the same lengths and qualities - a surface of a large diameter).
The values of the general tolerances of the shape and location (orientation) are established for three classes of accuracy, which characterize different conditions normal manufacturing accuracy, achieved without the use of additional processing of increased accuracy (table 3.18).
The class designations for general location tolerances are set by the standard as follows: H - fine, K - medium, L - rough. The choice of the accuracy class is carried out taking into account the functional requirements for the part and the production possibilities.
Table 3.18 - General tolerances of the shape and location of surfaces according to GOST 30893.2
| General tolerances for straightness and flatness | |||||||
| Accuracy class | Intervals of nominal lengths | ||||||
| To 10 | Over 10 to 30 | Over 30 to 100 | Over 100 to 300 | Over 300 | |||
| H K L | 0,02 | 0,05 | 0,1 | 0,2 | 0,3 | ||
| 0,05 | 0,1 | 0,1 | 0,4 | 0,6 | |||
| 0,1 | 0,2 | 0,4 | 0,8 | 1,2 | |||
| General squareness tolerances for the nominal length of the short side of a corner | |||||||
| H K L | Up to 100 | Over 100 to 300 | Over 300 to 1000 | Over 1000 | |||
| 0,2 | 0,3 | 0,4 | 0,5 | ||||
| 0,4 | 0,6 | 0,8 | 1,0 | ||||
| 0,6 | 1,0 | 1,5 | 2,0 | ||||
| General tolerances of symmetry of intersection of axes (in diametric terms) | |||||||
| H K L | 0,5 | ||||||
| 0,6 | 0,8 | 1,0 | |||||
| 0,6 | 1,0 | 1,5 | 2,0 | ||||
| General tolerances for radial and axial runout | |||||||
| H K L | 0,1 0,2 0,5 | ||||||
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 m is given for linear and angular dimensions according to GOST 30893.1, as well as the middle class for general tolerances of shape and location - K.
It is recommended that you selectively control deviations in shape and position of elements with general tolerances to ensure that normal manufacturing accuracy does not deviate from the originally established. The departure of deviations in the shape 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 Standardization of accuracy of keyed and spline 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 provide rotation gear wheels, pulleys and other parts mounted on shafts along transitional fits, in which, along with interference, there may be gaps. Sizes of keyways are standardized.
There are key joints with prismatic (GOST 23360), segment (GOST 24071), wedge (GOST 24068) and tangential (GOST 24069) keys. Keyed connections (Figures 4.1 and 4.2) with parallel keys are used in low-loaded low-speed gears (kinematic feed chains of machine tools), in large-sized products (forging equipment, flywheels of internal combustion engines, centrifuges, etc.). Tapered and tangential keys accommodate thrust reversal loads in heavily loaded joints. The most widely used are parallel keys.
Figure 4.1 - Keyed connection
The parallel keys are available in three versions (Figure 4.3). The type of key execution determines the shape of the groove on the shaft (Figure 4.4). Version 1 - for a closed groove, for normal connection in the conditions of serial and mass production types; version 2 - for an open groove with control keys, when the sleeve moves along the shaft when free connection; version 3 - for a half-open groove with keys installed on the end of the shaft with tight connection, a pressed-on sleeve on the shaft, in single and small-scale production types. The size of the key depends on the nominal size of the shaft diameter and is determined in accordance with GOST 23360 (see table 4.1).
Figure 4.2 - Cross-section of the key and grooves:
a - section of the key; b- the section of the grooves ( r- corresponds to its maximum value)
a B C)
Figure 4.3 - Types of key designs:
a- version 1; b- version 2; v- version 3
a B C)
Figure 4.4 - Forms of grooves on shafts:
a- closed; b- open; v- half-open
Table 4.1 - Dimensions of connections with parallel keys in accordance with GOST 23360 (limited), mm
| Shaft diameter d | Key dimensions | Depth of keyway with deviation | Radius of curvature r or chamfer S 1 max | ||||
| Cross section | Chamfer S min | Length intervals l | |||||
| b | h | on the shaft t 1 | in the sleeve t 2 | ||||
| 6 to 8 | 0,16 | 6 to 20 | 1,2 +0 ,1 | 1,0 +0 , 1 | 0,16 | ||
| Over 8''10 | " 6 " 36 | 1,8 +0 , 1 | 1,4 + 0,1 | ||||
| " 10" 12 | " 8" 45 | 2,5 +0 , 1 | 1,8 +0,1 | ||||
| " 12" 17 | 0,25 | " 10" 56 | 3,0 + 0,1 | 2,3 +0,1 | 0,25 | ||
| " 17" 22 | " 14" 70 | 3,5 + 0,1 | 2,8 + 0,1 | ||||
| " 22 " 30 | " 18 " 90 | 4,0 + 0,2 | 3,3 + 0,2 | ||||
| " 30" 38 | 0,40 | " 22 " 110 | 5,0 +0,2 | 3,3 +0,2 | 0,40 | ||
| “ 38 " 44 | " 28 " 140 | 5,0 + 0,2 | 3,3+0,2 | ||||
| " 44 " 50 | "36 " 160 | 5,5 + 0,2 | 3,8 +0,2 | ||||
| " 50 " 58 | "45 " 180 | 6,0 +0,2 | 4,3 + 0,2 | ||||
| " 58 " 65 | " 50" 200 | 7,0 + 0,2 | 4,4 + 0,2 | ||||
| " 65 " 75 | 0,60 | "56 " 220 | 7,5 + 0,2 | 4,9 + 0,2 | 0,60 | ||
| " 75 " 85 | "63 " 250 | 9,0 + 0,2 | 5,4 + 0,2 | ||||
| " 85 " 95 | 14. | " 70" 280 | 9,0 + 0,2 | 5,4 + 0,2 | |||
| " 95 "110 | " 80 " 320 | 10 +0,2 | 6,4 +0,2 | ||||
| " 110"130 | " 90" 360 | 11 +0,2 | 7,4 + 0,2 | ||||
| Note. 1. The length of the key is selected from a number of integers: 6; eight; 10; 12; 14; sixteen; eighteen; twenty; 22; 25; 28; 32; 36; 40; 45; 50; 56; 63; 70; 80; 90; one hundred; 110; 125; 140; 160; 180; 200; 220; 250; 280; 320; 360. |
Examples of legend key:
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).
The main landing dimension is the width of the key b. According to this size, the key mates with two grooves: a groove on the shaft and a groove in the bushing.
The keys are usually fixedly connected to the grooves of the shafts, and with the grooves; bushings - with a gap. The preload is necessary so that the keys do not move during operation, and the gap is necessary to compensate for the inaccuracy of the dimensions and the relative position of the grooves. Keys, regardless of fit, are made in dimension b with a tolerance h 9, which makes it possible to manufacture them centrally. The rest of the dimensions are less important: the height of the key h- on h 11, key length l- on h 14, the length of the keyway L - by H 15.
The layouts of the tolerance fields for connections with parallel and segment keys are shown in Figure 4.5.
a B C)
Figure 4.5 - Layouts of tolerance fields for dimension b of the keyed connection:
a- free; b- normal; v- dense; - key tolerance; - shaft groove tolerance; - sleeve groove tolerance
Landings of the keys are carried out along the shaft system ( Сh). The standard allows various combinations of tolerance fields for the grooves on the shaft and in the sleeve with the key width tolerance field.
The most common is the normal connection when the bush (gear) is located in the middle of the shaft.
Loose connection is used for guide keys (the gear moves along the shaft).
A tight connection is used when the shaft is reversible or when the key is located at the end of the shaft.
4.1.3. Requirements for the design of keyed connections
Maximum dimensional deviations 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 keyed connection on the assembly drawing, the cross-sections of the shaft and bushing involved in the connection with the parallel key are shown in Figures 4.6 and 4.7.
1 - bushing; 2 - key; 3 - shaft
Figure 4.6 - Performing keyway connection:
a- complete cross-section; b- key section
When making the cross-section of the keyed connection, it is necessary to indicate the fits, 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 sleeve, it is necessary to indicate the surface roughness, tolerance fields for dimensions b, d and D in mixed form, and also the dimensions of the depth of the grooves should 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 sleeve, it is necessary to limit the accuracy of the shape and the relative position of the surfaces to tolerances. Requirements are made for permissible deviations 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). The parallelism tolerance should be taken equal to 0.5 IT 9, the tolerance of symmetry in the presence of one key in the connection - 2 IT 9, and with two keys located diametrically - 0.5 IT 9 of the nominal size b of the key. Symmetry tolerances can be dependent on high volume and mass production.
Figure 4.7 - Cross-sections:
a- shaft, keyway execution 2; b- bushings
4.2 Splined joints
4.2.1 Purpose, a brief description of 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 location of the teeth (splines) around the circumference.
Depending on the profile of the teeth, spline connections are divided into straight-sided, involute and triangular. The most widespread are spline joints with a straight-sided tooth profile (Figure 4.8), having even number teeth (6, 8, 10, 16, 20). Straight-side spline joints are performed in accordance with GOST 1139, in which three gradations of the height of the number of teeth for the same diameter are set. Accordingly, the compounds are divided into light, medium and heavy series (table 4.3). The choice of series depends on the size 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 - section of the shaft
Splined joints with involute tooth profile (GOST 6033) are standardized for modules t = 0.5 ... 10 mm, for diameters 4 ... 500 mm and number of teeth z= 6 .. .82. Tooth profile angle α = 30 °.
Splined joints with an involute profile of the teeth, in comparison with straight-sided ones, transmit large torques, have a lower (by 10 ... 40%) stress concentration at the base of the teeth, increased cyclic strength and durability, provide better centering and direction of parts, are easy to manufacture, so how they can be milled using the running-in method. Spline joints with involute tooth profile are widely used in the automotive industry. Example of designation when centering on the flanks of the teeth: 50 × 2 × 9 H/9g GOST 6033 indicates that the nominal diameter is 50 mm, modulus t = 2 mm, fit on the lateral sides of the teeth 9 H/ 9g.
Spline joints with a triangular profile are not standardized, they have fine teeth. The profile angle is characterized by the angle of the groove on the shaft 2β. The main parameters of this type of joints are: t = 0.3 ... 0.8 mm; z = 15 ... 70; 2β = 90 ° or 72 °.
Splined joints with a triangular profile are most often used instead of interference fits, when the latter are undesirable, and also with thin-walled bushings for transmitting small torques.
Table 4.3 - Basic dimensions according to GOST 1139 of straight-sided spline joints, mm
| Z × d × D | b | d 1 | R | Z × d × D | b | d 1 | R | Z × d × D | b | d 1 | R |
| Light series | Medium series | Heavy series | |||||||||
| 6 × 23 × 26 | 22,1 | 0,2 | 6 × 11 × 14 | 3,0 | 9,9 | 0,2 | 10 × 16 × 20 | 2,5 | 14,1 | 0.2 | |
| 6 × 26 × 30 | 24,6 | " | 6 × 13 × 16 | 3,5 | 12,0 | " | 10 × 18 × 23 | 3,0 | 15,6 | " | |
| 6 × 28 × 32 | 26,7 | " | 6 × 16 × 20 | 4,0 | 14,5 | " | 10 × 21 × 26 | 3,0 | 18,5 | " | |
| 8 × 32 × 36 | 30,4 | 0,3 | 6 × 18 × 22 | 5,0 | 16,7 | " | 10 × 23 × 29 | 4,0 | 20,3 | " | |
| 8 × 36 × 40 | 34,5 | " | 6 × 21 × 25 | 5,0 | 19.5 | " | 10 × 26 × 32 | 4,0 | 23,0 | 0,3 | |
| 8 × 42 × 46 | 40,4 | " | 6 × 23 × 28 | 6,0 | 21.3 | " | 10 × 28 × 35 | 4,0 | 24,4 | " | |
| 8 × 46 × 50 | 44,6 | " | 6 × 26 × 32 | 6,0 | 23,4 | 0,3 | 10 × 32 × 40 | 5,0 | 28,0 | " | |
| 8 × 52 × 58 | 49,7 | 0,5 | 6 × 28 × 34 | 7,0 | 25.9 | " | 10 × 36 × 45 | 5,0 | 31,3 | " | |
| 8 × 56 × 62 | 53,6 | " | 8 × 32 × 38 | 6,0 | 29,4 | " | 10 × 42 × 52 | 6,0 | 36,9 | " | |
| 8 × 62 × 68 | 59,8 | " | 8 × 36 × 42 | 7,0 | 33,5 | " | 10 × 46 × 56 | 7,0 | 40,9 | 0,5 | |
| 10 × 72 × 78 | 69.6 | " | 8 × 42 × 48 | 8,0 | 39.5 | 16 × 52 × 60 | 6,0 | 47,0 | " | ||
| 10 × 82 × 88 | 79,3 | " | 8 × 46 × 54 | 9,0 | 42,7 | 0.5 | 16 × 56 × 65 | 5,0 | 50,6 | " | |
| 10 × 92 × 98 | 89,4 | " | 8 × 52 × 60 | 10,0 | 48,7 | " | 16 × 62 × 72 | 6,0 | 56,1 | " | |
| 10 × 102 × 108 | 99,9 | " | 8 × 56 × 65 | 10,0 | 52,2 | " | 16 × 72 × 82 | 7,0 | 65,9 | " | |
| 10 × 112 × 120 | 108,8 | " | 8 × 62 × 72 | 12,0 | 57.8 | " | 20 × 82 × 92 | 6,0 | 75,6 | " | |
| 10 × 72 × 82 | 12,0 | 67,4 | " | 20 × 92 × 102 | 7,0 | 85,5 | " | ||||
| 10 × 82 × 92 | 12,0 | 77,1 | 20 × 102 × 115 | 8,0 | 94,0 | " | |||||
| 10 × 92 × 102 | 14,0 | 87,3 | 20 × 112 × 125 | 9,0 | 104,0 | ||||||
| 10 × 102 × 112 | 16,0 | 97,7 | " | " | |||||||
| 10 × 112 × 125 | 18,0 | 106,3 | " | " | |||||||
| Note: Dimension R corresponds to the maximum value |
| Parameter name | Meaning |
| Topic of the article: | Dependent tolerance |
| Category (thematic category) | Standardization |
Levels of relative geometric accuracy of shape and surface position tolerances
This is the relationship between the shape and location tolerance and the element size tolerance:
A - normal relative geometric accuracy (shape or location tolerances are approximately 60% of the size tolerance);
B - increased relative geometric accuracy (shape or location tolerances are approximately 40% of the size tolerance);
C - high relative geometric accuracy (shape or location tolerances are approximately 25% of the size tolerance).
The shape tolerances of cylindrical surfaces (for deviations from cylindricity, roundness and longitudinal section profile) corresponding to levels A, B and C are approximately 30, 20 and 12% of the size tolerance, since the shape tolerance limits the radius deviation, and the size tolerance limits the diameter deviation surface. If the tolerances of the shape and location are limited by the size tolerance field, then they are not indicated.
For non-mating and easily deformable surfaces of elements, the form tolerance must be greater than the size tolerance.
14 Unspecified form and position tolerances
set based on the quality or accuracy class, which corresponds to the size tolerance. The tolerance can also be specified in the technical requirements.
If unspecified form tolerances are not assigned, then any form deviations are allowed within the tolerance range of the size of the element in question. Except where tolerances for parallelism, perpendicularity, tilt, or end runout are specified. The unspecified flatness and straightness tolerance is then equal to the tolerance of these deviations.
WITH unspecified location tolerances the matter is more complicated. Here, for cases of deviation from parallelism, perpendicularity, alignment, symmetry, location, separate requirements are imposed.
- ϶ᴛᴏ variable tolerance, at which the suitability of an element is assessed based on the actual dimensions of the influencing elements obtained for each specific part. Dependent tolerances are needed to increase the yield of suitable parts by increasing the collection of parts, the actual dimensions of which are shifted towards the minimum metal. The drawing indicates the minimum values tolerances that ensure the collectibility of the compound.
Dependent location tolerances are predominantly assigned to the center-to-center distances of the fastening holes, the alignment of the stepped hole sections, the symmetry of the keyway slots, etc. These tolerances are controlled by complex location gauges, which are prototypes of mating parts.
In the conditions of single and small-scale production, it is inappropriate to standardize dependent tolerances.
16 Protruding fields of location tolerances
This is a tolerance field or a part of it that limits the deviation of the location of the element under consideration outside the extent of this element (the normalized section protrudes beyond the length of the element).
If it is extremely important to set the protruding tolerance field of the location, then after the numerical value of the tolerance, indicate the symbol P in a circle. The contour of the protruding part of the normalized element is limited by a thin solid line, and the length and location of the protruding tolerance field - by dimensions (Fig. 4).
Figure 4 - An example of the designation of a protruding tolerance zone
1 Influence of surface microgeometry on product quality, optimal roughness .
Roughness and waviness surfaces of parts affect the indicators of fluid friction; gas-dynamic resistance and erosional wear; friction and sliding wear; rolling friction, wear and vibration; static and dynamic impermeability, etc.
In mobile landings, roughness and waviness disrupt lubrication and reduce bearing capacity oil layer.
Due to the roughness of the surface, the contact of the surfaces of the parts occurs along the tops of the irregularities. The ratio of the actual contact area to the nominal (Fig. 3) during turning, reaming and grinding is 0.25-0.3, with superfinishing and fine-tuning - 0.4 and more.
With such a contact, at first elastic, and then plastic deformation of the irregularities occurs, the tops of some irregularities break off. There is intense wear of parts and an increase in the gap between the mating surfaces.
Irregularities reduce the fatigue strength of parts. So, with a decrease in the roughness of the cavity of the cut or ground thread of bolts with Ra= 1.25 to Ra= 0.125, the permissible limiting amplitude of the stress cycle increases by 20-50%.
Smoothing the surfaces by 25-40% increases the fatigue strength and 15-30% wear resistance of alloy steel parts.
Corrosion of metal occurs and spreads faster on rough-cut surfaces, which reduces strength several times. The roughness of the surface is a controllable factor, it can be obtained with a given characteristic for all parts of the batch.
In stationary landings, undulation and roughness weaken the bond strength.
In the operation of the machine, a break-in period is distinguished. normal work and catastrophic wear and tear. The resulting roughness after running-in, which ensures minimal wear and remains in the process of long-term operation of machines, is usually called optimal... Optimum roughness increases the durability of the machine and maintains its accuracy.
The optimum roughness is characterized by the height, pitch and shape of the irregularities. Its parameters depend on the quality of the lubricant and other operating conditions of the rubbing parts, their structures and material. The optimum roughness is not necessarily low.
2 Parameters and characteristics of surface roughness; base length, altitude and step parameters .
Surface roughness- a set of irregularities with relatively small steps, highlighted by the base length. Surface roughness can be considered for any surface other than fluffy and porous. Roughness refers to the microgeometry of the surface.
The numerical values of the surface roughness are determined from a single base, for which it is taken middle line profile. The base line has the form of a nominal profile and is drawn so that within the base length the average standard deviation the profile to this line is minimal. This method of roughness control is called the centerline system.
To highlight irregularities of different sizes that characterize the surface roughness, the concept was introduced baseline length l: 0.01; 0.03; 0.08; 0.25; 0.80; 2.5; eight; 25 mm.
For a quantitative assessment of roughness, six parameters have been established: three high-altitude, two step, and the relative reference length of the profile:
The arithmetic mean of the absolute values of the profile deviation Ra within base length l:
Ra = |y (x) | dx; (1)
Ra = |y i|, (2)
where l- basic length;
n- the number of selected points of the profile at the base length.
Profile deviation y is the distance between any point in the profile and the midline.
Parameter Ra preferred, normalized to values from 0.008 to 100 μm from the range R 10;
The height of the irregularities of the profile at ten points Rz, i.e., the sum of the average absolute values of the heights of the five largest profile protrusions and the depths of the five largest profile valleys within the base length l... Values set Rz from 0.025 to 1600 microns;
The highest profile irregularities Rmax, i.e., the distance between the line of the profile protrusions and the line of the profile valleys within the base length l;
Figure 1 - Scheme for understanding the average pitch of irregularities Sm
The average value of the step of irregularities Sm profile within base length l... (from 0.002 to 12.5 microns);
Figure 2 - Scheme for understanding the average pitch of local protrusions S
The average value of the step of the local protrusions of the profile S within base length l... The numerical values of the roughness parameters are standardized;
Figure 3 - Scheme for understanding the relative reference length of the profile tp
Relative reference length of the profile tp (p- the value of the level of the profile section, Fig. 3.2).
Dependent tolerance - concept and types. Classification and features of the category "Dependent tolerance" 2017, 2018.
