Hole system and shaft system. Tolerances and fits. Measuring tool Shaft system and hole system how to distinguish

When transferring fits from the hole system to the shaft system, use the following rule: when transferring, the quality of the accuracy of the shaft and hole is preserved, the main deviations change - the non-main shaft becomes the main shaft h, and the main hole H is replaced by a non-main hole.

In accordance with this rule, in our example, the fit into the shaft system will be translated as follows: Ø45 P7/h6.

We repeat all previous calculations for the shaft system

6.2.1 Nominal shaft and bore diameters

6.2.2 We find the maximum deviations of the shaft with tolerance range h6 from Table 7 of GOST 125347 - 82 for quality 6 (for an interval measuring over 40 to 50 mm):

es = 0; ei = -16µm

We find the maximum deviations of hole P7 similarly in Table 8 of GOST 125347 - 82, they are equal to:

ES = -17 µm; EI = -42 µm

6.2.3 Determine the maximum dimensions of the shaft and hole:

6.2.4 Find the tolerance of the shaft and hole:

6.2.5 Let us determine the nature of the fit, since the dimensions of the shaft are larger than the dimensions of the hole, an interference is formed in the connection, we find N max, N min. They are equal

6.2.6 The fit tolerance is

Examination:

The calculation was done correctly.

Calculations have shown that when transferring a fit from a hole system to a shaft system, the tolerances of the shaft and hole, as well as the nature of the fit, do not change.

6.2.7 Similarly, we construct a diagram of the location of tolerance fields for landing Ø45 P7/h6, Figure 13.

6.2.8 The designation of tolerance fields and fits on the drawings is presented in Figure 14.

Figure 12 – Scheme of tolerance fields for fit Ø 45 H7/p6 (in the hole system)

Figure 13 – Scheme of tolerance fields for fit Ø 45 Р7/h6 (in the shaft system)

Figure 14 – Examples of designation of tolerance fields and fits in drawings

Control questions

1 Mating and non-mating surfaces, male and female, shapes of mating surfaces.

2 What sizes are called nominal, actual, limit, symbols of sizes.

3 Limit deviations, their purpose, symbol, cases of specifying deviations and graphical location of deviations relative to the zero line.

4 What is called tolerance is a symbol of tolerance, determination of tolerance based on specified maximum dimensions and deviations (formulas). Can the tolerance be negative or zero?

5 Landing. Types of landings. Landing permission. Designation of landings in the drawing.

6 Location of tolerance fields for the hole and shaft in each fit, characteristics of fits, formulas for determining gaps and interference.

7 What is called the main deviation, what does it determine, how the main hole and the main shaft are designated: definition, symbol, graphic image. Symmetrical tolerance field, symbol and graphic representation.

8 Define quality, list the qualities. How does one qualification differ from another?

9 Hole system and shaft system, definition. Transfer of planting from one system to another.

10 Ways to indicate dimensions in the drawing. What is called the tolerance zone, give a definition.

11 Tables of maximum deviations, ranges, intervals. What units of measurement are specified in? maximum deviations and tolerances in reference books?

Chapter 1. Hole system and shaft system. Peculiarities,

differences, advantages…………………………………………………………….3

1.1.The concepts of “shaft” and “hole”………………………………………………………………...3

1.2. Calculation of fit parameters and calibers for mating in

hole and shaft systems…………………………………………………………….6

Chapter 2. Tolerances and fits of keyed connections………………………...10

2.1. Thread tolerances………………………………………………………………………………15

2.2. Size tolerance. Tolerance field…………………………………………..18

2.3. Formation of fields of tolerances and landings……………………………..19

Chapter 3. Tolerance and landing systems………………………………………………………..21

3.1. Layout of tolerance fields for standard interfaces……….23

List of used literature……………………………………………………..30

Chapter 1. Hole system and shaft system. Features, differences, advantages

1.1.The concepts of “shaft” and “hole”

Structurally, any part consists of elements (surfaces) of different geometric shape, some of which interact (form mating fits) with the surfaces of other parts, and the rest of the elements are free (non-mating). In the terminology of tolerances and fits, the dimensions of all elements of parts, regardless of their shape, are conventionally divided into three groups: shaft dimensions, hole dimensions, and dimensions not related to shafts and holes.

Shaft is a term conventionally used to designate the external (male) elements of parts, including non-cylindrical elements, and, accordingly, mating dimensions.

Hole is a term conventionally used to designate internal (enclosing) elements of parts, including non-cylindrical elements, and, accordingly, mating dimensions.

For mating elements of parts, based on the analysis of working and assembly drawings, and, if necessary, product samples, the female and male surfaces of the mating parts and, thus, the membership of the mating surfaces in the “shaft” and “hole” groups are established.

For non-mating elements of parts, the establishment of a shaft or a hole is carried out using the technological principle that if, when processing from the base surface, the size of the element increases, then this is a hole, and if the size of the element decreases, then this is a shaft.

The composition of the group of dimensions and elements of parts that do not relate to either shafts or holes is relatively small (for example, chamfers, rounding radii, fillets, protrusions, depressions, distances between axes (etc.).

During assembly, the parts to be connected come into contact with each other by separate surfaces, which are called mating surfaces. The dimensions of these surfaces are called mating dimensions (for example, the diameter of the bushing hole and the diameter of the shaft on which the bushing is seated). A distinction is made between female and male surfaces and, respectively, male and female dimensions. The enclosing surface is usually called the hole, and the male surface is called the shaft.

The interface has one nominal size for the hole and shaft, and the maximum sizes are usually different.

If the actual (measured) dimensions of the manufactured product do not go beyond the largest and smallest maximum dimensions, then the product meets the requirements of the drawing and is made correctly.

The designs of technical devices and other products require different contacts of mating parts. Some parts must be movable relative to others, while others must form fixed connections.

The nature of the connection of parts, determined by the difference between the diameters of the hole and the shaft, creating greater or less freedom of their relative movement or the degree of resistance to mutual displacement, is called fit.

There are three groups of landings: movable (with a gap), fixed (with interference) and transitional (a gap or interference is possible).

The gap is formed as a result of the positive difference between the dimensions of the hole diameter and the shaft. If this difference is negative, then the fit will be an interference fit.

There are the largest and smallest gaps and interferences. The largest clearance is the positive difference between the largest limiting hole size and the smallest limiting shaft size

The smallest gap is the positive difference between the smallest limiting hole size and the largest limiting shaft size.

The greatest interference is the positive difference between the largest maximum shaft size and the smallest maximum hole size.

The minimum interference is the positive difference between the smallest maximum shaft size and the largest maximum hole size.

The combination of two tolerance fields (hole and shaft) determines the nature of the fit, i.e. the presence of a gap or interference in it.

The system of tolerances and fits establishes that in each mate one of the parts (the main one) has any deviation equal to zero. Depending on which of the mating parts is accepted as the main one, a distinction is made between fits in the hole system and fits in the shaft system.

Fittings in a hole system are fittings in which various clearances and tensions are obtained by connecting different shafts to the main hole.

Fittings in the shaft system are landings in which various clearances and interferences are obtained by connecting various holes with the main shaft.

The use of a hole system is preferable. The shaft system should be used where design or economic considerations make sense (for example, multiple bushings, flywheels or wheels with different landings on one smooth shaft).

1.2. Calculation of fit parameters and gauges for mating in hole and shaft systems

1. Deviations of the hole and shaft according to GOST 25347-82:

ES = +25 µm, es = -80 µm

EI = 0; ei = -119 µm

Fig.1. Layout of landing tolerance fields

2. Limit dimensions:

3. Hole and shaft tolerances:

4. Clearances:

5. Average clearance:

6. Clearance tolerance (fit)

7. Designation of maximum dimensional deviations on design drawings:

a) symbol of tolerance fields

b) numerical values of maximum deviations:

c) symbol of tolerance fields and numerical values of maximum deviations:

8. Designation of dimensions on working drawings:

9. Calculation of gauges for checking holes and shafts.

Tolerances and deviations of calibers according to GOST 24853-81:

a) for plug gauges

Z = 3.5 µm, Y = 3 µm, H = 4 µm;

b) for clamp gauges

Z 1 = 6 µm, Y 1 = 5 µm, H 1 = 7 µm;

Rice. 2 Layout of caliber tolerance fields

Bore testing gauges

Plug PR

Executive plug size PR:

Average wear
µm;

Workers can wear the plug up to the following size:

Wear of the plug by the shop inspector is permissible up to the following size:

Cork NOT

Executive plug size NOT:

Shaft test gauges

Executive size of bracket PR:

Average wear
µm;

Wear of the bracket by workers is permissible up to the following size:

Wear of the bracket by the shop inspector is permissible up to the following size:

Executive staple size NOT

Chapter 2. Tolerances and fits of keyed joints

A keyed connection is one of the types of connections between a shaft and a bushing using an additional structural element (key) designed to prevent their mutual rotation. Most often, a key is used to transmit torque in connections between a rotating shaft and a gear or pulley, but other solutions are also possible, for example, protecting the shaft from rotating relative to a stationary housing. Unlike tension connections, which ensure mutual immobility of parts without additional structural elements, keyed connections are detachable. They allow the structure to be disassembled and reassembled with the same effect as during initial assembly.

The key connection includes at least three fits: shaft-bushing (centering mate), shaft key-groove, and bushing key-groove. The accuracy of centering of parts in a keyed connection is ensured by the fit of the sleeve on the shaft. This is a conventional smooth cylindrical mating that can be installed with very small clearances or interferences, therefore transitional fits are preferred. In the mating (dimensional chain) along the height of the key, a nominal clearance is specially provided (the total depth of the grooves of the sleeve and shaft is greater than the height of the key). Another connection is possible - along the length of the key, if a parallel key with rounded ends is placed in a blind groove on the shaft.

Keyed connections can be movable or fixed in the axial direction. In moving joints, guide keys are often used and are secured to the shaft with screws. A gear (gear wheel block), half-coupling or other part usually moves along a shaft with a guide key. Keys attached to the bushing can also serve to transmit torque or to prevent the bushing from rotating as it moves along a stationary shaft, as is done in the bracket of a heavy rack for measuring heads such as microcators. In this case, the guide is a shaft with a keyway.

According to their shape, keys are divided into prismatic, segmental, wedge and tangential. The standards provide for different designs of some types of keys.

Parallel keys make it possible to obtain both movable and fixed connections. Segment keys and wedge keys, as a rule, are used to form fixed joints. The shape and dimensions of the sections of keys and grooves are standardized and selected depending on the diameter of the shaft, and the type of key connection is determined by the operating conditions of the connection.

The maximum deviations of the groove depths on the shaft t1 and in the sleeve t2 are given in table No. 1:

Table No. 1

Widths b – h9;

Heights h – h9, and for h over 6 mm – H21.

Depending on the nature (type) of the keyway connection, the standard establishes the following tolerance fields for the groove width:

To ensure the quality of the key connection, which depends on the accuracy of the location of the symmetry planes of the grooves of the shaft and sleeve, symmetry and parallelism tolerances are assigned and indicated in accordance with GOST 2.308-79.

Numerical values of location tolerances are determined by the formulas:

T = 0.6 T sp

T = 4.0 T sp,

where T sp – tolerance for the width of the keyway b.

Calculated values are rounded to standard values according to GOST 24643-81.

The roughness of the keyway surfaces is selected depending on the tolerance margins of the keyway dimensions (Ra 3.2 µm or 6.3 µm).

The symbol for parallel keys consists of:

The words "Spline";

Designations of version (version 1 are not indicated);

Section dimensions b x h and key length l;

Standard designations.

An example of a symbol designation for a feather key, version 2, with dimensions b = 4 mm, h = 4 mm, l = 12 mm

Key 2 - 4 x 4 x 12 GOST 23360-78.

Parallel guide keys are secured in the shaft grooves with screws. A threaded hole is used to press out the key during dismantling. An example of a symbol for a prismatic guide key version 3 with dimensions b = 12 mm, h = 8 mm, l = 100 mm Key 3 - 12 x 8 x 100 GOST 8790-79.

Segment keys are used, as a rule, to transmit small torques. The dimensions of segment keys and keyways (GOST 24071-80) are selected depending on the diameter of the shaft.

Dependence of the tolerance fields of the groove width of a segmental key connection on the nature of the key connection:

For heat-treated parts, maximum deviations of the shaft groove width are allowed according to H11, and the bushing groove width is D10.

The standard establishes the following tolerance fields for key sizes:

Widths b – h9;

Heights h (H2) - H21;

Diameter D - H22.

The symbol for segmental keys consists of the word “Key”; execution designations (version 1 is not indicated); section dimensions b x h (H2); standard designations.

Wedge keys are used in fixed joints when the requirements for the alignment of the parts being connected are low. The dimensions of wedge keys and keyways are standardized by GOST 24068-80. The length of the groove on the shaft for a taper key of design 1 is made equal to 2l; for other designs, the length of the groove is equal to the length l of the embedded key.

The maximum deviations of dimensions b, h, l for wedge keys are the same as for prismatic keys (GOST 23360-78). According to the width of the key b, the standard establishes connections along the width of the groove of the shaft and sleeve using tolerance fields D10. The length of the shaft groove L is H15. The maximum depth deviations t1 and t2 correspond to the deviations for parallel keys. Limit deviations of the angle of inclination of the upper edge of the key and groove ± AT10/2 according to GOST 8908-81. An example of a symbol for a wedge key, version 2, with dimensions b = 8 mm, h = 7 mm, l = 25 mm: Key 2 - 8 x 7 x 25 GOST 24068-80.

Inspection of keyed connection elements using universal measuring instruments is significantly difficult due to the smallness of their transverse dimensions. Therefore, calibers are widely used to control them.

In accordance with the Taylor principle, a pass gauge for checking a hole with a keyway is a shaft with a key equal to the length of the keyway or the length of the keyway. This caliber provides comprehensive control of all sizes, shapes and locations of surfaces. The set of no-go gauges is designed for element-by-element control and includes a no-go gauge for monitoring the centering hole (a smooth no-go plug of full or partial profile) and templates for element-by-element control of the width and depth of the keyway.

The pass-through gauge for checking a shaft with a keyway is a prism (“rider”) with a protrusion-key equal to the length of the keyway or the length of the keyway. The set of no-go gauges is designed for element-by-element control and includes a no-go gauge-bracket for monitoring the dimensions of the centering surface of the shaft and templates for element-by-element control of the width and depth of the keyway.

2.1.Thread tolerances

The connection between a screw and a nut depending on the accuracy of their threads. All threads accepted in mechanical engineering, with the exception of pipe threads, have gaps at the tops and bottoms, and if executed correctly threaded connection the screw and nut are in contact only with their sides (Fig. 167, a) For complete contact of the sides of the profile of all thread turns involved in this connection, the main importance is the accurate execution (within certain limits) of the dimensions of the average diameter of the thread of the screw and nut, the pitch of this thread and the angle of its profile. The accuracy of the outer and inner diameters of the screw and nut is less important, since there is no contact between the thread surfaces along these diameters.

If the gap along the average diameter is too large, the contact of the thread turns occurs only on one side (Fig. 167, b). If the clearance along the average diameter is too small for screwing together threaded parts, one of which has an incorrect thread pitch, it is necessary that the turns of one of the parts cut into the turns of the other. For example, if the pitch of the screw is greater than expected or, as they say, “stretched,” then in order to connect such a screw with a nut with the correct thread, the turns of the nut must cut into the turns of the screw (Fig. 167, V). This is obviously impossible, and the screwability of these parts can be achieved only by reducing the average diameter of the screw (Fig. 167, d) or increasing the average diameter of the threaded parts, one of which has an incorrect thread pitch; it is necessary that the turns of one of the parts cut into the turns another. For example, if the pitch of the screw is greater than expected or, as they say, “stretched,” then in order to connect such a screw with a nut with the correct thread, the turns of the nut must cut into the turns of the screw (Fig. 167, V). This is obviously impossible, and make-up of these parts can only be achieved by reducing the average diameter of the screw (Fig. 167, d) and or by increasing the average diameter of the nut. In this case, it may happen that only one outer turn of the nut will touch the corresponding turn of the screw and not along its entire lateral surface.

In the same way, you can ensure the screwability of the threads of parts if the angle of the profile of one of them or the position of this profile is incorrect. For example, if the profile angle of the screw is less than expected, which excludes the possibility of the screw being screwed together with the correct nut (Fig. 167, d), then by reducing the average diameter of this screw, these parts can be screwed together (Fig. 167, e). In this case, the contact of the screw thread and the nut occurs only along the upper sections of the side of the screw thread profile and along the lower sections of the nut thread profile.

By reducing the average diameter of a screw with an incorrect profile position (Fig. 167, and) It is also possible to obtain the screwability of a given screw with a nut, however, even in this case, the contact surface of the threads of the screw and the nut may be insufficient for a high-quality threaded connection (Fig. 167, h).

Construction of thread tolerances. Difficulties associated with checking the thread being cut arise mainly when measuring its pitch and profile. Indeed, if all three diameters external thread can be checked with sufficient accuracy in most cases of practice using micrometers, then for an appropriate (accuracy) check of the pitch and angle of the thread profile, more complex measuring instruments and even instruments are required. Therefore, when manufacturing threaded parts, tolerances are set only for thread diameters; permissible errors in the pitch and profile are taken into account in the tolerance for the average diameter, because, as shown above, errors in the pitch and profile can always be eliminated by changing the average diameter of one of the threaded parts.

The tolerance on the average diameter is set so that with small errors in the pitch or profile angle, the screw and nut are screwed together without compromising the strength of the threaded connection.

Tolerances on the outer and inner diameters of the screw and nut are assigned such that a gap is obtained between the top of the screw thread profile and the corresponding root of the nut thread.

The numerical values of these tolerances are assumed to be large, exceeding approximately twice the tolerances for the average diameter.

Tolerances metric and inch threads. For metric threads with large and small pitches for diameters from 1 to 600 mm, according to GOST 9253-59, three accuracy classes are established: first (cl./), second (Cl. 2) and third (cl. 3), and for threads with fine pitches also class 2a (Cl. 2a). These designations were indicated on previously released drawings. In the new GOST 16093-70, accuracy classes are replaced by accuracy grades, which are assigned the designations: h, g, e And d for bolts and N And G for nuts.

For inch and pipe threads, two accuracy classes are established - the second (Cl. 2) and third (Cl. 3).

Tolerances of trapezoidal threads. For trapezoidal threads, three accuracy classes are established, designated: class 1, cl. 2, class 3, cl. ZH.

2.2. Size tolerance. Tolerance field

Size tolerance is the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations. The tolerance is denoted by IT (International Tolerance) or TD - hole tolerance and Td - shaft tolerance.

The size tolerance is always positive. The size tolerance expresses the spread of actual dimensions ranging from the largest to the smallest limiting dimensions; it physically determines the magnitude of the officially permitted error in the actual size of a part element during its manufacturing process.

The tolerance field is a field limited by upper and lower deviations. The tolerance field is determined by the size of the tolerance and its position relative to the nominal size. With the same tolerance for the same nominal size, there may be different tolerance fields.

For a graphical representation of tolerance fields, allowing one to understand the relationship between nominal and maximum dimensions, maximum deviations and tolerance, the concept of a zero line has been introduced.

The zero line is the line corresponding to the nominal size, from which the maximum deviations of dimensions are plotted when graphically depicting tolerance fields. If the zero line is located horizontally, then on a conventional scale, positive deviations are laid upward, and negative deviations are laid down from it. If the zero line is located vertically, then positive deviations are plotted to the right of the zero line.

The tolerance fields of holes and shafts can occupy different locations relative to the zero line, which is necessary to create different fits.

There is a distinction between the beginning and the end of the tolerance field. The beginning of the tolerance field is the boundary that corresponds to the largest volume of the part and makes it possible to distinguish suitable parts from correctable unsuitable parts. The end of the tolerance zone is the boundary that corresponds to the smallest volume of the part and allows us to distinguish suitable parts from irreparable unsuitable ones.

For holes, the beginning of the tolerance field is determined by the line corresponding to the lower deviation, the end of the tolerance field by the line corresponding to the upper deviation. For shafts, the beginning of the tolerance field is determined by the line corresponding to the upper deviation, the end of the tolerance field - by the line corresponding to the lower deviation.

2.3. Formation of tolerance and landing fields

The tolerance field is formed by a combination of one of the main relations with tolerance for one of the qualifications, therefore the symbol of the tolerance field consists of the symbol of the main deviation (letter) and the number of the qualification.

Preferred tolerance fields are provided by cutting tools and calibers according to a normal series of numbers, and recommended ones are provided only by calibers. Additional tolerance fields are fields of limited application and are used when the use of the main tolerance fields does not allow the requirements for the product to be met.

The ESDP provides for all groups of fits: with clearance, interference and transitional. Plantings do not have names reflecting structural, technological or operational properties, but are presented only in symbols combined tolerance fields of the hole and shaft.

Fittings are typically used in a hole system (preferably) or a shaft system.

All fits in the hole system for the given nominal dimensions of the mates and their qualities are formed by the tolerance fields of the holes with unchanged main deviations and no different main deviations of the shafts.

For fits with a gap in the system, holes are used according to shaft tolerances with main deviations from a to h inclusive.

For transitional fits in the hole system, no shaft tolerances are used with the main deviations k, t, p.

For interference fits in the hole system, shaft start fields with main deviations from p to zc are selected.

For fits in the shaft system for given nominal sizes and mating qualities, tolerance fields with constant main deviations h of the shaft and different main deviations of the holes are used.

For clearance fits in the shaft system, hole tolerance fields with main deviations from A to H inclusive are selected.

For transitional fits in the shaft system, fields up to the openings of the holes with the main deviations Js, K, M, N are used.

For the range from 1 to 500 mm, 69 recommended fits are identified in the hole system, of which 17 are preferred, and in the shaft system there are 59 recommended fits, including 11 preferred.

Chapter 3. Tolerance and landing systems

Taking into account usage experience and requirements national systems Tolerances ESDP consists of two equal systems of tolerances and fits: the hole system and the shaft system.

The identification of the named systems of tolerances and landings is caused by the difference in the methods of forming landings.

Hole system - a system of tolerances and fits in which the maximum hole dimensions for all fits for a given nominal size dH of mate and quality remain constant, and the required fits are achieved by changing the maximum shaft dimensions.

Shaft system is a system of tolerances and fits in which the maximum shaft dimensions for all fits for a given nominal mating size and quality remain constant, and the required fits are achieved by changing the maximum hole dimensions.

The hole system has a wider application compared to the shaft system, which is due to its technical and economic advantages at the design development stage. To process holes of different sizes, it is necessary to have different sets of cutting tools (drills, countersinks, reamers, broaches, etc.), and shafts, regardless of their size, are processed with the same cutter or grinding wheel. Thus, the hole system requires significantly lower production costs both in the process of experimental mating processing and in conditions of mass or large-scale production.

The shaft system is preferable to the hole system, when the shafts do not require additional marking processing, but can be assembled after the so-called blank technological processes.

The shaft system is also used in cases where the hole system does not allow the required connections to be made with given design solutions.

When choosing a landing system, it is necessary to take into account the tolerances for standard parts and components of products: in ball and roller bearings, the fit of the inner ring on the shaft is carried out in the hole system, and the fit of the outer ring in the product body is in the shaft system.

A part whose dimensions do not change for all fits, with unchanged nominal size and quality, is usually called the main part.

In accordance with the pattern of formation of fits, in the hole system the main part is the hole, and in the shaft system the main part is the shaft.

The main shaft is a shaft whose upper deviation is zero.

The main hole is a hole whose lower deviation is zero.

Thus, in the hole system the non-main parts will be shafts, in the shaft system - holes.

The location of the tolerance fields of the main parts must be constant and independent of the location of the tolerance fields of non-main parts. Depending on the location of the tolerance field of the main part relative to the nominal size of the mate, extremely asymmetrical and symmetrical tolerance systems are distinguished.

ESDP is an extremely asymmetrical tolerance system, in which the Tolerance is set “into the body” of the part, i.e. plus - in the direction of increasing the size from the nominal one for the main hole and minus - in the direction of decreasing the size from the nominal one for the main shaft.

Extremely asymmetrical tolerance and fit systems have some economic advantages over symmetrical systems, which is associated with providing the main parts with extreme calibers.

It should also be noted that in some cases non-systemic fits are used, i.e. the hole is made in the shaft system, and the shaft is made in the hole system. In particular, a non-system fit is used for the sides of straight spline joints.

3.1. Layout of tolerance fields for standard interfaces

1 Smooth cylindrical connection

Parameter	Meaning









Td = dmax - dmin = es – ei =
TD = Dmax – Dmin = ES - EI =
Smax = Dmax - dmin =
Smin= Dmin – dmax =
Scp = (Smax + Smin) / 2 =
TS= Smax – Smin =
Nature of pairing
Landing system	Main hole

Parameter	Meaning









Td = dmax - dmin = es – ei =
TD = Dmax – Dmin = ES - EI =
Nmin = dmin - Dmax
Nmax = dmax - Dmin
Ncp = (Nmax + Nmin) / 2 =
TN = Nmax – Nmin =
Nature of pairing
Landing system	Main shaft

Parameter	Meaning









Td = dmax - dmin = es – ei =
TD = Dmax – Dmin = ES - EI =
Smax = Dmax - dmin =
Nmax = dmax - Dmin =
Scp = (Smax + Smin) / 2 =
TS = Smax – Smin =
Nature of pairing	Transitional
Landing system	Main hole

For a combined fit, we determine the probability of the formation of interference fits and clearance fits. We will perform the calculation in the following sequence.

Let's calculate the standard deviation of the gap (preference), µm

let's define the integration limit

table value of the function Ф(z)= 0.32894

Probability of interference in relative units

P N " = 0.5 + Ф(z) = 0.5 + 0.32894 = 0.82894

Probability of tension in percent

P N = P N " x 100% = 0.82894*100%= 82.894%

Probability of clearance in relative units

P Z "= 1 – P N = 1 - 0.82894 = 0.17106

Probability of gap in percent

P Z = P Z "x 100% = 0.17103*100% = 17.103%

List of used literature

1. Korotkov V.P., Taits B.A. “Fundamentals of metrology and theory of accuracy of measuring devices.” M.: Publishing house of standards, 1978. 351 p.

2. A. I. Yakushev, L. N. Vorontsov, N. M. Fedotov. “Interchangeability, standardization and technical measurements”: – 6th ed., revised. and additional – M.: Mechanical Engineering, 1986. – 352 p., ill.

3. V. V. Boytsova “Fundamentals of standardization in mechanical engineering.” M.: Publishing house of standards. 1983. 263 p.

4. Kozlovsky N.S., Vinogradov A.N. Basics of standardization, tolerances, fits and technical measurements. M., “Mechanical Engineering”, 1979

5. Tolerances and fits. Directory. Ed. V.D. Myagkov. T.1 and 2.L., “Mechanical Engineering”, 1978

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Main hole landing system or simply hole system - this is a set of fits in which the maximum deviations of the holes are the same (with the same nominal size and quality), and different fits are achieved by changing the maximum deviations of the shafts.

Main hole- this is a hole, which is indicated by the letter H and whose lower deviation is zero (EI = 0). When designating fits in a hole system, the numerator will always contain the main hole “H”, and the denominator will always contain the main shaft deviation intended to form a particular fit.

For example:

– fit a hole in the system with a guaranteed gap;

– fit in the hole system, transitional;

– fit the hole in the system with guaranteed interference.

Main shaft landing system or simply shaft system - this is a set of fits in which the maximum deviations of the shafts are the same (with the same nominal size and the same quality), and different fits are achieved by changing the maximum deviations of the holes.

Main shaft- this is a shaft, which is designated by the letter “ h» and whose upper deviation is zero (es = 0).

When designating fits in a shaft system, the denominator (where the shaft tolerance field is always written) will include the main shaft “ h", and in the numerator is the main deviation of the hole intended to form a particular fit.

For example:

– fit in the shaft system with guaranteed clearance;

– landing in the shaft system, transitional;

– fit in the shaft system with guaranteed interference.

The standard allows any combination of tolerance fields for holes and shafts, for example: ; and etc.

And at the same time, recommended fits have been established for all size ranges, and for sizes 1 – 500 mm the preferred fits have been identified, for example: H7/f7; H7/n6, etc. (see tables 1.2 and 1.3).

Unification of landings makes it possible to ensure uniformity of design requirements for connections and facilitate the work of designers in determining the purpose of landings. Combining various options preferable tolerance fields for shafts and holes, you can significantly expand the system’s capabilities to create various fits without increasing the set of tools, gauges and other technological equipment.

System of admissions and landings called a set of series of tolerances and fits, naturally built on the basis of experience, theoretical and experimental research and issued in the form of standards.

The system is designed to select the minimum necessary, but sufficient for practice, options for tolerances and fits of typical connections of machine parts, makes it possible to standardize cutting tools and gauges, facilitates the design, production and achievement of interchangeability of products and their parts, and also improves their quality.

Currently, most countries in the world use ISO tolerance and landing systems. ISO systems were created to unify national tolerance and fit systems in order to facilitate international technical connections in the metalworking industry. The inclusion of ISO international recommendations in national standards creates conditions for ensuring the interchangeability of similar parts, components and products manufactured in different countries. Soviet Union joined ISO in 1977, and then switched to a unified system of tolerances and landings (USDP) and basic interchangeability feeds, which are based on ISO standards and recommendations.

Basic standards of interchangeability include systems of tolerances and landings on cylindrical parts, cones, keys, threads, gears, etc. ISO and ESDP tolerance and fit systems for standard machine parts are based on common principles of construction, including:

system of formation of landings and types of interfaces;
system of main deviations;
accuracy levels;
tolerance unit;
preferred fields of tolerances and landings;
ranges and intervals of nominal sizes;
normal temperature.

The system of formation of landings and types of interfaces provides fits in the hole system (SA) and in the shaft system (SV).

Landings in the hole system- these are fits in which various gaps and tensions are obtained by connecting different shafts to the main hole (Fig. 3.1, a).

Fittings in the shaft system- these are fits in which various gaps and tensions are obtained by connecting various holes to the main shaft (Fig. 3.1, b).

The combination of the main deviation and quality forms the tolerance field of the part size . For example:

e8, k6, r6 – shaft tolerance fields (Table 1.2);

D10, M8, R7 – hole tolerance fields (Table 1.3).

Fittings in the drawings are indicated by a fraction: the hole tolerance field is written in the numerator, and the shaft tolerance field is written in the denominator.

The landings are provided in two systems: the main hole landing system and the main shaft landing system.

Main hole - this is a hole, which is indicated by the letter H and whose lower deviation is zero (EI = 0). When designating fits in a hole system, the numerator will always contain the main hole “H”, and the denominator will always contain the main shaft deviation intended to form a particular fit.

For example:

– fit a hole in the system with a guaranteed gap;

– fit in the hole system, transitional;

– fit the hole in the system with guaranteed interference.

Main shaft - this is a shaft, which is designated by the letter “ h» and whose upper deviation is zero (es = 0).

For example:

– fit in the shaft system with guaranteed clearance;

– landing in the shaft system, transitional;

– fit in the shaft system with guaranteed interference.

The standard allows any combination of tolerance fields for holes and shafts, for example: ; and etc.

Unification of landings makes it possible to ensure uniformity of design requirements for connections and facilitate the work of designers in determining the purpose of landings. By combining various options for the preferred tolerance fields of shafts and holes, you can significantly expand the system’s ability to create various fits without increasing the set of tools, gauges and other technological equipment.

For economic reasons, landings should be prescribed mainly in the hole system and less often in the shaft system. This reduces the range of cutting and measuring instruments, intended for processing and inspection of holes. Precise holes are machined with expensive cutting tools (countersinks, reamers, broaches). Each of them is used to process only one size with a certain tolerance range. Shafts, regardless of their size, are processed with the same cutter or grinding wheel. In the system, the holes of different maximum sizes are smaller than in the shaft system, and therefore the range is smaller cutting tool required for machining holes.

However, in some cases, for design reasons, it is necessary to use a shaft system, for example, when it is necessary to alternate connections of several holes of the same nominal size, but with different fits on the same shaft, or the socket in the housing for installing the bearing is made according to the shaft system.

In the recommended and preferred fits of precise quality for sizes from 1 to 3150 mm, the hole tolerance is, as a rule, one or two qualities greater than the shaft tolerance, since an accurate hole is technologically more difficult to obtain than an accurate shaft, due to worse heat dissipation conditions, insufficient rigidity, increased wear and difficulty in guiding the cutting tool to process holes.

Tolerances for dimensions up to 500 mm

Nominal size, mm

Quality

Tolerance designation

Tolerance, µm

6 – 10

10 – 18

18 – 30

30 – 50

50 – 80

80 – 120

180 – 250

The property of independently manufactured parts (or assemblies) to take their place in the assembly (or machine) without additional processing during assembly and to perform their functions in accordance with technical requirements to the operation of this unit (or machine)
Incomplete or limited interchangeability is determined by the selection or additional processing parts during assembly

Hole system

A set of fits in which different clearances and interferences are obtained by connecting different shafts to the main hole (a hole whose lower deviation is zero)

Shaft system

A set of fits in which various clearances and interferences are obtained by connecting various holes to the main shaft (a shaft whose upper deviation is zero)

In order to increase the level of interchangeability of products and reduce the range of standard tools, tolerance fields for shafts and holes for preferred applications have been established.
The nature of the connection (fit) is determined by the difference in the sizes of the hole and the shaft

Terms and definitions according to GOST 25346

Size— numerical value of a linear quantity (diameter, length, etc.) in selected units of measurement

Actual size— element size determined by measurement

Limit dimensions- two maximum permissible sizes of an element, between which the actual size must be (or can be equal to)

Largest (smallest) limit size— the largest (smallest) allowable element size

Nominal size- the size relative to which deviations are determined

Deviation- algebraic difference between the size (actual or maximum size) and the corresponding nominal size

Actual deviation- algebraic difference between the real and the corresponding nominal sizes

Maximum deviation— algebraic difference between the limit and the corresponding nominal sizes. There are upper and lower limit deviations

Upper deviation ES, es- algebraic difference between the largest limit and the corresponding nominal dimensions
ES— upper deviation of the hole; es— upper shaft deflection

Lower deviation EI, ei— algebraic difference between the smallest limit and the corresponding nominal sizes
EI— lower deviation of the hole; ei— lower shaft deflection

Main deviation- one of two maximum deviations (upper or lower), which determines the position of the tolerance field relative to the zero line. In this system of tolerances and landings, the main deviation is that closest to the zero line

Zero line- line corresponding to the nominal size, from which deviations of dimensions are plotted when graphic representation fields of tolerances and landings. If zero line is located horizontally, then positive deviations are laid up from it, and negative ones - downwards

Tolerance T- the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations
Tolerance is an absolute value without sign

IT standard approval- any of the tolerances established by this system of tolerances and landings. (Hereinafter, the term “tolerance” means “standard tolerance”)

Tolerance field- a field limited by the largest and smallest maximum dimensions and determined by the tolerance value and its position relative to the nominal size. In a graphical representation, the tolerance field is enclosed between two lines corresponding to the upper and lower deviations relative to the zero line

Quality (degree of accuracy)- a set of tolerances considered to correspond to the same level of accuracy for all nominal dimensions

Tolerance unit i, I- a multiplier in tolerance formulas, which is a function of the nominal size and serves to determine the numerical value of the tolerance
i— tolerance unit for nominal sizes up to 500 mm, I— tolerance unit for nominal dimensions St. 500 mm

Shaft- a term conventionally used to designate the external elements of parts, including non-cylindrical elements

Hole- a term conventionally used to designate the internal elements of parts, including non-cylindrical elements

Main shaft- a shaft whose upper deviation is zero

Main hole- a hole whose lower deviation is zero

Maximum (minimum) material limit- a term relating to that of the limiting dimensions to which the largest (smallest) volume of material corresponds, i.e. the largest (smallest) maximum shaft size or the smallest (largest) maximum hole size

Landing- the nature of the connection of two parts, determined by the difference in their sizes before assembly

Nominal fit size- nominal size common to the hole and shaft making up the connection

Fit tolerance- the sum of the tolerances of the hole and shaft making up the connection

Gap- the difference between the dimensions of the hole and the shaft before assembly, if the size of the hole larger size shaft

Preload- the difference between the dimensions of the shaft and the hole before assembly, if the shaft size is larger than the hole size
The interference can be defined as the negative difference between the dimensions of the hole and the shaft

Clearance fit- a fit that always creates a gap in the connection, i.e. the smallest limit hole size is greater than the largest size limit shaft or equal to it. When shown graphically, the tolerance field of the hole is located above the tolerance field of the shaft

Pressure landing - a landing in which interference is always formed in the connection, i.e. The largest maximum hole size is less than or equal to the smallest maximum shaft size. When shown graphically, the tolerance field of the hole is located below the tolerance field of the shaft

Transitional fit- a fit in which it is possible to obtain both a gap and an interference fit in the connection, depending on the actual dimensions of the hole and shaft. When graphically depicting the tolerance fields of the hole and shaft, they overlap completely or partially

Landings in the hole system

— fits in which the required clearances and interferences are obtained by combining different tolerance fields of the shafts with the tolerance field of the main hole

Fittings in the shaft system

— fits in which the required clearances and interferences are obtained by combining different tolerance fields of the holes with the tolerance field of the main shaft

Normal temperature— the tolerances and maximum deviations established in this standard refer to the dimensions of parts at a temperature of 20 degrees C