Interchangeability, standardization and technical measurements of Yakushev. Interchangeability, standardization and technical measurements. Interference fit calculation
INTERCHANGEABILITY, STANDARDIZATION AND TECHNICAL MEASUREMENTS
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Chapter 1. Basic concepts of interchangeability and systems of tolerances and fits
1.1. The concept of interchangeability and its types
1.2. The concept of nominal, actual and limiting dimensions, maximum deviations, tolerances and fits
1.3. Unified principles for constructing systems of tolerances and fits for typical joints of machine parts and other products
1.4. Functional interchangeability
1.5. Principles for the selection of tolerances and fits
Chapter 2. Basic concepts of standardization
2.1. State system of standardization
2.2. Brief information on international standardization
Chapter 3. Methodological foundations of standardization
3.1. Principles defining the scientific organization of standardization work
3.2. Standardization of parametric series of machines
3.3. Unification and aggregation of machines. Indicators of the level of unification and standardization
3.4. Comprehensive and forward-looking standardization
3.5. Complex systems of general technical standards
3.6. Classification and coding of technical and economic information
3.7. Standardization of products and assembly units for non-geometric parameters
3.6. The role of unification, aggregation and standardization in improving the quality of machines and the efficiency of their production, Economic efficiency of standardization
Chapter 4. Standardization and quality of machines
4.1. The concept of quality and product quality indicators
4.2. Methods for assessing the level of quality of machines. Optimum quality level
4.3. Statistical indicators of product quality
4.4. Statistical methods of product quality management
4.5. Product quality management systems
4.6. Industrial product quality certification
4.7. Mathematical model of optimization of parameters of standardization objects
Chapter 5. Metrology and technical measurements
5.1. General concepts
5.2. Standards. Measures of length and angular measures
5.3. Universal measuring instruments
5.4. Measurement planning methods
5.5. Criteria for evaluating measurement errors
Chapter 6. Principles of construction of measuring and control instruments
6.1. Choice of precision
6.2. Inversion principle
6.3. Principles of constructing measuring and control instruments
6.4. The principle of combining control functions with technological process control functions
Chapter 7. Automation of processes of measurement, control, selection and processing of results
7.1. Automated fixture
7.2. Control semi-automatic machines and automatic systems
7.3. Active control devices I self-adjusting control systems
7.4. Automation of measurement results processing and design of control processes
Chapter 8. Rationing, methods and tools for measuring and controlling deviations in shape, location, roughness and waviness of the surfaces of parts
6.1. Classification of deviations of geometric parameters of parts
8.2. The system for standardizing deviations in the shape and location of surfaces
8.3. Designation in the drawings of the tolerances of the shape and location of the surfaces of parts
8.4. Standardization system and designation of surface roughness
8.5. Waviness of the surfaces of parts
8.6. The influence of roughness, waviness, deviations in the shape and location of the surfaces of parts on the interchangeability and quality of machines
8.7. Methods and tools for measuring and monitoring shape deviations, location and surface roughness
Chapter 9. Interchangeability, methods and means of measurement in the control of smooth cylindrical joints
9.1. Basic operational requirements and system of tolerances for landings of smooth cylindrical joints
9.2. Designation of limit deviations and landings in the drawings
9.3. Calculation and choice of landings
9.4. Computer use for calculating landings
9.6. System of tolerances and fits for rolling bearings
9.6. Smooth gauges for sizes up to 600 mm
Chapter 10. Tolerances of angles. Interchangeability of tapered connections
10.1. Corner tolerance system
10.2. System of tolerances n landings of conical connections
10.3. Methods and means of control of angles and tapers
Chapter 11. Calculation of tolerances of dimensions included in dimensional chains
11.1. Dimensional chain classification. Basic terms and definitions
11.2. Method for calculating dimensional targets, ensuring complete interchangeability
11.3. Probability-theoretic method for calculating dimensional ispey
11.4. Group interchangeability method. Selective assembly
11.5. Adjustment and fit techniques
116. Calculation of flat and spatial dimensional chains
11.7. Computer application for solving dimensional chains
Chapter 12. Interchangeability, methods and means of measurement and control of threaded connections
12.1. Basic operational requirements for threaded connections
12.2. Main parameters and brief characteristics of fastening cylindrical threads
12.3. General principles for ensuring the interchangeability of cylindrical threads
12.4. Tolerance and fit systems for metric threads
12.5. Influence of thread manufacturing accuracy on the strength of threaded connections
12.6. Characteristics and interchangeability of kinematic threads
12.7. Methods and means of control and measurement of the accuracy of cylindrical threads
Chapter 13. Interchangeability, methods and means of measuring and control of gear and worm gears
13.1. Basic operational and precision requirements for gear drives
13.2. Tolerance system for spur gears
13.3. Tolerances of bevel gears
13.4. Tolerances of helical worm gears
13.5. Methods and means of measuring and control of cogwheels and gears
Chapter 14. Interchangeability of keyed and spline connections
14.1. Keyway tolerances and fits
14.2. Tolerances and fits of spline connections
14.3. Accuracy control of spline connections
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Introduction
1. Calculation and selection of landings of smooth cylindrical joints with a gap
2. Calculation and selection of landings for rolling bearings
3. Choice of landings of the keyed connection
4. Choice of landings of the spline connection
5. Calculation of linear dimensional chains
List of sources used
Introduction
To improve the technical level and quality of products, increase labor productivity, save labor and material resources, it is necessary to develop and improve standardization systems in all sectors of the national economy based on the introduction of the achievements of science, technology and practical experience.
It is necessary to strengthen the effective and active influence of standards on the output of products that meet the highest world level in terms of their technical and economic indicators.
Today, when the production of one machine requires cooperation between hundreds of enterprises of various industries, product quality issues cannot be resolved without expanding work on improving the interchangeability system, metrological support, and improving methods and means of product control. Therefore, the training of a modern engineer includes mastering a wide range of issues related to standardization, interchangeability and technical measurement. The course "Interchangeability, standardization and technical measurements" is the logical conclusion of the cycle of general technical courses in the theory of mechanisms and machines, metal technology, resistance of materials, machine parts. If other courses of the cycle serve as a theoretical basis for the design of machines and mechanisms, the use of standard machine parts, their strength and stiffness calculations, then this course considers the issues of ensuring the accuracy of geometric parameters as a necessary condition for interchangeability and such important quality indicators as reliability and durability. The tasks of improving the quality of manufacturing, operation and repair of agricultural machinery can be considered comprehensively, using the principles of standardization, interchangeability and control of established technical conditions.
The purpose of the discipline is to develop knowledge and practical skills of future engineers in using and complying with the requirements of complex systems of general technical standards, performing precision calculations and metrological support in the manufacture, operation and repair of agricultural machinery.
As a result of studying the course and in accordance with the qualification characteristics, an agricultural mechanical engineer should know: basic provisions, concepts and definitions in the field of standardization; the state system of standardization and its role in accelerating scientific and technological progress, intensifying production, improving the quality of agricultural machinery and the economic efficiency of its use; the main issues of the theory of interchangeability and technical measurements, the rules for designating accuracy standards in design and technological documentation; methods for calculating and selecting standard landings for typical joints of machine parts; calculation of dimensional chains; device for measuring linear and angular quantities, their adjustment, operating rules and selection procedure.
1. CALCULATION AND SELECTION OF FITS FOR SMOOTH CYLINDRICAL JOINTS WITH A CLEARANCE
Initial data:
Determine the product hS:
m2 or 4764 μm2.
We calculate the most advantageous clearance:
We find the value of the design gap:
According to the table in Appendix 8, we select a fit that satisfies the condition:
The above condition is satisfied by the standard fit 40H8 / d8, made in the hole system according to the tenth quality: side deviations for the hole; separate deviations for the shaft.
For the specified fit:
Determine the smallest oil layer thickness with the largest gap
We make a check for the sufficiency of the lubricant layer providing fluid friction:
The condition of fluid friction is met, which means that the fit is ripped out correctly.
We determine the limiting dimensions and tolerances for the processing of connection parts according to the selected fit:
a) holes:
Determine the landing tolerance:
We draw assembly and detailed sketches of the parts to be connected with an indication of the fit, maximum deviations and roughness on sheet 1.
The choice of universal measuring instruments. We choose universal measuring instruments, considering that we make measurements in individual production. In this case, the following condition must be met:
where is the maximum error of the measuring instrument, μm;
Permissible measurement error, microns.
The permissible error in measuring linear dimensions depends on the nominal size and quality.
For the connection in question, DH (dH) \u003d 40 mm. Then, according to Appendix 3, it has:
for hole microns;
for the shaft μm;
These requirements are met (Appendix 4) for the hole - an indicator bore gauge, and for the shaft - a class 1 micrometer, the characteristics of which are given in Table 1.1.
Table 1.1 - Characteristics of measuring instruments
Calculation of the executive dimensions of calibers. Limit gauges are special scaleless measuring instruments designed to establish the suitability of machine parts without determining the actual values \u200b\u200bof the controlled dimensions.
Limit calibers are used mainly to control the dimensions of parts manufactured in conditions of large-scale and mass production. They are divided into gauges for hole inspection and gauges for inspection of shafts, have a through and non-through sides, designated respectively by the symbols PR and NOT.
The hole sizes are controlled by plugs. Structurally, they can be double-sided or separately through and non-through side.
The dimensions of the shafts are controlled with clamps. Calibers-staples can be double-sided or one-sided (in the latter case, the through and non-through sides are combined), sheet, stamped or cast, adjustable and non-adjustable. Adjustable staple gauges are most often used to inspect parts in repair production. They are used when the size of the part being produced or repaired does not fit into the dimensions of a standard rigid gauge. Adjustable gauges for shaft inspection can be adjusted to overhaul dimensions for which rigid gauges are not manufactured. Compared to rigid gauges, adjustable gauges have less accuracy and reliability, therefore they are recommended to be used for inspection of parts with dimensions up to 180 mm and accuracy starting from the 8th grade and coarser.
In order to increase the service life of the gauges-plugs and gauges-staples, the lengths of their through sides are made larger than the lengths of the non-through sides. In addition, to reduce the cost of calibers and increase their service life, the through sides are supplied with hard alloy, thus increasing the wear resistance of calibers by 50 ... 150 times compared to the wear resistance of conventional steel calibers.
The nominal size of the passage side of the plug corresponds to the minimum size of the controlled hole (Dmin), and the no-passage side corresponds to its maximum size (Dmax). On the other hand, in the bracket, the nominal size of the lead-through side is equal to the maximum diameter of the controlled shaft (dmax), and the no-pass one - its minimum diameter (dmin). If, when inspecting a hole or shaft, the through side of the gauge does not pass, this means that the actual size of the hole is less than its minimum value (Dd By designation, limit calibers are divided into working, receiving and control ones. Working gauges are used to control parts directly at the workplace during their manufacture. Reception gauges are used by the customer's representatives when accepting finished products. In contrast to working calibers, it is customary to denote them: the passable side through the P-PR, and the non-passable through the P-NOT. Control gauges, designated K-PR and K-NOT, are used to check new working calibers-staples. There are also control gauges (K-I) to check the amount of wear on the bore of the working gauge-staples. Counter gauges-plugs K-I are made with dimensions corresponding to the maximum permissible wear of the passage sides of the working brackets and are non-passage. If the K-I gauge passes through the controlled bracket, then it is worn out over the established limit and must be removed. There are no control gauges for checking new and worn working plug gauges. The dimensions of the working gauge plugs are checked by universal measuring instruments. The executive ones are the limiting dimensions of the caliber, according to which a new caliber is made. The gauges control shafts and holes with tolerances according to IT6 and coarser. The dimensions of the parts, made with tolerances more accurate than IT6, are checked with universal measuring instruments. Deviations of calibers are counted from the corresponding limiting dimensions of the products. So, deviations of through passages for shafts are counted from the largest limiting shaft size, and deviations of no through passages - from the smallest limiting shaft size. Accordingly, deviations of bore passages for holes are counted from the smallest limiting hole size, and deviations of no-pass gauges - from the largest limiting hole size. The calculated parameters included in the formulas mean (respectively for the plug gauge and the staple gauge): Dmax and d max - the largest limiting dimensions of the hole and shaft; D min and d min - the smallest limiting dimensions of the hole and shaft; Н and H1 - tolerances for the manufacture of calibers; Z and Z1 are the coordinates of the midpoints of the tolerance fields for the manufacture of calibers; Y and Y1 - wear limits of the passing sides of the calibers. We calculate the working gauges for checking the connection details Determine the limiting and working dimensions of the plug gauge to control the hole. According to the table in Appendix 2, we find the data for calculating the plug caliber: H \u003d 4 μm; Z \u003d 6μm; Y \u003d 5 μm. Lead-through side of the plug gauge Rmax \u003d Dmin + Z + (1.2.1) Rmax \u003d 40 + 0.006 + \u003d 40.008 (mm) PRmin \u003d Dmin + Z- (1.2.2) PRmin \u003d 40 + 0.006- \u003d 40.004 (mm) PRIV \u003d Dmin -Y (1.2.3) PRISN \u003d 40-0.005 \u003d 39.995 (mm) The executive dimensions of the through and non-through sides of smooth working calibers for holes (plugs) are their largest limiting dimensions with a numerical tolerance equal to the manufacturing tolerance H directed into the caliber body (in "minus"). Then, for the through side of the plug, the operating size App. \u003d 40.008 -0.004 Non-passable side of the plug gauge HEmax \u003d Dmax + (1.2.4) HEmax \u003d 40.039 + \u003d 40.041 (mm) HEmin \u003d Dmax- (1.2.5) HEmin \u003d 40.039- \u003d 40.037 (mm) For the non-passage side of the plug, operating size Leading side of staple gauge Rmax \u003d dmax-Z1 + (1.2.6) PRMax \u003d 39.92-0.006 + \u003d 39.9175 (mm) PRmin \u003d dmax-Z1- (1.2.7) PRmin \u003d 39.92-0.006- \u003d 39.9105 (mm) PRIV \u003d dmax + Y1 (1.2.8) Lifetime \u003d 39.92 + 0.005 \u003d 39.925 (mm) The executive dimensions of the through and non-through sides of the working calibers for shafts (brackets) are their smallest limiting dimensions with a tolerance numerically equal to the manufacturing tolerance H1 directed to the caliber body (in "plus"). Then, for the passing side of the bracket, the executive size will be the following: PRisp \u003d 39.9105 + 0.007. Non-passable side of the staple gauge HEmax \u003d dmin + (1.2.9) HEmax \u003d 39.881 + \u003d 39.8845 (mm) HEmin \u003d dmin- (1.2.10) HEmin \u003d 39.881- \u003d 39.8775 (mm) For the non-passable side of the bracket, the effective size will be the following: FAIL \u003d 39.8775 +0.007. When calculating the working and working dimensions of calibers, dimensions ending in 0.25 and 0.75 microns should be rounded to multiples of 0.5 microns in the direction of reducing the manufacturing tolerance. The layouts of the tolerance fields and a sketch image of the gauges for controlling the hole and shaft are shown on sheet 2. 2. CALCULATION AND SELECTION OF FITTINGS FOR ROLLING BEARINGS Ball bearing No. 410. The shaft rotates, the body is stationary. The body is cast iron, one-piece. Radial load on the support R \u003d 16200 N. The bearing operating mode is normal (moderate shocks and vibrations, overload up to 150%). According to Appendix 2 of the methodological instructions, we find the main dimensions of the bearing: Determine the type of loading of the rings of a given bearing. Since the shaft rotates, and the housing is stationary, the inner ring of the bearing will experience a circulating load, the outer one will be local. We calculate and select the fit of the circulatingly loaded ring. We determine the intensity of the radial load of the landing surface by the formula: where is the dynamic landing coefficient, depending on the nature of the load, in our case we take KP \u003d 1; The coefficient taking into account the degree of weakening of the landing interference, in our case, we take F \u003d 1; The coefficient of uneven distribution of the radial load R between the rows of rollers in double-row tapered roller bearings or between double ball bearings in the presence of an axial load A on the support, in our case there is no axial load, we take FA \u003d 1; B is the width of the ring; r is the width of the chamfer. According to the table in Appendix 4, we find the shaft diameter tolerance field corresponding to the obtained PR values. For a bearing of accuracy class 0, we take the tolerance field k6. Then we write down the fit of the inner ring on the shaft as follows:. According to the table in Appendix 5, we take the tolerance field of the hole in the housing H7. Fitting the outer ring into the body in the conditional notation has the form. According to tables 1 and 2 and Appendix 6 of the methodological instructions, we find the numerical values \u200b\u200bof the maximum deviations of the connecting diameters of the bearing rings and the seats of the shaft and housing. We have: Let's calculate the limiting value of the connecting diameters and their tolerances. We summarize the calculation data in Table 2.1. Inner ring: Outer ring: Housing hole: Connection: "inner ring - shaft" Connection: "outer ring - body" The schemes of the mutual arrangement of the tolerance fields are shown on sheet 3. According to the tables in Appendix 7 and 8, we establish the permissible deviations of the shape, the relative position of the landing surfaces, their roughness. We have: Deviations from the cylindricity of the shaft journal - 8 microns, holes in the housing - 20 microns. The runout of the ends of the shaft shoulders is no more than 20 microns, the holes in the housing are no more than 50 microns. Roughness of shaft seating surfaces Ra not more than 1.25 microns; holes in the Ra housing are not more than 2.5 µm. The roughness of the landing surfaces of the ends of the shoulders Ra is not more than 2.5 microns. We draw sketches of the bearing assembly and parts connected to the bearing with all the necessary designations applied (sheet 3). Name of bearing connection elements Limit deviations, mm Limit dimensions, mm Tolerances, μm Limit gaps, microns Connecting diameters: inner ring Shaft neck outer ring case holes Connections: "Inner ring-shaft" Outer ring-body 3
... SELECTING THE KEY JOINT FITTING Initial data: According to Appendix 10, we find the main dimensions of the keys and grooves. Set the fit of the key into the groove of the shaft and into the groove of the sleeve from Appendix 13. Then the landings in the groove of the shaft and in the groove of the sleeve in general form can be written as follows: The numerical values \u200b\u200bof the maximum deviations of the width of the key and grooves are found from the tables in Appendix 15, we have: The tolerances and maximum deviations of the non-conjugate dimensions of the keyed connection elements are found from Table. Appendices 1 and 14. Let's calculate the limiting values \u200b\u200bof all basic dimensions taught in the connection of the key with the grooves: Bushing groove We calculate the clearances and tightness obtained in the connection of the key with the grooves in width. Compound: "Key - shaft groove" "Key - bushing groove" The calculation results are summarized in table. 3.1. We draw sketches of the keyway connection and its parts sheet 4. Name of keyed connection elements Nominal size in mm and tolerance range (fit) Limit deviations, mm Limit dimensions, mm Tolerances, μm Limit gaps, microns Shaft groove: Sleeve groove: Connections: "Key-groove of the shaft" Bushing key-groove 4
... SELECTING SPLINE FITTINGS Spline connection: We make a transcript of its conditional notation. The specified spline connection is centered on the outer diameter, has the number of teeth z \u003d 8, the nominal value of the inner (non-centering) diameter d \u003d 56 mm, the outer (centering) diameter - D \u003d 65 with the fit H7 / js6, the thickness of the shaft tooth (width of the sleeve cavity) b \u003d 10 with landing D9 / f7. According to the tables in Appendices 1 and 2, as well as in Appendix 19, we find the maximum deviations of the dimensions of the spline connection: We calculate the limiting dimensions and tolerances of all elements, as well as the gaps obtained in the joints according to the centering diameter and dimension b: for splined sleeve: inner diameter outside diameter cavity width for splined shaft: inner diameter outside diameter tooth thickness Connection: "sleeve - splined shaft": by centering diameter: by size b: We enter all the dimensional characteristics of the spline connection in the table. 4.1. Name of spline connection elements Nominal size in mm and tolerance range (fit) Limit deviations, mm Limit dimensions, mm Tolerances, μm Limit gaps, microns A. Centering element. outer diameter of the sleeve shaft outer diameter bushing cavity width shaft cavity width B. Non-centering ale. inner diameter of bushings. inner diameter of the shaft B. Connection: by centering diameter by size b bearing connection dimensional chain 5. CALCULATION OF LINEAR DIMENSIONAL CHAINS BY THE METHOD OF TOTAL INTERCHANGEABILITY The sequence of calculating the dimensional chain when solving the direct problem by the method of complete interchangeability is as follows: 1. For the closing link specified in the node drawing, identify the constituent links of the dimensional chain; 2. Build a geometric diagram of the dimensional chain and determine the nature of the constituent links (establish which of them are increasing and decreasing); 3. Using the basic equation, check the correctness of drawing up the dimensional chain; 4. Determine the tolerance of the closing link, and then, using the formulas, calculate the value of the accuracy coefficient of the dimensional chain ac; 5. Comparing ac with standard a values, set the quality and assign tolerances to the dimensions of the constituent links, having previously selected the correcting link; 6. Determine the tolerance value of the correcting link, and set the maximum deviations for the remaining component links according to the assigned tolerances; 7. Determine the coordinates of the midpoints of the tolerance fields of the closing and all constituent links, and then calculate the coordinate of the middle of the tolerance field of the correcting link; For an assembly dimensional chain with a master link \u003d determine the tolerances and maximum deviations of the constituent links. In a given dimensional chain, the closing link is the gap formed by the end of the body and the end of the sleeve. This gap is necessary to compensate for temperature changes in the dimensions of the parts of the assembly and, therefore, its value must be maintained within strictly specified limits. Let's build a dimensional chain, that is, find its constituent links. Making a detour along the contour from the closing link, we establish the tangency surfaces (assembly bases) of the adjacent parts, and through them - dimensional links. The size of the gap is determined by the relative position of the end surface of the body and the end surface of the sleeve. The sleeve with its left end touches the gear, which in turn rests against the shaft. The shoulder of the shaft is in contact with the bearing. Which rests against the body. Let's write dimensional relationships as follows: master link - spacer sleeve spacer sleeve - gear gear - shaft shaft - body body is a closing link. The dimensional chain is made up of the dimensions between the touching surfaces of each of the specified parts: the length of the spacer sleeve - link A1 \u003d 15 mm, the width of the gear wheel link A2 \u003d 65 mm, the length of the shaft section link A3 \u003d 105 mm and the size of the body (distance between the inner and outer surface of the sidewall) - link A4 \u003d 22 mm. Consequently, the dimensional chain includes nine constituent links, of which the A1, A2, A4 links are decreasing, and the A3 link is increasing. The geometric diagram of the dimensional chain is presented on sheet 5. Let's check the correctness of drawing up the dimensional chain, for which we use the formula: A3- (A1 + A2 + A4) (5.1) 105-15-65-22 \u003d 3mm. The obtained value of the nominal size of the closing link corresponds to the given one. Therefore, the dimensional chain is composed correctly. We now determine the accuracy coefficient of the dimensional chain, having previously calculated the tolerance of the closing link. Closing link tolerance ma \u003d - \u003d 200 - (- 200) \u003d 400 μm. We calculate the accuracy coefficient of the dimensional chain, since the dimensional chain contains links with known tolerances (rolling bearings): In the denominator, under the sign of the sum, the values \u200b\u200bof the tolerance units of the sizes of the links A1, A2, A3, A4 should be included, which we find from the table. 2.1., Then Comparing the obtained value of ac with the data in Table. 2.2., We establish that it is in the range of ac values \u200b\u200bcorresponding to the 10th and 11th qualifications (a10 \u003d 64, a11 \u003d 100). In this case, it is advisable to assign tolerances for the component links to the 10th grade and, since ac\u003e a10, choose the link that is most difficult to manufacture as a corrective link. Let's take the body size as a corrective link - link A3 \u003d 105 mm, and assign standard tolerances to the rest. According to the table. 2.3., We have the following: T1 \u003d 70 microns, T2 \u003d 120 microns; T4 \u003d 84 microns. The non-standard tolerance of the correcting link T3 is found using the formula (2.10).,: T3 \u003d T- (T1 + T2 + T4) (5.3) T3 \u003d 400 - (70 + 120 + 84) \u003d 126 microns. The maximum deviations of the constituent links (excluding the correcting one) are assigned, following the above rule. Then A1 \u003d 15-0.07, A2 \u003d 65-0.12, A4 \u003d 22-0.084 We determine the coordinate of the middle of the tolerance field of the correcting link, having previously determined its value for all other links in the chain. The coordinates of the middle of the tolerance fields of the closing and constituent links are found by the formula: We have: c1 \u003d -0.035mm; c2 \u003d -0.06 mm; c4 \u003d - 0.042 mm; \u003d 0mm. We find the coordinate of the middle of the tolerance field of the correcting link by the formula: 0.035-0.06-0.042-0 \u003d -0.137 mm. Now we set the maximum deviations of the A3 link Thus, the correcting link has maximum deviations. We check the correctness of the calculations, for which we use the equations: The resulting maximum deviations of the closing link correspond to the specified ones. Therefore, the dimensional chain is dimensioned correctly. LIST OF USED SOURCES 1. Interchangeability, standardization and technical measurements. Part 1: Guidelines for course design for the calculation and selection of landings of smooth cylindrical joints / Comp. V. A. Orlovsky; Belarusian agricultural acad. Gorki, 1986. - 47p. 2. Gray I.S. Interchangeability, standardization and technical changes. - M .: Agropromizdat, 1987 .-- 368 p. 3. Calculation of the executive dimensions of smooth working calibers: Methodical instructions for laboratory work on interchangeability, standardization and technical measurements / Comp. N. S. Troyan, V. A. Orlovsky; Belarusian agricultural acad. Gorki, 1987 .-- 16 p. 4. Interchangeability, standardization and technical measurements. Part 2. Guidelines for course design for the calculation and selection of landings for typical connections / Comp. N. S. Troyan; Belarusian agricultural acad. Gorki, 1986. - 48p. 5. Interchangeability, standardization and technical measurements. Part 3. Guidelines and tasks for the calculation of dimensional chains in course design / Comp. N. S. Troyan; Belarusian agricultural acad. Gorki, 1991. - 48p. Posted on Allbest.ru Basic provisions, concepts, definitions in the field of standardization. General information, the procedure for calculating and choosing landings for rolling bearings. Calculation of linear dimensional chains by the probabilistic method. Selection of landings for smooth cylindrical joints with a gap. tutorial, added 01/21/2012 The choice of fits of smooth cylindrical joints, for spline joints with a straight tooth profile. Calculation and selection of interference fits. Calculation of the dimensional chain by the method of complete interchangeability and the probabilistic method. Solution of linear dimensional chains. term paper, added 04/09/2011 The choice of landings for smooth cylindrical joints located on the low-speed shaft, the rationale for the choice of the system and qualities. Calculation and selection of interference fits. Solution of linear dimensional chains by the method of complete interchangeability and the probabilistic method. term paper, added 03/10/2011 Smooth cylindrical joints. Calculation of interference fits. The choice of transitional landings. Calculation of rolling bearings and straight-sided splined joints. Calculation by the method of complete interchangeability of dimensional chains. Indicators of gear and worm connections. term paper, added 03/27/2015 Choice of landings of smooth mates. Selection of rolling bearing landings, their characteristics. Fitting the sleeve on the shaft, the cover in the body. Calculation of the executive dimensions of calibers Selection and designation of landings for threaded and spline connections. Calculation of dimensional chains. term paper, added 04/28/2014 Determination of clearances, tightness and tolerances of landings in smooth cylindrical joints. Calculation of landings in the system of main holes, shafts, holes, smooth limiting dimensions of calibers. Solution of dimensional chains by the method of complete interchangeability. term paper added 07/11/2015 Methodology and main stages of solving dimensional chains by the method of complete interchangeability, the procedure for conducting direct and reverse calculations. Determination of the coordinates of the middle of the tolerance field of the closing link, the tolerance of the closing link according to the known dependence. test, added 01/20/2010 Selection and calculation of fits for connections. Calculation of the loading intensity. Fit the spacer sleeve and gear to the shaft. Requirements for the surfaces of the housing and shaft intended for the seating of rolling bearings. The choice of measuring instruments. test, added 11/16/2012 Calculation of landings with a clearance in plain and rolling bearings. The choice of gauges for the control of parts of smooth cylindrical joints, landings of keyway and straight-sided spline joints. Standardization of the accuracy of cylindrical gears and gears. term paper added on 05/28/2015 Determination of elements of a smooth cylindrical connection. Calculation and selection of landings with a clearance. Calculation and selection of interference fits. Determination of tolerances and fit of keyed connections. Calculation and selection of rolling bearing landings. Calculation of dimensional chains. Introduction 1 Purpose of work 2 Calculation data 4 Calculation of the screw connection 5 Landings of rolling bearings 6 Calculation of dimensional chains Literature Introduction With the modern development of science and technology, with organized mass production, standardization based on the widespread introduction of the principles of interchangeability is one of the most effective means of promoting progress in all areas of economic activity and improving the quality of products. This course work is done with the aim of consolidating the theoretical provisions of the course, set out in the lectures and teaching independent work with reference literature. 1 Purpose of work 1.1 For the mate specified in the task, calculate and select a standard fit with an interference or clearance 1.2 For a rolling bearing unit with a constant load in the direction, calculate the fit for the circulating-loaded ring and select the fit for the locally loaded ring. 1.3 Draw diagrams of the location of the tolerance fields for the bearing rings, shaft and housing. For a given threaded connection, determine all nominal values \u200b\u200bof thread parameters, tolerances and deviations. 2 Calculation of interference fit The calculation of interference fits is carried out in order to ensure the strength of the connection, that is, the absence of displacement of the mating parts under the influence of external loads, and the strength of the mating parts. The initial data for the calculation are taken from the task and are summarized in Table 1. Table 1 - Initial data for calculating interference fits Designation in formulas Nominal connection size Poisson's ratio Riala bushings Poisson's ratio Riala Vala The smallest calculation of the interference is determined from the condition of ensuring the strength of the connection (immobility), from the condition of ensuring the service purpose of the connection / 1, p.333 /. Only on action T only on action F and With simultaneous action F a and T: According to the obtained values R the required value of the smallest design interference is determined where E 1, E 2 - the modulus of elasticity of the materials of the male (shaft) and female (holes) parts, respectively, in N / m 2; from 1, from 2 Are the Lamé coefficients determined by the formulas The value of the minimum allowable tightness is determined / 1, p.335 / where g w- a correction that takes into account the crushing of the irregularities of the contact surfaces of the parts during the formation of the connection, g t - correction, taking into account the difference in the working temperature of parts t 0
and t d and build temperatures t Sat, the difference in the coefficients of linear expansion of the materials of the parts to be joined ( a D and a d), Here Dt D =
t D - 20
°
- the difference between the working temperature of the part with the hole and the normal temperature; Dt d =
t d - 20
°
- the difference between the temperature of the shaft and the normal temperature; a D, a d –
coefficients of linear expansion of materials of parts with a hole and shaft. g c - a correction that takes into account the weakening of the tightness under the action of centrifugal forces; for solid shaft and identical materials of jointed parts where u - peripheral speed on the outer surface of the sleeve, m / s; r - the density of the material, r/cm 3 . g P - an additive that compensates for the decrease in tightness during repeated pressings; determined empirically. Determine the maximum permissible specific pressure As The value of the largest design interference is determined The value of the maximum permissible tightness is determined, taking into account the amendments where g oud - coefficient of increase in specific pressure at the ends of the covering part; g t - a correction for the operating temperature, which should be taken into account if the interference increases. The fit is selected from the tables of the system of tolerances and fits /1, p.153/. The conditions for selecting the fit are as follows: - maximum tightness - minimum interference The required force is calculated when pressing the assembled parts, where f n - coefficient of friction during pressing, f n=(1,15…1,2)f; P max - maximum specific pressure at maximum tightness Based on the data obtained (Appendix B), we draw a diagram of the location of the "hole" and "shaft" tolerance fields. The scheme for calculating an interference fit is shown in Figure 1. Figure 1 - Scheme for the calculation of interference fit The calculation of interference fits was carried out on a computer and the result of the calculation is given in (Appendix B). We choose the fit according to the tables of the tolerance and fit system. The selection conditions are as follows: a) the maximum interference N max in the selected fit should not be more: b) the minimum interference N min in the fitted fit should be greater: Since the minimum condition is satisfied, we choose this fit. The graphic location of the d50 H8 / g8 fit tolerance fields is shown in Figure 2. Test 22... Landing tolerance is determined by the formula: Test 7... Control standards: establish organizational, methodological and, in general terms, technical provisions for a specific industry of standardization, as well as terms and definitions, in general terms, technical requirements, norms and rules; establish requirements for a group of homogeneous or specific products, services that ensure its compliance with its purpose; establish the basic requirements for the sequence and methods of performing different work in the processes that are used in the types of activities and ensure the compliance of the process with its purpose; establish a sequence of works, a method and technical means of implementation for varieties and objects of control of products, processes, services. Test 8... Decipher the designation of the DSTU ISO standard state standards of Ukraine approved by the State Standard of Ukraine; state standards through which the standards of the International Organization for Standardization are implemented; state standard of Ukraine, adopted by the Interstate Council; state standards are approved by the Ministry of Construction and Architecture of Ukraine. Test 15... Which constructive group does the internal micrometer belong to? To the group of lever-mechanical tools To the group of indicator instruments To the group of micrometric instruments To the group of optical-mechanical instruments Test 20... Micrometric screw is threaded with precise pitch Test 21... Complete interchangeability is characterized by the fact that ... Parts for high precision joints are made with deliberately reduced accuracy or allow one of the parts to be fitted The part, besides the fact that it takes its place in the machine without additional processing operations, also performs its functions in accordance with the technical requirements. In the process of drawing up, there should be no adjusting or adjusting operations. Interchangeability in size, shape, relative position of surfaces and axes of parts and roughness of their surfaces Test 22... The smallest interference fit is determined from the dependence: 69 In the drawing of the part, the maximum deviations are indicated as follows: D - 0.012. Please enter the correct tolerance. 70 In the drawing of the part, the size is indicated as follows: Ф 24 - 0.012. Specify the largest size limit. 71 In the drawing of the part, the size is indicated as follows: Ф 24 - 0.012. Please indicate the smallest size limit. 72 Given: nominal size d n \u003d 40 mm, the largest limiting size d m a x \u003d 40.016 mm, tolerance Td \u003d 0.026 mm. Determine the smallest size limit 73 Specified: nominal size d n \u003d 230 mm, lower deviation - 0.016 mm, tolerance Td \u003d 0.026 mm. Determine the upper deviation 74 Given: nominal size d n \u003d 10 mm, the smallest limiting size d m i n \u003d 10.015 mm, tolerance Td \u003d 0.026 mm. Determine the largest size limit 75 In the drawing, the hole size is marked F 56 + 0.00 5, the actual size is 56.15 mm. Determine the suitability of the hole 2) the marriage is irreparable 3) we fix the marriage 76 In the drawing, the hole size is marked F 56 + 0.00 5, the actual size is 56.010 mm. Determine the suitability of the hole 2) the marriage is irreparable 3) we fix the marriage 77 In the drawing, the hole size is marked F 56 + 0.00 5, the actual size is 56.00 mm. Determine the suitability of the hole 2) the marriage is irreparable 3) we fix the marriage 78 In the drawing, the size of the shaft is affixed to Ф 35, the actual size is 35.00 mm. Determine the suitability of the shaft 2) the marriage is irreparable 3) we fix the marriage 79 In the drawing, the size of the shaft is affixed to F 35 + 0.00 5, the actual size is 35.00 mm. Determine the suitability of the shaft 2) the marriage is irreparable 3) we fix the marriage 80 In the drawing, the size of the shaft is affixed to F 35 + 0.00 5, the actual size is 35.15 mm. Determine the suitability of the shaft 2) the marriage is irreparable 3) we fix the marriage 81 In the drawing, the size of the shaft is affixed to Ф 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 82 In the drawing, the size of the shaft is affixed to Ф 35 + 0.00 5, the dimensions of the measured part are 35.008 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 83 In the drawing, the size of the shaft is affixed to Ф 35 + 0.00 5, the dimensions of the measured part are 35.00 mm and 35.005 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 84 In the drawing, the size of the shaft is affixed to Ф 35 + 0.00 5, the dimensions of the measured part are 35.019 mm and 35.020 mm. Determine the suitability of the shaft if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 85 In the drawing, the hole size is marked F 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.005 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 86 In the drawing, the hole size is marked F 35 + 0.00 5, the dimensions of the measured part are 35.014 mm and 35.010 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 87 In the drawing, the hole size is marked F 35 + 0.00 5, the dimensions of the measured part are 35.015 mm and 35.018 mm. Determine the suitability of the hole if the deviation from roundness is not more than half the tolerance. 2) the marriage is irreparable 3) we fix the marriage 88 The hole diameter in the drawing is designated 100 + 0.02. At which of the indicated actual dimensions should the part be rejected? Introduction To improve the technical level and quality of products, increase labor productivity, save labor and material resources, it is necessary to develop and improve standardization systems in all sectors of the national economy based on the introduction of the achievements of science, technology and practical experience. It is necessary to strengthen the effective and active influence of standards on the output of products that correspond in their technical and economic indicators to the highest world level Today, when the production of one machine requires cooperation between hundreds of enterprises of various industries, product quality issues cannot be resolved without expanding work on improving the interchangeability system, metrological support, and improving methods and means of product control. Therefore, the training of a modern engineer includes mastering a wide range of issues related to standardization, interchangeability and technical measurement. The course "Interchangeability, standardization and technical measurements" is the logical conclusion of the cycle of general technical courses in the theory of mechanisms and machines, metal technology, resistance of materials, machine parts. If other courses of the cycle serve as a theoretical basis for the design of machines and mechanisms, the use of standard machine parts, their strength and stiffness calculations, then this course considers the issues of ensuring the accuracy of geometric parameters as a necessary condition for interchangeability and such important quality indicators as reliability and durability. The tasks of improving the quality of manufacturing, operation and repair of agricultural machinery can be considered comprehensively, using the principles of standardization, interchangeability and control of established technical conditions. The purpose of the discipline is to develop knowledge and practical skills of future engineers in using and observing the requirements of complex systems of general technical standards, performing precision calculations and metrological support in the manufacture, operation and repair of agricultural machinery. As a result of studying the course and in accordance with the qualification characteristics, an agricultural mechanical engineer should know: basic provisions, concepts and definitions in the field of standardization; the state system of standardization and its role in accelerating scientific and technological progress, intensifying production, improving the quality of agricultural machinery and the economic efficiency of its use; the main issues of the theory of interchangeability and technical measurements, the rules for designating accuracy standards in design and technological documentation; methods for calculating and selecting standard landings for typical joints of machine parts; calculation of dimensional chains; device for measuring linear and angular quantities, their adjustment, operating rules and selection procedure. 1. Calculation and selection of landings of smooth cylindrical joints with a gap Calculation and selection of landings of smooth cylindrical joints is carried out in the following sequence. 2. Select universal measuring instruments for the parts to be connected. The initial data for the calculation are: Nominal connection diameter, d H \u003d 30 mm; Connection (bearing) length, l \u003d 50 mm; Angular velocity, \u003d 70 rad / s; Absolute viscosity of oil at operating temperature, \u003d 0.03 N-s / m 2; Average specific pressure on the support, g \u003d 0.45 N / M 2 R zD \u003d 4 μm and R zd \u003d 2. 5 microns - the value of the surface roughness of the sleeve and shaft. Fig. 1.1 Scheme for calculating landings for a movable connection From the hydrodynamic theory of lubrication it is known that the ratio between the values \u200b\u200bof h and S (Fig. 1.1) in bearings of finite length is expressed by the relationship \u003d where h is the thickness of the oil layer at the place of the closest approach of the surfaces of the shaft and the bearings in working condition, m; is the gap between the shaft and the bearing at rest, m. hS \u003d Knowing the value of the product hS, determine the value of the most advantageous gap in the joint: Taking into account the presence of surface roughness of the parts to be joined, the value of the design gap is found: Spac \u003d According to the size of the design clearance according to the tables of maximum deviations of holes and shafts (Appendices 4 and 5), a fit is selected that satisfies the condition The above condition is satisfied by the standard fit 30, made in the hole system: maximum deviations for hole 30H8 (); limit deviations for shaft 30e8 (). For the specified fit: S max \u003d ES-ei \u003d 33 - (- 0.073) \u003d 106 (μm) (1.5) S min \u003d EI- es \u003d 0 - (- 40) \u003d 40 (μm) (1.6) The selected fit should be checked for fluid friction. The smallest thickness of the lubricant layer is determined at the largest clearance of the selected fit We make a check for the sufficiency of a lubricant layer that provides fluid friction, checked according to the condition The condition of fluid friction is met, which means that the fit is selected correctly. We determine the limiting dimensions and tolerances for the processing of connection parts according to the selected fit: a) holes: D max \u003d D H + ES (1.9) max \u003d 30 + 0. 033 \u003d 30. 033 (mm) mln \u003d D H + EI (1.10) mln \u003d 30 + 0 \u003d 30 (mm); D \u003d D max - D mln \u003d ES-EI; (1.11) D \u003d 30. 033-30 \u003d 0.033 (mm) max \u003d d H + es (1.12) max \u003d 30 + (- 0.040) \u003d 29. 96 (mm) min \u003d d H + ei (1.13) min \u003d 30 + (- 0.073) \u003d 29. 927mm) d \u003d d max -d mln \u003d es-ei (1.14) d \u003d 29. 96-29.927 \u003d 0.033 (mm) Determine the landing tolerance: s \u003d S max -S min \u003d T D + Td (1.5) Ts \u003d 33 + 33 \u003d 66 (mm). We choose universal measuring instruments for the parts to be joined, assuming that the measurement is carried out in individual production. The choice of universal measuring instruments is made taking into account metrological, design and economic factors. When choosing universal measuring instruments, it is necessary that the limiting error of the measuring instruments, lim, be equal or less than the permissible measurement error. that is, so that the condition is met: For the considered connection d H \u003d 30 mm, T D \u003d 33 μm, T d \u003d 33 μm, we choose from the table of Appendix 3 for the hole 30H8 \u003d 10 μm; for shaft 30e8 \u003d 10 microns. These requirements are met (Appendix 4) for a hole - an indicator bore gauge with a measuring head with a valuable division of 0.001 mm, and for a shaft a lever micrometer with a division value of 0. 002 mm, the characteristics of which are entered in table. eleven. Table 1. 1. Initial data and characteristics of the selected measuring instruments Part tolerance, IT part, μm Permissible error, microns Limiting error of measuring instruments, μm Name of measuring instruments and their metrological characteristics Hole Indicator bore gauge with an indicator of zero accuracy class when working within one turn of the hand with a valuable division of 0.01 mm Indicator bracket with a fine graduation of 0.01 mm 1.2 Calculation of the executive dimensions of smooth gauges In the manufacture of limiting calibers, their executive dimensions must be maintained within the tolerances for calibers established by the standards GOST 24853 - 81 (Art. SEV 157 - 75). Let's calculate the working gauges for checking the connection details: Since for parts made with an accuracy of more than 6-20 qualifications (shaft according to IT6), control using calibers (calibers of the staple) is carried out according to separate, limiting and operating dimensions of the plug caliber. Determine the limiting and operating dimensions of the caliber - plugs: According to Appendix 1 for IT6 and the size interval 18 ... 30 mm, we find the data for calculating the caliber - plug. \u003d 5μm, Y \u003d 4μm, H \u003d 4μm. The through side of the gauge is plugs. PR max \u003d D min + Z + H / 2 \u003d 30 + 0. 005 + 0. 004/2 \u003d 30. 007 (mm). (1. 16) PR min \u003d D min + Z-H / 2 \u003d 30 + 0.005-0.004 / 2 \u003d 30. 001 (mm). (1. 17) PR meas \u003d D min -Y \u003d 30 - 0.004 \u003d 29. 996 (mm). (1. 18) The executive dimensions of the through and non-through sides of the gauge - plugs are their largest limiting dimensions with a tolerance numerically equal to the tolerance for the manufacture of the gauge (minus). Then, for the through side of the gauge - plugs, the working size is: PR isp \u003d 30. 007 -0. 004 (mm). Non-passage side of plug gauge: NOT max \u003d D max + H / 2 \u003d 30. 033 + 0. 004/2 \u003d 30. 035 (mm). (1. 19) NOT min \u003d D max -H / 2 \u003d 30. 033-0. 004/2 \u003d 30. 031 (mm). (1.20) Then for the non-passage side of the gauge - plugs the working size: NOT use \u003d 30. 035 -0.004 (mm). We calculate the caliber - shafts for checking the shaft ø25f6. According to Appendix 1 for IT6 and size range 18… 30mm. we find data for calculating the caliber - staples. 1 \u003d 5μm. Y 1 \u003d μm. H 1 \u003d 4μm. Leading side of the gauge - staples: PR max \u003d d max -Z 1 + H 1/2 \u003d 29. 96-0. 005 + 0. 004/2 \u003d 29. 957 (mm). (1.21) PR min \u003d d max -Z 1 -H 1/2 \u003d 29. 96-0.005-0.004 / 2 \u003d 29. 953 (mm). (1.22) PR meas \u003d d max + Y 1 \u003d 29. 96 + 0. 004 \u003d 29. 964 (mm). (1.23) For the lead-through side of the bracket, operating size: PR isp \u003d 29. 957 +0. 004 (mm). Non-passable side of the gauge - staples: NOT max \u003d d min + H 1/2 \u003d 29. 927 + 0. 004/2 \u003d 29. 929 (mm). (1.24) NOT min \u003d d min -H 1/2 \u003d 29. 927-0. 004/2 \u003d 29. 925 (mm). (1.25) For the non-passable side of the bracket, the working size is: NOT use \u003d 29. 929 +0. 004 (mm). Limit executive gauges - plugs and staples are summarized in table 1.2 Table 1.2 Calculation results of measuring instruments Control detail The value of the elements of working calibers Passing side Bad side Nominal size Limit sizes, mm. Executive size Nominal size Limit size in, mm. Executive size Hole 2. Calculation and selection of landings for rolling bearings 1 General Rolling bearings operate in a wide variety of operating conditions and are designed to provide the required accuracy and uniformity of rotation of moving parts of machines. As standard units, rolling bearings have full external interchangeability for connecting surfaces determined by the outer diameter of the outer and inner diameters of the inner rings. Full interchangeability of rolling bearings along the connecting surfaces ensures their easy and quick assembly and disassembly, while maintaining the good quality of machine assemblies. The quality of the rolling bearings themselves is determined by a number of indicative ones, depending on the value of which by GOST standards. 520-71, five accuracy classes are established, designated in order of increasing accuracy: О, 6, 5, 4 and 2. The bearing accuracy class is selected based on the requirements for the rotation accuracy and the operating conditions of the mechanism. In mechanical engineering and instrumentation at medium and low loads, with normal rotation accuracy, bearings of accuracy class O are usually used. For the same conditions, but with increased requirements for rotation accuracy, bearings of accuracy class 6 are used. Bearings of accuracy classes 5 and 4 are used only at high speeds and strict requirements for the accuracy of rotation, and accuracy class 2 - only in special cases. Accuracy class (except for class 0) is indicated by a dash in front of the bearing designation, for example: 6 - 209 In order to reduce the nomenclature, bearings are manufactured with deviations in the connecting diameters, which do not depend on the landings along which they are mounted on shafts and in housings. This means that the outer diameter of the outer ring and the inner diameter of the inner ring are taken, respectively, for the diameters of the main shaft and the main hole and, therefore, the connections of the outer ring with the body are carried out according to fits in the shaft system, and the inner ring to the shaft - according to fits in the hole system. The bore diameter of the inner ring taken as the main bore has a tolerance direction similar to that of the main shaft. The inverted arrangement of the tolerance field for the diameter of the inner ring bore eliminates the need for the development and use of special fits to obtain connections of the rings with shafts with small interference. In this case, the required tightness values \u200b\u200bare provided as a result of the use of standard transitional landings in accordance with GOST 25347-82. Landings of rolling bearings on shafts and housings are selected depending on their types and sizes, operating conditions, the magnitude and nature of the loads acting on them and the type of loading of the rings. There are three main types of loading of rolling bearing rings: local, circulating and oscillatory. In practice, it most often happens that one of the bearing rings, as a rule, is rotating, experiences a circulating load, and the other (stationary) is local. A ring under circulating load should be connected to the shaft or body along landings that provide low interference values, and a stationary, locally loaded ring should be connected through landings with a small clearance. Landings of circulation-loaded bearing rings on shafts and in housings are selected according to the intensity of the radial load on the seating surface, which is determined by the following formula: K p - dynamic landing coefficient, depending on the nature of the load (with strong shocks and vibration, overload up to 300% Kp \u003d 1.8); - coefficient taking into account the degree of weakening of the landing interference with a hollow shaft or a thin-walled body (for a shaft F varies from 1 up to 3, for the body - from 1 to 1.8; with a solid shaft and a massive thick-walled body F \u003d l); A is the coefficient of uneven distribution of the radial load R between the rows of rollers in double-row tapered roller bearings or between double ball bearings in the presence of axial load A on the support (coefficient F A varies from 1 to 2, and in the absence of axial load F A \u003d \u200b\u200b1). For locally loaded bearing rings, landings are selected depending on the operating conditions and, first of all, on the nature of the load and the speed. The seating surfaces of shafts and housing bores for rolling bearings are subject to increased requirements in terms of shape deviations and roughness. 2.2 The procedure for calculating and choosing landings According to the initial data, the following must be done: Establish the basic dimensions of the bearing and determine the nature of the loading of its rings. Determine the numerical values \u200b\u200bof the maximum deviations of the connecting diameters of the bearing and the seats of the shaft and housing. Determine the numerical values \u200b\u200bof the maximum deviations. 3. Connecting diameters of the bearing and seats of the shaft and housing according to the selected fits. 5. Determine the deviations of the shape, relative position, roughness of the surfaces of the shaft and housing seats. Ball bearing No. 209. The housing rotates, the shaft is stationary. The body is cast iron, one-piece. Radial load pa support R \u003d 19. 5 kH. The bearing operating mode is normal. According to Appendix 2, we find the main dimensions of the bearing: outer diameter D \u003d 85mm, inner diameter d \u003d 45 mm, ring width B \u003d 19 mm, chamfer radius r \u003d 2 mm Determine the type of loading of the rings for a given bearing. Since the housing rotates, and the shaft is stationary, the outer ring of the bearing will experience a circulating load, internal-local. We calculate and select the fit of the circulatingly loaded ring. Determine the intensity of the radial load of the landing surface by the formula According to the table in Appendix 4, we find the tolerance field for the hole in the body of the part corresponding to the obtained value of P R. The fit of the outer ring into the hole of the part body in the conditional notation has the form. According to the table in Appendix 5, we take the tolerance field of the shaft diameter. Then we write down the fit of the inner ring on the shaft of the part as follows:. According to the tables of GOST 25347-82 Appendix 6, we find the numerical ones. the values \u200b\u200bof the maximum deviations of the connecting diameters of the bearing rings and the seats of the shaft and housing. We have: inner ring shaft journal outer ring. hole in the housing. The calculation of the limiting values \u200b\u200bof the connecting diameters, their tolerances, as well as the gaps and tightness obtained in the joints, are taken down to table 2.1. a) inner ring Dmax \u003d D H + ES \u003d 45 + 0 \u003d 45 (mm) (2.2) \u003d D H + EI \u003d 45 + (- 0.012) \u003d 44.988 (mm) (2.3) T D \u003d D max -D mln \u003d ES-E (2.4) D \u003d 45-44. 988 \u003d 0. 012 (mm) b) shaft journal D H + es \u003d 45 + 0. 018 \u003d 45. 018 (mm) (2.5) d min \u003d d H + ei \u003d 45 + 0. 002 \u003d 45. 002 (mm) (2.6) T d \u003d D max -D mln \u003d es - ei (2.7) d \u003d 45.018-45. 002 \u003d 0. 016 (mm) c) hole in the case ax \u003d D H + ES \u003d 85 + (- 0.010) \u003d 84. 99 (mm) (2.8) Dmin \u003d D H + EI \u003d 85 + (- 0.045) \u003d 84. 955 (mm) (2.9) T D \u003d D max -D mln \u003d ES-EI (2.10) T D \u003d 84. 99-84. 955 \u003d 0.035 (mm) d) outer ring D H + es \u003d 85 + 0 \u003d 85 (mm) (2.11) d min \u003d d H + ei \u003d 85 + (- 0.020) \u003d 84. 98 (mm) T d \u003d D max -D mln \u003d es - ei T d \u003d 85-84. 98 \u003d 0.02 (mm) Determine the limiting clearance (interference) of the inner ring-journal of the shaft N max \u003d es- EI \u003d -0. 012-0.018 \u003d -0.03 (mm) (2.12) S max \u003d ES - ei \u003d 0-0. 002 \u003d -0. 002 (mm) (2.13) Determine the landing tolerance; T s (N) \u003d S max + N max \u003d T D + T d (2.14) Ts (N) \u003d -0. 002 + (- 0.03) \u003d -0. 032 (mm). hole in the body - outer ring max \u003d ES-ei \u003d -0. 010 - (- 0.020) \u003d 0.01 (mm) (2.15) N max \u003d es- EI \u003d -0. 045-0 \u003d -0. 045 (mm) (2.16) Determine the landing tolerance; T s (N) \u003d S max + N max \u003d T D + T d (2.17) Ts (N) \u003d 0.01 + (- 0.045) \u003d -0. 035 (mm). According to the tables in Appendices 7 and 8, we establish the permissible deviations of the shape, the relative position of the landing surfaces, their roughness We have: a) deviation from the cylindricity of the shaft journal - 8 microns, holes in the body - 15 microns; b) beating of the ends of the shaft shoulders - 20 microns, holes in the body - 40 microns; c) the roughness of the shaft seating surfaces R a 1.25 and the hole in the housing R a no more. 1.25μm; d) also the ends of the shaft shoulders R a 2.5 µm, and the holes in the housing R a 2.5 µm. Name of bearing connection elements Limit deviations, mm Limit dimensions, mm Dopski, μm Limit gaps, microns Connecting diameters: inner ring Shaft neck outer ring case holes Connections: "Inner ring-shaft" Outer ring-body 3. Choice of landings of the keyed connection 3.1 General In general mechanical engineering, as well as in automotive and agricultural engineering, key connections with parallel and segment keys are most widely used. The dimensions of the keyed connection elements depend on the shaft diameter and are regulated by the relevant standards. To facilitate the conditions and ensure the required assembly quality when creating movable or fixed joints, the key with its lateral faces (size b) can simultaneously be connected to the grooves of the shaft and the complete sleeve according to various fits. Taking into account the technically feasible accuracy for the formation of various landings in the connection of the parallel key with grooves in size b, the GOST 23360-78 standard establishes the following tolerance ranges: for the key width - H9; for the width of the shaft groove - H9, N9, P9; for the width of the bushing groove - D10, J S 9 and P9. The combination of the tolerance fields of the grooves with the tolerance field of the key must be such that the following three types of connections are formed: a) a free connection, which ensures the relative axial movement of the sleeve on the shaft (guide key) or is used to form fixed connections of the sleeves with the shafts under difficult assembly conditions and the action of small uniform loads; b) a normal connection, used under favorable assembly conditions to ensure relative immobility of the bushings and shafts connected to each other, operating without loads or with small irreversible loads; c) a tight connection used to obtain fixed connections of bushings and shafts, which does not require frequent disassembly and works with significant alternating loads; this connection is characterized by the presence of approximately the same small interference between the key and the grooves. In addition to dimension b, all other sizes of keyed connection elements are non-mating or non-seated. The tolerances for these dimensions are also standardized. The GOST 24071 80 standard establishes only two purposes of the segment keys. They can be used to transmit torques or to simply hold parts. In this regard, for the formation of landings in the connection of the segment key with the grooves, the standard regulates the size b of the grooves not in three, as for parallel keys, but in two tolerance fields: N9 and P9 - for the shaft groove and J b 9 and P9 - for the groove bushings. Tolerance field H9 is set for the key width. The preferred combination of the indicated groove tolerance fields with the segment key tolerance field provides two types of connections: normal and tight. The GOST 24071-80 standard also establishes tolerances for non-mating dimensions of connection elements with a segment key. The quality of the keyed connections depends on the presence of distortions and displacements in the arrangement of the keyways of the shafts and bushings relative to the section plane. However, the tolerances for these errors are not standardized by the standards. The choice of their values \u200b\u200bis determined by the specific assembly conditions. Usually, with a symmetrical arrangement of the field, the tolerance for the misalignment of the keyway along its length at the shaft and sleeve is taken equal to 0.5 Tb, and the tolerance for displacement is 2T b, where T b is the tolerance for the width of the groove of the shaft or sleeve. The standards do not standardize the surface roughness of the key joint elements either. Its values \u200b\u200bare determined by accepted methods of key and shaft finishing. Usually, the roughness of the side (seating) surfaces of the grooves and keys is taken equal to R z 20 μm, and for shafts and key surfaces in height h - R z 40 μm. 3.2. The procedure for selecting and calculating the landings of the keyed connection To solve the problem, the diameter of the shaft on which the key is arranged, the type of the key (prismatic or segmental), the type of keyway connection (free, normal or tight) must be known. In the presence of the specified initial data, the choice of landings and subsequent calculations must be performed in the following order: 1. Select the main structural dimensions of the keyed connection elements with a parallel or keyway. 2. In accordance with the type of keyway, select the fit of the key in the groove of the shaft and in the groove of the sleeve. 3. Find the numerical values \u200b\u200bof the maximum deviations of the width of the key and grooves, the tolerances and maximum deviations of non-mating dimensions. 4. Determine the limiting dimensions, as well as the tightness clearances obtained in the joints of the key with the grooves by dimension b ;. shaft diameter d \u003d 16 mm; key type - segmented, keyway type - normal, appointment - 1. Then, according to the table in Appendix 10, we find the main dimensions of the key and grooves: section of the key bXhXd \u003d (5X6. 5 X 16) mm; shaft groove depth t 1 \u003d 4. 5 mm; bushing groove depth t 2 \u003d 2. 3 mm. We install the fit of the key into the groove of the shaft and into the groove of the sleeve. The width of the key and grooves with a normal connection has the following tolerance ranges: keys - b \u003d 5h9, shaft groove - b \u003d 5N9 and sleeve groove - b \u003d 5Js9. Then the fit of the key into the groove of the shaft and into the groove of the sleeve in general form can be written as follows: In the groove of the shaft 5 and the groove of the sleeve 5 The numerical values \u200b\u200bof the maximum deviations of the width of the key and grooves are found from the table of the standard (Appendix 15) for key 5h9 for shaft groove - 5N9 for sleeve groove -5Js9 Tolerances and maximum deviations of non-mating dimensions of keyed connection elements are found from tables 1 and 12: key height h \u003d 6.5h11 (-0.090) key diameter d \u003d 16h12 (-0.18) shaft groove depth t 1 \u003d 4. 5 (+0. 2) bushing groove depth t 2 \u003d 2. 3 (+0. 1) We calculate the limiting values \u200b\u200bof all basic dimensions and the gaps or tightness obtained in the connection of the key with the grooves. the calculation results are summarized in table. 3.1. a) Keys for key width B H + es \u003d 5 + 0 \u003d 5 (mm) (3.1) min \u003d b H + ei \u003d 5 + (- 0.030) \u003d 4. 97 (mm) (3.2) T b \u003d b max -b mln \u003d es-ei (3.3) T b \u003d 5-4. 97 \u003d 0. 03 (mm) For key height hmax \u003d h H + es \u003d 6. 5 + 0 \u003d 6. 5 (mm) (3.4) h min \u003d h H + ei \u003d 6.5 + (- 0.09) \u003d 6. 41 (mm) (3.5) T h \u003d h max -h mln \u003d es-ei (3.6) T h \u003d 6.5-6. 41 \u003d 0. 09 (mm) For key diameter d d max \u003d d H + es \u003d 16 + 0 \u003d 16 (mm) (3.7) min \u003d d H + ei \u003d 16 + (- 0.18) \u003d 15. 82 (mm) (38) T l \u003d d max - d mln \u003d es-ei (3.9) T l \u003d 16-15. 82 \u003d 0. 18 (mm) b) Shaft groove for the width of the shaft groove Bmax \u003d B H + ES \u003d 5 + 0 \u003d 5 (mm) (3.10) Bmin \u003d B H + EI \u003d 5 + (- 0.03) \u003d 4. 97 (mm) (3.11) T B \u003d B max -B mln \u003d ES-EI (3.12) B \u003d 5-4. 97 \u003d 0. 03 (mm) For shaft groove depth t 1 min \u003d t 1 + EI \u003d 4.5 + 0 \u003d 4. 5 (mm) (3.14) T t 1 \u003d t 1 max - t 1 mln \u003d ES-EI (3.15) 1 \u003d 4. 7-4. 5 \u003d 0. 2 (mm) c) Sleeve groove for sleeve groove width Bmax \u003d B H + ES \u003d 5 + 0. 015 \u003d 5. 015 (mm) (316) \u003d B H + EI \u003d 5 + (- 0.015) \u003d 4. 985 (mm) (3.17) T B \u003d B max -B mln \u003d ES-EI; (3.18) T B \u003d 5. 015-4. 985 \u003d 0. 03 (mm) For bushing groove depth 2max \u003d t 2H + ES \u003d 2. 3 + 0. 1 \u003d 2. 4 (mm) (3.9) 2min \u003d t 2H + EI \u003d 2.3 + 0 \u003d 2. 3 (mm) (3.20) T t 2 \u003d t 2max - t 2mln \u003d ES-EI (3.21) T H \u003d 2.4-2. 3 \u003d 0.1 (mm) Determine the gaps a) Shaft groove keys S max \u003d ES-ei \u003d 0 - (- 0.03) \u003d 0. 03 (mm) (3.22) N max \u003d es-EI \u003d 0 - (- 0.03) \u003d 0.03 (mm) (3.23) Determine the landing tolerance; T s (N) \u003d S max + N max \u003d T D + T d (3.24) Ts (N) \u003d 0.03 + 0. 03 \u003d 0.06 (mm). b) Bushing groove keys max \u003d ES-ei \u003d 0.015 - (- 0.03) \u003d 0. 045 (mm) (3.25) max \u003d es-EI \u003d 0 - (- 0.015) \u003d 0. 015 (mm) (3.26) Determine the landing tolerance; T s (N) \u003d S max + N max \u003d T D + T d (3.27) Ts (N) \u003d 0.015+ 0.045 \u003d 0.06 (mm). Table 3 1 Dimensional characteristics of the keyed connection
Name of keyed connection elements Nominal size in mm and tolerance range (fit) Limit deviations, mm Limit dimensions, mm Tolerances, μm Limit gaps, microns Shaft groove: Sleeve groove: Connections: "Key-groove of the shaft" Bushing key-groove 4. Choice of landings of the spline connection 4.1 General Splined joints are used for the same purposes as keyed ones, but unlike the latter, they have a number of advantages. Connections of this type are capable of withstanding significantly higher loads and provide a higher degree of centering of the bushings on the shafts. Among the known types of spline joints, the most widespread, especially in automotive and agricultural engineering, are joints with a straight-sided tooth profile. The nominal dimensions and the number of teeth of the spline connection of the straight-sided profile are regulated by the GOST 1139-80 standard. Depending on the magnitude of the transferred loads, these standards establish three series of straight-sided spline joints: light, medium and heavy (Appendix 16). Light series couplings have small heights and number of teeth. These include fixed, lightly loaded connections. Medium series couplings have higher heights and number of teeth compared to light series couplings and are used to transfer medium loads. Heavy series couplings have the highest height and number of teeth and are designed for heavy duty applications. For straight-sided spline joints, depending on the operational and technical requirements imposed on them, three methods of centering the bushings on the shafts are used: but with the outer diameter D, along the inner diameter d and along the side surfaces of the teeth b. The system of tolerances and landings is regulated by standards and GOST 1139 - 80 and applies to critical movable and fixed joints of a straight-sided profile. According to GOST 1139-80, landings are formed by a combination of the provided tolerance fields of bushings and shafts and are assigned, depending on the adopted centering method, to the centering diameter and side surfaces of the teeth. When centering on D, the fits are assigned to dimensions D and b. when centered on d - on d and b. If the spline parts are centered on the flanks of the teeth, the fit is assigned to dimension b only. The tolerance fields of bushings and shafts for the formation of landings of centering surfaces for various methods of centering spline joints of a straight-sided profile are given in Appendix 18. The GOST 1139-80 standard also provides for tolerances of non-centering diameters of the shaft and sleeve.Tolerances of non-centering diameters are given in Appendix 17. The roughness of the surfaces of the elements of spline joints is not regulated by standards and can be selected depending on the purpose of the joint and the operational requirements imposed on it, taking into account the applied methods of processing parts. Usually, for all centering methods, the roughness of the centering surfaces of the shaft is recommended to be kept within R a 1.25. ... ... 0.32 microns, and the bushings are R a 2.5. ... 1.25 microns. Roughness of non-centering surfaces of the shaft and sleeve R z 20.. ... 10 microns. In the accepted designations of straight-sided spline joints, their shafts and bushings, the following should be indicated: the letter denoting the centering surface, the number of teeth, the nominal values \u200b\u200bof the inner d, outer D diameters and width b in the joint, tolerance fields or fit for diameters and dimension b, placed after the corresponding sizes. The standard allows not to indicate tolerances of non-centering diameters in the designation. 4.2 The procedure for calculating the landings of a spline connection The choice of landings for the projected spline joints is a complex technical and economic task, since it requires the performers to use calculations taking into account all the data that comprehensively characterize the operation of the joints under operating conditions. Therefore, for educational purposes in course design, the student is given a spline connection in a finished form with the necessary landings and the solution to the problem is reduced to the following: For a given symbol, give a decoding of the straight-sided splined connection and determine the nominal dimensions of its elements. 2. According to the tables of standards, find the maximum deviations of the tolerance fields of the centering and non-centering diameters, as well as the size b. 3. Calculate the limiting dimensions of all elements, their tolerances and the limiting values \u200b\u200bof the clearances or interference obtained in the joints along the centering diameter and flank surfaces of the teeth. Given: Spline connection d-6x18x22 x 5 Let's decipher its conditional notation. A given spline connection is centered on the inner diameter d, has the number of teeth z \u003d 6, the nominal value of the inner diameter d \u003d 18mm with fit, outer D \u003d 22 with fit, the thickness of the shaft tooth (width of the sleeve cavity) b \u003d 5 mm with fit According to the tables of the GOST 25347-82 standard, we find the maximum deviations of the diameters and size b of the sleeve and shaft. We have: a) for splined sleeve: inner diameter d \u003d 18H7 (+0. 018) outer diameter D \u003d 22H12 (+0.21) valley width b \u003d 5F8 () b) for a splined shaft: inner diameter d \u003d 18h7 (-0. 018) outer diameter D \u003d 22a11 () tooth thickness b \u003d 5d8 () We calculate the limiting dimensions and tolerances of all elements, as well as the clearances obtained in the joints along the centering diameter and flank surfaces of the teeth. a) for splined sleeve inner diameter dmax \u003d d H + ES \u003d 18 + 0. 018 \u003d 18. 018 (mm) (4.1) \u003d d H + EI \u003d 18 + 0 \u003d 18 (mm) (4.2) d \u003d d max d \u003d ES-EI (4.3) d \u003d 18. 018-18 \u003d 0. 018 (mm) outside diameter Dmax \u003d D H + ES \u003d 22 + 0. 21 \u003d 22. 21 (mm) (4.4) \u003d D H + EI \u003d 22 + 0 \u003d 22 (mm) (4.5) D \u003d D max -D mln \u003d ES-EI (4.6) D \u003d 22. 21-22 \u003d 0. 21 (mm) cavity width Bmax \u003d B H + ES \u003d 5 + 0. 028 \u003d 5. 028 (mm) (4.7) \u003d B H + EI \u003d 5 + 0. 01 \u003d 5. 01 (mm) (4.8) T B \u003d B max -B mln \u003d ES-EI (4.9) T B \u003d 5. 028-5. 01 \u003d 0. 018 (mm) b) for a splined shaft: inner diameter dmax \u003d d H + es \u003d 18 + 0 \u003d 18 (mm) (4.10) d min \u003d d H + ei \u003d 18 + (- 0.018) \u003d 17. 982 (mm) (4.11) T d \u003d D max -D mln \u003d ES-EI; T d \u003d 18-17. 982 \u003d 0. 018 (mm) (4.12) outside diameter D H + es \u003d 22 + (- 0.3) \u003d 21. 7 (mm) (4.13) D min \u003d D H + ei \u003d 22 + (- 0.43) \u003d 21. 57 (mm) (4.15) T d \u003d D max -D mln \u003d ES-EI (4.16) T d \u003d 21.7-21. 57 \u003d 0. 13 (mm) tooth thickness B H + es \u003d 5 + (- 0.03) \u003d 4. 97 (mm) (4.17) b min \u003d b H + ei \u003d 5 + (- 0.048) \u003d 4. 952 (mm) (4.18) T b \u003d b max -b mln \u003d ES-EI (4.19) b \u003d 4.97-4. 952 \u003d 0.018 (mm) Determine the gaps a) inner diameter S max \u003d ES-ei \u003d 0. 018 - (- 0.018) \u003d 0. 036 (mm) (4.20) N max \u003d es- EI \u003d 0- 0 \u003d 0 (mm) (4.21) Determine the landing tolerance; T s (N) \u003d N max + S max \u003d T D + T d (4.21) (N) \u003d 0.036 + 0 \u003d 0. 036 (mm) b) outer diameter max \u003d ES-ei \u003d 0.21 - (- 0.43) \u003d 0. 64 (mm) (4.22) S min \u003d EI- es \u003d 0 - (- 0.3) \u003d 0. 3 (mm) (4.23) Determine the landing tolerance; T s \u003d S max -S min \u003d T D + T d (4.24) Ts \u003d 0.64-0. 3 \u003d 0.34 (mm) c) by size b S max \u003d ES-ei \u003d 0.028 - (- 0.048) \u003d 0.076 (mm) (4.25) S min \u003d EI- es \u003d 0.01 - (- 0.03) \u003d 0. 04 (mm) (4.26) Determine the landing tolerance; T s \u003d S max -S min \u003d T D + T d (4.27) Ts \u003d 0.076-0. 04 \u003d 0.036 (mm) 5. Calculation of linear dimensional chains by the probabilistic method For an assembly dimensional chain with a closing link Г ∆, determine the tolerances and maximum deviations of the constituent links. 1. The closing link has a tolerance: Г ∆ \u003d 1 () 2. The dispersion of the actual dimensions of all links obeys the normal law. The percentage of the risk of the size of the closing link going beyond the tolerance limits - Р \u003d 0.1% Let's build a dimensional chain, that is, find its constituent links. Making a detour along the contour from the master link, we establish the contact surfaces of the adjacent parts. Let's write dimensional relationships as follows: master link - right bearing cover; right bearing cover - gasket; gasket - body; body - left side of the body; left housing wall - left bushing; left sleeve - drum; drum - shaft journal; shaft journal - right bearing; right bearing - right spacer sleeve; the right spacer sleeve is the master link. The dimensional chain is made up of the dimensions between the touching surfaces of each of the specified parts: G 1 \u003d 334mm; G 2 \u003d 27 mm; G 3 \u003d 58 mm; G 4 \u003d 255mm; D 5 \u003d 24 mm; G 6 \u003d 23 -0. 1 mm; G 7 \u003d 6 mm; D 8 \u003d 18 mm; D 9 \u003d 24 mm. The dimensional chain will include nine constituent links, of which the links Г 1, Г 2, Г 9 are decreasing, and the links Г 3 ... Г 8 are increasing. Let's check the correctness of drawing up the dimensional chain according to the formula: Where m is the number of increasing links, n is the number of decreasing links. Г ∆ \u003d (Г 1 + Г 2 + Г 9) - (Г 3 + Г 4 + Г 5 + Г 6 + Г 7 + Г 8) \u003d \u003d (334 + 27 + 24) - (58 + 255 + 24 + 23 + 6 + 18) \u003d 1 mm. The obtained value of the nominal size of the closing link corresponds to the given one. Therefore, the dimensional chain is composed correctly. Determine the tolerance of the closing link: T ∆ \u003d B ∆ - H ∆ \u003d 300 - (-900) \u003d 1200 microns. Determine the accuracy coefficient of the dimensional chain by the formula: where is the average value of the coefficient of relative dispersion of the sizes of the constituent links. Since by the condition the dispersion of the actual dimensions of the links obeys the normal law, we take \u003d 1/3; Risk coefficient, \u003d 3. 29 (see table 3. 1.). The value of the tolerance units (see table 2. 1.), microns. 1 \u003d 3. 54 microns; i 2 \u003d 1. 31 microns; i 3 \u003d 1. 86 microns; i 4 \u003d 3. 22 microns; i 5 \u003d 1. 31 microns; i 7 \u003d 0. 73 microns; i 8 \u003d 1. 08 microns; i 9 \u003d 1. 31 microns. Then: Comparing the obtained value and with the data in Table. 2. 2, we establish that it differs slightly from the standard value a, corresponding to the 12th grade. Therefore, we will assign unknown tolerances according to this quality, and we will perform the adjustment of the tolerances at the expense of the link that is the easiest to manufacture. Let's take the size of the body length as a corrective link - link Г 1 \u003d 334 mm, and for the rest (except for Г 6, we assign standard tolerances). s 1 \u003d (s 2 + s 9) - (s 3 + s 4 + s 5+ s 6 + s 7 + s 8) - s ∆ \u003d \u003d (-0.105 -0. 105) - (-0. 15 + 0-0. 26-0. 05-0. 06-0. 09) + 0.3 \u003d 0.7 mm. Now we set the maximum deviations of the link E 3: Thus, the correcting link has maximum deviations: We check the correctness of the calculation of the dimensional chain The resulting value of the risk coefficient corresponds to the risk percentage P \u003d 0.1%, which is equal to the specified one. This means that for a given accuracy of the closing link, the tolerances for the dimensions of the constituent links assigned according to the 12th grade are quite acceptable. fit bearing clearance standardization Literature 1. Interchangeability, standardization and technical measurements. Part 1 Method. decree. / Comp. V. A. Orlovsky. , Belorusskaya s. -x. acad. ... -Gorki, 1986.47s. Gray I. S. Interchangeability, standardization and technical measurements -M. : Agropromtizdat 1987.-365p. Interchangeability, standardization and technical measurements: Method. decree. Part 2 / Comp. N. S. Troyan, Belorusskaya s. -x. acad. ... -Gorki, 1986. -48s. ... Interchangeability, standardization and technical measurements: Method. decree. Part 3 / Comp. N. S. Troyan. , Belorusskaya s. -x. acad. ... -Gorki, 1991. -36s.Table 2.1 -Dimensional characteristics of rolling bearings
Table 3.1 - Dimensional characteristics of the keyed connection
Table 4.1 - Dimensional characteristics of the spline connection
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3 Calculation of calibers
Name of quantity Numerical value unit of measurement
Torque T
256
H×
m
Axial force F a
0
H
d ns
50
mm
Shaft inner diameter D 1
40
mm
Outside diameter of the sleeve D 2
72
mm
Mate length l
40
mm
Friction coefficient f
0,08
Modulus of elasticity of the bushing material E 1
0.9 × 10 11 N / m 2
Modulus of elasticity of the shaft material E 2
2 × 10 11 N / m 2
m 1
0,33
m 2
0,3
Bushing material yield strength s T 1
20 × 10 7 N / m 2
Yield Strength of Shaft Material s T 2
800 × 10 7 N / m 2
Roughness of the sleeve R zD
2,5
micron
Shaft roughness R zd
1,3
micron
Tests with answers in the discipline "Interchangeability, standardization and technical measurements" Option number 2
Design problems tests
(1.1)
(μm 2)
\u003d 79 (μm)
(1.3)
(1.7)
(1.8)
(2.1)
Table 2.1 Dimensional characteristics of rolling bearings
mm; (5.1) 
(5.2)
