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 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 batch and single production, and their control is carried out by 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 given limit deviations± δL coordinating dimensions;
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 batch production Required to provide correct functioning connections (centering, tightness, balancing and other requirements) Inspection universal means Type of connections: Responsible connections 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".
The numerical values of positional tolerances do not have degrees of accuracy and are determined from the base series of numerical values according to GOST 24643. The base series consists of 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 tolerance (symmetry) with respect to 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 NS) 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 on 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 relative to the common plane of 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 constructive form details. 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 length is taken, which ensures reliable installation of the part during measurement (for example, for the tolerance of coaxiality, the base will be a shaft step of a greater 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 conventional manufacturing accuracy achieved without the use of additional processing 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 keyway 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, engine flywheels internal combustion, 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; ten; 12; fourteen; 16; eighteen; twenty; 22; 25; 28; 32; 36; 40; 45; 50; 56; 63; 70; 80; 90; 100; 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 size 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 clearance is necessary to compensate for inaccuracies in dimensions and mutual disposition 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). Allowed by the standard various combinations tolerance fields for grooves on the shaft and in the bushing with a key tolerance field in width.
Most widespread has a normal connection when the hub (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 mixed dowels 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 of version 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 tooth profile 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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
, (4)
, (5)
, (7)
|
Determined value |
||
|
for shafts |
for holes |
|
|
d MMC - d a |
d a - d MMC |
|
|
TR Ma |
TF M min + TF z |
TF M min + TF z |
|
TF M max |
TF M min + T d |
TF M min + T d |
|
d MMC + TF M min |
d MMC - TF M min |
|
Note. Formulas for TF z and TR ma, given in table. 1, correspond to the condition when all local dimensions of the element are the same, and for cylindrical elements there are no deviations from roundness. If these conditions are not met, the values TF z and TR ma can be estimated only roughly (for example, if in the formulas instead of d a substitute values d a max for shafts or d a min for holes). It is critical that the condition is met so that the real surface does not go beyond the current limiting contour, the size of which is d υ.
3. DEPENDENT POSITIONING TOLERANCES
3.1. Dependencies can be assigned the following location tolerances:
The perpendicularity tolerance of an axis (or plane of symmetry) relative to a plane or axis;
Tilt tolerance of an axis (or plane - symmetry) relative to a plane or axis;
Alignment tolerance;
Symmetry tolerance;
Axis intersection tolerance;
Positional tolerance of an axis or plane of symmetry.
3.2. With dependent location tolerances, the maximum deviations of the size of the element and base in question are interpreted in accordance with GOST 25346.
3.3. The permissible excess of the minimum value of the dependent position tolerance is determined depending on the deviation of the mating size of the element and / or base in question from the corresponding maximum material limit.
Depending on the requirements for the part and the way the dependent tolerance is indicated in the drawing, the dependent tolerance condition may extend:
On the element under consideration and the base at the same time, when the expansion of the location tolerance is possible both due to deviations in the size of the mate of the element in question, and due to deviations in the size of the mate of the base;
Only on the element under consideration, when the expansion of the location tolerance is possible only due to the deviation of the size at the conjugation of the element under consideration;
Only to the base, when the expansion of the location tolerance is possible only due to the deviation of the size on the base mate.
3.4. Formulas for calculating the permissible excess of the minimum value of the dependent location tolerance, when the condition of the dependent tolerance is extended to the element in question, as well as for determining the actual and maximum values of the dependent location tolerance and the limiting effective size of the element under consideration are given in Table. 2 and 3.
3.5. If dependent tolerances are established for the relative position of two or more elements under consideration, then the values indicated in table. 2 and 3, are calculated for each considered element separately according to the dimensions and tolerances of the corresponding element.
table 2
Calculation formulas for dependent position tolerances in diametric terms (exceeding the minimum value of the dependent tolerance due to deviations in the size of the element in question)
|
Determined value |
||
|
for shafts |
for holes |
|
|
d MMC - d p |
d p - d MMC |
|
|
TR Ma |
TP M min + TP z |
TP M min + TP z |
|
TF M max |
TP M min + T d |
TP M min + T d |
|
d MMC + TP M min |
d MMC - TP M min |
|
Table 3
Calculation formulas for dependent position tolerances in radial expression (exceeding the minimum value of the dependent tolerance due to deviations in the size of the element in question)
|
Determined value |
||
|
for shafts |
for holes |
|
|
0,5 (d MMC - d p) |
0,5 (d p - d MMC) |
|
|
RTR Ma |
RTP M min + RTP z |
RTP M min + RTP z |
|
RTP M max |
RTP M min + 0,5 T d |
RTP M min + 0,5 T d |
|
d MMC + 2 RTP M min |
d MMC - 2 RTP M min |
|
3.6. When the condition of the dependent tolerance extends to the base, then deviation (displacement) of the base axis or plane of symmetry relative to the element (or elements) in question is additionally allowed. Formulas for calculating the actual and maximum values of the dependent tolerance of the location of the base, as well as the limiting effective size of the base are given in table. 4.
Table 4
Calculation formulas for dependent tolerances of base location
|
Determined value |
||
|
for shafts |
for holes |
|
|
TP zo = TRMao |
d MMCo - d po |
d po - d MMCo |
|
TR M max o |
||
|
Positioning tolerances in diametric terms |
||
|
RTP zo = RTP Mao |
0,5 (d MMCo -d po) |
0,5 (d po - d MMCo) |
|
RТР М max о |
0,5 T do |
0,5 T do |
|
Limit effective base size |
||
3.7. If, in relation to this base, a dependent tolerance of the location of one considered element is established, then the actual value of this tolerance can be increased by the actual value of the dependent tolerance of the location of the base according to table. 4 taking into account the lengths and location in the axial direction of the element and base in question (see Appendix 1, example 7).
If relative tolerances of the location of several elements are established relative to a given base, then the dependent tolerance of the location of the base cannot be used to increase the actual value of the dependent tolerance for the relative position of the elements under consideration (see Appendix 1, example 8).
4. DEPENDENT TOLERANCES OF COORDINATING SIZES
4.1. Dependent can be assigned tolerances of the following coordinating dimensions that determine the location of the axes or planes of symmetry of elements:
Distance tolerance between the plane and the axis (or plane of symmetry) of the element;
Distance tolerance between the axes (planes of symmetry) of two elements.
4.2. With dependent tolerances of coordinating dimensions, the maximum deviations of the dimensions of the elements in question are interpreted in accordance with GOST 25346.
4.3. The permissible excess of the minimum value of the dependent position tolerance is determined depending on the deviation of the mating size of the element (or elements) in question from the corresponding maximum material limit.
4.4. The formulas for calculating the permissible excess of the minimum value of the dependent tolerance of the coordinating size, the actual and maximum values of the dependent tolerance of the coordinating size, as well as the limiting effective dimensions of the elements under consideration are given in table. 5.
Table 5
Calculation formulas for dependent tolerances of coordinating dimensions
|
Determined value |
|||
|
for shafts |
for holes |
||
|
TL M max |
d MMC - d p TL M min + TL z TL M min + T d d MMC + TL M min |
d MMC - d p TL M min + TL z TL M min + T d d MMC + TL M min |
|
|
TL M max d 1υ d 2υ |
|d 1MMC - d 1p | + |d 2MMC - d 2p | TL M min + TL z TL M min + T d 1 + T d 2 |
||
|
d 1MMC + 0,5 TL M min d 2MMC + 0,5 TL M min |
d 1MMC - 0,1 TL M min d 2MMC - 0,5 TL M min |
||
5. ZERO DEPENDENT POSITIONING TOLERANCES
5.1. The constrained positioning tolerances can be set to zero. In this case, location deviations are allowed within the element size tolerance range and only on condition that the mating size deviates from the maximum material limit.
5.2. With a zero dependent location tolerance, the dimension tolerance is the cumulative dimension and location tolerance of the feature. In this case, the limit of the maximum material limits the size of the mate and is the limiting effective size of the element, and the limit of the minimum material limits the local dimensions of the element.
In extreme cases, the field of the total tolerance of size and location can be fully used for location deviations if the mating dimension is made at the limit of the minimum material, or for size deviations if the location deviation is zero.
5.3. The assignment of separate tolerances for the size of an element and the dependent tolerance of its location can be replaced by the assignment of a total tolerance of size and location in combination with a zero dependent tolerance for location, if, according to the conditions of assembly and functioning of the part, it is permissible that for this element the limit size for mating coincides with the limit effective size determined according to separate tolerances of size and location. Equivalent replacement is provided by increasing the size tolerance by shifting the maximum material limit by an amount equal to the minimum value of the dependent positioning tolerance in diametrical terms, while maintaining the minimum material limit, as shown in Fig. 2. Examples of equivalent replacement of separate tolerances of size and location are shown in fig. 3, as well as in Appendix 1 (example 10).
Compared to the separate assignment of size and position tolerances, the zero dependent positioning tolerance allows not only to increase the position deviation due to the size deviations from the maximum material limit, but also to increase the size deviation with a corresponding decrease in the position deviation.
Note. Replacing the separate tolerances of size and location with the total tolerance of size and location with a zero dependent location tolerance is not allowed for elements that form a fit during assembly, in which there is no guaranteed clearance that compensates for the minimum value of the dependent separate location tolerance, for example, for tolerances of the location of threaded holes in connections type B according to GOST 14143.
5.4. The relationship between deviations in size and location within the total tolerance (with zero dependent location tolerances) is not regulated. If necessary, it can be set in the technological documentation, taking into account the peculiarities of the manufacturing process by assigning an element-by-element limit to the maximum material for the local size or mating size ( d ′ MMC to hell. 2). Monitoring compliance with this limit during the acceptance control of products is not mandatory.
5.5. Zero dependent positioning tolerances can be set for all types of positioning tolerances specified in clause 3.1.
Notes:
1. Zero dependent form tolerance corresponds to the interpretation of the limiting dimensions in accordance with GOST 25346 and it is not recommended to assign it.
2. Instead of zero dependent tolerances of coordinating dimensions, zero dependent positional tolerances should be assigned.
6. INSPECTION OF PARTS WITH DEPENDENT TOLERANCES
6.1. Parts with dependent tolerances can be inspected in two ways.
6.1.1. Complex method, in which the observance of the principle of maximum material is monitored, for example, with the help of gauges to control the location (shape), instruments for coordinate measurements, in which the limiting effective contours are simulated and the measured elements are aligned with them; projectors by superimposing the image of real elements on the image of the limiting operating contours. Independently of this check, the dimensions of the element in question and the base are controlled separately.
Note. Caliber tolerances for position control and calculation of their dimensions are in accordance with GOST 16085.
6.1.2. Separate measurement of deviations in the size of the considered element and / or base and deviations of location (shape or coordinating size), limited by the dependent tolerance, followed by calculating the actual value of the dependent tolerance and checking the condition that the actual deviation of the location (shape or coordinating size) does not exceed the actual value of the dependent tolerance.
6.2. In case of discrepancies between the results of complex and separate control of deviations in shape, location or coordinating dimensions, limited by dependent tolerances, the results of complex control are arbitration.
ANNEX 1
Reference
EXAMPLES OF ASSIGNMENT OF DEPENDENT TOLERANCES AND THEIR INTERPRETATION
The dependent tolerance of the straightness of the hole axis is specified according to Fig. 4a.
The local dimensions of the hole should be between 12 and 12.27 mm;
The real surface of the hole should not go beyond the limiting effective contour - a cylinder with a diameter
d υ = 12 - 0.3 = 11.7 mm.
Actual values of the dependent tolerance of the straightness of the axis at different meanings local hole sizes are given in the table in fig. 4.
In extreme cases:
If all local dimensions of the hole are made equal to the smallest limiting dimension d mms= 12 mm, then the tolerance of the straightness of the axis will be 0.3 mm (the minimum value of the dependent tolerance, Fig. 4b);
If all values d a holes are made equal to the largest limit size d LMc= 12.27 mm, then the tolerance of the straightness of the axis will be 0.57 mm (the maximum value of the dependent tolerance, Fig. 4c).
|
12,00 d MMc |
|
The dependent tolerance of the flatness of the symmetry surface of the plate is set according to Fig. 5a.
The part must meet the following requirements:
The thickness anywhere should be between 4.85 and 5.15 mm;
Surfaces A the plates should not go beyond the limiting effective contour - two parallel planes, the distance between which is 5.25 mm.
Actual values of the dependent flatness tolerance at different meanings local plate thicknesses are given in the table in fig. 5. In extreme cases:
If the thickness of the plate in all places is made equal to the largest limit size d mms= 5.15 mm, then the flatness tolerance of the symmetry surface will be 0.1 mm (the minimum value of the dependent tolerance, Fig.5b),
If the thickness of the plate in all places is made equal to the smallest limiting size d LMc= 4.85 mm, then the flatness tolerance of the symmetry surface will be 0.4 mm (the maximum value of the dependent tolerance, Fig. 5c).
|
5,15 d MMc |
|
|
4,85 d LMc |
The dependent tolerance of the perpendicularity of the axis of the protrusion relative to the plane is specified according to Fig. 6a.
The part must meet the following requirements:
Local diameters of the protrusion should be between 19.87 and 20 mm, and the diameter of the protrusion in conjunction should be no more than 20 mm;
The surface of the protrusion should not go beyond the limiting effective contour - a cylinder with an axis perpendicular to the base A, and diameter
d υ = 20 + 0.2 = 20.2 mm.
|
20,00 d MMc |
|
|
19,87 d LMc |
The actual values of the dependent tolerance of the perpendicularity of the axis for different values of the diameter of the protrusion along the mate are given in the table in fig. 6 and graphically shown in the diagram (Fig. 6b).
In extreme cases:
If the diameter of the protrusion along the mating is made equal to the largest limit size d mms= 20 mm, then the tolerance of the perpendicularity of the axis will be 0.2 mm (the minimum value of the dependent tolerance, Fig. 6c);
If the diameter of the mating protrusion and all local diameters are made equal to the smallest limiting size d LMc = 19.87 mm, then the perpendicularity tolerance of the axis will be 0.33 mm (the maximum value of the dependent tolerance, Fig. 6d).
The tolerance of the slope of the symmetry plane of the groove relative to the plane is specified A according to the devil. 7a.
The part must meet the following requirements:
The local dimensions of the groove must lie between 6.32 and 6.48 mm, and the mating dimension must be at least 6.32 mm;
The side surfaces of the groove should not go beyond the limiting effective contour - two parallel planes located at an angle of 45 ° to the reference plane A and spaced apart from each other
d υ= 6.32 - 0.1 = 6.22 mm.
The actual values of the dependent tolerance of the slope of the plane of symmetry of the groove, depending on its size in conjunction, are given in the table in fig. 7 and graphically shown in the diagram (Fig. 7b).
In extreme cases:
If the width of the groove at the mate is equal to the smallest limit size d mms= 6.32 mm, then the tolerance of the slope of the plane of symmetry of the groove will be 0.1 mm (the minimum value of the dependent tolerance, Fig. 7c);
If the width of the mating groove and all local dimensions of the groove are equal to the largest limit size d LMc= 6.48 mm, then the tolerance of the inclination of the plane of symmetry will be 0.26 mm (the maximum value of the dependent tolerance, Fig. 7d).
|
6,32 d mms |
|
|
6,48 d LMc |
The dependent tolerance of the coaxiality of the outer surface relative to the base hole is set according to Fig. 8a; the condition of the dependent tolerance applies only to the element in question.
The part must meet the following requirements:
The local diameters of the outer surface should lie between 39, 75 and 40 mm, and the mating diameter should not be more than 40 mm;
The outer surface should not go beyond the limiting active contour - a cylinder with a diameter of 40.2 mm, coaxial with the base hole.
The actual values of the dependent alignment tolerance in diametric terms depending on the diameter at the mating of the outer surface are given in the table in fig. 8 and shown in the diagram (Fig. 8b).
In extreme cases:
If the diameter at the mating of the outer surface is equal to the largest limit size d mms= 40 mm, then the alignment tolerance is Ø 0.2 mm
(the minimum value of the dependent tolerance, Fig. 8c);
If the mating diameter and all local diameters of the outer surface are equal to the smallest limit size d LMc= 39.75 mm, then the alignment tolerance will be Ø 0.45 mm (the maximum value of the dependent tolerance, Fig. 8d).
|
40,00 d mms |
|
|
39,75 d LMc |
The dependent positional tolerance of the axes of the four holes in relation to each other is set according to Fig. 9a.
The part must meet the following requirements:
The local diameters of all holes must be between 6.5 and 6.65 mm, and the diameters at the interface of all holes must be at least 6.5 mm
d υ= 6.5 - 0.2 = 6.3 mm,
whose axes occupy a nominal position (in a precise rectangular lattice with a size of 32 mm). The actual values of the positional tolerance in the diametric expression for the axis of each hole, depending on the diameter at the mating of the corresponding hole, are given in the table in fig. 9 and shown in the diagram (Fig. 9b). In extreme cases:
d mms= 6.5 mm, then the positional tolerance of the axis of this hole will be Ø 0.2 mm (the minimum value of the dependent tolerance, Fig. 9b);
d mms= 6.65 mm, then the positional tolerance of the axis of this hole will be Ø 0.35 mm (the maximum value of the dependent tolerance, Fig. 9c).
The gauge diagram for controlling the location of the axes of the holes, which implements the limiting effective contours, is shown in Fig. 9d.
|
6,50 d mms |
|
|
6,65 d LMc |
The dependent tolerance of the coaxiality of the outer surface of the sleeve relative to the hole is set according to Fig. 10a; the condition of the dependent tolerance is specified for the base.
The part must meet the following requirements:
The local diameters of the outer surface should be between 39, 75 and 40 mm, and the mating diameter should be no more than 40 mm;
The local diameters of the base hole should be between 16 and 16.18 mm, and the mating diameter should be at least 16 mm;
The outer surface should not go beyond the limiting effective contour - a cylinder with a diameter
d υ= 40 + 0.2 = 40.2 mm,
whose axis coincides with the axis of the base hole, if its mating diameter is equal to the smallest limit size d mms about = 16 mm. The actual values of the dependent tolerance of alignment, depending on the size at the conjugation of the outer surface, are given in the table in fig. 10 (column 2) and measured from Ø 0.210 mm (at d mms= 40 mm) up to Ø 0.45 mm (at d LMc= 39.75 mm);
The surface of the base hole should not go beyond the contour of the maximum material - a cylinder with a diameter of 16 mm ( d mms o), coaxial with the limiting effective contour of the outer surface. Valid Tolerance Values TR mao on the displacement of the base axis relative to the axis of the maximum material contour, depending on the diameter at the mating of the base hole, are given in the table in fig. 10 (4th line from the top) and vary from 0 (at d mms o= 16 mm) up to Ø 0.18 mm (at d LMco= 16.18 mm).
|
Total value TR 'ma = TR ma +TP Mao |
||||||
The total actual value of the dependent tolerance of the coaxiality of the outer surface relative to the hole, depending on the size deviations of both the considered element and the base for a given configuration of the part (both elements have the same length and the same location in the axial direction) is
TR ′ ma = TR Ma + TR mao
The values TR ′ ma at different sizes on the conjugation of the element in question and the base are given in the table in fig. 10. In extreme cases:
If the dimensions for mating elements are made according to the maximum material limit ( d p = 40 mm, d po = 16 mm), then TR ′ ma =Ø 0.2 mm (the minimum value of the dependent tolerance, Fig. 10b);
If the dimensions of the mate and all local dimensions of the elements are made according to the minimum material limit ( d p= 39.75 mm; d po= 16.18 mm), then TR ′ ma =Ø 0.63 mm (maximum value of the dependent tolerance, Fig. 10c).
With other configurations of parts, when the element in question and the base are spaced apart in the axial direction, the total actual value of the dependent tolerance of alignment depends on the length of the elements, the magnitude of their separation in the axial direction, as well as on the nature of the deviation from alignment (the ratio between parallel and angular displacement of the axes).
For example, for the detail shown in damn. 11a, in the case of angular displacement of the element axes (Fig.11b), the maximum value of the dependent alignment tolerance will be equal to
TR ′ max= 2
However, with a parallel offset of the axes (Fig. 11c), the maximum value of the dependent alignment tolerance will be different:
TR ′ max= 2
If the nature of the deviation of the axes is unknown, it is decisive to observe the principle of maximum material, for example, when checking with a gauge shown in fig. 11d.
The dependent positional tolerance of the axes of the four holes is set in relation to each other and relative to the axis of the base hole according to Fig. 12a; the condition of the dependent tolerance is specified for the base.
|
5,5 d mms |
7,00 d mmso |
||
|
5,62 d LMco |
|||
|
7,15 d LMco |
The part must meet the following requirements:
The local diameters of the four peripheral holes must be between 5.5 and 5.62 mm, and the diameters at the mating of these holes must be at least 5.5 mm;
The local diameters of the base hole must be between 7 and 7.15 mm, and the mating diameter must be at least 7 mm;
The surfaces of the peripheral holes should not go beyond the limiting effective contours - cylinders with a diameter
d υ = 5.5 - 0.2 = 5.3 mm,
whose axes occupy a nominal position (in a precise rectangular lattice with a size of 32 mm); the central axis of symmetry of the lattice coincides with the axis of the base hole if its size in conjunction is made according to the smallest limiting size ( dmmsO = 7 mm). Actual values of the dependent positional tolerance of the axis of each hole considered TR ma depending on the mating diameter of the corresponding hole are given in the table in fig. 12 and vary from Ø 0.2 mm (at dmms = 5.5 mm) up to Ø 0.32 mm (with d LMc= 5.62 mm), fig. 12b, c;
The surface of the base hole should not go beyond the contour of the maximum material - a cylinder with a diameter of 7 mm ( d υ o = d MMCo), whose axis coincides with the central symmetry axis of the limiting active contours of the four holes. Actual values of the positional tolerance of the datum hole axis TR mao depending on the diameter at the mating of this hole are given in the table in fig. 12 and vary from 0 (at dmmsO = 7 mm) up to Ø 0.15 mm (at d LMco= 7.15 mm), fig. 12b, c. This positional tolerance cannot be used to widen the positional tolerances of peripheral holes relative to each other.
The gauge scheme for controlling the location of the axes of the holes, which implements the limiting effective contours of the four peripheral holes and the contour of the maximum material of the base hole, is shown in Fig. 12g.
The dependent tolerance of the distance between the axes of the two holes is specified according to the drawing. 13a.
The part must meet the following requirements:
The local diameters of the left hole must be between 8 and 8.15 mm, and the mating diameter must be at least 8 mm;
The local diameters of the right hole must be between 10 and 10.15 mm, and the mating diameter must be at least 10 mm;
The surfaces of the holes should not go beyond the limiting effective contours - cylinders with diameters of 7.8 and 9.8 mm, the distance between the axes of which is 50 mm. The actual values of the dependent tolerance of the distance between the axes corresponding to this condition, depending on the diameters at the conjugation of both holes, are given in the table in fig. 13.
In extreme cases:
If the diameters at the mating of both holes are equal to the smallest limit size d 1Mms = 8 mm and d 2Mms= 10 mm, then the maximum deviations of the distance between the axes will be ± 0.2 mm (the minimum value of the dependent tolerance, Fig. 13b);
If the mating diameters and all local diameters of both holes are equal to the largest limit size d 1 L ms= 8.15 mm and d 2 L ms = 10.15 mm, then the maximum deviations of the distance between the axes of the holes will be ± 0.35 mm (the maximum value of the dependent tolerance, Fig. 13c).
The gauge scheme for controlling the distance between the axes of two holes, which implements the limiting effective contours of the holes, is shown in fig. 13d.
|
d 1 p |
d 2p |
|||
|
± 0.5 T LMa |
||||
The zero dependent positional tolerance of the axes of the four holes in relation to each other is specified according to Fig. 14a.
V this example for the part considered in example 6 (Fig. 8), an equivalent replacement of the separate tolerances of size and location with an extended tolerance of size with a zero dependent tolerance of location was made.
The part must meet the following requirements:
The local dimensions of all holes must be between 6.3 and 6.65 mm, and the diameters at the interface of all holes must be at least 6.3 mm;
The surfaces of all holes should not go beyond the limiting effective contours - cylinders with a diameter
d υ= 6.3 - 0 = 6.3 mm,
whose axes occupy a nominal position (in a precise rectangular lattice with a size of 32 mm).
The actual values of the positional tolerance in the diametric expression for the axis of each hole, depending on the diameter at the mating of the corresponding hole, are given in the table in fig. 14 and shown in the diagram (Fig. 14b).
In extreme cases:
If the diameter at the mate of this hole is equal to the smallest limit size d mms= 6.3 mm, then the axis of the hole should occupy the nominal position (positional deviation is zero); in this case, the entire field of the total tolerance of the size and location of the element can be used for deviations of the local diameter and deviations of the hole shape;
If the diameter at the conjugation of this hole and all of its local diameters are equal to the largest limiting size d LMc= 6.65 mm, then the positional tolerance of the axis of this hole will be Ø 0.35 mm (the maximum value of the dependent tolerance); in this case, the entire total tolerance of the size and position of the element can be used for position deviations.
The gauge diagram for controlling the location of the axes of the holes, which implements the limiting effective contours, is shown in Fig. 14c.
|
6,30 d mms |
|
|
6,65 d LMc |
APPENDIX 2
Reference
TECHNOLOGICAL ADVANTAGES OF DEPENDENT TOLERANCES
1. Technological advantages dependent tolerances of the shape and location in comparison with independent ones consist primarily in the fact that they allow the use of less accurate, but more economical ways processing and equipment, and reduce waste from scrap. If the field of technological dispersion of location deviations exceeds the value of the location tolerance (independent or dependent), then with dependent location tolerances, the proportion of suitable parts increases in comparison with independent tolerances due to:
Parts with deviations in shape and location exceeding the minimum value, but not exceeding the actual value of the dependent tolerance;
Parts for which deviations in shape and location, although they exceed the actual value, do not exceed the maximum value of the dependent tolerance; these parts are recoverable defects and can be converted into usable ones by additional processing of the element for a corresponding change in its size towards the limit of the minimum material, for example, by boring or reaming holes (see example in Fig. 15).
2. If the field of technological dispersion of location deviations is limited, proceeding from the condition that there is practically no correctable or final marriage due to location deviations (that is, so that its share does not exceed a given percentage of risk), then this field will be larger for the dependent location tolerance, according to compared to independent.
Its increase can be determined taking into account the laws of distribution of deviations in size and location, the share of risk, the ratio between the tolerances of size and location. Tentatively, to assess the possible field of technological dispersion, it can be taken equal to the actual value of the dependent location tolerance when the actual dimensions of the elements are fulfilled in the middle of the dimensional tolerance field.
3. If the condition of dependent tolerance applies to the base, then this makes it possible to simplify the design of the basing elements of technological devices, for example, conductors, and calibers, since their basing elements can be made not self-centering, but rigid with a constant size corresponding to the maximum limit of the base material. The displacement of the base of the part due to the gap between it and the base element of the fixture or gauge, which occurs when the size of the base deviates from the maximum material limit, in this case is allowed by the dependent position tolerance.
4. With dependent location tolerances, the manufacturer has the ability, if necessary, to increase (in the technological documentation) the minimum value of the dependent location tolerance due to a corresponding reduction in the size tolerance field on the side of the maximum material.
5. Dependent tolerances make it possible to reasonably use gauges to control the location (shape, coordinating dimensions) in accordance with GOST 16085, assessing the suitability of a part by entering it. The principle of operation of such calibers is fully consistent with the concept of dependent tolerances.
With independent tolerances of the location, the use of calibers may turn out to be impossible or require a preliminary recalculation of an independent tolerance into a dependent one (mainly in technological documentation) or the use of a special method for calculating the executive dimensions of calibers.
Independent location tolerance
Dependent location tolerance
INFORMATION DATA
1 . DEVELOPED AND INTRODUCED by the All-Union Scientific Research and Design Institute of Measuring Instruments in Mechanical Engineering
DEVELOPERS
A.V. Vysotsky, Cand. tech. sciences; M.A. Paley(topic leader), Cand. tech. sciences; L.A. Ryabinin; O.V. Buyanina
2 . APPROVED AND PUT INTO EFFECT by the Decree of the State Standard of Russia dated 28.07.92 No. 794
3 ... The period of the first inspection is 2004, the frequency of the inspection is 10 years.
4 . The standard complies with the international standard ISO 2692-88 in terms of terminology (p.1.1.1 - 1.1.5 , 1.1.9 ) and examples (examples1 , 3 , 4 , 6 , 7 (heck.11 ), 8 , 10 )
5 . INTRODUCED FOR THE FIRST TIME
6 . REFERENCE REGULATORY AND TECHNICAL DOCUMENTS
1.1, 1.2, 3.2, 4.2, 5.5
ISO 1101 / 2-74
Deviations in the location of surfaces and coordinating dimensions, as well as deviations in dimensions (diameters, widths, etc.) can manifest themselves both jointly and independently of each other. Their mutual influence is possible both in the manufacturing process and in the control process. Therefore, it is customary to consider independent and dependent tolerances for the location of surfaces and coordinating dimensions.
Independent admission- the tolerance of the relative position or shape, the numerical value of which is constant and does not depend on the actual dimensions of the surfaces or profiles under consideration.
Dependent location or shape tolerance Is a variable tolerance, the minimum value of which is indicated in the drawing or technical requirements and which is allowed to be exceeded by an amount corresponding to the deviation of the actual size of the part surface from the maximum material limit (the largest limit size shaft or smallest hole size limit). To designate the dependent tolerance, after its numerical value in the box, write the letter M in a circle à.
According to GOST R 50056-92, the concepts are established - the minimum and maximum value of the dependent tolerance.
The minimum value of the dependent tolerance- the numerical value of the dependent tolerance, when the considered (normalized) element and (or) base have dimensions equal to the maximum material limit.
The minimum value of the dependent tolerance can be zero. In this case, location deviations are allowed within the element size tolerance range. With a zero dependent location tolerance, the dimension tolerance is the cumulative dimension and location tolerance.
Maximum value of dependent tolerance- the numerical value of the dependent tolerance, when the considered element and (or) base have dimensions equal to the minimum material limit.
Constrained tolerances are assigned only to elements (their axes or planes of symmetry) that are holes or shafts.
The following dependent shape tolerances exist:
- the tolerance of the straightness of the axis of the cylindrical surface;
- flatness tolerance of the surface of symmetry of flat elements.
Dependent position tolerances:
- 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.
Dependent tolerances of coordinating dimensions:
- the tolerance of the distance between the plane and the axis or plane of symmetry;
- the tolerance of the distance between the axes (planes of symmetry) of the two elements.
Dependent location tolerances are assigned mainly in cases where it is necessary to ensure the collection of parts that mate simultaneously on several surfaces with specified gaps or interference. The use of dependent tolerances of shape and location reduces the cost of manufacturing and simplifies the acceptance of products.
The numerical value of the dependent tolerance can be related to:
1) with the actual dimensions of the element in question;
2) with the actual dimensions of the base element;
3) with the actual dimensions of both the base and the considered elements.
When denoting the dependent tolerance in the drawings in accordance with GOST 2.308-79, the symbol à is used.
If the dependent tolerance is related to the actual size of the element in question, conventional sign is indicated after the numerical value of the tolerance.
If the dependent tolerance is related to the actual size of the base feature, the symbol is specified after letter designation base.
If the dependent tolerance is related to the actual size of the element in question and the dimensions of the base element, then the à sign is indicated twice after the numerical value of the tolerance and after the letter designation of the base.
Constrained tolerances are usually controlled by complex gauges that are prototypes of the mating parts. These calibers are straight through only and guarantee a fit-free assembly of products. Complex gauges are rather complicated and expensive to manufacture, therefore the use of dependent tolerance is advisable only in serial and mass production.
| 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).
Shape tolerances cylindrical surfaces(for deviations from cylindricity, roundness and longitudinal section profile), corresponding to the 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. 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 distinction is made between running-in, a period of normal operation and catastrophic wear. The resulting roughness after running-in, ensuring minimal wear and being retained in the process long-term operation machines, it is customary to call 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 the middle line of the profile. The base line has the form of a nominal profile and is drawn so that within the base length the standard deviation of 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 quantify roughness six parameters are set: three height, 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;
Highest height irregularities in the profile 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.
