An independent tolerance for the location of the axes of the holes is a tolerance, the numerical value of which is constant for a large number parts of the same name (for example, a batch of parts) and does not depend on the actual size (diameter) of the hole or (or maybe "and") on the size of the base. If there is no indication on the drawing, then the tolerance is considered independent.

The meaning of the given concept boils down to the fact that with an independent measurement tolerance, it is necessary to determine the location error in such a way that the value of the size (diameter) of the hole does not affect the value of the location deviation.

In the previous figures, the positioning tolerances are independent, i.e. the center-to-center distances must be maintained within the tolerances specified by positional deviations, or by the maximum deviations and do not depend on what the actual diameters of the holes are (but, of course, the holes, in turn, must be made within their permissible dimensions).

Dependent location tolerance is a tolerance indicated on a drawing or in other technical documents in the form of a minimum value that can be exceeded by a value depending on the deviation of the actual size of the element (hole) and / or base under consideration from the maximum material limit, i.e. for a hole from the smallest limiting hole size.

The dependent location tolerance is highlighted by the symbol M,

standing next to the location tolerance or / and with the base.

The full value of the dependent location tolerance is determined by the formula:

,

where is the minimum value of the tolerance indicated in the drawing (part of the dependent tolerance, which is constant for all parts);

- additional value of the tolerance, depending on the actual dimensions of the holes.

If the hole is made with the maximum size (diameter), then it will be the maximum and it will be determined as

, ,

where is the hole tolerance.

Interpreting the above, it can be argued that the minimum guaranteed clearance for the passage of the fastener can be increased (which occurs when the actual dimensions of the mating elements deviate from the flow limits), while the correspondingly increased location deviation allowed by the dependent tolerance becomes acceptable.

Let us explain the above with specific examples.

In fig. 7, and the positional tolerance of the location is independent (there are no indications in the drawing). This means that the center of the hole ø10H12 must be within a circle with a diameter of 0.1 mm and not go beyond the limits, regardless of what the actual diameter of the hole is.

In fig. 7, b the positional tolerance is dependent (this is indicated by the M symbol next to the location tolerance). This means that the minimum positioning tolerance is 0.1 mm (for a hole diameter).

With an increase in the diameter of the hole, the location tolerance can be increased (due to the resulting gap in the joint). The maximum value of the location tolerance can be when the hole will be made at the upper limit size, i.e. when = 10.15 mm. Eventually

,

and then, i.e. the center of the hole ø 10H12 can be in a circle with a diameter of 0.25 mm.

5 Numerical values ​​of tolerances

hole locations

For connection (Fig. 1, a, type A) in both plates 1 and 2 to be connected, through holes are provided for the passage of fasteners. For connection of type B - through holes only in the 1st plate. The diametral clearance between the fastener and the hole in the plate must ensure free passage of the bolt (rivet) into the hole to ensure assembly. The guarantee can be achieved when the actual hole size is obtained close to the minimum hole size, and the shaft (bolt, rivets) - to the maximum size (usually, where d is the nominal size of the bolt). The difference between the dimensions and is the minimum gap, which is guaranteed, since with a larger gap, the more assembly will be ensured. The minimum diametral clearance is taken as the positional tolerance of the hole arrangement, and:

- for type A connections:;

- for type B connections: (gap in one plate only).

Here T is the main positional tolerance in diametrical terms (twice the maximum displacement from the nominal location according to GOST 14140-81).

For standard fasteners, there are developed tables with the diameters of through holes for them and the corresponding smallest (guaranteed) clearances (GOST 11284-75). One of these tables is given in Appendix 1.

2. When setting the dimensions, "ladder" with reference to the assembly base:

For type A connections - ;

For type B connections - .

Appendix 2 “Recalculation of positional tolerances for limit deviations dimensions coordinating the axis of the holes. System of rectangular coordinates ”according to GOST 14140-81, the numerical values ​​of the maximum deviations are given depending on the specified positional tolerance for some dimensioning schemes.

Appendix 3 shows examples of translating positional tolerances into maximum deviations for some sizing schemes with tolerance symbols in the drawings.

Positioning or shape tolerances for shafts or holes can be dependent or independent.

Addicted called the tolerance of the shape or location, the minimum value of which is indicated in the drawings or technical requirements and which is allowed to exceed by an amount corresponding to the deviation of the actual size of the part from the flow limit (the largest limiting shaft size or the smallest limiting hole size):

T zav = T min + T add,

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

Dependent position tolerances are established for parts that mate with counter parts simultaneously on two or more surfaces and for which the interchangeability requirements are reduced to ensuring assembly, i.e. the ability to connect parts on all mating surfaces. Dependent tolerances are associated with the gaps between the mating surfaces, and their maximum deviations should be in accordance with the smallest limiting size of the female surface (holes) and the largest limiting size of the male surface (shafts). Constrained tolerances are usually controlled by complex gauges that are prototypes of the mating parts. These calibers are always straight-through, which guarantees a fit-free assembly of products.

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

At highest values actual hole sizes T add max = 30.2–30 + 20.1 –20 = 0.3. In this case, T zav max = 0.1 + 0.3 = 0.4.

Figure 24 - Dependent hole alignment tolerance

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

End of work -

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Dependent tolerance in accordance with GOST R 50056-92 is a variable tolerance of the shape, location or coordinating size, the minimum value of which is indicated on the drawing or in the technical requirements and which is allowed to exceed by an amount corresponding to the deviation of the actual size of the considered and (or) base element of the part from maximum limit material. According to GOST 25346-89, the maximum material limit is a term referring to that of the limiting dimensions to which the largest volume of material corresponds, i.e. the largest limiting shaft size d max or the smallest limiting hole size D min.

Dependent can be assigned the following tolerances:

• shape tolerances:
  • - the tolerance of the straightness of the axis of the cylindrical surface;
  • - tolerance of flatness of the surface of symmetry of flat elements;
• location tolerances (orientation and location):
• - tolerance of perpendicularity of an axis or plane of symmetry relative to a plane or axis;
• - the tolerance of the inclination of the axis or plane of symmetry relative to the plane or axis;
• - alignment tolerance;
• - symmetry tolerance;
• - the tolerance of the intersection of the axes;
• - positional tolerance of an axis or plane of symmetry;
• tolerances of coordinating dimensions:
• - the tolerance of the distance between the plane and the axis or plane of symmetry of the element;
• - the tolerance of the distance between the axes or planes of symmetry of two elements.

Full value of dependent tolerance:

where T t in is the minimum dependent tolerance value specified by

on the drawing, mm;

Gdop - permissible excess of the minimum value of the dependent tolerance, mm.

Dependent tolerances are recommended to be assigned, as a rule, for those elements of parts to which requirements are imposed collection in joints with a guaranteed clearance. Tolerance T t [P calculated based on the smallest joint gap, and the permissible excess of the minimum value of the dependent tolerance is determined as follows:

For shaft

For hole

where d a and /) d - actual dimensions of the shaft and hole, respectively, mm.

The value of G add can vary from zero to the maximum value. d

If the shaft is in actual size d min, and the hole D max, then

For shaft

For hole

where TdwTD- the tolerance of the size of the shaft and hole, respectively, mm.

In this case, the dependent tolerance has a maximum value:

For shaft

For hole

If the dependent tolerance is related to the actual dimensions of the considered and base elements, then

where Gd 0P.r and Gd 0P.b are the permissible exceedances of the minimum value of the dependent tolerance, depending on the actual dimensions of the considered and base elements of the part, respectively, mm.

Examples of using dependent tolerances include:

• - positional location tolerance through holes for fasteners (Fig. 2.17, a);
• - Tolerances of alignment of stepped bushings and shafts (see.Fig.2.17, b, v), assembled with a gap;
• - the tolerance of the symmetry of the location of the grooves, for example, keyway (see Fig. 2.17, d);
• - tolerance of perpendicularity of the axes of holes and end surfaces of body parts for glasses, plugs, lids.

Rice. 2.17.a - positional tolerance of holes for fasteners; b, c - the alignment of the surfaces of the stepped sleeve and the shaft; G - symmetry of the keyway relative to the shaft axis

Dependent position tolerances are more economical and profitable for production than independent ones, since they expand the tolerance value and allow the use of less accurate and labor-intensive manufacturing technologies for parts, as well as reduce losses from rejects. The control of parts with dependent position tolerances is carried out, as a rule, using complex bore calibers.

The dependent tolerance of the shape or location is indicated in the drawing by a sign, which is placed in accordance with GOST 2.308-2011:

• - after the numerical value of the tolerance (Fig.2.17, a), if the dependent tolerance is associated with the actual dimensions of the element in question;
• - after the letter designation of the base or without the letter designation in the third field of the frame (see Fig. 2.17, b), if the dependent tolerance is related to the actual dimensions of the base feature;
• - after the numerical value of the tolerance and the letter designation of the base (see Fig. 2.17, G) or without letter designation (see.

rice. 2.17, v), if the dependent tolerance is related to the actual dimensions of the considered and base elements.

Since 01.01.2011 GOST R 53090-2008 (ISO 2692: 2006) has been put into effect. This GOST partially duplicates the current GOST R 50056-92 from 01.01.1994 in terms of rationing and indicating the requirements of the maximum material (MMR - maximum material reguirement) in the drawings in cases where it is necessary to ensure the assembly of parts in joints with a guaranteed gap. Requirements of the minimum material (LMR - least material reguirement), due to the need to limit minimum thickness the walls of the parts were not previously shown.

MMR and LMR requirements combine dimensional and geometric tolerance constraints into one complex requirement that more closely matches the intended use of the parts. This complex requirement allows, without prejudice to the performance of the part of its functions, to increase the geometric tolerance of the normalized (considered) element of the part, if the actual size of the element does not reach the limit value determined by the established size tolerance.

The requirement for the maximum material (as well as the dependent tolerance according to GOST R 50056-92) is indicated on the drawings by the sign and the requirement for the minimum material is indicated by the sign (L), placed in a frame to indicate the geometric tolerance of the normalized element after the numerical value of this tolerance or (and) the conventional designation of the base ...

Calculating Geometric Tolerance Values T m, providing the requirement for a maximum of material, can be performed in a similar way to the calculation of dependent tolerances (see formulas 2.10-2.15).

By designating, similarly to the dependent tolerances T m, geometric tolerances subject to minimum material requirements - T L, you can write:

where T m in is the minimum geometric tolerance specified by the

on the drawing, mm;

Tdop - permissible excess of the minimum value of the geometric tolerance, mm.

The values ​​of T add are determined as follows:

For shaft

For hole

d min, a hole D max, then

If the shaft is in actual size d max, and hole Z) min, then

For shaft

For hole

In this case, the geometric tolerance has a maximum value:

For shaft

For hole

If the geometric tolerance is associated with the actual dimensions of the normalized and basic elements, then the value of Gop is found from dependence (2.15).

Examples of the application of the maximum material requirements are examples of the assignment of dependent tolerances according to GOST R 50056-92 in Fig. 2.17. An example of the application of the minimum material requirement is shown in Fig. 2.18, a.

Both the maximum material requirements and the minimum material requirements can be supplemented by the reciprocity requirement (RPR), which allows an increase in the size tolerance of the part element, if the actual geometric deviation (deviation of shape, orientation or location) of the standardized element does not fully exploit the restrictions imposed by the requirements. MMR or LMR. Example of Application of Material Minimum Requirements and Interaction of Size 05 Tolerance O_ o, oz9 and concentricity tolerance is shown in Fig. 2.18, b, and an example of the application of the requirement of the maximum material and the interaction of the size 16_o, q and the perpendicularity tolerance is shown in Fig. 2.18, v.

Example 2.2. The dependent tolerance of the alignment of the hole 016 + OD8 relative to the outer surface 04O_o, 25 of the sleeve shown in Fig. 2.19.

It can be seen from the legend that the alignment tolerance depends on the actual size of the element, the axis of which is the reference axis, i.e. surfaces 04O_ о 25.

Rice. 2.18.a- minimum material; b - minimum material and interaction; v- maximum material and interaction

Rice. 2.19.

The minimum value of the alignment tolerance indicated in the drawing (7pcs = 0.1 mm) corresponds to the limit of the maximum material of the outer surface, in this case the size d a = d max = 40 mm, i.e. at d a = d max = 40 mm

If the outer surface is the actual size d a = d min, the alignment tolerance can be increased:

Intermediate size values d a and their corresponding tolerance values T m are given in table. 2.9, and in Fig. Figure 2.20 is a graph showing alignment tolerance versus actual bushing outer surface size.

Rice. 2.20.

Dependent alignment tolerance values, mm(see fig. 2.20)

Positioning or shape tolerances for shafts or holes can be dependent or independent.

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

T zav = T min + T add,

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

Dependent position tolerances are established for parts that mate with counter parts simultaneously on two or more surfaces and for which the interchangeability requirements are reduced to ensuring collection, i.e. the possibility of joining parts along all mating surfaces. Dependent tolerances are associated with the gaps between the mating surfaces, and their maximum deviations should be in accordance with the smallest limiting size of the female surface (holes) and the largest limiting size of the male surface (shafts). Constrained tolerances are usually controlled by complex gauges that are prototypes of the mating parts. These calibers are always straight-through, which guarantees a fit-free assembly of products.

Example. In fig. 2.22 shows a detail with holes of different sizes Æ20 +0.1 and 30 +0.2 with an alignment tolerance T min = 0.1 mm. The additional part of the tolerance is determined by the expression T add = D1 act - D1 min + D2 act - D2 min.

With the largest values ​​of the actual dimensions of the holes T add max = 30.2 –30 + 20.1 –20 = 0.3. In this case, T zav max = 0.1 + 0.3 = 0.4.

Rice. 2.22. Dependent hole alignment tolerance

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

Numerical values ​​of the tolerances of the shape and location of surfaces.

According to GOST 24643 - 81, 16 degrees of accuracy are established for each type of tolerance of the shape and location of surfaces. The numerical values ​​of the tolerances from one degree to another change with an increase factor of 1.6. Depending on the relationship between the size tolerance and the shape or location tolerances, the following levels of relative geometric accuracy are established: 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%. Size tolerance); C - high relative geometric accuracy (shape or location tolerances are approximately 25% of the size tolerance).

The shape tolerances of the cylindrical surfaces 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 surface diameter deviation. Shape and position tolerances can be limited to the size tolerance field. These tolerances are indicated only when, for functional or technological reasons, they should be less than the size tolerances or unspecified tolerances in accordance with GOST 25670 - 83.

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 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 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
Alignment (symmetry) tolerance relative to the axis 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 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:

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 = ± 3400 (corner mine T NS) T add = TD
	Three or more holes are located in a circle (no assembly base) Three or more holes are located in a circle, central element is an assembly base	T add = TD T p = 1.4 δα δα = ± 0.7 T R (corner mine T NS) 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
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).