1. Smooth mates and calibers

1.1 Calculation of tolerances and fits of smooth cylindrical mates

1.2 Gauges for the control of smooth cylindrical joints

2. Calculation and selection of rolling bearing fits

3. Roughness, deviation of shape and location of surfaces

4. Tolerances and fits of keyed and splined connections

4.1 Keyed connection

4.2 Straight spline connection

4.3 Involute spline connection

Literature

1. Smooth mates and calibers

1. The specified landing is Æ56H6/k5.

Transitional landing.

Limit deviations of hole Æ56H6: upper ES=+19 µm; lower EI=0.

Maximum shaft deviations Æ56k5: upper es=14 µm; lower ei=+1 µm.

Dmax = D + ES = 56 + 0.019 = 56.019 mm;

Dmin = D + EI = 56 + 0 = 56 mm;

dmax = d + es = 56 +0.014 = 56.014 mm;

dmin = d + ei = 56 + 0.001 = 56.001 mm;

TD = IT6 = 19 µm;

Td = IT5 = 13 µm;

Smax = ES - ei = 19- 1 = 18 µm;

Smin = EI - es = 0 - 14 = -14 µm;

TS = Smax - Smin = 18 + 14 = 32 µm.

Check: TS = Td+TD 32= 19 + 13

2. The specified landing is Æ70S6/h7.

Landing with clearance.

Limit deviations of hole Æ70S6: upper ES=-59 µm; lower EI=-78.

Maximum shaft deviations Æ70h7: upper es=0 µm; lower ei=-30 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 70 + (-0.059) = 69.941 mm;

Dmin = D + EI = 70 + (-78) = 69.922 mm;

dmax = d + es = 70 + 0 = 70 mm;

dmin = d + ei = 70 + (0.030) = 69.970 mm;

Hole and shaft dimensional tolerances:

TD = IT6 = 19 µm;

Td = IT7 = 30 µm;

Fit parameters (with clearance).

Nmax = dmax - Dmin = -0.078 mm;

Nmin = dmin - Dmax = -0.029 mm;

TN = Nmax - Nmin = -0.0678 + 0.029 = -0.049 mm.

Check: TN = Td+TD 0.049 = 0.019 + 0.030

3. The landing is Æ105F7/h7.

Landing with clearance.

Limit deviations of hole Æ53H7: upper ES=+30 µm; lower EI=0.

Maximum shaft deviations Æ53k5: upper es=+15 µm; lower ei=+2 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 53 + 0.030 = 53.030 mm;

Dmin = D + EI = 53 + 0 = 53 mm;

dmax = d + es = 53 + 0.015 = 53.015 mm;

dmin = d + ei = 53 + 0.002 = 53.002 mm;

Hole and shaft dimensional tolerances:

TD = IT7 = 30 µm;

Td = IT5 = 13 µm;

Landing parameters (transitional).

Smax = Dmax - dmin = 53.030 - 53.002 = 0.028 mm;

Nmax = dmax - Dmin = 53.015 - 53 = 0.015 mm;

Smin = -Nmax = -0.015 mm;

Nmin = -Smax = -0.028 mm;

TS(N) = Smax + Nmax = 0.028 - 0.015 = 0.043 mm.

Check: TS(N) = Td+TD 0.043 = 0.013 + 0.030

4. The landing is set to Æ21H8/h7.

Landing with clearance.

Limit deviations of hole Æ21H8: upper ES=+33 µm; lower EI=0.

Maximum shaft deviations Æ21h7: upper es=0 µm; lower ei=-21 µm.

Limit dimensions of hole and shaft:

Dmax = D + ES = 21 + 0.033 = 21.033 mm;

dmax = d + es = 21 + 0 = 21 mm;

dmin = d + ei = 21 + (-0.021) = 20.979 mm;

Hole and shaft dimensional tolerances:

TD = IT8 = 33 µm;

Td = IT7 = 21 µm;

Landing parameters (with clearance).

Smax = Dmax - dmin = 21.033 - 20.979 = 0.054 mm;

Smin = Dmin - dmax = 21 - 21 = 0;

TS = Smax - Smin = 0.054 - 0 = 0.054 mm.

Check: TS = Td+TD 0.054 = 0.021 + 0.033

We enter the obtained data for all landings in Table 1.1.

Table 1.1 Types and parameters of plantings

Designation Landing	Limit dimensions				Limit dimensions				Fit type	Fit tolerance
	Holes
									transitional

Figure 1.1 - Landing diagram No. 1 with a gap

Figure 1.2 - Scheme of landing No. 2 with interference

Figure 1.4 – Landing diagram No. 4 with a gap

Figure 1.5 – Sketches of mating parts: a) holes; b) shafts;

1.2 Gauges for testing smooth cylindrical joints

We will develop limit gauges to control the Æ34H7/s7 interface. We establish tolerances for the production of maximum calibers according to tables 3 and 4.

Initial data:

For hole Æ34H7: Н=4 µm; Z=3.5 µm; α=0.

For shaft: Æ34s7: H 1 =4 µm, Z1=3.5 µm, H p =1.5 µm, α 1 =0, Y1=3 µm.

Executive size of the passage side of the plug gauge:

Prmax= Dmin+Z+=34+0.0035+0.004/2=34.0055 mm;

size in the drawing Æ34.0055 -0.004 mm.

The standard size of the non-pass side of the plug gauge:

Notmax= Dmax- α +=34.025-0+0.004/2=34.027 mm;

size in the drawing Æ34.027 -0.004 mm.

Executive size of the passage side of the staple gauge:

Prmin= dmax-Z 1 - =34.068-0.0035-0.004/2=34.0625 mm;

size in the drawing Æ34.0625 +0.004 mm.

The standard size of the non-pass side of the staple gauge:

Notmin= dmin+ α 1 - =34.043+0-0.004/2=34.041 mm;

size in the drawing Æ34.041 +0.004 mm.

Executive size of control gauge:

K-Imax= dmax+ Y 1 - α 1 +=34.068+0.003-0+0.0015/2=34.07025 mm;

size in the drawing Æ34.0702 -0.0015 mm.

Executive size of the pass-through control gauge:

K-Prmax= dmax-Z 1 +=34.068-0.0035+0.0015/2=34.06525 mm;

size in the drawing Æ34.0652 -0.0015 mm.

Executive size of a no-go control gauge:

K-Hemax= dmin+ α 1 +=34.043+0+0.0015/2+0=34.04375 mm;

size in the drawing Æ34.0437 -0.0015 mm.

Roughness of working surfaces of calibers:

R a ≤ 0.012T size (H 1 ,H), H 1 =H=4 µm;

R a = 0.012 ۰ 4 = 0.048 µm;

We accept R a from the standard series

For both calibers: R a =0.05 µm.

Figure 1.6 Schemes of tolerance fields of maximum calibers

2. Calculation and selection of bearing fits

Initial data:

bearing 409;

accuracy class 0;

radial force F=4000 N;

It is the inner ring that rotates.

1. Bearing parameters 409: d=45 mm; D=120 mm; B=29 mm; r=3.0 mm.

In the unit under consideration, the rotating ring is the inner ring of the bearing, so we fit it onto the shaft with an interference fit, and install the outer ring in the housing with a gap.

2. Determination of the minimum required interference for the inner ring of the bearing:

where coefficient k=2 for the heavy bearing series.

3. Determination of the maximum permissible tension of the inner ring of the bearing:

Using Table 9, we determine the maximum size deviations:

for hole: ES=0; EI=–12 µm;

for the shaft: es=+25 µm; ei=+9 µm;

5. Determination of the minimum and maximum interference in the connection:

Since >(9 µm > 4.522 µm), and >(37 µm< 205,2 мкм), можно заключить, что посадка внутреннего кольца подшипника выполнена правильно.

6. Select the fit for the outer ring of the bearing from the recommended ones: Æ 120H7/l0. Limit deviations:

for hole:

TD=35 µm;

for shaft:

ei=–15 µm.

Td=15 µm;

Maximum clearance for selected fit:

S max =ES–ei=35–(–15)=50 µm.

Minimum clearance for selected fit:

Smin=EI–es=0–0=0 µm.

7. We build a diagram of the tolerance fields of the selected fits for the rolling bearing rings:

8. Sketch of the assembly unit

Figure 2.2 Assembly

3. Roughness, deviations in shape and location of surfaces

Initial data:

1. Æ 45k6; Td=16 µm;

2. Æ 50n7; Td=25 µm;

3. Æ 45k6; Td=16 µm;

4. Æ 25r7; Td=21 µm;

5. Æ 53 -0.3; Td=300 µm;

6. Æ 55 -0.3; Td=300 µm;

7. 18h6; Td=11 µm;

8. 9h15; Td=580 µm;

9. Æ 14N9; Td=43 µm;

3.1 We find the roughness of the marked surfaces in accordance with the purpose of these surfaces and the tolerance of their size

3.1.1 Determine the roughness for the seats of rolling bearings

we take R a =0.63 μm from the standard series.

Surface Æ 45k6: Td=16 µm

Similar to the previous surface R a =0.63 µm.

3.1.2 Roughness for critical surfaces that form certain fits with the mating surfaces of other parts

IN general case the selected surfaces can be considered surfaces of normal geometric accuracy, for which the roughness parameter T Æ .

we take R a =1.25 µm from the standard series.

Surface Æ 25r7: Td=21 µm;

we take R a =1.00 µm from the standard series.

Surface Æ 18h6: Td=11 µm;

we take R a =0.32 µm from the standard series.

3.1.3 Determination of the roughness of surfaces that do not have high requirements

Surface Æ 53 -0.3: Td=300 µm;

Surface Æ 55 -0.3: Td=300 µm;

we take R a =12.5 µm from the standard series.

Surface Æ 9h15: Td=580 µm;

we take R a =25 µm from the standard series.

The roughness of the keyway surfaces is assumed to be within the range of R a = 3.6...12.5 µm, and large values correspond to the bottom of the groove.

3.2 Tolerances for deviation of the shape and location of surfaces will also be determined using an approximate method

3.2.1 Calculation of tolerances for deviations from roundness and cylindricity of surfaces

Surface Æ 45k6: Td=16 µm;

T µm, take T = 4 µm from the standard series.

T µm, take T = 4 µm.

Surface Æ 50n7: Td=25 µm;

T µm, take T = 6 µm.

Surface Æ 25r7: Td=21 µm;

T µm, take T = 6 µm.

3.2.2 Permit radial runout surface relative to the AB surface

Surface Æ 50n7:

T mm, take T =0.02 mm;

Surface Æ 25r7:

T mm, take T =0.02 mm;

3.2.3 The tolerance for deviation from the perpendicularity of the surface end Æ50 -0.3 for fixing the bearing depends on the size tolerance for the width of the bearing

T µm, take T = 6 µm.

T µm, take T = 120 µm.

3.2.4 Tolerance for deviation from the symmetry of the keyway location

T µm, take T = 120 µm,

3.2.5 Tolerance for deviation from parallelism of the keyway

T // µm, take T // =120 µm.

where T B - when determining the perpendicularity tolerance, is the tolerance for the width of the bearing; when determining the tolerance for deviation from the symmetry of the sides of the keyway, this is the tolerance for the width of the shaft groove.

Draw a sketch of the shaft

4. Tolerances and fits of keyed and splined joints.

4.1 Keyed connections.

Initial data: d=35 mm, connection type 3 (tight connection).

According to GOST 23360-78, we select the main connection dimensions:

b=10 mm, h=8 mm;

The depth of the groove of the shaft and sleeve, respectively: t 1 = 5 mm, t 2 = 3.3 mm;

Type of execution 1;

Key length l=50 mm;

Key designation: Key 1-10 ĥ 8 ĥ 50 GOST 23360-78.

Application conditions – tight, characterized by the probability of obtaining approximately equal small interference in the connection of the keys with both grooves; assembly is carried out by pressing, used for rare disassembly and reverse loads.

For a given connection type, we assign tolerance fields for keyed connection parts:

shaft tolerance field s6,

hole tolerance H7,

key width tolerance range b - h9,

key height tolerance range h - h11,

tolerance range of key length l - h14,

tolerance range of groove width on the shaft and in the bushing - P9,

We determine the maximum deviations using the standard for smooth joints:

shaft diameter 35

sleeve diameter 35

key width 10

key height 8

key length 50

width of the groove on the shaft 10

groove width in sleeve 10

shaft groove depth

Bushing groove depth

We build diagrams of the location of tolerance fields (Figure 4.1).

4.2 Straight spline connection

Initial data: b-6 ĥ 28H11/ ≥ 26.7 ĥ 32H12/a11 ĥ7F8/js7 GOST 1139-80

Straight spline connection: centering along the side surfaces of the teeth b;

tolerance range of centering diameter D=32 mm

H12 - bushings,

number of straight-sided splines 6;

internal diameter of connection d=28 mm;

slot width b=7 mm,

bushing spline width tolerance range F8,

Shaft spline width tolerance range js7.

Centering along b is used when special alignment accuracy is not required, when transmitting significant moments, in cases where large gaps between the side surfaces of the shaft and bushing are unacceptable; the simplest and most economical way.

According to GOST 1139-80, we assign tolerance fields for the bushing and shaft according to the non-centering diameter:

H11 bushings,

maximum shaft deviation along the non-centering diameter d is not less than 26.7 mm.

Values ​​of maximum deviations of diameters and widths of straight-sided splines:

For bushing b-6 ĥ 28H11 ĥ 32H12 ĥ7F8 GOST 1139-80

centering diameter;

non-centering diameter;

groove width;

For shaft b-6 ĥ ≥ 26.7 ĥ 32a11 ĥ7js7 GOST 1139-80

centering diameter;

non-centering diameter mm;

groove width;

We build diagrams of the location of tolerance fields (Figure 4.2).

4.3 Involute spline connections

Initial data: 48 ĥ H7/h6 ĥ 2 GOST 6033-80

Nominal diameter D=48 mm,

Module m=2 mm,

type of centering along the outer diameter,

tolerance range of the outer diameter of the shaft d a - h6.

Centering along the outer diameter D is the most technologically advanced, since in this case, the final operation of the hole is broaching, and when processing the shaft, grinding is performed. This centering is used in parts with a non-hardened hole.

We determine according to GOST 6033-80 the missing parameters of the involute connection:

Number of teeth Z=22;

Pitch diameter:

Diameter of spline shaft grooves

Inner sleeve diameter

We assign a tolerance field for the bushing cavity width e - 9H, a tolerance field for the shaft tooth thickness S - 9d: fit 9H/9d.

The tolerance field of the bushing and shaft for non-centered diameter with a flat shape of the bottom of the cavity: for bushing D a - H11, for shaft d f - h16, fit H11/h16.

Values ​​of maximum deviations of diameters, maximum deviations on the sides of the teeth:

For bushing 48 ĥ H7 ĥ 2 GOST 6033-80:

centering diameter;

depression width

e - 9H: ES=+71µm;

EJ e =+26 µm;

For shaft 48 ĥ h6 ĥ 2 GOST 6033-80:

centering diameter;

tooth thickness

S - 9d: es=-44 µm;

es e = -70 µm;

We build diagrams of the location of tolerance fields (Figure 4.3).

Literature

1. Markov N.N., Osipov V.V., Shabalina M.B. Standardization of accuracy in mechanical engineering: Textbook. for mechanical engineering specialist. universities / Ed. Yu.M. Solomentseva. – 2nd ed., revised. and additional – M.: Higher. school; Publishing center "Academy", 2001. – 335 pp.: ill.

2. Yakushev A.I. etc. Interchangeability, standardization and technical measurements: Textbook for colleges / A.I. Yakushev, L.N. Vorontsov, N.M. Fedotov. – 6th ed., revised. and additional – M.: Mechanical Engineering, 1987. – 352 p.: ill.

3. V.I. Anuriev "Handbook of mechanical engineering designer": in 3 volumes - 8th edition: - M.: Mechanical Engineering, 2001.

Standardization of dimensional accuracy in mechanical engineering

Basic concepts about sizes, deviations and fits

Creators of mechanisms and machines, based on the purpose of parts, based on calculations of various nature and the results of experimental studies, determine the geometric parameters of the elements of the parts. The degree of possible deviations of its geometric parameters from the specified ones, from the point of view of the performance of each part, is determined by the designer. Naturally, some elements of parts need to be performed more accurately than others in accordance with their purpose.

At the same time, it is known that it is impossible to absolutely accurately produce the geometric elements of a part due to a number of reasons inherent in any technological process.

1. Size – numerical value of a linear quantity (diameter, length, etc.) in selected units of measurement. In other words, the size of a part element is the distance between two characteristic points of this element.

2. The size of an element, established by measurement with a permissible error, is called actual size . The actual size is determined experimentally (measurement) with an acceptable error, which is determined by any regulatory documents. The actual size is found in cases where it is necessary to determine the compliance of the dimensions of the elements of a part with the established requirements. When such requirements are not established and measurements are not carried out for the purpose of product acceptance, then it is possible to use the term measured size, i.e. the size obtained as a result of measurements.

3. True Size - a size obtained as a result of manufacturing and the meaning of which is unknown to us, although it exists. We approach the value of the true size as the accuracy of measurements increases, therefore the concept of “true size” is often replaced by the concept of “actual size”, which is close to the true one under the conditions of the goal.

4. Nominal size – the size relative to which deviations are determined. For the parts that make up the connection, the nominal size is common to the hole and shaft. The nominal size is determined by the designer as a result of calculations for strength, rigidity, when determining dimensions, etc. or taking into account design and technological considerations. This size is indicated in the drawing.

5. Taking into account the processing error, the designer indicates not one size, but two maximum permissible size elements between which the actual size must lie (or be equal to them). These two sizes are called the largest limit size (the largest allowable size of a part element) and the smallest limit size (the smallest allowable size of a part element). The difference between the largest and smallest limit sizes is called processing tolerance or tolerance, denoted T d:

;

.

Tolerance– this is an essentially positive quantity; it cannot be negative. This is the interval of size values ​​between which the size of a suitable part element must lie.

; .

Consequently, the tolerance shows, as it were, the permitted processing error, pre-provided for and reflected in the drawing of the part. In this case, suitable and interchangeable parts will be those whose size obtained after processing is within the tolerance.

The smaller the tolerance, the more accurately the standardized element of the part must be manufactured and the more difficult, complex and therefore more expensive it is to manufacture. The larger the tolerance, the rougher the requirements for the part element and the easier and cheaper it is to manufacture.

Thus, to establish (normalize) the accuracy of a size means to indicate its two possible (permissible) limit values.

The correctness of the dimensions obtained during processing is checked by measuring them.

To measure a size means to compare its value with the value taken as a unit (for linear dimensions the unit of measurement is the meter).

All instruments and devices used for measurements have common name– measuring instruments. Errors may occur during measurements, and therefore it is impossible to accurately determine the size of the part.

Measurement error is called the deviation of the measurement result from true meaning measured quantity. Measurement errors can be caused by: errors introduced by installation standards and samples; SI inaccuracies or wear and tear individual parts; temperature influences; errors associated with the experience and skills of the person who carries out the measurement, etc.

The organization of serial production of products required a reduction in the embodied labor invested in them. It was possible to achieve a reduction in the cost of products by simplifying the design (primarily by eliminating excesses - expensive materials, labor-intensive decorations, low-tech parts and assembly units) and changing technology (providing division of labor and cooperation production).

The division of labor in its ultimate form can be represented as division technological process manufacturing a product for operations - the simplest actions, each of which is performed by one worker (operator). You can learn how to perform such an operation within a few minutes, and acquire sufficient work skills in 2...3 work shifts. The benefit from such an organization of work is high productivity with minimum requirements to the employee's qualifications.

To ensure a certain level of quality for mass-produced products, it is necessary that all processed parts for the same purpose (nomenclature, standard size) are practically the same. The differences between the parts must be so insignificant that any of them can be assembled with the corresponding ones, and when assembled together they form a product that is indistinguishable from others in operation. Parts and more complex products, if they meet the specified requirements, are called interchangeable.

In the everyday sense, interchangeability can be considered as the sameness of products, but since absolutely identical products do not exist, it is obvious that during production one should only prevent such differences that go beyond the agreed standards. These standards are recorded in documentation (design documentation, technical descriptions, passports, etc.). Standardization is widely used to give the most frequently used norms official status. They standardize complex products and processes, their components, down to the elementary ones. Everyone knows not only standard houses and cars, but also standard voltage of the electrical network, standard sizes of magnetic tape, magnetic and optical disks, speed of recording and playback of information.

To obtain standard products of a given level of quality, it is necessary to organize an extensive regulatory framework. Standardization is regulatory framework interchangeability mass-produced products and repeatedly reproducible processes.

In technology, the interchangeability of products implies the possibility of equivalent (from the point of view of specified conditions) replacement of one with another during the manufacturing or repair process. The more detailed and rigidly the parameters of products are standardized, the easier the replacement is, but the more difficult it is to ensure interchangeability.

Interchangeability of products and their components(assemblies, parts, elements) should be considered as the only possibility ensuring economical serial and mass production of products of a given level of quality. The same (fluctuating within the limits of differences negligible for the consumer) level of quality of the final products of a particular production is ensured by fulfilling a certain set of requirements. Requirements apply to all elements of parts and interfaces that provide normal work products. Ensuring interchangeability, and therefore a given level of product quality, implies:

Establishing a set of requirements for all parameters that affect the interchangeability and quality of products (standardization of nominal values ​​and accuracy of parameters);

Compliance with established standards during production, uniform for identical objects, and effective control of standardized parameters.

At the same time, gaps in the assignment of standards or an incorrect, unclearly defined choice of their boundaries can lead to a violation of the interchangeability of manufactured products, and, consequently, to non-compliance with the specified level of product quality. An incorrect or incomplete set when standardizing the nomenclature of parameters or their limit values ​​will lead to a violation of interchangeability (even to the point of bullying the customer: ... the dog could have grown up during the journey), in which the manufacturer cannot formally be accused of non-compliance with the standards.

So, highest achievement standardization of product parameters will ensure complete interchangeability of similar products in any manufactured batch. Full interchangeability implies the interchangeability of products according to all standardized parameters. Parameters and properties that are not of fundamental importance for the functioning of products are not standardized. For example, a housewife is of little interest in the particle size of granulated sugar, which is sold by weight, while for pasta the shape and size may be sufficient significant properties, since noodles and vermicelli cook differently. Interchangeability (full interchangeability) implies compliance during the manufacturing process of a product with all its standardized parameters within specified limits. Standardized product parameters may include:

Geometric (size, shape, location and surface roughness);

Physico-mechanical (hardness, mass, reflectivity, etc.);

Economic (cost, limit price, productivity, etc.);

Other (ergonomic, aesthetic, environmental, etc.).

You can refuse interchangeability even during the design process by incorporating a compensator into the design, which ensures a change within certain limits (regulation) of the normalized parameter. Everyone knows the adjustable supports (legs) of appliances and furniture, which allow you to compensate not only for inaccuracies in the manufacture of the products themselves, but also for the imperfections of the base surfaces (table, floor).

Functional interchangeability is an analogue of complete interchangeability, which is not understood in the literal sense (identicality of parameters), but is limited to a necessary and sufficient set of requirements for the operation (functions) of the product. For example, a pencil, a ballpoint or fountain pen, a piece of chalk, a typewriter, or a computer may be functionally interchangeable if you need to write down short message(the list is compiled without taking into account economic costs and qualifications). The imposition of economic restrictions can sharply shorten such a list. The feature that the term functional interchangeability emphasizes is the priority of the functions performed by the product (pencil, chalk, pen...writing) with possible significant technical differences in the objects used. The following can be considered functionally interchangeable under a certain problem statement (timely attendance at work): vehicles like a tram, trolleybus, bus, taxi, bicycle or your own legs.

Functionally interchangeable in terms of the content of recorded information for the computer owner can be files recorded on a hard disk, floppy disks, CDs (if appropriate drives are available), as well as a hard copy of the corresponding file, although the parametric differences between the storage media are very significant. In particular, the printout can also be used when the computer stops working due to a temporary lack of electricity, a technical malfunction, or a virus infection.

From the examples considered, two accentuated features of functional interchangeability emerge: focus on results with an almost indifferent attitude to the process (goal-providing interchangeability), or guaranteeing results by reproducing functions (procedural interchangeability). In particular, we may be indifferent to where and how to obtain the necessary textual information, as long as its completeness and accessibility are ensured. On the other hand, if this information is subject to editing or other modification (partial borrowing, combining with additional information, etc.), not only the form of its presentation (printout or electronic copy on a floppy disk), but also the system becomes very important for us its coding. An electronic copy of the text becomes useless if we do not have the appropriate environment on our computer (the so-called word processor, the version of which is compatible with the one used). IN in this case We are talking about procedural interchangeability, since the fundamentally described operations can be implemented using typewriting, but without a computer there is a slide into incomplete interchangeability due to difficulties in using fonts, mathematical symbols and other symbols. The picture drawn can be continued until a return to individual rewriting of texts with quill pens.

Parts for mechanical engineering products (as opposed to a number of radio-electronic, optical, etc.) products pass the first test of interchangeability during the assembly process. Imprecisely manufactured parts may not fit together or may break if you try to assemble them by force, so for mechanical parts and assemblies, the first aspect that is considered is geometric interchangeability.

The arrays of geometric parameter values ​​used for standardization are usually formatted in the form of standards. For example, you can use the standards for parameters of macrogeometry of surfaces (dimensions, shape, location) and microgeometry (roughness). The standards are suitable for normalizing the geometric parameters of any standard parts and surfaces in a very wide range.

The suitability of a product for a given parameter Q is assessed by comparing the actual value of the parameter Q d STV with its maximum permissible values. Determining suitability is called parameter control, and if measuring instruments are used, then control is called measuring. Measurement control is usually carried out in two stages:

Determining the actual value of the parameter;

Comparison of the actual value of the parameter with normalized values ​​and determination of the suitability of the object based on the controlled parameter.

To obtain the actual value of a controlled parameter specified by a physical quantity, it is necessary to compare its real value with the unit of the corresponding physical quantity - this is the essence of any measurement. Units physical quantities standardized, they are reproduced using standard standards, and from them are transferred to standard and non-standardized working measuring instruments.

"Regulation of accuracy in mechanical engineering"

For course work in the discipline “Normalization of accuracy in mechanical engineering.”

Initial data for option No. 23.

• 1. Calculate the parameters and graphically depict the fit of smooth joints.
• 2. Select bearing fits for the outer and inner rings.
• 3. Draw a sketch of the threaded connection and give an explanation of the thread symbol.
• 4. Draw sketches of a straight-sided spline connection and standardize for accuracy for three centering methods.
• 5. On the working drawing of the part, indicate the tolerances of linear dimensions, the necessary deviations of shape and location. Assign surface roughness. Decipher the notation.

Calculation of landings of smooth joints

The quality of mechanical engineering products depends on the geometric accuracy of the parts included in them. Accuracy is a collective concept, and can be assessed by the accuracy of the dimensions of the elements of a part, the accuracy of the shape of surfaces and their relative position, waviness and roughness. Standardization of dimensional accuracy is carried out by the standards of the Unified System of Tolerances and Landings (USDP) through the system of GOSTs (State Standards). Available in sizes: nominal- the size relative to which the maximum dimensions are determined and which serves as the starting point for deviations is assigned from among the standard ones according to GOST 6636 “Normal linear dimensions”, limit (largest and smallest)- two maximum permissible sizes, between which the actual size of a suitable part must lie; valid- size established by measurement with permissible error.

Accepted designations:

· - nominal size of the hole (shaft);

· , - hole (shaft) size, largest (maximum), smallest (minimum), actual;

· - upper deviation of the hole (shaft); - lower deviation of the hole (shaft);

· - gap, largest (maximum), smallest (minimal), average, respectively;

· - interference, greatest (maximum), smallest (minimum), average, respectively.

During processing, each part acquires its actual size and can be assessed as acceptable if it is within the range of maximum sizes, or rejected if the actual size is outside these limits.

The condition for the suitability of parts can be expressed by the following inequality:

The difference between the largest and smallest limit sizes is called size tolerance. Tolerance is always positive.

For hole;

For the shaft.

Tolerance is a measure of dimensional accuracy. The smaller the tolerance, the smaller the permissible fluctuation in actual dimensions, the higher the accuracy of the part and, as a result, the complexity of processing and its cost increase. The position of the tolerance relative to the nominal size is determined by the deviations.

Size deviation is called the algebraic difference between the size (real, limit) and the nominal size. From here, deviations can be real or maximum, and maximum deviations can be upper ES (es) and lower EI (ei):

for the hole,

for the shaft,

Deviations can be: positive (with a plus sign), if

negative (with a minus sign), if

and equal to zero if

In the connection of elements of two parts, one of them is internal (male), the other is external (male). In ESDP, every external element is called a shaft, every internal element is called a hole. The terms "hole" and "shaft" also apply to non-mating elements.

The difference between the sizes of the hole and the shaft before assembly determines the nature of the connection of the parts, i.e. landing. The gap characterizes greater or lesser freedom of relative movement of the parts of the connection, and the interference is the degree of resistance to the mutual displacement of the parts in the connection:

The designer assigns fits in the form of a certain combination of tolerance fields of the hole and shaft, and the nominal size of the hole and shaft is common (the same) and is called nominal connection size. There are three types of fits: with clearance, interference and transitional, which can be assigned in the hole system (CH) or in the shaft system (CH). The choice of system is dictated by design, technological or economic considerations.

In the system, landing holes are made between the main hole with the main deviation H and the shafts with different main deviations (a....zc).

In the shaft system, fits are made between the main shaft with the main deviation h and holes with different main deviations (A....ZC).

Of the two systems, CH is preferable, since it is more expensive to machine an accurate hole than an accurate shaft, and to produce holes of different accuracy in the CH system, many measuring cutting tools (drills, countersinks, reamers, broaches, etc.) and control equipment are required .

The shaft system is used less frequently, in economically justified cases: on shafts made from calibrated cold-drawn rod without cutting the seating surfaces; in connecting a long section of a shaft of the same nominal size with holes in several parts with different fit characteristics; in connections of standard parts and assemblies made in the shaft system (bearing outer ring, width key, etc.). Fitments can be made with clearance -S, interference - N and transition - S(N).

They are distinguished, which quantify the landing and are calculated using the formulas:

Clearance fit tolerance

The value is sometimes called the guaranteed clearance. Landings with a gap also include landings in various grades, in which bottom line hole tolerance range coincides with upper limit shaft tolerance fields. For them = 0.

IN interference fit The tolerance field of the hole is located below the tolerance field of the shaft, i.e. The actual size of the shaft before assembly is larger than the actual size of the hole. Requires the use of force or thermal effects(heating the sleeve or cooling the shaft).

Interference fit tolerance

where is the guaranteed interference.

Transitional landing called a fit in which, during assembly, it is possible to obtain both a gap and an interference fit. These fits ensure precise centering (coincidence of axes) of the bushing relative to the shaft axis. In such a fit, the tolerance fields of the hole and shaft partially or completely overlap each other

Transitional plantings are characterized highest values interference and clearance

Transitional fit tolerance

In a transitional fit, the average interference fit (clearance) is calculated using the formula:

A result with a minus sign will mean that the average value for the fit corresponds to The fit tolerance is always equal to the sum of the hole and shaft tolerances.

Initial data:

Nominal diameter: D=20 mm.

Hole tolerance range: E8; F7; JS6; N8; P6; S7.

Shaft tolerance fields: d8; f7; js6; n6; p6; r6.

According to GOST 25347-82 “Unified system of tolerances and landings. Tolerance fields and recommended fits” we will describe the maximum upper (es, ES) and lower (ei, EI) deviations for the given tolerance fields.

1) For tolerance range E8:

Upper deviation ES = + 73 µm

Lower deviation EI = + 40 µm

Tolerance T = 33 µm

2) For tolerance range F7:

Upper deviation ES = + 41 µm

Lower deviation EI = + 20 µm

Tolerance T = 21 µm

3) For tolerance zone JS6:

Upper deviation ES = + 6.5 µm

Lower deviation EI = - 6.5 µm

Tolerance T = 13 µm

4) For tolerance zone N8:

Upper deviation ES = - 3 µm

Lower deviation EI = - 36 µm

Tolerance T = 33 µm

5) For tolerance range P6:

Upper deviation ES = - 18 µm

Lower deviation EI = - 31 µm

Tolerance T = 13 µm

6) For tolerance range S7:

Upper deviation ES = - 27 µm

Lower deviation EI = - 48 µm

Tolerance T = 21 µm

7) For tolerance range d8:

Upper deviation es = - 65 µm

Lower deviation ei = - 98 µm

Tolerance T=33 µm

8) For tolerance range f7:

Upper deviation es = - 20 µm

Lower deviation ei = - 41 µm

Tolerance T=21 µm

9) For tolerance field js6:

Upper deviation es = + 6.5 µm

Lower deviation ei = - 6.5 µm

Tolerance T=13 µm

10) For tolerance range n6:

Upper deviation es = + 28 µm

Lower deviation ei = +15 µm

Tolerance T=13 µm

11) For tolerance range p6:

Upper deviation es = + 35 µm

Lower deviation ei = + 22 µm

Tolerance T=13 µm

12) For tolerance range r6:

Upper deviation es = + 41 µm

Lower deviation ei = +28 µm

Tolerance T=13 µm

Figure 1. Layout of hole tolerance fields

Figure 2. Layout of shaft tolerance fields

Let us express the absolute values ​​of size deviations:

a) Through the maximum dimensions:

Hole Ш20Э8:

b) Through the maximum deviations of the hole (shaft):

Formation of landings in the hole system

With a gap	Transitional fit	With interference

Let us graphically depict three types of plantings.

Federal state budget educational institution

higher professional education

"Altai State Technical University

named after I.I. Polzunov"

V.A. Wagner,

V.P. Zvezdakov,

V.V. Sobachkin

STANDARDING PRECISION IN MECHANICAL ENGINEERING

Tutorial

in the discipline "Metrology, standardization and certification"

Approved by the Educational and Methodological Association of Universities for University Polytechnic Education as a manual for higher education students educational institutions students studying in mechanical engineering areas of training

From AltSTU

Barnaul – 2011

Vagner V.A. Standardization of accuracy in mechanical engineering. Textbook for the discipline “Metrology, standardization and certification” / V.A. Wagner, V.P. Zvezdakov, V.V. Sobachkin. - Barnaul: Publishing house Alt.gos.tekhn. University named after I.I. Polzunova. - 2011, 84 p.: ill.

IN textbook information is presented on the standardization of accuracy in mechanical engineering when developing machine parts and assemblies.

The purpose of the work is to study theoretical issues in the “interchangeability” section of the discipline “Metrology, standardization and certification”, developing students’ independent activity skills to practically consolidate the tasks discussed in the theoretical part of the course, as well as working with reference literature and standards.

The textbook is intended for students of higher educational institutions of all specialties, studying in mechanical engineering areas of full-time, part-time and correspondence courses, studying the course “Metrology, standardization and certification”.

Reviewers:
Professor of the Department of Metrology and Interchangeability, MSTU. N.E. Bauman,

Doctor of Technical Sciences Pronyakin V.I.
Professor of the Department of Machine Parts, Ural Federal University,

Doctor of Technical Sciences Chechulin Yu.B.

1 Determination of the nominal dimensions of parts of an assembly unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 General information about dimensions, tolerances, fits and maximum deviations. . . . . . . . . . . . . . . . . . . . . .

3 Tolerances and landings in the “Unified System of Tolerances and Landings”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Choice of landings when designing structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1 Landings with clearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Transitional landings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Interference fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Calculation of interference fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Tolerances and fits of keyed joints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Connections with parallel keys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2 Connections with segmental keys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Tolerances and fits of gear (spline) connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.1 Toothed connection with straight splines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.2 Gear connection with involute splines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 Fittings of rolling bearings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 Dimensional chains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Standardization of the accuracy of the shape and location of surfaces of typical machine parts, determination of the required surface roughness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1 Form tolerances and relative position surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2 Roughness of surfaces of parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 Tolerances for the location of the axes of holes for fasteners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12 Justification of the technical requirements for the drawing of the assembly unit. . . . . . . . . . . . . . . . . . . . . . . . . . .

12.1 General provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2 Determination of technical requirements values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2.1 Determination of the values ​​of lateral clearances in engagement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.2.2 Determination of the completeness of contact of the mating side surfaces of the teeth. . . . . . . . . . . . . . . . . .

13 Instructions for drawing up technical requirements and preparing a working drawing of a gear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13.2 Recommendations for drawing up technical requirements for spur and bevel gears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 Instructions for drawing up technical requirements and preparing a working drawing of the gearbox shaft

15 Recommendations for drawing up technical requirements, developing and designing a drawing of the bearing cover and cup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
INTRODUCTION

In accordance with the educational standard for students of technical specialties in mechanical engineering, studying the discipline “Metrology, standardization and certification” in the interchangeability section, a course work or calculation assignment is provided.

Purpose course work(calculation task) is to consolidate the knowledge gained from the theoretical course and acquire skills in their practical application, therefore this work provides both theoretical information on the main sections of the discipline and examples of solving typical problems of the course. The appendix to the work provides reference material necessary for solving problems.

Coursework is completed according to individual assignments issued by the teacher.

Requirements for the content and design of coursework (calculation assignment) are set out in methodological recommendations.

1 Determination of the nominal dimensions of parts of an assembly unit

The dimensions of the parts that make up the assembly unit depend on the assignment and option for the course work. To determine their nominal values, it is necessary to calculate the scale factor. It is calculated as follows. In the drawing of the course work assignment, the size corresponding to the diameter of the shaft under the rolling bearing (d 3 measured) is measured. The target size (d 3 given) is divided by this measured size to obtain the scale factor μ

By measuring all other dimensions of the parts of the assembly unit and multiplying them by this scale factor, the calculated dimensions are determined.

To reduce the number of standard sizes of workpieces and parts, cutting and measuring tools, the values ​​of nominal dimensions obtained by calculation must be rounded to the values ​​​​specified in GOST 6636-69 “Normal linear dimensions” (Table A.1). After this, the rounded values ​​of nominal sizes should be entered in Table 1.1. The dimensions associated with the rolling bearing should be taken according to the standard for this product, regardless of the design size. To do this, you need to decipher symbol of a given rolling bearing, determining its series, type and design features, and then, according to GOST 520-2002 or reference books, write down all the parameters of the rolling bearing necessary for further calculations (connecting diameter of the outer ring, width of the rings, dynamic load capacity of the bearing).

Then the dimensions associated with the rolling bearing are assigned. These dimensions are size d 1 (fitting diameter of the through bearing cap), d 2 (diameter of the hole in the housing for installing the bearing), d 4 (inner diameter of the spacer sleeve), d 5 (fitting diameter of the blind bearing cap). Designations according to .

For example, if according to the assignment it is known that d 3 = 30 mm, bearing type 7300, then this means that the bearing size is 7306 (d 3 /5 = 30/5 = 6), tapered roller bearing and its outer diameter D = 72 mm . In accordance with this, the dimensions d 1 = d 2 = d 5 = 72 mm, and d 4 = d 3 = 30 mm.

When filling out Table 1.1, you should pay attention to the dimensions of standardized and standard parts, which must also be taken in accordance with the relevant regulatory documents. Such parts include seals of bearing units, keys, round spline nuts, through and blind bearing caps, bearing cups.

Based on the obtained dimensions, an assembly unit is drawn on the appropriate scale.

2 General information about dimensions, tolerances, fits and maximum deviations

Size– numerical value of a linear quantity (diameter, length, etc.) in selected units of measurement. In the drawings, all linear dimensions are indicated in millimeters.

Actual size – element size established by measurement with permissible error.

Limit dimensions– two maximum permissible sizes, between which the actual size of a suitable part must be or can be equal to. The larger one is called the largest limit size, and the smaller one is called the smallest limit size. They are designated D max and D min for the hole and d max and d min for the shaft.

Nominal size– the size relative to which deviations are determined. The size indicated in the drawing is nominal. The nominal size is determined by the designer as a result of calculations for strength and rigidity or taking into account design and technological features. For parts forming a landing connection, the nominal size is common.

IN
Table 1.1 - Assembly unit dimensions

No.	Size designation	Dimensions measured, mm	Design size, mm	Size according to GOST 6636-69
1	. . .	. . .	. . .	. . .
2	. . .	. . .	. . .	. . .
n	. . .	. . .	. . .	. . .

upper deviation ES, es – algebraic difference between the largest limit and the corresponding nominal dimensions.

ES = D max – D - for hole, (2.1)

es = d max – d - for the shaft. (2.2)

Lower deviation EI, ei – algebraic difference between the smallest limit and the corresponding nominal sizes.

EI = D min – D - for hole, (2.3)

ei = d min – d - for the shaft. (2.4)

Actual deviation – algebraic difference between real and nominal sizes.

Tolerance T – the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations.

T D = D max – D min = ES - EI - for holes, (2.5)

T d = d max – d min = es - ei - for the shaft. (2.6)

Tolerance is always positive. It determines the permissible dispersion field of the actual dimensions of suitable parts in a batch, that is, the specified manufacturing accuracy.

Tolerance field– a field limited by the largest and smallest limit sizes and determined by the tolerance value T and its position relative to the nominal size. At graphic representation the tolerance field is enclosed between two lines corresponding to the upper and lower deviations relative to the zero line (Figure 2.1).

Main deviation– one of two deviations (upper or lower), determining the position of the tolerance field relative to the zero line. The main one is the deviation closest to the zero line. The second deviation is determined through tolerance.

Zero line– a line corresponding to the nominal size, from which dimensional deviations are plotted when graphically depicting tolerances and fits.

Shaft– a term conventionally used to designate the external (male) elements of parts, including non-cylindrical elements.

Hole– a term conventionally used to designate the internal (encompassing) elements of parts, including non-cylindrical elements.

Hole tolerance denoted T D, and the shaft T d. In addition to female and male elements called holes and shafts, parts contain elements that cannot be attributed to either a hole or a shaft (ledges, distances between the axes of holes, etc.).

Landing- the nature of the connection of two parts, determined by the difference in their sizes before assembly. The fit characterizes the freedom of relative movement of the parts being connected or the degree of resistance to their mutual displacement. Based on the nature of the connection, three groups of fits are distinguished: fits with clearance, fits with interference, and transitional fits.

Gap S is the difference between the sizes of the hole and the shaft, if the size of the hole is larger than the size of the shaft. The gap allows relative movement of the assembled parts. The largest, smallest and average gaps are determined by the formulas:

S max = D max – d min = ES - ei; (2.7)

S

Figure 2.1. a – pairing

b – diagram of the location of the tolerance fields of the shaft and hole
min = D min – d max = EI - es (2.8)