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1 MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous educational institution higher education "NATIONAL RESEARCH TOMSK POLYTECHNICAL UNIVERSITY" A.S. Spiridonova, N.M. Natalinova WORKSHOP ON METROLOGY, STANDARDIZATION AND CERTIFICATION Recommended as a teaching aid by the Editorial and Publishing Council of Tomsk Polytechnic University Publishing house of Tomsk Polytechnic University 2014
2 UDC (076.5) LBC ya73 С72 С72 Spiridonova A.S. Workshop on metrology, standardization and certification: textbook / A.S. Spiridonova, N.M. Natalinova; Tomsk Polytechnic University. Tomsk: Publishing House of the Tomsk Polytechnic University, p. The manual contains six laboratory works and four practical exercises, which include the necessary theoretical materials and control questions to prepare for the defense of the work performed. Designed for students of all directions to consolidate theoretical foundations metrology, measurement methods, the procedure for measuring the values of physical quantities and the rules for processing measurement results, estimating the uncertainty of measurements, the regulatory framework of metrology, as well as the theoretical provisions of standardization activities, the principles of construction and rules for using standards, sets of standards and other regulatory documentation. UDC (076.5) LBC Ya73 Reviewers Candidate of Technical Sciences, Associate Professor of TSUAE A.A. Alekseev Candidate of Chemical Sciences, Associate Professor of TSU N.A. Gavrilenko FGAOU VO NR TPU, 2014 Spiridonova A.S., Natalinova N.M., 2014 Design. Publishing house of Tomsk Polytechnic University, 2014
3 INTRODUCTION Metrology and standardization are tools for ensuring the quality and safety of products, works and services, an important aspect of a multifaceted activity. Quality and safety are the main factors in the sale of goods. The purpose of teaching the discipline "Metrology, standardization and certification" is the presentation of concepts, the formation of students' knowledge, skills and abilities in the areas of standardization, metrology and conformity assessment to ensure the efficiency of production and other activities. As a result of studying the discipline, the student must have the following competencies: to know the goals, principles, areas of application, objects, subjects, means, methods, the regulatory framework for standardization, metrology, conformity assessment activities; be able to apply technical and metrological legislation; work with regulatory documents; recognize conformity confirmation forms; distinguish between international and national units of measurement; have experience in working with current federal laws, regulatory and technical documents necessary for the implementation of professional activities. The work complies with the requirements of the state educational standard of the highest vocational education(FSES HPE and standards of the TPU OOP) in the discipline "Metrology, standardization and certification" for students of all specialties. This manual is intended to consolidate the theoretical foundations of metrology, measurement methods, the procedure for measuring the values of physical quantities and the rules for processing measurement results, the legal framework of metrology, as well as the theoretical provisions of standardization and certification activities, the principles of construction and rules for using standards, sets of standards and other regulatory documentation. 3
4 SECTION 1. METROLOGY LABORATORY WORK 1 CLASSIFICATION OF MEASURING INSTRUMENTS AND RATED METROLOGICAL CHARACTERISTICS 1.1. Basic concepts and definitions In accordance with the RMG, a measuring instrument is a technical instrument intended for measurements, having normalized metrological characteristics, reproducing and (or) storing a unit of physical quantity, the size of which is taken unchanged (within a specified error) for a known time interval. Measuring instruments (SI) used in various fields of science and technology are extremely diverse. However, for this set, it is possible to single out some common features inherent in all SI, regardless of the field of application. These features form the basis of various SI classifications, some of which are given below. Classification of measuring instruments By technical purpose: A measure of a physical quantity is a measuring instrument designed to reproduce and (or) store a physical quantity of one or more given dimensions, the values of which are expressed in established units and are known with the required accuracy; The following types of measures are distinguished: a single-valued measure is a measure that reproduces a physical quantity of the same size (for example, a 1 kg weight, a capacitor of constant capacitance); multi-valued measure - a measure that reproduces a physical quantity of different sizes (for example, a dashed measure of length, a capacitor of variable capacitance); a set of measures a set of measures of different sizes of the same physical size, intended for practical use both individually and in various combinations (for example, a set of gauge blocks); store of measures - a set of measures structurally combined into a single device, in which there are devices for connecting them in various combinations (for example, a store of electrical resistances). 4
5 Measuring device is a measuring instrument designed to obtain the values of the measured physical quantity in the specified range. The measuring device, as a rule, contains a device for converting the measured value into a signal of measuring information and indexing it in the most accessible form for perception. In many cases, the display device has a scale with an arrow or other device, a chart with a pen or a digital display, thanks to which a reading or registration of the values of a physical quantity can be made. Depending on the type of output value, analog and digital measuring instruments are distinguished. An analog measuring instrument is a measuring instrument whose readings (or output signal) are a continuous function of the measured quantity (eg pointer voltmeter, mercury-in-glass thermometer). A digital meter is a meter whose readings are presented in digital form. In a digital device, the input analog signal of the measuring information is converted into a digital code, and the measurement result is displayed on a digital display. According to the form of presentation of the output value (according to the method of indicating the values of the measured value), measuring instruments are divided into indicating and recording measuring instruments. indicating measuring instrument a measuring instrument that allows only the reading of indications of the values of the measured quantity (micrometer, analog or digital voltmeter). recording measuring device measuring device in which the recording of readings is provided. The registration of the values of the measured value can be carried out in analog or digital form, in the form of a diagram, by printing on paper or magnetic tape (thermograph or, for example, a measuring device associated with a computer, display and device for printing readings). By action, measuring instruments are divided into integrating and summing. There are also direct action devices and comparison devices. A measuring transducer is a technical tool with standard metrological characteristics that serves to convert a measured value into another value or a measuring signal that is convenient for processing, storage, further transformations, indication or transmission. The resulting value 5
6 or the measurement signal are not directly accessible to the observer, they are determined through the conversion factor. A measuring transducer is either part of a measuring device (measuring setup, measuring system), or is used together with any measuring instrument. According to the nature of the conversion, analog, digital-to-analog, analog-to-digital converters are distinguished. According to the place in the measuring circuit, primary and intermediate converters are distinguished. There are also scale and transmitting converters. Examples: thermocouple in a thermoelectric thermometer, measuring current transformer, electro-pneumatic converter. Measuring installation is a set of functionally combined measures, measuring instruments, measuring transducers and other devices, designed to measure one or more physical quantities and located in one place. The measuring setup used for verification is called a calibration setup. The measuring setup that is part of the standard is called the reference setup. Some large measuring installations are called measuring machines, designed to accurately measure the physical quantities that characterize the product. Examples: installation for measuring the resistivity of electrical materials, installation for testing magnetic materials. Measuring system is a set of functionally combined measures, measuring instruments, measuring transducers, computers and other technical means located at different points of a controlled object, etc., with the aim of measuring one or more physical quantities inherent in this object, and generating measuring signals for different purposes . Depending on the purpose, measuring systems are divided into measuring information, measuring control, measuring control systems, etc. A measuring system that is reconfigured depending on a change in the measuring task is called a flexible measuring system (GIS). Examples: measuring system of a thermal power plant, which allows obtaining measuring information about a number of physical quantities in different power units. It can contain hundreds of measurement channels; a radio navigation system for determining the location of various objects, consisting of a number of measuring and computing complexes spaced apart in space at a considerable distance from each other. 6
7 Measuring and computing complex functionally integrated set of measuring instruments, computers and auxiliary devices, designed to perform a specific measurement task as part of a measuring system. Comparator means of comparison intended for comparison of measures of homogeneous quantities (lever balance, comparator for comparison of normal elements). According to the metrological purpose, all measuring instruments are divided into standards, working standards and working measuring instruments. The standard of a unit of physical quantity (standard) is a measuring instrument (or a set of measuring instruments) intended for reproducing and (or) storing a unit and transferring its size to measuring instruments lower in the verification scheme and approved as a standard in the prescribed manner. The design of the standard, its properties and the method of reproducing the unit are determined by the nature of the given physical quantity and the level of development of measuring technology in this area of measurement. The standard must have at least three essential features of immutability, reproducibility and comparability that are closely related to each other. Working standard A standard designed to transfer the size of a unit to working measuring instruments. If necessary, working standards are divided into categories (1st, 2nd, ..., nth). In this case, the transfer of the size of the unit is carried out through a chain of working standards subordinate in terms of digits. At the same time, from the last working standard in this chain, the size of the unit is transferred to the working measuring instrument. working tool measurement means of measurement intended for measurements not related to the transfer of the size of the unit to other means of measurement. According to the significance of the measured physical quantity, all measuring instruments are divided into main and auxiliary measuring instruments. The main means of measuring SI of that physical quantity, the value of which must be obtained in accordance with the measurement task. Auxiliary measuring instruments SI of that physical quantity, the influence of which on the main measuring instrument or object of measurement must be taken into account in order to obtain measurement results of the required accuracy (a thermometer for measuring gas temperature in the process of measuring the volume flow of this gas). 7
8 The classification of measuring instruments according to their technical purpose is the main one and is shown in Fig. 1.1 Metrological characteristic of a measuring instrument (MX SI): Characteristic of one of the properties of a measuring instrument that affects the measurement result and its error. For each type of measuring instruments, their metrological characteristics are established. The metrological characteristics established by normative and technical documents are called standardized metrological characteristics, and those determined experimentally are called valid metrological characteristics. The nomenclature of metrological characteristics and methods for their normalization are established by GOST. All metrological characteristics of MI can be divided into two groups: characteristics that affect the result of measurements (determining the scope of MI); characteristics affecting the accuracy (quality) of the measurement. The main metrological characteristics that affect the result of measurements include: measurement range of measuring instruments; 8
9 the value of a one-to-one or multi-valued measure; transmitter conversion function; the value of division of the scale of a measuring instrument or a multi-valued measure; type of output code, number of digits of the code, price of the unit of the smallest digit of the code of measuring instruments intended for issuing results in a digital code. Measuring range of a measuring instrument (measurement range) is the range of values within which the permissible error limits of a measuring instrument are normalized (for transducers, this is the conversion range). The values of the quantity that limit the measurement range from below and above (left and right) are called the lower measurement limit or the upper measurement limit, respectively. For measures, the limits of reproduction of values. Single digit measures have nominal and actual reproducible values. The nominal value of a measure is the quantity value assigned to a measure or batch of measures during manufacture. Example: resistors with a nominal value of 1 ohm, a weight with a nominal value of 1 kg. Often the nominal value is indicated on the measure. The actual value of a measure is the value of a quantity assigned to a measure based on its calibration or verification. Example: the composition of the state standard of the unit of mass includes a platinum-iridium weight with a nominal mass value of 1 kg, while the actual value of its mass is 1 kg, obtained as a result of comparisons with the international standard of the kilogram stored at the International Bureau of Weights and Measures (BIPM) (in in this case it is the calibration). The range of indications of a measuring instrument (range of indications) is the range of values of the instrument scale, limited by the initial and final values of the scale. Measuring range of a measuring instrument (range of measurements) is the range of values within which the permissible error limits of a measuring instrument are normalized. The values of the quantity that limit the measurement range from below and above (left and right) are called the lower measurement limit or the upper measurement limit, respectively. The scale division price (division price) is the difference between the values of the quantities corresponding to two adjacent marks on the scale of the measuring instrument. The metrological characteristics that determine the accuracy of measurement include the error of the measuring instrument and the accuracy class of the measuring instrument. 9
10 Measuring instrument error is the difference between the indication of the measuring instrument (x) and the true (real) value (x d) of the measured physical quantity. x x x d. (1.1) As x d is either a nominal value (for example, measures), or the value of a quantity measured more accurate (at least an order of magnitude, i.e., 10 times) SI. The smaller the error, the more accurate the measuring instrument. MI errors can be classified according to a number of features, in particular: in relation to the measurement conditions, basic, additional; according to the method of expression (by the method of normalization of MX) absolute, relative, reduced. The basic error of a measuring instrument (basic error) is the error of a measuring instrument used under normal conditions. As a rule, normal operating conditions are: temperature (293 5) K or (20 5) ºС; relative air humidity (65 15)% at 20 ºС; mains voltage 220 V 10% with a frequency of 50 Hz 1%; atmospheric pressure from 97.4 to 104 kPa. Additional error of a measuring instrument (additional error) is a component of the error of a measuring instrument that occurs in addition to the main error due to the deviation of any of the influencing quantities from its normal value or due to its going beyond the normal range of values. When normalizing the characteristics of the errors of measuring instruments, the limits of permissible errors (positive and negative) are established. The limits of permissible basic and additional errors are expressed in the form of absolute, reduced or relative errors, depending on the nature of the change in errors within the measurement range. The limits of the permissible additional error can be expressed in a form different from the form of expression of the limits of the permissible basic error. The absolute error of the measuring instrument (absolute error, expressed in unity of error) is the error of the measuring instrument in the values of the measured physical quantity. The absolute error is determined by formula (1.1). 10
11 The limits of the permissible basic absolute error can be specified as: a (1.2) or a bx, (1.3) where the limits of the permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x the value of the measured value at the input (output) of measuring instruments or the number of divisions counted on the scale; ab, positive numbers independent of x. The reduced error of the measuring instrument (reduced error) is the relative error expressed as the ratio of the absolute error of the measuring instrument to the conditionally accepted value of the quantity (normalizing value), which is constant over the entire measurement range or in part of the range. The reduced error of the measuring instrument is determined by the formula: 100%, (1.4) x N where the limits of the allowable reduced basic error, %; limits of permissible absolute basic error, established by formula (1.2); x N normalizing value expressed in the same units as. The limits of the allowed reduced basic error should be set in the form: p, (1.5) where p is an abstract positive number chosen from the series 1 10 n ; 1.5 10n; (1.6 10n); 2 10n; 2.5 10n; (3 10 n); 4 10n; 5 10n; 6 10 n (n = 1, 0, 1, 2, etc.). The normalizing value x N is taken equal to: the final value of the working part of the scale (x k), if the zero mark is on the edge or outside the working part of the scale (uniform or power); the sum of the final values of the scale (excluding the sign), if the zero mark is inside the scale; the modulus of the difference in measurement limits for SI, the scale of which has a conditional zero; the length of the scale or its part corresponding to the measurement range, if it is significantly non-uniform. In this case, the absolute error, like the length of the scale, must be expressed in millimeters. eleven
12 Relative error of the measuring instrument (relative error) error of the measuring instrument, expressed as the ratio of the absolute error of the measuring instrument to the measurement result or to the actual value of the measured physical quantity. The relative error of the measuring instrument is calculated by the formula: 100%, (1.6) x where the limits of the permissible relative basic error, %; limits of permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x value of the measured quantity at the input (output) of measuring instruments or the number of divisions counted on the scale. If bx, then the limits of the permissible relative basic error are set in the form: q, (1.7) where q is an abstract positive number selected from the series given a bx, then in the form: given above; or if x cd k 1, (1.8) x where x k is greater (in absolute value) from the measurement limits; cd, positive numbers chosen from the series above. In justified cases, the limits of the permissible relative basic error are determined by more complex formulas or in the form of a graph or table. The characteristics introduced by GOST 8.009 most fully describe the metrological properties of SI. However, at present, a fairly large number of measuring instruments are in operation, the metrological characteristics of which are normalized somewhat differently, namely on the basis of accuracy classes. The accuracy class of measuring instruments (accuracy class) is a generalized characteristic of this type of measuring instruments, as a rule, reflecting the level of their accuracy, expressed by the limits of permissible basic and additional errors, as well as other characteristics that affect accuracy. The accuracy class makes it possible to judge the limits of the measurement error of this class. This is important when choosing measuring instruments depending on the given measurement accuracy. 12
13 The designation of accuracy classes of SI is assigned in accordance with GOST. The construction rules and examples of the designation of accuracy classes in the documentation and on measuring instruments are given in Appendix B. The designation of the accuracy class is applied to dials, shields and SI cases, and is given in the regulatory documentation for SI. The range of standardized metrological characteristics of measuring instruments is determined by the purpose, operating conditions, and many other factors. The norms for the main metrological characteristics are given in the standards, in the technical specifications (TS) and operational documentation for SI The purpose of the work is to familiarize yourself with the technical documentation for SI and determine the main classification features and normalized metrological characteristics of the measuring instruments used; acquisition of skills in determining the main classification features, the measuring instruments used and their standardized metrological characteristics directly on the measuring instruments; consolidation of theoretical knowledge in the section "Classification of measuring instruments" of the studied discipline "Metrology, standardization and certification" Used equipment and instruments 1) oscilloscope; 2) digital voltmeter; 3) analog voltmeter; 4) generator; 5) amplifier; 6) power supply; 7) the element is normal temperature-controlled; 8) programmable source of calibrated voltages Work program Determine the classification features indicated in Table. 1.2 from the number of measuring instruments (SI) at the workplace Familiarize yourself with the technical documentation for the SI (operating manual, technical description with operating instructions or passport). 13
14 Determine the normalized metrological characteristics of MI directly by measuring instruments and technical documentation for them and fill in the table for each measuring instrument Compile a report on the work done (see Appendix A for an example of a title page). Table 1.2 Classification features Measuring instrument (indicate the type of MI) By type (by technical purpose) By type of output value By the form of information presentation (only for measuring instruments) By purpose By metrological purpose Normalized metrological characteristics 1.5. Control questions 1. Name the types of measuring instruments. 2. According to what classification criteria are SI subdivided. 3. Describe each type of SI. 4. What groups are the metrological characteristics of SI divided into. 5. What are metrological characteristics? 6. What are normalized and valid metrological characteristics and how do they differ from metrological characteristics? 7. Name the metrological characteristics that determine: the scope of the SI; measurement quality. 8. Name the types of errors. 9. What characteristic determines the accuracy of SI? 10. What is the function of standards? 11. What is the difference in the appointment of working SI and working standards? 1.6. Literature 1. RMG GSI. Metrology. Basic terms and definitions. Recommendations for interstate standardization. 2. GOST GSI. Normalized metrological characteristics of measuring instruments. 3. GOST GSI. Accuracy classes of measuring instruments. 4. Sergeev A.G., Teregerya V.V. Metrology, standardization and certification. M.: Yurayt Publishing House: ID Yurayt,
15 LABORATORY WORK 2 INDIRECT SINGLE MEASUREMENTS 2.1. Basic concepts and definitions Measurement is a set of operations for the use of a technical means that stores a unit of a physical quantity, providing a ratio (in an explicit or implicit form) of the measured quantity with its unit and obtaining the value of this quantity. Measurements are the main source of information about the compliance of products with the requirements of regulatory documents. Only the reliability and accuracy of measurement information ensure the correctness of decision-making about the quality of products, at all levels of production when testing products, in scientific experiments, etc. Measurements are classified: a) by the number of observations: a single measurement a measurement performed once. The disadvantage of these measurements is the possibility blunder miss; multiple measurement measurement of a physical quantity of the same size, the result of which is obtained from several successive measurements, i.e., consisting of a number of single measurements. Usually their number is n 3. Multiple measurements are carried out in order to reduce the influence of random factors on the measurement result; b) by the nature of accuracy (according to the conditions of measurement): equal-precision measurements of a series of measurements of any quantity, made with the same accuracy of measuring instruments in the same conditions with the same care; unequal measurements - a series of measurements of some quantity, performed by several measuring instruments differing in accuracy and (or) under different conditions; c) by expression of the measurement result: absolute measurement is a measurement based on direct measurements of one or more fundamental quantities and (or) the use of physical constant values (for example, the measurement of force F m g is based on the measurement of the basic quantity of mass m and the use of the physical constant of gravitational acceleration g (at the point of measurement of mass); relative measurement is the measurement of the ratio of a quantity to the quantity of the same name, which plays the role of a unit, or the measurement of a change
16 values in relation to the value of the same name, taken as the original; d) according to the method of obtaining the measurement result: direct measurement is a measurement in which the desired value of a physical quantity is obtained directly (for example, measuring the mass on a scale, measuring the length of a part with a micrometer); indirect measurement is the determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the sought value; cumulative measurements are simultaneous measurements of several quantities of the same name, in which the desired values \u200b\u200bof the quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations (for example, the mass value of individual weights of the set is determined by known value the mass of one of the weights and according to the results of measurements (comparisons) of the masses of various combinations of weights); joint measurements are simultaneous measurements of two or more dissimilar quantities to determine the relationship between them; e) by the nature of the change in the measured physical quantity: static measurement is the measurement of a physical quantity taken in accordance with a specific measurement task as unchanged throughout the measurement time. They are carried out with the practical constancy of the measured quantity; dynamic measurement measurement of a physical quantity that changes in size; f) according to the metrological purpose of the measuring instruments used: technical measurements measurements using working measuring instruments; metrological measurements measurements with the help of reference measuring instruments in order to reproduce units of physical quantities in order to transfer their size to working measuring instruments. The measurement results are approximate estimates of the values of quantities found by measurements, since even the most accurate instruments cannot show the actual value of the measured quantity. There is necessarily a measurement error, the causes of which can be various factors. They depend on the method of measurement, on the technical means by which measurements are taken, and on the perception of the observer making the measurements. 16
17 The accuracy of the measurement result is one of the characteristics of the quality of measurement, reflecting the closeness to zero of the error of the measurement result. The smaller the measurement error, the greater its accuracy. Measurement error x deviation of the measurement result x from the true or actual value (x i or x d) of the measured quantity: xx x id. (2.1) The true value of a physical quantity is the value of a physical quantity that ideally characterizes the corresponding physical quantity qualitatively and quantitatively. It does not depend on the means of our knowledge and is an absolute truth. It can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. The actual value of a physical quantity is the value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the given measurement problem. Measurement errors can also be classified according to a number of criteria, in particular: a) according to the method of numerical expression; b) by the nature of the manifestation; c) according to the type of source of occurrence (causes of occurrence). According to the method of numerical expression, the measurement error can be: The absolute measurement error (x) is the difference between the measured value and the actual value of this value, i.e. x x x d. (2.2) Relative measurement error () is the ratio of the absolute measurement error to the actual value of the measured quantity. The relative error can be expressed in relative units (in fractions) or as a percentage: x or x 100%. (2.3) x x The relative error shows the accuracy of the measurement. 17
18 Depending on the nature of the manifestation, there are systematic (s) and random (0) components of measurement errors, as well as gross errors (misses). A systematic measurement error (s) is a component of the measurement result error that remains constant or regularly changes during repeated measurements of the same physical quantity. Random measurement error (0) is the component of the measurement result error, which changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. Gross errors (misses) occur due to erroneous actions of the operator, a malfunction of the measuring instrument, or sudden changes in measurement conditions (for example, a sudden drop in voltage in the power supply network). The following components of the total measurement error are considered depending on the type of source of error: allowed simplifications in measurements. The instrumental components of the error are errors that depend on the errors of the measuring instruments used. The study of instrumental errors is the subject of a special discipline of the theory of accuracy of measuring devices. The subjective components of the error are errors due to the individual characteristics of the observer. Errors of this kind are caused, for example, by a delay or advance in signal registration, incorrect reading of tenths of a division of the scale, asymmetry that occurs when a stroke is set in the middle between two risks, etc. Approximate estimation of the error Single measurements. The vast majority of technical measurements are single. The performance of single measurements is substantiated by the following factors: production necessity (destruction of the sample, impossibility of repeating the measurement, economic feasibility, etc.); 18
19 the possibility of neglecting random errors; random errors are significant, but the confidence limit of the measurement result error does not exceed the permissible measurement error. For the result of a single measurement, a single reading value of the instrument reading is taken. Being essentially random, a single reading x includes instrumental, methodological and personal components of the measurement error, in each of which systematic and random components of the error can be distinguished. The components of the error of the result of a single measurement are the errors of the measuring instrument, the method, the operator, as well as the errors due to changes in the measurement conditions. The error of the result of a single measurement is most often represented by systematic and random errors. The error of MI is determined on the basis of their metrological characteristics, which must be specified in regulatory and technical documents, and in accordance with the RD Method and operator errors must be determined during the development and certification of a specific MIM. Personal errors in single measurements are usually assumed to be small and are not taken into account. indirect measurements. With indirect measurements, the desired value of the quantity is found by calculation based on direct measurements of other physical quantities that are functionally related to the desired quantity by the known dependence y f x1, x2,..., xn, (2.4) where x1, x2,..., x n subject to direct measurements function arguments y. The result of indirect measurement is an estimate of the value of y, which is found by substituting the measured values of the arguments x i into formula (4). Since each of the arguments x i is measured with some error, the problem of estimating the error of the result is reduced to summing the errors in the measurement of the arguments. However, a feature of indirect measurements is that the contribution of individual errors in the measurement of arguments to the error of the result depends on the type of function (4). 19
20 For estimation of errors, it is essential to divide indirect measurements into linear and non-linear indirect measurements. For linear indirect measurements, the measurement equation has the form: y n bi xi, (2.5) i1 where b i are constant coefficients at the arguments x i. The result of a linear indirect measurement is calculated by formula (2.5), substituting the measured values of the arguments into it. The measurement errors of the arguments x i can be set by their boundaries xi. With a small number of arguments (less than five), a simple estimate of the error of the result y is obtained by simply summing the marginal errors (ignoring the sign), i.e., substituting the boundaries x 1, x 2, x n into the expression: y x1x2 ... xn. (2.6) However, this estimate is overestimated, since such summation actually means that the measurement errors of all arguments simultaneously have a maximum value and coincide in sign. The probability of such a coincidence is practically zero. To find a more realistic estimate, they proceed to the static summation of the error of the arguments according to the formula: n 2 2 i i, (2.7) i1 yk b x where k is the coefficient determined by the accepted confidence probability (at P = 0.9 at k = 1.0; .95 at k = 1.1, P = 0.99 at k = 1.4). Nonlinear indirect measurements any other functional dependencies other than (2.5). With a complex function (2.4) and, in particular, if it is a function of several arguments, the determination of the law of distribution of the result error is associated with significant mathematical difficulties. Therefore, the approximate estimation of the error of nonlinear indirect measurements is based on the linearization of function (2.4) and further processing of the results, as in linear measurements. Let us write the expression for the total differential of the function y in terms of partial derivatives with respect to the arguments x i: y y y dy dx1 dx2... dxn. (2.8) x x x 1 2 n 20
21 By definition, the total differential of a function is the increment of a function caused by small increments of its arguments. Considering that the measurement errors of the arguments are always small compared to the nominal values of the arguments, we can replace in formula (2.8) the differentials of the arguments dx n with the measurement error xn, and the function differential dy with the error of the measurement result y: y y y y x x... xn. (2.9) x x x If we analyze formula (2.9), we can obtain a simple rule for estimating the error of the result of a non-linear indirect measurement . Errors in works and private. If the measured values x1, x2,..., x n are used to calculate y x... 1x2 xn or y 1, x2, then the relative errors y x1x2... xn are summed, where y y. y 2.3. Recording (rounding) error of a number The recording (rounding) error of a number is defined as the ratio of half of the unit of the least significant digit of the number to the value of the number. For example, for the normal acceleration of falling bodies g \u003d 9.81 m / s 2, the unit of the least significant digit is 0.01, therefore, the error in writing the number 9.81 will be equal to 0.01 5, \u003d 0.05%. 29, Purpose of work n x development of methods for conducting single direct and indirect measurements; mastering the rules for processing, presenting (recording) and interpreting the results of measurements; acquisition of practical skills in the use of measuring instruments of different accuracy, as well as analysis and comparison of the accuracy of the results of indirect measurements with the accuracy of the measuring instruments used in direct measurements; identification of possible sources and causes of methodological errors; 21
22 consolidation of theoretical material in the section "Metrology" of the discipline under study "Metrology, standardization and certification" Equipment used vernier caliper (hereinafter SC); micrometer; ruler. When recording the measuring instruments used, indicate their normalized metrological characteristics using the measuring instruments Work program Perform single measurements of the diameter and height of the cylinder with measuring instruments of various accuracy: calipers, micrometers and rulers. Record the measurement results in the table. As cylinder 1, select a cylinder of lower height. Record the results of direct measurements of the diameter and height of the cylinders in a table with the accuracy with which the measuring instrument allows you to measure. Table 2.1 Measurement results Measured Cylinder 1 (small) Cylinder 2 (large) parameter Diameter d, mm Height h, mm Volume V, mm Rel. V Abs. error V, mm 3 micrometer ШЦ ШЦ ruler Determine the volume of the cylinder using the ratio: 2 V d h, mm 3, (2.10) 4 where = 3.14 is a numerical coefficient; d cylinder diameter, mm; h cylinder height, mm Determine the relative measurement error, expressed in relative units V V. (2.11) V 22
23 To determine the relative measurement error V, it is necessary to transform formula (2.11) into a convenient one for calculation using formula (2.9) (see section 2.2). In the resulting formula, d, h are the errors of the measuring instruments used in the measurements. In indirect measurements of physical quantities, tabular data or irrational constants are very often used. Because of this, the value of the constant used in the calculations, rounded up to a certain sign, is an approximate number that contributes its share to the measurement error. This fraction of the error is defined as the error in recording (rounding off) the constant (see clause 2.3) Determine the error in calculating the volume using the formula V V, mm 3. (2.12) V Round off measurement errors and record the result of measurements of cylinder volumes V V V mm 3. (2.13) For in order to record the final result of indirect measurements, it is necessary to round off the measurement error V in accordance with MI 1317, agree on the numerical values of the result and measurement errors (see clause 2.4) Show in the figures the areas in which the results of volume measurements obtained by different measuring instruments are located for each of the cylinders. An example is shown in Figure 2.1. V 2 ΔV 2 V 2 V 1 ΔV 1 V 1 V 1 + ΔV 1 V 2 + ΔV 2 Then you need to select the scale and put down all the other points. Show the error of the method in the figure. 23
24 2.6.7 Prepare a report and draw a conclusion (see Appendix A for an example of a title page). In the conclusion, evaluate the results of measurements, identify possible sources and causes of methodological errors. Control questions 1. Name the main types of measurements. 2. By what criteria are measurement errors classified? 3. Name and describe the main types of measurement errors. 4. How to determine the error in writing a number? 5. How to determine the error of the result of indirect measurement? 2.8. Literature used 1. RMG Recommendations on interstate standardization. GSI. Metrology. Basic terms and definitions. 2. R Recommendations on metrology. GSI. Direct single measurements. Estimation of errors and uncertainty of the measurement result. M., Publishing house of standards, Borisov Yu.I., Sigov A.S., Nefedov V.I. Metrology, standardization and certification: textbook. Moscow: FORUM: INFRA-M, MI Guidelines. GSI. Results and characteristics of measurement errors. Submission Forms. Methods of use in testing product samples and monitoring their parameters. 24
25 LABORATORY WORK 3 PROCESSING THE RESULTS OF DIRECT MULTIPLE MEASUREMENTS 3.1. Introduction The need to perform direct multiple measurements is established in specific measurement procedures. During statistical processing of a group of results of direct multiple independent measurements, the following operations are performed: known systematic errors are excluded from the measurement results; calculating an estimate of the measurand; calculate the standard deviation of the measurement results; check for gross errors and, if necessary, exclude them; checking the hypothesis that the measurement results belong to a normal distribution; calculate the confidence limits of the random error (confidence random error) estimates of the measured value; calculate the confidence limits (boundaries) of the non-excluded systematic error in the estimate of the measured value; calculate the confidence limits of the error in estimating the measured value. The hypothesis that the measurement results belong to a normal distribution is tested with a significance level q from 10% to 2%. Specific values of significance levels should be specified in a specific measurement procedure. To determine the confidence limits of the error in estimating the measured value, the confidence probability P is taken equal to 0. Basic concepts and definitions Depending on the nature of the manifestation, systematic (C) and random (0) components of the measurement error are distinguished, as well as gross errors (misses). Gross errors (misses) arise due to erroneous actions of the operator, a malfunction of the measuring instrument, or sudden changes in measurement conditions, for example, a sudden drop in voltage in the power supply network. Closely adjoining them are the errors that depend on 25
26 observers and related to improper handling of measuring instruments. The systematic measurement error (systematic error C) is the component of the measurement result error that remains constant or regularly changes during repeated measurements of the same physical quantity. It is believed that systematic errors can be detected and eliminated. However, under real conditions, it is impossible to completely eliminate the systematic component of the measurement error. There are always some factors that need to be taken into account, and which will constitute a non-excluded systematic error. Non-excluded systematic error (NSE) is a component of the error of the measurement result, due to errors in the calculation and introduction of corrections for the influence of systematic errors or a systematic error, the correction for which is not introduced due to its smallness. Non-excluded systematic error is characterized by its boundaries. The boundaries of the non-excluded systematic error Θ with the number of terms N 3 are calculated by the formula: N i, (3.1) i1 where i-th border component of the non-excluded systematic i error. With the number of non-excluded systematic errors N 4, the calculation is carried out according to the formula k N 2 i, (3.2) i1 ; at P = 0.99, k = 1.4). Here Θ is considered as a confidence quasi-random error. Random measurement error (0) is the component of the measurement result error, which changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. 26
27 To reduce the random component of the error, multiple measurements are carried out. Random error is estimated by the confidence interval tp Sx, (3.3) where t P is the Student's coefficient for a given level of confidence Р d and sample size n (number of measurements). Confidence limits of the error of the measurement result of the boundary of the interval within which the desired (true) error value of the measurement result is located with a given probability. Sample a series of x measurement results (x i ), i = 1,..., n (n > 20), from which known systematic errors are excluded. The sample size is determined by the requirements of measurement accuracy and the possibility of repeated measurements. A variational series is a selection sorted in ascending order. Histogram of the dependence of the relative frequencies of the measurement results falling into the grouping intervals on their values, presented in graphical form. Estimation of the distribution law Estimation of the correspondence between the experimental distribution law and the theoretical distribution. It is carried out using special statistical criteria. When p< 15 не проводится. Точечные оценки закона распределения оценки закона распределения, полученные в виде одного числа, например оценка дисперсии результатов измерений или оценка математического ожидания и т. д. Средняя квадратическая погрешность результатов единичных измерений в ряду измерений (средняя квадратическая погрешность результата измерений) оценка S рассеяния единичных результатов x измерений в ряду равноточных измерений одной и той же физической величины около среднего их значения, вычисляемая по формуле: 1 n S 2 x x 1 i x n, (3.4) i1 где i x результат i-го единичного измерения; x среднее арифметическое значение измеряемой величины из n единичных результатов. Примечание. На практике широко распространен термин среднее квадратическое отклонение (СКО). Под отклонением в соответствии с приведенной выше формулой понимают отклонение единичных результатов в ряду измерений от их среднего арифметического значения. В метрологии это отклонение называется погрешностью измерений. 27
28 The mean square error of the measurement result of the arithmetic mean estimate S x of the random error of the arithmetic mean of the measurement result of the same value in a given series of measurements, calculated by the formula 2 i S Sx 1 x x x n nn1, (3.5) measurements obtained from a series of equally accurate measurements; n number of single measurements in a series Exclusion of gross errors To exclude gross errors, Grubbs' statistical test is used, which is based on the assumption that a group of measurement results belongs to a normal distribution. To do this, calculate the Grubbs criteria G 1 and G 2, assuming that the largest x max or smallest x min measurement result is caused by gross errors: xmax x x x G1, min S G. (3.6) x 2 Sx Compare G 1 and G 2 with the theoretical value G T of the Grubbs test at the chosen significance level q. A table of critical values of the Grubbs criterion is given in Appendix B. If G 1 > G T, then x max is excluded as an unlikely value. If G 2 > G T, then x min is excluded as an unlikely value. Next, the arithmetic mean and standard deviation of a number of measurement results are calculated again, and the procedure for checking for the presence of gross errors is repeated. If G1 G T, then x max is not considered a miss and is stored in the measurement series. If G 2 G T, then x min is not considered a miss and it is stored in a series of measurement results. The error limits for estimating the measured value (without taking into account the sign) are calculated by the formula 28
29 K S, (3.7) where K is a coefficient depending on the ratio of the random component of the error and the NSP. The total standard deviation S of the estimate of the measured value is calculated by the formula S S2 S2 x, (3.8) from formulas (3.1), or P S, (3.10) k 3 where P are the confidence limits of the NSP, which are determined by one of the formulas (3.2); k is a coefficient determined by the accepted confidence probability P, the number of NSP components and their relationship to each other. The coefficient K for substitution into formula (3.7), depending on the number of NSPs, is determined by the empirical formulas, respectively, K, P K. (3.11) S S S x x S 3.5. Algorithm for processing the results of observations Processing of the results of observations is carried out in accordance with GOST “GSI. Measurements are direct with multiple. Methods for processing measurement results. Basic Provisions» Determination of point estimates of the distribution law x 1 n x i ; 1 n S 2 x x 1 i x n ; S S x x. n n i Construction of the experimental law of distribution of the results of multiple observations a) in Table 3.2, write the variational series of the results of multiple observations x ; i i1 29
PRACTICAL LESSON 6 "Processing the results of equal-precision measurements, free from systematic errors" The lesson is devoted to solving problems of calculating the errors of equal-precision measurements
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Â. n. KAKENOVA, T. n. GRAPH, Å. Â. TÅSLÅNOKO, Å. A. COMPOSITION OF MONEY, STRATEGY AND SATURATION. PRACTICE Under the general editorship of V. N. Kainova Anogogo mashinostroyya (UMO AM) as a textbook for university students, about in the direction of preparation "Designer-technological spacecraft" Treatment of machine building Productions» SANC-PASTROROG MONOSCLA 2015 BBC 30.10-73 K 12 Kainova V. N., Grebneva T N., Teslenko E. V., Kulikova E. A. K 12 Metrology, standardization and certification: Workshop: Textbook / Ed. V. N. Kainoy. - St. Petersburg: Publishing house "Lan", 2015. - 368 p.: ill. - (Textbooks for universities. Special literature). ISBN 9785811418329 The textbook contains theoretical and reference & methodological material on the standardization of the geometric characteristics of products, as well as on the choice of measuring instruments and processing the results of single and multiple measurements performed by direct and indirect methods. Variants of tasks used in the performance of practical classes and independent work in the discipline "Metrology, standardization and certification" have been developed. Designed for students of higher educational institutions studying in the technical areas of training bachelors & masters and graduates. It may be useful for engineering and technical services of enterprises and organizations that develop and manufacture products in the field of mechanical engineering. BBK 30.10ya73 Reviewers: F. F. REPIN - Ph.D. P. M. KOROLEV - candidate of technical sciences, deputy. chief technologist of OAO NAZ "SOKOL". Cover by EA VLASOVA Protected by the RF copyright law. Reproduction of the entire book or any part of it is prohibited without the written permission of the publisher. Any attempt to break the law will be prosecuted. © Publishing house "La; н", 2015 © Collective of authors, 2015 © Publishing house "Lan", artistic design, 2015 FOREWORD The discipline "Metrology, standardization and certification" refers to the basic part of the professional cycle of full-time and part-time education of students of higher educational institutions studying in technical areas of training bachelors, masters and graduates. This manual was developed for the first time in the form of a workshop, previous editions contained theoretical material and reference data. The authors of the manual have extensive experience in studying the issues of standardization and control of the accuracy of geometric parameters, in issues of standardization in the field of design and technological documentation. Considering that modern curricula pay considerable attention to the performance of independent and practical work by students, it became necessary to create a teaching aid in the form of a workshop. In the manual on all the topics under consideration, the theoretical part, options for tasks and examples of their solution are briefly given. The manual consists of five chapters and appendices that contain reference tables from the standards needed to complete the tasks. T. N. Grebneva prepared the first chapter, sections on keyed and splined connections from the fourth chapter. The second and third chapters, as well as the section on the choice of means 4 The preface of measurements from the fifth chapter were compiled by E. V. Teslenko. E. A. Kulikova developed a section on the rationing of metric thread parameters from the fourth chapter and a section from the fifth chapter on the calculation of measurement errors. Sections of the fifth chapter on the basics of probability theory, mathematical statistics and processing of measurement results were compiled by VN Kainova. The general edition of the manual was completed by associate professor, candidate of technical sciences Valentina Nikolaevna Kainova. The authors express their deep gratitude for valuable suggestions and comments on improving the content of the textbook to Ph.D. Exact science is unthinkable without measure. DI Mendeleev The further unreliability is found from the designer's board, the more expensive it is. AA Tupolev INTRODUCTION Design documentation determines the design quality of products. It is the main type of documents that are used to design technological processes for processing and assembly, control and measurement operations, as well as when performing certification work. When developing design documentation, it is necessary to comply with the requirements of current standards. Accuracy significantly affects the quality of products, the complexity of their manufacture, and, consequently, the cost. The purpose of this tutorial is to help students in solving these problems. The manual consists of five chapters and appendices that contain reference tables from the standards needed to complete the tasks. The first chapter gives general concepts about the system of tolerances for smooth cylindrical joints (ESDP), as well as recommendations and examples for the selection and calculation of tolerances and fits, methods for calculating dimensional chains. The second chapter is devoted to the issues of surface roughness, the accuracy of the shape and location of the surfaces of machine parts, and also contains recommendations for calculating the numerical values of geometric tolerances and indicating them on the drawings. In the third chapter, joints with rolling bearings are considered, recommendations are given for choosing fits and drawing up drawings. 6 Introduction The fourth chapter contains information on feather keys, straight splines, threaded connections and spur gears. The fifth chapter covers the issues of metrological support for machine-building production: analysis of measurement errors, recommendations for choosing measuring instruments, the basics of probability theory and mathematical statistics, specific situations are considered. CHAPTER 1 REGULATION OF THE ACCURACY OF SMOOTH CYLINDRICAL JOINTS 1.1. ESDP. TOLERANCES AND FITTINGS OF SMOOTH JOINTS 1.1.1. TERMS AND DEFINITIONS ACCORDING TO GOST 25346-89 THEORETICAL PART FOR PRACTICAL LESSON 1.1 Standardization of the accuracy of linear dimensions is carried out by the standards of the Unified System of Tolerances and Fits (ESDP). The basic standard for this system is GOST 25346-89 “ONV. Unified system of tolerances and landings. General provisions, series of tolerances and basic deviations. Size - the numerical value of a linear quantity in the selected units of measurement. It is customary to divide the dimensions into free and mating, covered (shafts) and covering (holes). Hole - a term conventionally used to refer to the internal elements of parts, including non-cylindrical elements. Shaft is a term conventionally used to designate external elements of parts, including non-cylindrical elements. All shaft parameters are indicated by lowercase Latin letters, and all hole parameters are indicated by uppercase letters. The size can be actual, nominal or limit (largest or smallest). Actual size - the size of the element, set by the measurement with an allowable error. Limit dimensions - two maximum allowable dimensions of an element (largest and smallest), between which the actual size of a suitable part must be: Dmax, Dmin - the largest and smallest limit dimensions of the hole, respectively; dmax, dmin - the largest and smallest shaft dimensions, respectively. Nominal size - the size relative to which deviations are determined. The value of the nominal size is found according to the performed engineering calculations of the part for strength, rigidity, bending, etc. , taking into account the safety factor (equal to 2, 3 or more), with its further rounding in rows of normal linear dimensions according to GOST 6636-69: d - nominal shaft diameter; D is the nominal hole diameter. The nominal size serves as the starting point for deviations - actual or limit (upper and lower). All nominal sizes in the ESDP system are divided into a number of intervals,. Deviation - the algebraic difference between the size (actual, limit) and the corresponding nominal size. Limit deviation (upper or lower) - the algebraic difference between the limit and the corresponding nominal dimensions (Fig. 1.1): E, e - actual deviations of the hole and shaft, respectively; ES, es - upper limit deviations of the hole and shaft, respectively; EI, ei - lower limit deviations of the hole and shaft, respectively. ES = Dmax – D; es = dmax – d; EI = Dmin – D; (1.1) ei = dmin – d. (1.2) From here, the limiting dimensions can be determined as the algebraic sum of the nominal size and the corresponding limiting deviation according to the following formulas: Chapter 1. Rationing of the accuracy of smooth cylindrical joints 9 Fig. 1.1 Limit dimensions and deviations: a, b - shafts; in - holes. Dmax = D + ES; dmax = d + es; Dmin = D + EI; (1.3) dmin = d + ei. (1.4) The tolerance of the hole and the shaft (T) can be represented as the difference in the limiting dimensions or as the algebraic difference in the limit deviations: TD = Dmax - Dmin = ES - EI; (1.5) Td = dmax – dmin = es – ei. (1.6) The dependence of the tolerance on the nominal size is expressed in terms of the tolerance unit, which for sizes up to 500 mm is denoted by the letter i (µm), and for sizes over 500 mm - I (µm). It is a characteristic of accuracy (a function of the nominal size). Rounded values of the tolerance unit depending on the nominal size are presented in table 1.1. In accordance with GOST 25346-89, the standard tolerance (IT) is any of the tolerances established by this system of tolerances and fits, which is specified by the quality (degree of accuracy) and is conditionally designated taking into account the quality number ITn. 10 Metrology, standardization and certification T a b l e 1.1 Dimension intervals, mm Rounded values of tolerance units i, µm to 3 sv. 3 to 6 St. 6 to 10 St. 10 to 18 St. 18 to 30 St. 30 to 50 St. 50 to 80 St. 80 to 120 St. 120 to 180 St. 180 to 250 St. 250 to 315 St. 315 to 400 St. 400 to 500 i 0.6 0.8 0.9 1.1 1.3 1.6 1.9 2.2 2.5 2.9 3.2 3.6 4 Quality is a set of tolerances considered as appropriate the same level of accuracy for all nominal sizes. Size tolerances depending on the ranges of sizes and qualifications are given in Appendix B, Table B.1. The calculation was made for a normal temperature of 20°C with a probability of 0.997. Thus, the quality is understood as the totality of tolerances of all nominal sizes of a given range, which are characterized by a constant relative accuracy, expressed by the coefficient a, called the number of tolerance units (Table 1.2). The range of values of the coefficient a corresponds to the range R5 of preferred numbers. Table 1.2 Quality The values of the number of tolerance units a depending on the number of qualification 5 6 7 8 9 10 11 12 13 14 15 16 17 a 7 10 16 25 40 64 100 160 250 400 640 1000 1600 Number of tolerance units a for a given quality in the entire range of sizes is constant, and the tolerance value depends on the nominal size and quality number. Therefore, the tolerance value for grades 5 to 17, depending on the nominal size, can be determined by the formula ITn = a⋅i; (1.7) where a is the number of tolerance units; i - tolerance unit, microns. Chapter 1. Rationing the accuracy of smooth cylindrical joints 11 The tolerance unit, which is a function of the nominal size (hyperbolic dependence), is calculated by the formula i \u003d 0.453 D + 0.001D, where D \u003d Dmax Dmin, i.e. the geometric mean of the extreme dimensions of each interval (Dmax and Dmin), in mm. The standard establishes 20 qualifications: 01, 0, 1, 2, ..., 18. The qualifications from 01 to 4 are intended mainly for calibers. The executive dimensions in the drawings are given by the nominal size and the tolerance field. The tolerance field is limited by the largest and smallest limit sizes and is determined by the tolerance value and its position relative to the nominal size. With a graphical representation of tolerance fields, the position of the nominal size is depicted by a line called zero. The deviations are counted along the perpendicular to the zero line: up - with a positive sign, and down - with a negative sign. The horizontal lines limiting the tolerance field from above and below are the upper generatrices of cylindrical surfaces with the largest and smallest diameters, respectively. The position of the tolerance field is set by the main deviation, which in the ESDP is called one of the two limit deviations (upper or lower), closest to the zero line. Thus, for tolerance fields located above the zero line, the main deviation will be the lower deviation, and for tolerance fields located below the zero line, the upper deviation. The main deviations are indicated by letters of the Latin alphabet: lowercase - for shafts (a–zc), uppercase - for holes (A–ZC). For sizes up to 500 mm, 27 options are provided for the main deviations of shafts and holes (Table 1.3). The layout of the main deviations is shown in Figure 1.2. 12 Metrology, standardization and certification T a b l e 1.3 Designations of basic bore and shaft deviations Holes A B C D E EF F FG G H Js K Shafts a b c d e eff f fg g h js k m Holes N P R S T U V X Y Z ZA ZB ZC Shafts n p r s t u v x y z za zb zc M Fig. 1.2 Main deviations: a - holes; b - shafts; I - for landings with a gap; II - for transitional landings; III - for interference fit. Among the main deviations, a special place is occupied by deviations with the designation H, h, Js, js. The letters H, h Chapter 1. Rationing the accuracy of smooth cylindrical joints 13 denote the tolerance fields of the main hole and the main shaft, respectively. The main shaft (h) is a shaft whose main upper deviation is zero: es = 0. The main hole (H) is a hole whose main lower deviation is zero: EI = 0. The tolerance fields of the main hole and the main shaft are directed to the "body" details and determine the maximum size of the material. The term maximum material size refers to that of the limit sizes, which corresponds to the largest volume of the material of the part, i.e. the largest limit size of the outer (male) element (shaft) or the smallest limit size of the inner (female) element (hole). In GOST 25346, the term "material maximum limit" is used in approximately the same sense as the term "material maximum size" in accordance with GOST R 53090-2008. The designations Js, js correspond to the symmetrical (tolerance field) location of the deviations of the hole and the shaft, respectively (Fig. 1.2). The value of the basic deviation depends on the symbol and the value of the nominal size. The second deviation of the tolerance fields (Fig. 1.3) is defined as the algebraic difference or algebraic sum of the values of the main deviation and the standard tolerance ITn of the hole or shaft specified by the size qualification, according to the following formulas (taking into account the sign of the main deviation and its location): ES = EI + ITn ( from A to H); (1.8) EI = ES – ITn (from K to ZC); (1.9) ei = es – ITn (from a to h); (1.10) es = ei + ITn (from k to zc). (1.11) The numerical values of the main deviations are given in Appendix B, for shafts - in table B.2, for holes - in table B.3. 14 Metrology, standardization and certification Pic. 1.3 The layout of the tolerance fields: a - holes (ES and EI - positive); b - shaft (es and ei - negative). Due to the fact that the tolerance field is determined by the tolerance value and its position relative to the nominal size, its symbol in accordance with GOST 25436 should include the value of the nominal size, the designation of the main deviation and the quality number. For example: ∅30F7 and ∅30f6. The first dimension refers to the bore and the second dimension refers to the shaft. Tolerance fields and maximum deviations of dimensions on the drawings are indicated in accordance with ESKD according to GOST 2.307-2011 as follows: 1) the symbol of the tolerance fields (letter and number); recommended in mass production: ∅20m6, ∅50H7, ∅100f8, etc.; 2) numerical values of limit deviations (upper and lower deviations) in mm; recommended in single production: +0.025; ∅100−0.036; ∅20++0.021 0.008; ∅50 −0.090 3) mixed method; recommended in mass production and for educational purposes: To write in a mixed way means to indicate the tolerance field twice: first with conventional signs (letter and 15 Chapter 1. Rationing the accuracy of smooth cylindrical joints with a number), and then in brackets with the values \u200b\u200bof limit deviations. A parenthesis separates one way of writing a tolerance field from another. When drawing dimensions with maximum deviations on the drawings, the following rules should be observed: the upper and lower deviations are written in two lines in a font half the size of the main one, placing the upper deviation above the lower one: ∅30++0.075 0.051; the number of characters when recording the upper and lower deviations should be the same, for example, ∅30−−0.007 0.040; deviations equal to zero do not indicate, for example +0.021 ∅30; ∅30–0.033; with a symmetrical arrangement of deviations, their value is given after the “±” sign with digits equal in height to the digits of the nominal size, for example, ∅30 ± 0.026. ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.1 To get acquainted with the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.4. T a b l e 1.4 Variants of tasks for a practical lesson 1.1 No. of variant Dimensions No. of variant Dimensions No. of variant Dimensions 7 45h6 12 85S7 85h6 21 50H11 50d10 4 65g6 65H7 13 75s6 75H7 22 150h10 150E9 5 112G6 112h5 14 102D8 102h7 23 12P5 12h5 6 35M5 35h4 15 135m5 135H6 24 240G7 24 0h6 72E7 72h6 7 16 58e8 58H9 25 20s7 20H8 8 185m6 185H7 17 10Js9 10h9 26 24k6 24H7 9 28a11 18 32c11 32H12 27 210r6 210H7 28H12 Job. Calculate tolerances and maximum deviations of given dimensions and write down the tolerance fields in a mixed way (1st level of complexity); at the 2nd level of complexity to build layouts of tolerance fields. 16 Metrology, standardization and certification Solution. 1. Find in table 1.1 the value of the tolerance unit for the given nominal dimensions. 2. Determine the number of tolerance units according to table 1.2, depending on the given qualification number. 3. Calculate the tolerance value for given dimensions using formula (1.7). 4. Round off the calculated tolerance value to the standard one according to Table B.1 of Appendix B. 5. Determine the type and value of the main deviations (Tables B.2 and B.3), as well as the second deviations of the tolerance fields for given sizes according to the formulas (1.8) , (1.9) or (1.10), (1.11). 6. Write down the given dimensions, indicating the tolerance fields in a mixed way. 7. Construct layouts of tolerance fields for given dimensions similar to Figure 1.3. EXAMPLES OF PERFORMANCE OF PRACTICAL LESSON 1.1 Example 1 (1st level of complexity) Task. Calculate the tolerances and limit deviations of the dimensions ∅30H7 and ∅30f6 and write down the tolerance fields in a mixed way. Solution. 1. For size ∅30, find the value of the tolerance unit i = 1.3 µm from Table 1.1. 2. Determine the number of tolerance units according to table 1.2: for the 7th grade -a = 16; for the 6th grade -a = 10. 3. Calculate the tolerance value for the given dimensions according to the formula (1.7): for the hole IT7 = a ⋅ i = 1.3 ⋅ 16 = 20.8 µm; for the shaft IT6 = a ⋅ i = 1.3 ⋅ 10 = 13 µm. 4. According to Table B.1, find the standard tolerance values: IT7 = 21 µm; IT6 = 13 µm. 5. Determine the type and value of the main deviations and the second deviations of the tolerance fields for the given dimensions according to the formulas (1.8), (1.9) or (1.10), (1.11). Chapter 1. Rationing the accuracy of smooth cylindrical joints 17 5.1. Size ∅30H7 has a main deviation H (Table B.3), which corresponds to a lower deviation equal to EI = 0, the second deviation is determined by formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 5.2. Size ∅30f6 has a basic deviation f, which corresponds to the upper deviation equal to es = –20 µm (Table B.2). Lower shaft deflection according to formula (1.10): ei = es – ITn = –20 – 13 = –33 µm. 6. Write down the specified dimensions, indicating the tolerance field in a mixed way: ∅30H7 (+0.021); ∅30f 6 (−−0.020 . 0.033) Example 2 (2nd level of difficulty) Task. Calculate limit deviations, limit dimensions ∅30H7 and ∅30f6, write down the tolerance fields in a mixed way and build tolerance fields. Solution. For size ∅30H7 determine: 1. Type and value of the main deviation H: EI = 0 (Table B.3). 2. The value of the standard tolerance IT7 = 21 (Table B.1). 3. The value of the second deviation according to formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 4. Record the tolerance field in a mixed way: ∅30H7(+0.021). 5. Calculate the limit dimensions of the hole using formulas (1.3): Dmax = D + ES = 30.000 + 0.021 = 30.021; Dmin = D + EI = 30.000 + 0 = 30.000. For the size ∅30f6 determine: 1. Type and value of the main deviation f: es = –20 (Table B.2). 18 Metrology, standardization and certification Pic. 1.4 Schemes for the location of tolerance fields: a - holes ∅30H7; b - shaft ∅30f6. 2. The value of the standard tolerance IT6 = 13 µm (Table B.1). 3. The value of the second deviation according to formula (1.10): ei = es – IT6 = –20 – 13 = –33 µm. 4. Record the tolerance field in a mixed way: ∅30f 6 (−−0.020 . 0.033) 5. Calculate the maximum shaft dimensions using formulas (1.4): dmax = d + es = 30.000 - 0.020 = 29.980; dmin = d + ei = 30.000 - 0.033 = 29.967. 6. Build a layout of tolerance fields for the size ∅30H7 (Fig. 1.4a) and for the size ∅30f6 (Fig. 1.4b). 1.1.2. LANDINGS AND THEIR CHARACTERISTICS. LANDING SYSTEMS THEORETICAL PART TO PRACTICAL LESSON 1.2 Fitting is the connection of two parts, resulting in a gap or interference. The difference in dimensions Chapter 1. Rationing the accuracy of smooth cylindrical joints 19 of the hole and the shaft before assembly determines the nature of the connection of parts. Distinguish landings with a gap, landings with an interference fit and transitional landings. For the formation of landings, either the main hole H or the main shaft h is used. The main shaft is a shaft whose upper (basic) deviation is zero: es = 0 → h. Main hole - a hole whose lower (basic) deviation is zero: EI \u003d 0 → H. Nominal fit size - nominal size common to the hole and shaft that make up the connection. Fit characteristics include tightness, clearances and fit tolerance. Clearance (S) - the difference between the hole and shaft dimensions before assembly, if the hole size is larger than the shaft size. Preload (N) - the difference between the dimensions of the shaft and the hole before assembly, if the size of the shaft is larger than the size of the hole. Fit tolerance - the sum of the tolerances of the hole and the shaft that make up the connection: TS (TN) = TD + Td. Rice. 1.5 Layout of tolerance fields for clearance fits (1.12) 20 Metrology, standardization and certification Clearance fit - a fit in which a gap is always formed in the connection, since the smallest limit hole size is greater than or equal to the largest limit shaft size. With a graphic representation of the fit, the hole tolerance field is located above the shaft tolerance field (Fig. 1.5). The limiting characteristics of a fit with a gap are the largest and smallest gaps and the gap tolerance: Smax = Dmax - dmin = ES - ei; (1.13) Smin = Dmin – dmax = EI – es; (1.14) TS = Smax – Smin = TD + Td. (1.15) An interference fit is a fit in which an interference is always formed in the joint, i.e., the largest limit hole size is less than or equal to the smallest limit size of the shaft. With a graphical representation, the hole tolerance field is located below the shaft tolerance field (Fig. 1.6). The limiting characteristics of an interference fit are the largest and smallest interference and interference tolerance: Fig. 1.6 Layout of tolerance fields of interference fit Chapter 1. Accuracy standardization of smooth cylindrical joints 21 Fig. 1.6. 1.7 The layout of the transition fit tolerance fields Nmax = dmax - Dmin = es - EI; (1.16) Nmin = dmin – Dmax = ei – ES; (1.17) TN = Nmax – Nmin = TD + Td. (1.18) Transitional fit - a fit in which both clearance and interference are possible in the joint, depending on the ratio of the actual dimensions of the hole and the shaft. With a graphic representation of the tolerance field, the hole and the shaft overlap completely or partially (Fig. 1.7). The limiting characteristics of the transitional fit are the largest gap, the largest interference fit and the fit tolerance: Smax = Dmax - dmin = ES - ei; (1.19) Nmax = dmax – Dmin = es – EI; (1.20) TS/N = Smax + Nmax = TD + Td. (1.21) The diagram in Figure 1.8 illustrates the calculation of clearance fit tolerance, transitional fit and interference fit through limiting characteristics. Since the gaps and tensions are of the opposite nature, it is customary to lay the gaps in positive side from zero, and tension - in the negative direction. The problem, in accordance with the scheme, is solved as a geometric one, i.e., the fit tolerance is determined either as the difference between the segments equal to the limiting characteristics of the fit (for landings with a gap and landings with an interference fit), or as their sum (for a transitional fit). 22 Metrology, standardization and certification Pic. 1.8 Scheme for calculating the fit tolerance according to the limiting characteristics The fit designation is indicated after the nominal size of the fit. Landing is indicated by a fraction, in the numerator of which the symbol of the hole tolerance field is indicated, and in the denominator - the symbol of the shaft tolerance field. With a mixed designation method, after the symbol for the tolerance fields of the hole and the shaft, the numerical values \u200b\u200bof the maximum deviations of these tolerance fields are indicated, enclosed in brackets. For example: ∅40 H7/ k6; ∅40 H7 (+0.025) H7 ; ∅50 . k6 k6 (+0.018 +0.002) The system of tolerances and fits is a set of series of tolerances and fits, naturally built on the basis of theoretical and experimental studies. Landings can be assigned in two systems: in the hole system (СH) and in the shaft system (Сh). Landings of the hole system - landings in which the required gaps and interferences are obtained by combining shaft tolerance fields of different basic deviations with the tolerance field of the main hole H (EI \u003d 0). Thus, in order to change the nature of the connection, it is necessary to change the position of the shaft tolerance field, i.e. the main shaft deviation (Fig. 1.9), leaving the hole tolerance field (H) unchanged. Examples of landings in the hole system: ∅30N/k6; ∅30Н7/f6; ∅30Н7/р6. Landings of the shaft system - landings in which the required gaps and interferences are obtained by a combination of tolerance fields of holes that are different in terms of the main deviation with the tolerance field of the main shaft h (es \u003d 0). Chapter 1. Rationing the accuracy of smooth cylindrical joints 23 Fig.1. 1.9 Tolerance fields of the hole system Thus, in order to change the nature of the connection, it is necessary to change the main deviation of the hole, i.e. the position of the hole tolerance field (Fig. 1.10), leaving the shaft tolerance field (h) unchanged. Examples of landings in the shaft system: ∅30M7/h6; ∅30F7/h6; ∅30R7/h6. Similar landings of different systems with the same nominal size are interchangeable, since they have the same limiting characteristics. However, in some cases, the use of a shaft system is necessary. Examples of the application of the shaft system: 1) in the joints of a smooth shaft with several holes for landings of various nature; Rice. 1.10 Tolerance fields of the shaft system 24 Metrology, standardization and certification 2) in the connection of the outer ring of the bearing with the hole in the housing (the bearing is a standard product); 3) in the joints of the keys along the width with the grooves of the hole and the shaft; 4) the use of smooth cold-drawn calibrated bars as axles or shafts without additional machining in agricultural machines,. The standard allows any combination of tolerance fields for holes and shafts, but two narrower series of tolerance fields are recommended for use: the main series, in which an even narrower selection of preferred tolerance fields is highlighted (Tables 1.5 and 1.6), and an additional series of limited use. Table 1.5 Preferred tolerance fields in the hole system Main holes Shaft tolerance fields Number of fields H7 e8, f7, g6, h6, js6, k6, n6, p6, r6, s6 10 H8 d9, e8, h7, h8 4 H9 d9, h9 2 H11 2 d11, h11 Σ 18 Total Table 1.6 Preferred tolerance fields in the shaft system Main shafts Hole tolerance fields h6 F8, H7, Js7, K7, N7, P7 6 h7 H8 1 h8 E9, H9 2 h11 H11 1 Total Number of fields Σ 10 Hole system (СH) is preferred, as it allows to reduce the cost of processing parts by reducing the range of standard sizes of measuring cutting tools (drills, countersinks, reamers) and measuring tools (bore gauges for holes) . Chapter 1. Rationing the accuracy of smooth cylindrical joints 25 Landings are called basic if the following conditions are met: the tolerance fields (basic deviations) of the hole and the shaft belong to the same system; the accuracy of the hole and the shaft is the same, i.e. the numbers of the hole and shaft qualifications are the same or differ by one; in rare cases, a difference in qualification numbers equal to two is allowed. If these conditions or one of them are not met, the landing will be combined on both grounds or on one of them. Examples of basic and combined landings: 1) landing ∅45Н7/k6 - basic landing: tolerance fields belong to one system - the hole system, and the difference in qualification numbers is equal to one; 2) landing ∅45Н7/h6 - combined landing on the first sign. The tolerance fields belong to different systems: the hole tolerance field belongs to the hole system, the shaft tolerance field belongs to the shaft system. 3) landing ∅45F9/k6 - combined in two ways. The hole and shaft tolerance fields belong to different systems: the hole tolerance field belongs to the shaft system, and the shaft tolerance field belongs to the hole system. The difference between the numbers of qualifications is not more than three. The hole tolerance fields recommended by the standard for nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.4. The largest number of tolerance fields (10) is in the zone of 7-11 qualifications. Shaft tolerance fields recommended by the standard with nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.5. The largest number of tolerance fields (16) is in the zone of 6-11 qualifications. ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.2 Level of the first complexity - the solution of questions for one given landing, for two landings - the second level, and for three - the third level of complexity. 26 Metrology, standardization and certification Read the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.7. T a b l e 1.7 Landings Variant No. Variant No. Variants of tasks for the practical lesson 1.2 105Js7/h6 14 Landings 15 45H7/g6 76M7/h6 25H9/js9 22H7/r6 3 36G6/h5 85H8/x8 100M6/h5 16 30F7/h6 180K8/h7 4 22C11/h10 230H6/t5 18 K8/h7 17 25F7/h 6 10Js10/h9 45H7/ s6 5 40D11/h10 60H7/p6 105H7/js 7 18 32F9/h8 28N8/h7 175H6/t 5 6 118F10/h9 150H7/p6 130H6/m5 19 34D9/h8 240H5/k4 102H7/s6 7 76D8/h7 205H7/u7 90H7/m6 20 72F8/h7 18H8/z8 90H7/js6 8 25H9/f8 210T7/h6 55H7/k6 21 118U8/h7 15H10/h9 20H7/n7 9 90H8/g8 110H7/t6 65N7/h6 22 27M8/h7 36H10/f9 125H7/s7 10 185H8/k7 222N8/h7 70H10/d9 27H7/r6 112Js7/h7 23 95H11/d11 11 48H12/d11 42S7/h6 130H6/k5 24 114Js9/h9 50G7/h6 55H7/s6 12 80K8/h7 122H7/r6 25 145G7/h6 23H7/r6 108K7/h6 140H7/n6 40H9/x8 26 180H10/e9 105R7/h6 215H6/k5 50F8/h7 13 90H12/b11 When calculating the main deviations of the holes (K, M, N, as well as for P–Z up to the 7th grade), use the “Note” to Table B.3 of Appendix B. Task. Determine the maximum deviations of the tolerance fields for three given landings (with a gap, an interference fit and a transitional fit) according to a given option. 1. Determine the maximum deviations of the tolerance fields of given landings. To do this, according to tables B.1–B.3 of Appendix B, determine the tolerances and basic deviations. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance, as was done during the first practical work. 3. Write down the tolerance fields for the dimensions of the parts in a mixed way. 4. Calculate the limiting characteristics of the given fits, find the fit tolerance in two ways: according to Chapter 1. Rationing the accuracy of smooth cylindrical joints 27 limit gaps or interference, and perform the check according to the tolerances of the hole and shaft according to the formula (1. 12). 5. Build three layouts of tolerance fields for all three landings. EXAMPLE OF IMPLEMENTATION OF PRACTICAL LESSON 1.2 Task. Calculate the limiting characteristics of three given landings and build the layout of the tolerance fields for them: ∅40H7/f6; ∅40H7/k6; ∅40H7/r6. Solution. 1. Determine the maximum deviations of the tolerance fields of given landings. To do this, according to Table B.1 of Appendix B, determine the tolerances for the size ∅40: tolerance IT7 = 25 µm; tolerance IT6 = 16 µm. The main deviations are determined according to tables B.2, B.3 of Appendix B: for H → EI = 0; for f → es = –25 µm; for k → ei = +2 µm; for r → ei = +34 µm. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance: for H → ES = EI + IT7 = 0 + 25 = +25 µm; for f → ei = es – IT6 = –25 – 16 = –41 µm; for k → es = ei + IT6 = +2 + 16 = +18 µm; for r → es = ei + IT6 = +34 + 16 = +50 µm. 3. Write down the tolerance fields for the dimensions of the parts in a mixed way: +0.018 +0.050 ∅40H7 (+0.025); ∅40f 6 (−−0.025 0.041); ∅40k6 (+0.002); ∅40r 6 (+0.034). 4. Calculate the limiting characteristics of the given landings. 4.1. Calculate the limiting characteristics according to H7 (+0.025) of the cage with a gap in the hole system ∅40 along f 6 (−0.025) 0.041 formulas (1.13)–(1.15): Smax = ES – ei = +25 – (–41) = 66 µm ; 28 Metrology, standardization and certification Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; Check according to formula (1.12): TS = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transitional fit in the hole system ∅40 lam (1.12), (1.19)–(1.21): H7 (+0.025) according to the shape6 (++0.018 0.002) Smax = ES – ei = 25 – 2 = 23 µm; Nmax = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. Rice. 1.11 Schemes for the location of landing tolerance fields: a - with a gap; b - transitional; c - with tension. Chapter 1. Rationing the accuracy of smooth cylindrical joints 29 4.3. Calculate the limiting characteristics of an interference fit in the hole system ∅40 lam (1.12), (1.16)–(1.18): H7 (+0.025) r 6 (++0.050 0.034) according to the form - Nmin = ei – ES = 34 – 25 = 9 µm; Nmax = es – EI = 50 – 0 = 50 µm; TS/N = Nmax – Nmin = 50 – 9 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct the layout of the tolerance fields of the given landings (Fig. 1.11). 1.1.3. GENERAL AND SPECIAL RULES FOR THE FORMATION OF INTERCHANGEABLE SEATS THEORETICAL PART FOR PRACTICAL LESSON 1.3 GOST 25346 provides for the interchangeability of similar fits of the hole system and the shaft system with the same nominal dimensions. Such landings have the same limiting characteristics due to the use of general and special rules that establish the values of the same basic deviations of the shaft and hole. The general rule establishes the following ratios between the same (i.e., having the same letter designation) main deviations: EI \u003d -es → from A (a) to H (h); (1.22) ES = –ei → from K (k) to ZC (zc). (1.23) In accordance with the general rule, the main deviations of the hole and the shaft of the same name are equal in magnitude and opposite in sign, i.e., they are symmetrical with respect to 30 Metrology, standardization and certification Pic. 1.12 Scheme of the location of the main deviations of the same name of the zero line. A fragment of the layout of the main deviations of the same name is shown in Figure 1.12. The general rule applies to all clearance fits, to transitional fits from grade 9 and coarser, and to interference fits from grade 8 and coarser. A special rule applies to transitional landings up to the 8th grade inclusive and interference landings up to the 7th grade. It allows you to get the same limit gaps and tightness in the same fit, specified in the hole system and in the shaft system, in which the hole of a given quality is connected to the shaft of the nearest more accurate quality. Special rule: the main deviation of the hole is equal to the main deviation of the shaft, taken with the opposite sign, with the addition of the correction ∆: ES = –ei + ∆, (1.24) where ∆ = ITq – ITq–1 is the difference between the tolerances of adjacent qualifications, i.e. the difference between the tolerance of the considered quality (hole) and the tolerance of the nearest more accurate quality (shaft). The second deviation of the tolerance field of the hole or shaft is determined through the basic deviation and tolerance ITn in accordance with the formula for calculating the tolerance. When changing the system, the accuracy (quality) of the hole and the shaft does not change. Chapter 1. Rationing the accuracy of smooth cylindrical joints 31 ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.3 Familiarize yourself with the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.8. Table 1.8 Options for practical exercises 1.3 Variant No. Landing Variant No. Landing Variant No. Landing h5 12 58E9/h8 21 36G7/h6 4 25F9/h8 13 55K7/h6 22 12N9/h9 5 100F7/h6 14 60H7/p6 23 76H11/d10 6 45H7/g6 15 83R6/h5 24 210H6/ t5 7 100H6/m5 16 105H7/f6 25 36H7/g6 8 25H9/f8 17 55H7/k6 26 20Js9/h9 9 130H6/k5 18 27H7/r6 27 28N8/h7 For a given fit, form an interchangeable fit of the same name in another system. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name. Solution. 1. Determine the system of a given fit and assign the fit of the same name to it in another system. 2. Determine the value of the tolerance value, the type and value of the value of the main and second deviations for all tolerance fields forming similar landings (see note to Table B.3). Designate landings in a mixed way. 3. Calculate the limiting characteristics of both landings. 4. Build the layout of landing tolerance fields. 5. Make a conclusion about the interchangeability of landings. 32 Metrology, standardization and certification PRACTICAL EXAMPLES 1.3 Example 1 for the general rule (2nd level of complexity) Task. For a given fit ∅40Н7/f6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name and draw a conclusion. Solution. 1. A fit with a clearance in the hole system is specified, since there is a tolerance field for the main hole. It corresponds to the fit of the same name in the shaft system ∅40F7/h6. 2. Determine the value of the tolerance value, the type and value of the main and second deviations for all tolerance fields that form similar landings. 2.1. Calculate and round up to standard values according to Table B.1 the tolerance values of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 40 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a⋅i = 10 ⋅1.6 = 16 µm; IT7 = a⋅i = 16⋅1.6 = 25 µm. 2.2. Determine the type (upper or lower) and the values of the main deviations of holes with ∅40 (Tables B.2 and B.3 of Appendix B): H → EI = 0; F → EI = +25 µm. 2.3. Since landings with a gap are given, based on the general rule (EI = –es), we find the values of the main shaft deviations of the same name: h → es = 0; f → es = –25 µm. 2.4. Calculate the second deviations of the tolerance fields of the hole and the shaft through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES - EI; Td = es - ei. Chapter 1. Rationing the accuracy of smooth cylindrical joints 33 Calculate the second deviation of the tolerance fields: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; h6 → ei = es – IT6 = 0 – 16 = –16 µm; F7 → ES = EI + IT7 = +25 + 25 = +50 µm; f6 → ei = es – IT6 = –25 – 16 = –41 µm. 2.5. Designate landings in a mixed way: 3. Calculate the limiting characteristics of both landings. 3.1. Calculate the limiting characteristics of fit with a gap in the hole system ∅40 H7 (+0.025) f 6 (−−0.025 0.041): Smax = ES – ei = +25 – (–41) = 66 µm; Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 3.2. Calculate the limiting characteristics of a fit with a clearance in the shaft system ∅40 F7 (++0.050 0.025) h6 (−0.016) : Smax = ES – ei = +50 – (–16) = 66 µm; Smin = EI – es = +25 – 0 = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 4. Build the layout of the tolerance fields of the landings of the same name (Fig. 1.13). 34 Metrology, standardization and certification Pic. 1.13 The layout of the landing tolerance fields: a - in the hole system; b - in the shaft system. Conclusion. The considered examples have shown that the landings of the same name with the same nominal sizes, given in different systems , are interchangeable, since they have the same limiting characteristics. Thus, for landings ∅40Н7/f6 and ∅40F7/h6, the smallest and largest gaps are equal, respectively: Smin = 25 µm; Smax = 66 µm. Example 2 for a special rule (3rd level of complexity) Task. For a given fit ∅50H7/k6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name. Solution. 1. A transitional fit in the hole system is set not coarser than the 8th grade: ∅50H7/k6. It corresponds to the same-name fit in the shaft system ∅50K7/h6 2. Determine the value of the tolerance value, the type and value of the main and second deviations for the tolerance fields that form the same-name fit. 2.1. Calculate the tolerance values of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 50 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a ⋅ i = 10 ⋅ 1.6 = 16 µm; Chapter 1. Rationing the accuracy of smooth cylindrical joints 35 IT7 = a ⋅ i = 16 ⋅ 1.6 = 25 µm. 2.2. Determine the type (upper or lower) and the values of the main deviations of the hole and shaft tolerance fields for landing ∅50H7/k6 (Table B.2, B.3 of Appendix B): H → EI = 0; k → ei = +2 µm. 2.3. Calculate the second deviations of the tolerance fields of the hole and the shaft through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES - EI; Td = es - ei. Calculate the second deviation of the landing tolerance fields ∅50H7/k6: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; k6 → es = ei + IT6 = +2 + 16 = +18 µm. 2.4. To fit in the shaft system ∅50K7/h6, determine the main deviation of the tolerance field of the hole K7 according to a special rule, since the fit is transitional, not coarser than the 8th grade: ∆ = IT7 - IT6 = 25 - 16 = 9 microns; ES = –ei + ∆ = –2 + 9 = +7 µm, where ES is the main deviation of the hole tolerance field K7; ei - the main deviation of the tolerance field of the same name of the shaft k6. 2.5. Calculate the second deviation of the hole tolerance K7: EI = ES – IT7 = +7 – 25 = –18 µm. 2.6. The main deviation of the tolerance field of the main shaft h6 is es = 0. The second deviation is: ei = es – IT6 = 0 – 16 = –16 µm. 36 Metrology, standardization and certification 3. Designate fits in a mixed way: 4. Calculate the limiting characteristics of these fits. 4.1. Calculate the limiting characteristics of the transition fit in the hole system ∅50H7/k6: Smax = Dmax – dmin = ES – ei = 25 – 2 = 23 µm; Nmax = dmax – Dmin = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transition fit in the shaft system ∅50K7/h6: Smax = Dmax – dmin = ES – ei = +7 – (–16) = 23 µm; Nmax = dmax – Dmin = es – EI = 0 – (–18) = 18 µm; ТS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct the layout of the tolerance fields of the landings of the same name (Fig. 1.14). Rice. 1.14 Landing tolerance fields layout: a - ∅50H7/k6; b - ∅50K7/h6. Chapter 1. Rationing the accuracy of smooth cylindrical joints 37 Conclusion. The considered examples have shown that similar landings with equal nominal sizes, given in different systems, are interchangeable, since they have the same limiting characteristics. Thus, for landings ∅50H7/k6 and ∅50K7/h6, the largest gap and the largest interference, respectively, are equal to Smax = 23 µm; Nmax = 18 µm. 1.1.4. ASSIGNING LANDINGS BY THE METHOD OF SIMILARITY THEORETICAL PART TO PRACTICAL LESSON 1.4 Method of precedents (analogues) The method lies in the fact that the designer, designing new components and mechanisms, assigns the same landings in them that were used in the same type of previously designed and in operation product, . The similarity method It is a development of the precedent method and is based on the classification of machine parts according to their design and operational characteristics and the release of reference books with examples of the use of landings (Appendix B.6). The disadvantage of this method is a qualitative rather than quantitative description of operational features and the difficulty of their identification with the features of a newly designed structure. Recommendations for the appointment of landings by the similarity method Appointment of landings with a gap. Landings are characterized by a guaranteed minimum clearance Smin, necessary to place lubricant between mating surfaces in movable joints, to compensate for temperature deformations, shape and location errors in order to ensure the assembly of the product. The main requirements for landings with a gap: working temperature should not exceed 50°С; 38 Metrology, standardization and certification the ratio of the length of the conjugation to the diameter should not exceed the ratio l:d ≤ 1:2; the coefficients of linear expansion of the hole and the shaft must be close to each other; the value of the guaranteed gap should be the greater, the greater the angular velocity of rotation. Assignment of landings with an interference fit. Landings are intended for fixed one-piece connections without additional fastening with screws, pins, etc. Relative immobility is achieved due to stresses arising in the material of mating parts. The main methods of assembling parts with an interference fit are: longitudinal pressing - assembly under pressure due to axial force at normal temperature; transverse pressing - assembly with preliminary heating of the female part or cooling of the covered part to a certain temperature. Assignment of transitional landings. Transition fits are designed for fixed, but detachable connections of parts, provide good centering and are used with additional fastening. These landings differ from each other in the probability of obtaining gaps or interference (Table 1.9). T a b l e 1.9 Probability of getting gaps or tightness in transitional fit Designation of fit Name of fit Probability of gaps Probability of tightness H7/n6 blind 1% 99% H7/m6 tight 20% 80% H7/k6 tense 60% 40% H7/ js6 dense 99% 1% PROCEDURE FOR PRACTICAL LESSON 1.4 (3rd LEVEL OF Difficulty) Read the theoretical part of the section. Get a task (option) of practical work. Options are specified in Appendix A (A.1–A.12) for size D1 or D2. Chapter 1. Rationing the accuracy of smooth cylindrical joints 39 Task. Determine the fit for a given connection (options A.1–A.12); taking into account the requirements for it, calculate the limiting characteristics and landing tolerance, build a layout of the landing tolerance fields, record the landing in a mixed way. The task is presented in the form of a map of the initial data. Solution. 1. Determine which group the landing belongs to (according to the description of the nature of the connection and its purpose): with a gap, with an interference fit, or transitional. 2. Determine the fit system based on the joint design analysis. 3. Select the type of mating (combination of the main deviations of the hole and shaft tolerance fields) according to Table B.6. 4. Determine the fit accuracy: the degree of accuracy, taking into account the preference for the use of fits and tolerance fields according to tables B.4 and B.5. 5. Determine limit deviations and tolerances according to tables B.1–B.3. 6. Calculate limit characteristics and fit tolerance. 7. Build a layout of the fit tolerance fields and record the fit in a mixed way. EXAMPLE OF PERFORMING A PRACTICAL LESSON 1.4 Initial data map Name of initial data Value of initial data Nominal connection size and its value D = 65 mm Name of parts included in the connection Helical gear 4 and spindle 6 Requirements for the operation of the connection (from the description to the drawing) wheel 4 in D2 is well centered relative to the spindle axis and has two diametrically spaced feather keys Solution. 1. Determine the landing group. A fixed connection with additional fastening with two dowels is specified, in which it is required to ensure precise centering. These conditions correspond to the transition landing (Table B.6). 2. Assign a landing system. The connection includes a helical gear and a spindle. Since the shaft is connected to one hole along this diameter, and the inner surfaces are more difficult to machine, we choose the preferred CH hole system. Thus, we assign the tolerance field of the main hole H to the hole of the helical gear. 3. Select the type of conjugation. Using the similarity method, we assign the following type of fit H / js (Table B.6). For this species, gaps are more likely than tightness. It provides easy assembly and disassembly, precise centering and is used for interchangeable parts that require additional fastening in exact qualifications: shafts from 4th to 7th, and holes from 5th to 8th. 4. Determine the fit accuracy. Analyzing the design and operating conditions of this connection, we assign the landing H7 / js6. This fit is used in the following connections: bearing cups of the 4th, 5th accuracy classes in housings, gears connected to the shaft with two keys, tailstock quill of a lathe (Table B.6). 5. Determine the limit deviations and tolerances of the hole and shaft. According to table B.1, find the tolerances of the 6th and 7th grades in the size range from 50 to 80: IT6 = 19 microns; IT7 = 30 µm. The upper deviation for ∅65Н7 is equal to the tolerance, i.e. 30 µm. Shaft ∅65js6 has a symmetrical tolerance field, i.e. ±9.5 µm. 6. Calculate the limit characteristics and fit tolerance ∅65 H7(+0.030) . js6(±0.0095) Limit hole dimensions: Dmax = D + ES = 65 + 0.030 = 65.030 mm; Chapter 1. Rationing the accuracy of smooth cylindrical joints 41 Dmin \u003d D + EI \u003d 65 + 0 \u003d 65 mm. Maximum shaft dimensions: dmax = d + es = 65 + 0.0095 = 65.0095 mm; dmin \u003d d + ei \u003d 65 + (-0.0095) \u003d 64.9905 mm. Maximum interference: Nmax = dmax - Dmin = 65.0095 - 65 = 0.0095 mm. Maximum clearance: Smax = Dmax - dmin = 65.030 - 64.9905 = 0.0395 mm. Average probable gap: Sm = (Smax - Nmax) / 2 = (0.0395 - 0.0095) / 2 = 0.015 mm. Fit tolerance: TS/N = Smax + Nmax = 0.0095 + 0.0395 = 0.049 mm or TS/N = TD + Td = 0.030 + 0.019 = 0.049 mm. 7. Build a layout of landing tolerance fields (Fig. 1.15). Rice. 1.15 Location of landing tolerance fields 42 Metrology, standardization and certification 1.1.5. LANDING ASSIGNMENT BY THE CALCULATION METHOD THEORETICAL PART TO PRACTICAL LESSON 1.5 The calculation method is the most reasonable method of landing assignment. It is based on engineering calculations of joints for strength, stiffness, etc. However, the formulas do not always fully take into account the complex nature of the physical phenomena occurring in conjugation. The disadvantage of this method is the need to test prototypes before launching a new product into mass production and adjust the fit in the developed product. The calculation method is used when, according to the operating conditions of the mechanism, the limit values of gaps or interferences are limited, , for example, for plain bearings, critical press joints, etc. For example, when calculating a fit with a gap of the form H / h, used as a centering first of all, the maximum permissible eccentricity or thermal deformation of parts, if the operating temperature differs significantly from normal. When calculating transitional fits (mainly test fits), the probability of obtaining gaps and interferences in the joint, the largest gap according to the known maximum allowable eccentricity of the parts to be joined, or the greatest assembly force with the greatest fit interference are determined, and for thin-walled bushings, a strength calculation is performed. In interference fit, the minimum allowable interference is calculated based on the largest possible forces acting on the interface, and the maximum interference is calculated from the strength condition of the parts. After calculating the limiting characteristics, it is necessary to select a standard fit with limiting characteristics close to the calculated ones. Chapter 1. Rationing the accuracy of smooth cylindrical joints 43 The selection of a standard fit is carried out in the following sequence. 1. According to the results of the analysis of the design of the node, the landing system is determined. In most cases, landings are assigned in the hole system as the preferred one. Typical cases of assigning landings in the shaft system - see clause 1.1.4. 2. The landing tolerance is calculated with a gap, with an interference fit or a transitional fit according to the specified characteristics: Tpos = TS = Smax - Smin; (1.25) Tpos = TN = Nmax – Nmin; (1.26) Tpos = TS/N = Smax + Nmax. (1.27) 3. To determine the standard landing tolerance, it is necessary to determine the relative landing accuracy apos (number of landing tolerance units), based on formulas (1.7) and (1.12): Tpos = TD + Td = aD ⋅ i + ad ⋅ i = i ⋅ (аD + ad), (1.28) where aD + ad = apos, i.e. the sum of the numbers of tolerance units of the hole and the shaft is equal to the number of landing tolerance units; i = ipos - landing tolerance unit, the value of which depends on the nominal size of the landing (Table B.1). It follows from here that apos = Tpos/i. (1.29) 4. According to the known number of landing tolerance units, the numbers of qualifications for the hole and the shaft are determined in accordance with the second sign of the main fit: the numbers of the hole and shaft qualifications are the same or differ by one (rarely by two). Thus, aD = ad = apos/2. Then, according to Table B.1, the nearest to the calculated standard value of the number of tolerance units of the hole and the shaft is determined, according to which the qualification number is determined. 5. If the value of the number of tolerance units falls between two standard values, qualifications corresponding to these standard values are assigned to the hole and shaft (coarer - to the hole, more than 44 Metrology, standardization and certification accurate - to the shaft), while the sum is aD + ad should be close to the calculated value apos, for example apos = 35, then with aD = ad = 35/2 = 17.5 - the accuracy of the hole and shaft corresponds to ≈ IT7 (a = 16). 6. Landing can be combined according to qualifications if there is a mounting on the same diameter of the rolling bearing shaft. In this case, it is necessary to limit the accuracy of the shaft. For example, IT6 (ad = 10), then aD = 35 - 10 = 25, which corresponds to the accuracy of the hole IT8. 7. Tolerance fields for the hole and shaft are assigned depending on the selected fit system (СH or Сh) of the hole and shaft tolerances (Table B.1) and the value of one of the limiting characteristics of the fit, which is used to calculate the main deviation of the tolerance field of the non-main part ( shaft or hole) in the following sequence: first, determine the tolerances of the hole and shaft according to table B.1 and the second deviations of the main parts according to formulas (1.8) and (1.10) of practice 1.1: ES = EI + ITn (from A to H); ei = es – ITn (from a to h); for landings with a gap, with an interference fit and a transitional one, specified in the hole system, the main deviations are calculated respectively according to the following formulas: es = EI - Smin; (1. 30) ei = ES + Nmin; (1.31) ei = ES – Smax; (1.32) for landings with a gap, with an interference fit and transitional, given in the shaft system, the main deviations are calculated respectively by the following formulas: EI = es + Smin; (1.33) ES = ei – Nmin; (1.34) ES = ei + Smax. (1.35) Chapter 1. Rationing the accuracy of smooth cylindrical joints 45 Based on the calculated values of the main deviations of the shaft or hole in Tables B.2 and B.3, the nearest standard values are selected. 8. Then the second limit deviations of the non-main shaft or hole are determined according to the formulas (1.8) - (1.10) of practical lesson 1.1, depending on the group of landings. ORDER OF PERFORMANCE OF PRACTICAL LESSON 1.5 (3rd LEVEL OF COMPLEXITY) Familiarize yourself with the theoretical part of the section. Get a task (option) of practical work. Variants are specified in Appendix A (A.1–A.12) in size D3. Exercise. To select, according to the given limiting characteristics, a standard fit for a given connection by the calculation method. Calculate the limiting characteristics and tolerance of a standard fit, build a layout of the fit tolerance fields and record the fit in a mixed way. The task is presented in the form of a map of the initial data. Solution. 1. Determine which group the landing belongs to (according to the description of the nature of the connection and its purpose): with a gap, with an interference fit, or transitional. 2. Determine the fit system by analyzing the connection design. 3. Determine the fit accuracy. 3.1. Calculate the landing tolerance depending on its group according to the formula (1.26), or (1.27), or (1.28). 3.2. Determine the relative landing accuracy (number of landing tolerance units apos). Calculate by formula (1.29) the number of landing tolerance units. 3.3. According to table B.1, determine the qualities of the shaft and hole. When assigning qualifications to a hole and a shaft, it is necessary to strive to ensure the fulfillment of the second sign of the main fit, i.e., assign the same qualifications to the shaft and hole or with a difference in qualification numbers equal to one. 46 Metrology, standardization and certification 3.4. Find the hole and shaft tolerances according to Table B.1. 4. Determine the main and second deviations of the hole and shaft. 4.1. The selected fit determines the main part (main hole for CH and main shaft for Ch). The main part will have a main deviation equal to 0, and the second is determined depending on the type of main deviation (ES or ei) and tolerance. 4.2. Determine the position of the tolerance field of another (not the main) part using the formulas (1.30) - (1.32) or (1.33) - (1. 35) depending on the group of landings through the known values of Smin; Smax or Nmin; Nmax and taking into account the accepted deviations of the main part. 4.3. Select the standard main and second deviations of the tolerance fields of the hole and shaft (Table B.2 or B.3). Record tolerance fields in mixed form. 5. Calculate the limit characteristics and landing tolerance according to the formulas of the practical lesson 1.2. 6. Build a layout of landing tolerance fields. 7. Determine the error in the selection of fit according to the fit tolerance and limiting characteristics. The allowable error of selection according to the landing characteristics can be ± 10%. The formula for determining the error (∆Tpos) is: ∆Tpos Tset − Tst ⋅ 100% ≤ ±10% , Tset where ∆Tpos is the error in selecting the fit according to the fit tolerance, i.e. the relative value of the difference between the assigned standard tolerance field and the specified one; Tzad - specified landing tolerance; Tst - tolerance of the selected standard fit. Check the correctness of the fit selection by comparing the standard values of the limiting gaps (interferences) with the given ones: for landings with a gap Smax st ≤ Smax; Smin st ≈ Smin; for landings with interference Nmax st ≈ Nmax; Nmin st ≥ Nmin. Chapter 1. Rationing the accuracy of smooth cylindrical joints 47 EXAMPLE OF PERFORMING A PRACTICAL EXERCISE 1.5 Chart of initial data to Figure A.12 Name of initial data Value of initial data Nominal connection size and its value Name of parts included in the connection D = 36 mm Cutter 11 and spindle 6 Specified landing characteristics for the calculation method of landing assignment, µm: Smax= Smin= Requirements for the operation of the connection (from the description to the drawing) 42 2 Milling cutters 11 are installed at both ends of the spindle, periodically removed for sharpening or readjusting the machine Solution. 1. Determine the landing group. It is necessary to assign a standard fit with characteristics close to the specified ones. Limit clearances are set, therefore a clearance fit must be assigned. 2. Determine the landing system. Milling cutters 11 are installed at both ends of the spindle, periodically removed for sharpening or readjusting the machine. Also, along the diameter D, at the same end of the spindle, an adjusting washer and a protective ring for landings of a different nature are installed. Thus, we assign the shaft system Ch (Table B.6). 3. Determine the fit accuracy. 3.1. Calculate fit tolerance: TS = Smax - Smin = 42 - 2 = 40 µm. 3.2. Determine the relative fit accuracy (number of fit tolerance units aS). According to the nominal size, we find the unit of tolerance (tab. B.1) - i = 1.6 µm. Calculate the number of landing tolerance units: aS = TS 40 = ≈ 25. i 1.6 48 Metrology, standardization and certification 3.3. Determine the qualities of the shaft and hole. Based on the fact that aS = aD + ad and in accordance with the principle of basic fit on the equality of the accuracy of the hole and the shaft (the hole and shaft qualification numbers are the same or differ by one), we take aD = 16, ad = 10. This corresponds to the 7th quality for the hole and 6th for the shaft. 3.4. Find bore and shaft tolerances. According to Table B.1, we determine the hole tolerance TD = IT7 = 25 µm and the shaft tolerance Td = IT6 = 16 µm. 4. Determine the main and second deviations of the hole and shaft. 4.1. Since the fit is assigned in the shaft system, then on the shaft we assign the tolerance field of the main shaft h6 with the main deviation es = 0. 4.2. The second deviation of the shaft is determined taking into account the tolerance of the 6th grade according to Table B.2: ei = es – IT6 = 0 – 16 = –16 µm. Let's write the shaft tolerance field in a mixed way: 4.3. Determine the main deviation of the hole. Since a fit with a gap in the shaft system is assigned, the main deviation of the tolerance field of the hole will be the lower limit deviation, which is determined by the specified minimum gap: EI = Smin + es = 2 + 0 = +2 µm. 4.4. According to GOST 25346-89 (Table B.3), we select the standard hole tolerance field. There is no standard tolerance field for a hole with a basic deviation of EI = +2 µm. The closest to this location will be the tolerance field of the main hole H7 with a basic deviation EI = 0 µm. 4.5. The second deviation of the hole tolerance field is calculated depending on the tolerance of the 7th grade: ES = EI + IT7 = 0 + 25 = +25 microns. Chapter 1. Rationing the accuracy of smooth cylindrical joints 49 Let's write the hole tolerance field in a mixed way: ∅36Н7 (+0.025). Thus, we assign a fit to the “cutter-spindle” connection: ∅36 H7 (+0.025) . h6 (−0.016) The fit is combined by systems, since the hole is specified in the hole system, and the shaft is in the shaft system. 5. Calculate the limit characteristics and fit tolerance. The calculation of the characteristics consists in determining the maximum dimensions of the hole and the shaft and determining the values of the maximum clearances and fit tolerance. Limit hole dimensions: Dmax = D + ES = 36 + 0.025 = 36.025 mm; Dmin = D + EI = 36 + 0 = 36 mm. Maximum shaft dimensions: dmax = d + es = 36 + 0 = 36 mm; dmin \u003d d + ei \u003d 36 + (-0.016) \u003d 35.984 mm. Minimum clearance: Smin = Dmin - dmax = 36 - 36 = 0 mm. Maximum clearance: Smax = Dmax - dmin = 36.025 - 35.984 = 0.041 mm. Average probable clearance: Sm = (Smax + Smin)/2 = (0.041 + 0)/2 = 0.0205 mm. Fit tolerance: TS = Smax - Smin = 0.041 - 0 = 0.041 mm = 41 µm; TS = TD + Td = 25 + 16 = 41 µm = 0.041 mm. 50 Metrology, standardization and certification 6. Build a diagram of the location of the tolerance fields of the assigned fit (Fig. 1.16). 7. Checking the correctness of the calculation and selection of landing. Determine the error ∆Тpos of the fit selection according to the tolerance: ∆Tpos = Тset − Тst ⋅ 100%; Тzad ∆Tpos = 40 − 41 ⋅ 100% = 2.5%< 10%. 40 Проверить правильность подбора посадки сравнением стандартных значений предельных зазоров (натягов) с заданными: Smaх ст = 41 ≤ Smax = 42; Smin ст = 0 ≈ Smin = 2. Следовательно, посадка назначена верно. Рис. 1.16 Схема расположения полей допусков вала и отверстия посадки Глава 1. Нормирование точности гладких цилиндрических соединений 51 1.2. ДОПУСКИ РАЗМЕРОВ, ВХОДЯЩИХ В РАЗМЕРНУЮ ЦЕПЬ 1.2.1. ОСНОВНЫЕ ПОНЯТИЯ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКОМУ ЗАНЯТИЮ 1.6 Размерная цепь - совокупность геометрических размеров (звеньев), расположенных по замкнутому контуру и определяющих взаимные положения и точность элементов деталей при изготовлении, измерении и сборке. По области применения размерные цепи можно разделить на конструкторские (сборочные), технологические (операционные, детальные) и измерительные. Звено размерной цепи - один из размеров, образующих размерную цепь. Звенья размерной цепи обозначаются заглавной буквой русского алфавита с числовым индексом, определяющим порядковый номер звена в цепи. Размерная цепь состоит из составляющих звеньев и одного замыкающего звена. Простейшей размерной цепью будет соединение вала с отверстием (рис. 1.17а). Эта размерная цепь содержит наименьшее число размеров (три), которые расположены параллельно и получены в результате обработки вала и втулки: диаметр вала d (А2), диаметр отверстия втулки D (А1). В результате сборки этих деталей получается замыкающее звено - зазор S (А∆), если размер отверстия будет больше размера вала до сборки, или натяг N (А∆), если размер вала будет больше размера отверстия до сборки. Простейшая технологическая размерная цепь двухступенчатого валика (рис. 1.17б) состоит из габаритного размера А1, ступени вала А2 и замыкающего звена, оставшейся части вала А∆, которая получается за счет обтачивания меньшего диаметра на длину А2. Схема размерной цепи - графическое изображение размерной цепи. Замыкающее звено - звено, получаемое в размерной цепи последним в результате решения поставленной задачи, 52 Метрология, стандартизация и сертификация Рис. 1.17 Виды размерных цепей: а - конструкторская (сборочная); б - технологическая (операционная). в том числе при изготовлении, сборке и измерении. В размерной цепи должно быть только одно замыкающее звено, которое получается последним в результате сборки, обработки или измерения (размер контролируемой детали). Составляющее звено - звено размерной цепи, изменение которого вызывает изменение замыкающего звена. Все составляющие звенья по характеру влияния на замыкающее звено делятся на увеличивающие и уменьшающие. Увеличивающие звенья - звенья, при увеличении которых замыкающее звено увеличивается. Уменьшающие - звенья, при увеличении которых замыкающее звено уменьшается. На рисунке 1.18 представлена схема размерной цепи, в которой звенья А1–А6 - составляющие звенья, А∆ - замыкающее звено. Для определения характера составляющего звена используют правило обхода по контуру размерной цепи. Для этого предварительно выбирают направление обхода размерной цепи (может быть любое). Оно совпадает с направлением левонаправленной стрелки (←), проставленной над замыкающим звеном. Обходя цепь в этом направлении, над Глава 1. Нормирование точности гладких цилиндрических соединений 53 составляющими звеньями расставляют стрелки в направлении обхода. Увеличивающие звенья обозначаются стрелкой над буквой, направленной вправо а уменьшающие - стрелкой, направленной влево Правило. Все составляющие звенья, имеющие такое же направление стрелок, которое имеет стрелка над замыкающим звеном, являются уменьшающими звеньями, а звенья, имеющие противоположное направление, - увеличивающими . По взаимному расположению размеров цепи делятся на плоские (звенья цепи расположены произвольно в одной или нескольких произвольных параллельных плоскостях) и пространственные (звенья цепи расположены произвольно в пространстве). В зависимости от вида звеньев цепи делятся на линейные (звенья цепи - линейные размеры, расположенные на параллельных прямых) и угловые (звенья цепи представляют собой угловые размеры, отклонения которых могут быть заданы в линейных величинах, отнесенных к условной длине, или в градусах). По месту в изделии цепи делятся на детальные (определяют точность относительного положения поверхностей или осей одной детали) и сборочные (определяют точность относительного положения поверхностей или осей деталей, образующих сборочную единицу). По характеру звеньев цепи делятся на скалярные (все звенья - скалярные величины), векторные (все Рис. 1.18 Схема размерной цепи 54 Метрология, стандартизация и сертификация звенья - векторные погрешности) и комбинированные (часть звеньев - векторные погрешности, остальные - скалярные величины). Перед тем как построить размерную цепь, следует выявить замыкающее звено. Для этого по чертежам общих видов и сборочных единиц выявляются и фиксируются все требования к точности, которым должно удовлетворять изделие или сборочная единица, например: точность взаимного расположения деталей, обеспечивающая качественную работу изделия при эксплуатации (перпендикулярность оси шпинделя станка к рабочей плоскости стола); точность взаимного расположения деталей, обеспечивающая собираемость изделия , . При выявлении замыкающих звеньев их номинальные размеры и допускаемые отклонения устанавливаются по стандартам, техническим условиям, на основании опыта эксплуатации аналогичных изделий, а также путем теоретических расчетов и специально поставленных экспериментов. Для нахождения составляющих звеньев после определения замыкающего звена следует идти от поверхностей (осей) деталей, образующих замыкающее звено, к основным базам (осям) этих деталей, от них - к основным базам деталей, образующих первые детали, и т. д. до образования замкнутого контура. В число составляющих звеньев необходимо включать размеры деталей, непосредственно влияющих на замыкающее звено, и стремиться к тому, чтобы от каждой детали в линейную цепь входил только один размер. Каждая размерная цепь должна состоять из возможно меньшего числа звеньев (принцип «кратчайшей» размерной цепи). 1.2.2. МЕТОДЫ РЕШЕНИЯ РАЗМЕРНЫХ ЦЕПЕЙ При решении размерных цепей могут быть использованы два метода расчета: метод расчета размерной цепи на max-min; вероятностный метод расчета. Глава 1. Нормирование точности гладких цилиндрических соединений 55 Метод расчета размерной цепи на max-min - метод расчета размерной цепи, при котором требуемая точность замыкающего звена размерной цепи получается при любом сочетании размеров составляющих звеньев. При этом предполагают, что в размерной цепи одновременно могут оказаться все звенья с предельными значениями, причем в любом из двух наиболее неблагоприятных сочетаний (все увеличивающие звенья имеют наибольшее предельное значение, а все уменьшающие звенья - наименьшее предельное значение или наоборот). В результате размер замыкающего звена будет максимальным или минимальным. Преимущества такого метода заключаются в простоте, наглядности, небольшой трудоемкости вычислительных работ, полной гарантии от брака из-за неточности замыкающего звена. Недостатком является то, что полученные по этому методу результаты часто не соответствуют фактическим. Метод экономически целесообразен лишь для цепей малой точности или для точных цепей с небольшим числом составляющих звеньев. Вероятностный метод расчета - метод расчета размерной цепи, учитывающий явление рассеяния и вероятность различных сочетаний отклонений составляющих звеньев. Этот метод допускает малый процент изделий, у которых замыкающее звено выйдет за рамки поля допуска. При этом расширяются допуски составляющих цепь размеров и тем самым снижается себестоимость изготовления деталей. В данном практическом занятии используется только метод расчета размерной цепи на max-min, а вероятностный метод расчета рассматривается в спецкурсах. Уравнения размерных цепей устанавливают взаимосвязь между параметрами замыкающего звена и составляющих звеньев. Для конструкторских (сборочных) линейных скалярных цепей передаточное отношение принимается для увеличивающих звеньев ξ = +1, для уменьшающих звеньев - ξ = –1. Тогда уравнения размерных цепей при расчете на max-min можно представить в следующем виде. 56 Метрология, стандартизация и сертификация 1. Уравнение номиналов. По определению размерной цепи следует, что сумма всех номинальных размеров, включая и замыкающее звено, равна нулю: Исходя из этого равенства, можно найти номинальный размер замыкающего звена: где ξ = ±1 - передаточное отношение; ρ - число составляющих звеньев. Или с учетом характера звена (передаточного отношения) получим уравнение номиналов для расчета размерной цепи на max-min (номинал замыкающего звена равен разности суммы номиналов увеличивающих звеньев и суммы номиналов уменьшающих звеньев): (1.36) где n - число увеличивающих звеньев; k - число уменьшающих звеньев. 2. Уравнение допусков. Допуск замыкающего звена (или поле рассеяния размера замыкающего звена) равен сумме допусков составляющих звеньев: (1.37) где p = n + k - число составляющих звеньев; 3. Уравнения предельных отклонений: верхнее отклонение замыкающего звена равно разности суммы верхних отклонений увеличивающих звеньев и суммы нижних отклонений уменьшающих звеньев: (1.38) Глава 1. Нормирование точности гладких цилиндрических соединений 57 нижнее отклонение замыкающего звена равно разности суммы нижних отклонений увеличивающих звеньев и суммы верхних отклонений уменьшающих звеньев: (1.39) При расчете конструкторских размерных цепей обычно решаются две задачи: прямая и обратная. Прямая задача заключается в том, что по предельным размерам и допуску замыкающего звена определяются допуски и предельные отклонения составляющих звеньев. Это основная задача, решаемая при проектировании. Дано: А∆; Т∆; ЕS∆; EI∆ (параметры замыкающего звена). Найти: Аj; Тj; ЕSj; EIj (параметры составляющих звеньев). Обратная задача заключается в том, что по размерам, предельным отклонениям и допускам составляющих звеньев определяется размер, допуск и предельные отклонения замыкающего звена. Эта задача используется при проверочных расчетах. Дано: Аj; Тj; ЕSj; EIj (параметры составляющих звеньев) Найти: А∆; Т∆; ЕS∆; EI∆ (параметры замыкающего звена). Нахождение точности составляющих звеньев при решении прямой задачи может осуществляться двумя способами: 1. Способ равных допусков. Этот способ применим в случае, когда все размеры цепи входят в один интервал размеров. Тогда допуски составляющих звеньев будут равны среднему допуску Тm: ТА1 = ТА2 = ... = ТАp = Тm. Средний допуск определяется по формуле (1.40) 58 Метрология, стандартизация и сертификация 2. Способ одного квалитета. Все размеры могут быть выполнены по какому-либо одному квалитету (или двум ближайшим квалитетам), который определяется нахождением среднего числа единиц допуска аm (средней относительной точности). Величины допусков при этом будут определены в зависимости от номинального размера (табл. Б.1). Известно, что допуск есть произведение единицы допуска на число единиц допуска. Это справедливо для любого звена размерной цепи: Tj = ijaj, где ij - единица допуска для каждого звена, мкм; aj - число единиц допуска каждого звена. Следовательно, уравнение допусков размерной цепи можно представить в следующем виде при условии, что число единиц допуска a у всех звеньев одинаковое (т. е. точность звеньев одинаковая): Так как допуски составляющих звеньев неизвестны, на основании уравнения размерных цепей (1.37) сумму допусков составляющих звеньев заменим допуском замыкающего звена, который задан по условию задачи. Определим среднее число единиц допуска размерной цепи - аm: (1.41) Если в размерную цепь включены стандартные звенья (ширина подшипника), необходимо из допуска замыкающего звена исключить сумму допусков стандартных звеньев, так как допуск этих звеньев уже известен и изменять его нельзя. В этом случае число единиц допуска определяется только для нестандартных звеньев - аmнест: Глава 1. Нормирование точности гладких цилиндрических соединений 59 (1.42) где t - число стандартных звеньев; p - число всех составляющих звеньев; (ρ − t) - число нестандартных звеньев; Tjст - допуск стандартного звена; ijнест - единица допуска нестандартного звена. Для определения полей допусков на размеры составляющих звеньев, кроме квалитета, необходимо назначить основные отклонения в зависимости от вида размеров: для охватываемых - h, охватывающих - H, остальных - js. Например, на рисунке 1.17а размер - охватывающий, размер - охватываемый; на рисунке 1.17б размер - охватывающий, относится к группе остальных размеров, т. е. не относится ни к охватываемым, ни к охватывающим. ПОРЯДОК ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 1.6 (РАСЧЕТ РАЗМЕРНОЙ ЦЕПИ НА MAX-MIN) (3-Й УРОВЕНЬ СЛОЖНОСТИ) Задание. По предельным размерам и допуску замыкающего звена определить допуски и предельные отклонения составляющих звеньев. Выполнить проверку, решив обратную задачу. Даны предельные размеры замыкающего звена и номинальные размеры составляющих звеньев. Варианты заданий указаны в Приложении А.13. 1. Решить прямую задачу. 1.1. Представить схему размерной цепи и указать, какие звенья охватываемые, а какие охватывающие. 1.2. Определить номинальный размер, предельные отклонения и допуск замыкающего звена. 1.3. Определить номинальный размер (номинал) замыкающего звена по уравнению номиналов размерной цепи (1.36). 60 Метрология, стандартизация и сертификация 1.4. Определить предельные отклонения через предельные размеры и номинал замыкающего звена. 1.5. Рассчитать допуск замыкающего звена по предельным размерам или предельным отклонениям. 1.6. Определить характер составляющих звеньев (увеличивающие или уменьшающие звенья). 1.7. Определить точность составляющих звеньев, используя способ равных квалитетов (формулы 1.41 и 1.42). Назначить одинаковый квалитет на все звенья. 1.8. Определить вид и значения (табл. Б.1) основных отклонений полей допусков составляющих звеньев в зависимости от вида размера (для охватываемых - h; охватывающих - H; остальных - js). 2. Решить обратную задачу. 2.1. Выполнить проверку по уравнению допусков (1.37). При большой разнице между полем рассеяния и допуском замыкающего звена выполнить согласование по квалитетам (изменить квалитет у одного звена). 2.2. Выполнить проверку по предельным отклонениям (1.38), (1.39). Для корректировки расположения поля рассеяния замыкающего звена выбрать самое простое по конструкции согласующее звено. Рассчитать новые предельные отклонения согласующего звена, подставив в левую часть Т а б л и ц а 1.10 Номинальный размер звена, мм Значение единицы допуска ij, мкм Обозначение размеров размерной цепи, Аj Расчет размерной цепи методом на «максимум - минимум» после назначения полей допусков по расчетному значению аm 55 1,9 55Js10(±0,06) 55Js10(±0,06) 3 0,6 3h10(–0,04) 3h10(–0,04) 22 1,3 22h10(–0,084) 22h11(–0,13) 22h11(–0,13) 32 1,6 32h10(–0,10) 32h10(–0,10) 32h10(–0,10) ω∆ = 0,344 ω∆ = 0,39 ω∆ = 0,4 Т∆ 0,4 A∆ 2–0,4 - Принятые значения звеньев размерной цепи ω∆ < T∆ после согласования значений допусков после согласования предельных отклонений 55Js10(±0,06) 2–0,4 Глава 1. Нормирование точности гладких цилиндрических соединений 61 уравнений требуемые значения предельных отклонений замыкающего звена. 2.3. Представить результаты расчета размерных цепей в виде таблицы (табл. 1.10). ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 1.6 (РАСЧЕТ РАЗМЕРНОЙ ЦЕПИ НА MAX-MIN) Задание. Необходимо обеспечить собираемость деталей с валом (Приложение А.13, табл. А.25, рис. А.13; вариант 13-1). Исходные данные: 1) предельные размеры замыкающего звена (зазор между торцами вала 13 и зубчатого колеса 3): А∆min = 1,6 мм; A∆max = 2,0 мм; 2) номинальные размеры составляющих звеньев: длина ступени вала 13 - А1 = 53 мм; буртик втулки 7 - А2 = 3 мм; длина втулки 7 - А3 = 22 мм; длина (высота) зубчатого колеса 3 - А4 = 32 мм. Решение. 1. Решить прямую задачу. 1.1. На рисунке 1.19 представлена схема размерной цепи, в которую включены размеры, влияющие на замыкающее звено, по одному от каждой детали. Размеры А2, А3, А4 - охватываемые; размер А1 не относится ни к охватываемым, ни к охватывающим (группа остальных размеров). Рис. 1.19 Схема размерной цепи 62 Метрология, стандартизация и сертификация Для обеспечения полной взаимозаменяемости сборки решение следует вести методом расчета на max-min, так как цепь невысокой точности. 1.2. Определить номинальный размер, предельные отклонения и допуск замыкающего звена. 1.3. Определить номинальный размер замыкающего звена: А∆ = (32 + 22 + 3) – 55 = 2 мм. 1.4. Определить предельные отклонения замыкающего звена через его предельные размеры и номинал: ES∆ = A∆max – А∆ = 2 – 2 = 0; EI∆ = А∆min – A∆ = 1,6 – 2 = –0,4 мм. 1.5. Определить допуск замыкающего звена: Т∆ = A∆max – А∆min = 2 – 1,6 = 0,4 мм = 400 мкм. Записать номинал и предельные отклонения замыкающего звена в виде исполнительного размера: А∆ = 2–0,4 (нулевое отклонение не обозначается). 1.6. Определить характер составляющих звеньев. Для этого обходим цепь слева направо в соответствии с левонаправленной стрелкой, указанной над замыкающим звеном. Расставляем стрелки над составляющими звеньями в направлении обхода. В соответствии с правилом обхода по контуру размерной цепи определяем характер составляющих звеньев: звено - уменьшающее; звенья - увеличивающие. 1.7. Определить точность составляющих звеньев. Так как номинальные размеры составляющих звеньев относятся к разным интервалам размеров, для определения точности составляющих звеньев используем способ одного квалитета, т. е. рассчитаем среднее число единиц допуска с учетом отсутствия в цепи стандартных звеньев по формуле (1.41): Глава 1. Нормирование точности гладких цилиндрических соединений 63 Ближайшее к рассчитанному значению аm = 74 стандартное число единиц допуска равно аm = 64, что соответствует 10-му квалитету. Поэтому принимаем для всех звеньев 10-й квалитет. 1.8. Определить вид и значения основных отклонений полей допусков составляющих звеньев в зависимости от вида размера (для охватываемых - h; охватывающих - H; остальных - js). Так как звено А1 относится к третьей группе размеров, назначим на него поле допуска js10, а для звеньев А2, А3, А4 (как на охватываемые) поле допуска h10. Составляющие звенья будут иметь следующие размеры: 2. Решить обратную задачу 2.1. Выполним проверку по допускам. Рассчитаем поле рассеяния замыкающего звена: ω∆ = 120 + 40 + 84 + 100 = 344 = 0,344 < 0,4 на 0,056 мм. Так как разница между полем рассеяния ω∆ = 0,344 мм и заданным допуском замыкающего звена T∆ = 0,4 мм получилась слишком большая, изменим 10-й квалитет звена А3 на 11-й квалитет. Тогда Это позволяет расширить поле рассеяния замыкающего звена на следующую величину: IT11 – IT10 = 0,130 – 0,084 = 0,046 мм, т. е. поле рассеяния при этом будет равно ω∆ = 0,39 мм. Примечание. Звено А3 выбрано потому, что разница между допусками 10-го и 11-го квалитетов для номинального размера этого звена наиболее близко приближает поле 64 Метрология, стандартизация и сертификация рассеяния замыкающего звена к полю допуска замыкающего звена. 2.2. Выполним проверку по предельным отклонениям: ES∆ = – [–0,060] = +0,060 мм; EI∆ = [(–0,040) + (–0,13) + (–0,10)] – [(+0,06)] = –0,33 мм. Следовательно, поле рассеяния замыкающего звена по предельным отклонениям равно: ω∆ = ES∆ – EI∆ = 0,06 – (–0,33) = 0,39 мм. Это совпадает со значением поля рассеяния, полученным по уравнению допусков: ω∆ = 0,39 мм, т. е. расчет предельных отклонений замыкающего звена выполнен правильно. Однако расположение поля рассеяния замыкающего звена, полученное по отклонениям (рис. 1.20а), не соответствует заданному положению поля допуска (рис. 1.20б). 2.3. Для обеспечения заданного расположения поля допуска замыкающего звена выберем самое простое по конструкции согласующее звено. Таким звеном будет звено А2 (высота буртика втулки). Принимаем его отклонения за неизвестные и решаем уравнения отклонений размерной цепи относительно этих неизвестных, подставив в левую часть уравнений требуемые отклонения (А∆ = 3–0,4) замыкающего звена. 0 = – [(–0,06)]; Рис. 1.20 Расположение поля допуска замыкающего звена: а - полученное по отклонениям; б - заданное. Глава 1. Нормирование точности гладких цилиндрических соединений 65 ESA2 = –0,06 мм; –0,4 = – [(+0,06)]; EIA2 = –0,11 мм. В результате для звена А2 получили новые предельные отклонения и допуск звена: TA2 = 0,05 мм. Таким образом, расширение допуска компенсирующего звена и изменение его предельных отклонений позволили получить замыкающее звено в заданных пределах (рис. 1.20б). Все расчеты внесем в таблицу 1.10. ГЛ А В А 2 НОРМИРОВАНИЕ ТРЕБОВАНИЙ К ШЕРОХОВАТОСТИ ПОВЕРХНОСТИ И ГЕОМЕТРИЧЕСКИМ ДОПУСКАМ 2.1. ШЕРОХОВАТОСТЬ ПОВЕРХНОСТИ И ЕЕ НОРМИРОВАНИЕ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЮ 2.1 Н а поверхности детали после обработки остаются следы от кромок режущего инструмента в виде неровностей и гребешков, близко расположенных друг от друга. Шероховатостью поверхности называется совокупность неровностей с относительно малыми шагами, выделенная на базовой длине (l). Нормирование шероховатости поверхности по ГОСТ 2789-73 выполнено с учетом рекомендаций международных стандартов. Установлены (рис. 2.1) шесть параметров: три высотных (Ra; Rz; Rmax), два шаговых (Sm; S) и параметр относительной опорной длины профиля (tp) , , . Рис. 2.1 Профилограмма шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 67 Характеристика параметров шероховатости: Ra - среднее арифметическое отклонение профиля, мкм: (2.1) где yi - расстояние между любой точкой профиля и средней линией m, cредняя линия имеет форму номинального профиля и проводится так, что в пределах базовой длины среднее квадратическое отклонение профиля до этой линии минимально; n - количество рассматриваемых точек профиля на базовой длине. Rz - высота неровностей профиля по 10 точкам, мкм: (2.2) где Himax; Himin - высота наибольшего выступа и глубина наибольшей впадины, мкм. Соотношение между Ra и Rz колеблется в пределах от 4 до 7 раз; Rz больше, чем Ra. Rmax - наибольшая высота профиля - расстояние между линией выступов и линией впадин, мкм; Sm - средний шаг неровностей профиля по средней линии в пределах базовой длины, мм: (2.3) где n - количество шагов в пределах базовой длины; Smi - шаг неровностей профиля по средней линии. S - средний шаг местных выступов профиля (по вершинам) в пределах базовой длины, мкм: (2.4) где n - количество шагов в пределах базовой длины; Si - шаг местных выступов профиля. tp - относительная опорная длина профиля в %: 68 Метрология, стандартизация и сертификация (2.5) где p - уровень сечения профиля в процентах - это расстояние между линией выступов и линией, пересекающей профиль эквидистантно линии выступов; за 100% принимается Rmax; bi - длина отрезка, отсекаемая на заданном уровне в материале, мм; l - базовая длина, мм. Направления неровностей обработки зависят от метода и технологии изготовления, влияют на работоспособность, износостойкость и долговечность изделия. Условные обозначения направления неровностей (табл. 2.1) указывают на чертеже при необходимости. Т а б л и ц а 2.1 Условное обозначение направлений неровностей Тип направления неровностей Обозначение Тип направления неровностей Параллельное Произвольное Перпендикулярное Кругообразное Перекрещивающееся Радиальное Обозначение Точечное Выбор параметров производится в зависимости от эксплуатационных свойств поверхности. Предпочтительным принят параметр Ra - среднее арифметическое отклонение профиля, так как он определяет шероховатость по всем точкам профиля (табл. В.1). Глава 2. Нормирование требований к шероховатости поверхности 69 Точечное направление неровностей дают поверхности, полученные методом порошковой металлургии, электроискровым методом, травлением и др. Средняя высота неровностей по 10 точкам Rz используется в тех случаях, когда нельзя измерить Ra на приборах типа профилометр путем ощупывания поверхности алмазной иглой (острые кромки, мягкий материал, особо чистая поверхность). Шаговые параметры влияют на виброустойчивость, сопротивление в волноводах и электропроводность в электротехнических деталях. Параметр tp необходимо учитывать при высоких требованиях к контактной жесткости и герметичности. В ГОСТ 2789-59 предусматривалось 14 классов шероховатости в порядке уменьшения значений параметров. В сравнительной таблице В.1 даны соотношения между классами шероховатости и другими высотными параметрами. С 1983 г. для всех классов введен ряд значений Ra предпочтительного применения по 1-му варианту. Определение значений параметров шероховатости может быть выполнено методом подобия и расчетным методом. Метод подобия (табл. В.2) ориентируется на экономическую точность, которая устанавливает зависимость шероховатости и формы поверхности от допуска размера и применяемого отделочного метода обработки. Минимальные требования к шероховатости поверхности в зависимости от допусков размера и формы даны в таблице В.3 . Примеры выбора числовых значений Ra в зависимости от вида соединения даны в таблице В.4. При расчетном методе учитывается зависимость параметров шероховатости поверхности от допуска размера, так как при обеспечении требуемой точности размера изменяется шероховатость и точность геометрической формы поверхности. Для деталей жесткой конструкции (L ≤ 2d) соотношение допусков размера (Т) и формы поверхности (Тф) установлены три уровня относительной геометрической точности (ГОСТ 24643-81): А - нормальный, используемый наиболее часто в машиностроении для поверхностей без особых требований 70 Метрология, стандартизация и сертификация к точности формы при низкой скорости вращения или перемещения; В - повышенный, используемый для поверхностей, работающих при средних нагрузках и скоростях до 1500 об/мин, при оговоренных требованиях к плавности хода и герметичности уплотнений. Поверхности, образующие соединения с натягом или по переходным посадкам при воздействии больших скоростей и нагрузок, при наличии ударов и вибраций; С - высокий, рекомендуемый для поверхностей, работающих в подвижных соединениях при высоких нагрузках и скоростях свыше 1500 об/мин, при высоких требованиях к плавности хода, герметичности уплотнения и при необходимости трения малой величины; при высоких требованиях к точности центрирования, прочности соединения в условиях воздействия больших нагрузок, ударов и вибраций. Значения коэффициентов формы (Kф) и шероховатости (Kr) приведены в таблице 2.2. Т а б л и ц а 2.2 Значения коэффициентов Kф и Kr Уровень относительной геометрической точности цилиндрические поверхности плоские поверхности Значение коэффициента Kф Значение коэффициента Kr А 0,3 0,6 0,05 В 0,2 0,4 0,025 С 0,12 0,25 0,012 Значение Ra можно рассчитать по формуле Ra = KrТ, (2.6) где Т - допуск на размер, ограничивающий данную поверхность (Td или TD); Kr - коэффициент шероховатости поверхности по таблице 2.2. Расчетное значение округлить в сторону уменьшения до величины, указанной в таблице В.1, вариант 1. Указание требований к шероховатости поверхностей производится на чертежах согласно ЕСКД по ГОСТ 2.30973 «ЕСКД. Обозначения шероховатости поверхностей». Глава 2. Нормирование требований к шероховатости поверхности 71 Рис. 2.2 Место и порядок записи параметров шероховатости Обозначение шероховатости состоит из условного значка и числовых значений . Структура обозначения шероховатости поверхности приведена на рисунке 2.2. При применении знака без указания параметра и способа обработки его изображают без полки. В обозначении шероховатости применяют один из знаков: - основной знак, когда метод обработки поверхности чертежом не регламентируется; - знак, соответствующий поверхности, полученной удалением слоя металла (точением, сверлением, фрезерованием, шлифованием и т. д.); - знак, соответствующий поверхности в состоянии поставки, без удаления слоя металла (литье, штамповка, поковка и т. д.). Согласно ГОСТ 2.309-73 с 01.01.2005 г. при задании параметров шероховатости: обязательно указывать символы (Ra, Rz, S, tp) перед их числовым значением; все параметры записывать под полочкой. Под полочкой могут быть указаны: условные обозначения неровностей, базовая длина и все параметры шероховатости по строчкам, начиная с Ra; над полочкой указывают способ обработки и другие дополнительные требования (например, полировать); 72 Метрология, стандартизация и сертификация знак «остальное» для поверхностей, обрабатываемых с одинаковыми требованиями, указывать в верхнем правом углу чертежа, например, или; обработку поверхностей сложного контура «кругом» указывать так: . Знак шероховатости может указываться на контурной линии чертежа, на размерных линиях или на их продолжениях, на рамке допуска формы, на полках линий - выносок (рис. 2.3а). При указании двух и более параметров шероховатости поверхности в обозначении шероховатости значения параметров записывают сверху вниз в следующем порядке (рис. 2.3б): параметры высоты неровностей профиля; параметры шага неровностей профиля; относительная опорная длина профиля. При нормировании требований к шероховатости поверхности параметрами Ra, Rz, Rmax базовую длину в обозначении шероховатости не приводят, если она соответствует ГОСТ 2789-73 для выбранного значения параметра шероховатости (табл. В.1). В данном примере указано (рис. 2.3б): среднеарифметическое отклонение профиля Ra не более 0,1 мкм на базовой длине l = 0,25 мм (в обозначении Рис. 2.3 Примеры обозначения шероховатости: а - возможное размещение знака шероховатости; б - указание нескольких параметров. Глава 2. Нормирование требований к шероховатости поверхности 73 Рис. 2.4 Варианты обозначения шероховатости в правом углу чертежа: а - все поверхности имеют одинаковую шероховатость; б - часть поверхностей имеет одинаковую шероховатость (остальные); в - часть поверхностей по данному чертежу не обрабатывается (полочка не рисуется, параметры не указываются. базовая длина не указана, так как соответствует значению, определенному стандартом для данной высоты неровностей); средний шаг неровностей профиля Sm должен находиться в пределах от 0,063 до 0,040 мм на базовой длине l = 0,8 мм; относительная опорная длина профиля на 50%-ном уровне сечения должна находиться в пределах 80 ± 10% на базовой длине l = 0,25 мм. Примеры задания требований к шероховатости поверхности: означает Ra ≤ 1,6 мкм, метод обработки поверх ности чертежом не регламентируется; означает Rz≤ 40 мкм, обработка резанием; означает Ra ≤ 12,5 мкм, поверхность без удале ния слоя металла (литье, штамповка, поковка и т. д.). Обозначение шероховатости поверхностей повторяющихся элементов изделия (отверстий, пазов, зубьев и т. д.), количество которых указано на чертеже, а также обозначение шероховатости одной и той же поверхности, независимо от числа изображений или поверхностей, имеющих одинаковую шероховатость и образующих контур, наносят один раз. В правом верхнем углу чертежа указывают общие требования к поверхностям детали, варианты задания таких требований указаны на рисунке 2.4. 74 Метрология, стандартизация и сертификация ПОРЯДОК ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 (1-Й УРОВЕНЬ СЛОЖНОСТИ) Ознакомиться с теоретической частью раздела. Получить задание (вариант) практической работы. Варианты заданы в таблице 2.3. Т а б л и ц а 2.3 Варианты заданий к практическому занятию 2.1 № варианта Обозначение шероховатости поверхности № варианта 1 15 2 16 3 17 4 18 5 19 6 20 Обозначение шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 75 П р о д о л ж е н и е т а б л. 2.3 № варианта Обозначение шероховатости поверхности № варианта 7 21 8 22 9 23 10 24 11 25 12 26 13 27 14 28 Обозначение шероховатости поверхности 76 Метрология, стандартизация и сертификация Задание. По заданному варианту расшифровать условное обозначение шероховатости. Решение. 1. Указать вид условного значка, обозначающего требования к шероховатости поверхности. 2. Определить тип направления неровностей. 3. Определить наименование параметров шероховатости, их условное обозначение и числовое значение. 4. Указать базовую длину и объяснить ее назначение. ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 Задание. По заданному варианту расшифровать условное обозначение шероховатости. Дано: Решение. 1. Использован знак - метод обработки поверхности чертежом не регламентируется. 2. Направление неровностей не регламентируется, т. е. соответствует методу обработки. 3. Шероховатость нормируется по: параметру Ra (среднее арифметическое отклонение профиля), значение которого не должно превышать 0,1 мкм; средний шаг неровностей профиля по средней линии Sm в пределах (0,063–0,040) мм; относительная опорная длина профиля tp, задана на уровне 50% и должна составлять 80 ± 10%; 4. Базовая длина l = 0,25 мм для Ra не указывается, так как ее числовое значение соответствует числовому значению параметра Ra (табл. В.1); базовая длина l = 0,8 мм для Sm указана, базовая длина l = 0,25 мм для tp указана, так как эти параметры на приборах профилометр - профилограф измеряются на больших базовых длинах. Глава 2. Нормирование требований к шероховатости поверхности 77 2.2. НОРМИРОВАНИЕ ОТКЛОНЕНИЙ ФОРМЫ ПОВЕРХНОСТИ 2.2.1. ТЕРМИНЫ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЯМ 2.2, 2.3, 2.4 В ГОСТ 24642 (не действует в РФ) даны термины и определения, относящиеся к допускам формы; на территории России введен в действие с 01.01.2012 г. ГОСТ Р 53442, который устанавливает определения и правила указания на чертежах геометрических допусков (формы, ориентации, месторасположения и биения). Однако необходимо рассмотреть некоторые понятия ГОСТ 24642-81, так как аналогичных им в новом стандарте нет. Отклонением формы EF (∆ф) называется отклонение формы реального элемента от номинальной формы, оцениваемое наибольшим расстоянием от точек реального элемента по нормали к прилегающему элементу (рис. 2.5). Шероховатость поверхности в отклонение формы не включается. Номинальная поверхность - это идеальная поверхность, форма которой задана чертежом или другой технической документацией. Реальная поверхность - это поверхность, ограничивающая тело и отделяющая его от environment. Form deviations are evaluated over the entire surface (over the entire surface form deviation Fig. 2.5 Scheme for determining the surface form deviation 78 Metrology, standardization and certification of the profile) or in a normalized area, if the area, length or angle of the sector is given, and, if necessary, its location on the surface. If the location of the site is not specified, then it is considered any within the entire surface or profile. The deviations of the surface shape are counted along the normal to the adjacent surface as the greatest distance from the points of the real surface to the adjacent one, which is considered as nominal. Adjacent surface - a surface having the shape of a nominal surface, in contact with the real surface and located outside the material of the part so that the deviation from it of the most distant point of the real surface within the normalized area has a minimum value. Profile shape deviations are evaluated similarly - from the adjacent line. Form tolerance TF (Tf) is the largest allowable form deviation value. Shape tolerances can be: complex (flatness, cylindricity, roundness, shape tolerance preset profile); elementary (convexity, concavity, ovality, faceting, cone-shape, saddle-shape, barrel-shape). Roundness deviation ∆cr - the greatest distance from the points of the real profile to the adjacent circle (Fig. 2.6). The main types of private profile deviations cross section cylindrical surfaces - ovality (Fig. 2.7a) and faceting (Fig. 2.7b). Partial deviations of the profile of the longitudinal section - conical (Fig. 2.8a), barrel-shaped (Fig. 2.8b), saddle-shaped (Fig. 2.8c). For all cases, the shape deviation is determined in the radius expression: 2.6 Deviation from roundness 2.7 Particular types of deviations from roundness: a - ovality; b - faceting. Rice. 2.8 Particular types of deviations in the shape of the profile of the longitudinal section: a - taper; b - barrel-shaped; in - saddle shape. 79 80 Metrology, standardization and certification be smaller than the size tolerance. Types of shape tolerances and other geometric tolerances are presented in Table B.5. The name of the geometric tolerance consists of the word "tolerance" and the geometric characteristic of the element normalized by it, for example, "straightness tolerance". The exception is the positioning tolerance, which in current practice is called "positional tolerance". The numerical values of the tolerances of the shape and location of the surfaces are established by GOST 24643-81 according to 16 degrees of accuracy (Tables B.6 and B.7). The tables consider 12 degrees, since for rough surfaces GOST 30893.2 is applied for general tolerances. The numerical values of the surface shape tolerances can be determined by the calculation method and the similarity method. 2.2.2. DETERMINATION OF THE NUMERICAL VALUES OF THE SURFACE SHAPE TOLERANCES The similarity method is used when the quality of the accuracy of the size of the surface under consideration is known. The degree of accuracy of the surface shape is determined according to the conditions of economic accuracy for a rigid structure (Table B.2). The degree of accuracy is reduced by one if L/d is between 2 and 5; two degrees of accuracy coarser if L/d > 5. The calculation method is based on the ratio of dimensional tolerances to shape tolerances and surface roughness. When considering the relationship between the size tolerance and the shape tolerance for cylindrical parts, the diameter of the surface under consideration is taken, and for flat parts - the tolerance for the thickness of the part, since the largest error is equal to this tolerance, i.e. 100%. Tf max = Td. For cylindrical parts, the shape tolerance is given in terms of radius, so the largest shape error is taken equal to 50% of the diameter tolerance: Тf max = Тd/2. Chapter 2. Rationing of requirements for surface roughness 81 For level A, the shape tolerance (
The textbook discusses the means and methods of carrying out work on various types of standardization and certification. Scientific-technical, normative-methodical and organizational bases of standardization and certification of production and services are stated. In order to harmonize work in the field of standardization and certification, the methodology and practice of certification abroad are considered in detail. Given big number examples and reference data in the form of tables and diagrams. After each chapter are given control questions and tasks.
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A.G. Sergeev
M.V. Latyshev
V.V. Teregerya
WORKSHOP
ON METROLOGY, STANDARDIZATION, CERTIFICATION
Vladimir 2005
A.G. Sergeev, M.V. Latyshev, V.V. Teregerya
WORKSHOP
ON METROLOGY, STANDARDIZATION, CERTIFICATION
Tutorial
Vladimir 2005
UDC 621.753(076) + 658.516(075.8)
Reviewer
Workshop on metrology, standardization, certification / Comp.: A.G. Sergeev, M.V. Latyshev, V.V. Teregerya; Vladim. state un-t. Vladimir, 2005. p.
Compiled in accordance with the program of the course "Metrology, standardization, certification" for specialties 120301, 114000, 210200
The sections of the training manual contain materials for practical classes on the following topics of the course "Metrology, standardization, certification": the legal basis for standardization, the classification of scientific and technical documentation, the development of technical specifications for products and services, the control of the accuracy of manufacturing parts, the basic concepts of connections and landings, the state standard ESDP , the choice of methods and means of measuring linear dimensions, processing the results of direct multiple measurements, the basics of certification.
Designed for full-time students of the named specialties.
Il. Tab. . Bibliography name
UDC 621.753(076 + 658.516
1. STANDARDIZATION
1.1. LEGAL FRAMEWORK AND REGULATORY DOCUMENTS ON STANDARDIZATION OF THE RUSSIAN FEDERATION
Key points. The main document in the Russian Federation for standardization is the law "On technical regulation", as well as the laws "On ensuring the uniformity of measurements", "On the protection of consumer rights" and the decrees of the Government of the Russian Federation adopted to implement these Laws of the Russian Federation.
The Law "On Technical Regulation" establishes the legal basis for standardization in the Russian Federation, defines the rights and obligations of participants regulated by the Federal Law of Relations. It regulates relations arising from the development, adoption, application and use of mandatory requirements for products, production processes, operation and disposal, as well as the development, adoption, application and use on a voluntary basis of requirements for products, production processes, operation, storage, transportation, sale and disposal, performance of work or provision of services. Other Federal laws and regulations of the Russian Federation relating to the scope of standardization (including those directly or indirectly providing for monitoring compliance with the requirements of technical regulations) are applied to the extent that they do not contradict the main document. Federal executive authorities have the right to issue in the environment of technical regulation acts of only a recommendatory nature, except in the case of regulation in relation to defense products (works, services) and products (works, services), information about which constitutes a state secret. If an international treaty of the Russian Federation in the field of technical regulation establishes other rules than those provided for by the main Federal Law, the rules of the international treaty are applied, and if it follows from the international treaty that its application requires the issuance of a domestic act, the rules of the international agreement and the adoption on its basis of the legislation of the Russian Federation (see Appendix 1).
To strengthen the role of standardization in scientific and technological progress, improve product quality and cost-effectiveness of its production, the Russian National Standardization System (RNSS) has been developed. The basis of the RNSS is the State Standardization System (GOST R 1.0 - 92.
GSS RF. Basic provisions; GOST 1.5 - 2002. GSS RF. Standards. General requirements for construction, presentation, design, content and designation; GOST R 1.8 - 2002. GSS RF. Interstate standards. Rules for the development, application, updating and termination of work carried out in the Russian Federation; GOST R 1.9 - 95. GSS RF. The procedure for labeling products and services with a sign of compliance with state standards; GOST R 1.12 - 99. GSS RF. Terms and Definitions. etc.) as amended in the light of the Federal Law "On Technical Regulation". The RNSS establishes the legal framework for standardization in the Russian Federation, for all government bodies, as well as enterprises and entrepreneurs, public associations, and determines measures for state protection of the interests of consumers and the state through the development and application of regulatory documents on standardization.
Standardization, as defined by ISO/IEC, is the establishment and application of rules for the purpose of streamlining activities in a certain area for the benefit and with the participation of all interested parties, in particular to achieve optimal overall economy while observing the conditions of operation (use) and safety requirements.
According to the Federal Law “On Technical Regulation”, standardization is carried out in order to: increase the level of safety of life or health of citizens, property of individuals or legal entities, state or municipal property, environmental safety, safety of life or health of animals and plants and promote compliance with the requirements technical regulations; increasing the level of security of facilities, taking into account the risk of natural and technical emergencies; ensuring scientific and technological progress; increasing the competitiveness of products, works and services; rational use of resources; technical and information compatibility; comparability of the results of research (tests) and measurements, technical and economic-statistical data; interchangeability of products. Standardization is guided by the following principles: voluntary application of standards; maximum consideration in the development of standards of the legitimate interests of stakeholders; application of an international standard as the basis for the development of a national standard, unless such application is recognized as impossible due to the inconsistency of the requirements of international standards with the climatic and geographical features of the Russian Federation, technical and (or) technological features, or for other reasons, or the Russian Federation in
in accordance with established procedures, opposed the adoption of an international standard or a separate provision of it; the inadmissibility of creating obstacles to the production and circulation of products, the performance of work and the provision of services to a greater extent than is the minimum necessary to fulfill the goals of standardization; the inadmissibility of establishing such standards that are contrary to technical regulations; providing conditions for the uniform application of standards.
Standardization activity is regulated by normative documents. A normative document on standardization is a document that establishes rules, principles, norms, characteristics regarding the objects of standardization, various types of activities or their results, and is available to a wide range of users. The list of the main normative documents on standardization is shown in Fig. 1.1.1.
International Standards are developed and published by the International Organization for Standardization. Based on international standards, national standards are created, they are also used for international economic relations. The main purpose of these standards is to promote the favorable development of standardization in the world in order to facilitate the international exchange of goods and develop mutual cooperation in the field of intellectual, scientific, technical and economic activities.
International as well as national foreign standards are introduced in the Russian Federation through the adoption of a state standard or technical regulations.
International standards are widely used in the world, their number currently exceeds 12 thousand, and about a thousand standards are adopted or revised annually. They are not binding on member countries of the international organization for standardization. The decision on their application is connected with the degree of participation of a particular country in the international division of labor and the state of its foreign trade. In Russia, there is currently an active process of introducing international standards into the national standardization system.
On fig. 1.1.2 provides a list of international organizations for standardization.
Rice. 1.1.1. List of main regulatory documents on standardization
|
Regulations |
|
STP is the standard of enterprises and organizations. |
Rice. 1.1.1. Ending
Rice. 1.1..2. International organizations for standardization
Work assignment. To study the main legal documents on standardization (Federal Law “On Technical Regulation”, see Appendix 1), categories and types of regulatory documents on standardization. Familiarize
tsya with the concept of "international standards" and with the activities of international organizations for standardization.
Practical tasks. Answer the questions:
concept of standardization.
standardization goals.
Russian national standardization system.
definition of a standard.
international standardization.
international standardization bodies.
Determine the correct test control answers.
1. Name the regulatory document on the legal basis for the standardization of the Russian Federation:
"Law on technical regulation";
"Law on Ensuring the Uniformity of Measurements";
"International Acts";
"Regulatory and technical documents on standardization".
2. What is the nature of the requirements of technical regulations:
only some of them are obligatory;
they are mandatory;
3. Specify the main international organization in the field of standardization:
International Electrotechnical Commission (IEC);
European Committee for Standardization (CEN);
International Organization for Standardization (ISO).
4. What is called a standard:
a document in which, for the purpose of voluntary multiple use, product characteristics, implementation rules and characteristics of the processes of production, operation, storage, transportation, sale and disposal, performance of work or provision of services are established;
this is a planned activity to establish mandatory rules, norms and requirements for the object of standardization.
5. What is called technical regulation:
document indicating only technical requirements to the object of standardization;
a regulatory document developed for specific production processes and their elements related to solving the problems of organizing and managing work on standardization, metrology, certification, accreditation, licensing, state control and supervision of compliance with the mandatory requirements of technical regulations, state and international standards.
this is a planned activity to establish mandatory rules, norms and requirements for the object of standardization.
