Kolchkov V.I. METROLOGY, STANDARDIZATION AND CERTIFICATION. M.: Tutorial
2. Standardization
2.3. Methodological foundations of standardization
2.3.3. parametric series
Production of new types of products, for example: machines, technological equipment, household appliances etc. may lead to the release of an unnecessarily large range of products that are similar in purpose and slightly different in design and size. Rational reduction in the number of types and sizes of manufactured products, unification and aggregation components can significantly reduce the cost of production.
Cost reduction is achieved with a simultaneous increase in serialization, development of specialization, inter-industry and international cooperation in production, which is achieved by developing standards for parametric series of similar products. Satisfaction of market demand and quality assurance remains the main condition. Any product is characterized by parameters that reflect the diversity of its properties, while there is a certain list of parameters that it is advisable to standardize. The range of standardized parameters should be minimal, but sufficient to evaluate performance characteristics of this type products and modifications.
Analyzing the parameters, allocate main and basic parameters of products.
chief name the parameter that determines the most important operational indicator of the product. The main parameter does not depend on technical improvements of the product and manufacturing technology, it determines the indicator of the direct purpose of the product.
For example, the main parameter overhead crane is the carrying capacity. Main parameters lathe are the height of the centers and the distance between the centers of the front and rear headstock, which determine the overall dimensions of the workpieces being processed. The gearbox is characterized by a gear ratio, an electric motor - by power, measuring instruments - by a measurement range, etc.
The main parameter is taken as a basis for constructing a parametric series. The choice of the main parameter and the determination of the range of values of this parameter must be technically and economically justified, the extreme numerical values of the series are chosen taking into account the current and future needs for these products, for which marketing research is carried out.
Parametric series is a set of numerical values of the main parameter of a product of one functional purpose and principle of operation, regularly constructed in a certain range. The main parameter serves as the basis for determining the numerical values of the main parameters, since it expresses the most important operational property.
Main name the parameters that determine the quality of the product as a set of properties and indicators that determine the conformity of the product to its intended purpose. For example, for metal-cutting equipment, the following can be taken as the main ones: machining accuracy, power, spindle speed, productivity.
Formeasuring instruments the main parameters are: measurement error, scale division value, measuring force.
The main and main parameters are interrelated, so it is sometimes convenient to express the main parameters in terms of the main parameter. For example, the main parameter of a reciprocating compressor is the cylinder diameter, and one of the main parameters is the performance, which are interconnected by a certain relationship.
The parametric series is called standard size or simply size range, if its main parameter refers to the geometric dimensions of the product. On the basis of standard size parametric series, constructive series of specific types or models of products of the same design and one functional purpose are developed.
Parametric, standard and structural series of machines are built on the basis of a proportional change in their performance indicators (power, productivity, traction force, etc.), taking into account the theory of similarity. In this case, the geometric characteristics of the machines (working volume, cylinder diameter, wheel diameter for rotary machines, etc.) are derived from performance indicators and within a number of machines can change according to patterns that are different from the patterns of changes in performance indicators.
Rice. 2.1. Structural range of piston machine
When constructing parametric, standard and structural series of machines, it is advisable to observe the mechanical and thermodynamic similarity of the working process, which ensures the equality of the parameters of thermal and power tension of machines as a whole and their parts. This approach leads to geometric similarity. For example, for engines internal combustion the following similarity conditions apply: a) the equality of the average effective pressure re, depending on the pressure and temperature of the fuel mixture at the suction; b) equality average speed piston v n = S n/30 (S- piston stroke; n- engine speed) or the equality of the product D n, where D is the diameter of the cylinder. Based on the theory of similarity, it is possible to move from the thermal and power parameters of the engine to its geometric parameters. Then, the main parameter will be D(Fig. 2.1), which makes it possible to create a number of geometrically similar engines with the ratio S/ D = const, in which the indicated thermodynamic and mechanical similarity criteria of the working process will be observed. In this case, all geometrically similar engines will have the same efficiency, fuel consumption, thermal and power intensity and power. Cylinder wall thickness gradation h and diameter D in the ranks will be the same.
Standards for parametric series provide for the production of products that are progressive in their characteristics. Such rows should have properties to set intratype and intertype unification and aggregation of products, as well as the possibility of creating various modifications of products based on aggregation. In most cases, the numerical values of the parameters are chosen from the series of preferred numbers, especially when the series is evenly saturated in all its parts; an example of such a series with a slight rounding of numbers is shown in Fig. 2.2.
Rice. 2.2. Structural range of presses
In mechanical engineering, the most widely used series of preferred numbers R 10. For example, for longitudinal grinding machines, the largest width AT processed products forms a series R 10, i.e. B is equal to: 200; 250; 320; 400; 500 630; 800; 1000; 1250; 1600; 2000; 2500; 3200 mm.
Row R 10 is also set for the rated powers of electrical machines. By row R 10 diameters of triangular cutters are accepted, D equals: 50; 63; 80; 100 mm. In some cases, rows are used R 20 and R 40, for example, for reciprocating compressors with a cylinder diameter of 67.5 mm, the nominal capacity is set according to the series R 20/3.
Parametric and standard series are series of products that ensure the performance of the amount of work corresponding to their passport data, with established specifications quality indicators, while minimizing costs and maximizing profits. Thus, it is achieved intersectoral unification.
Structurally unified series is a regularly constructed set of products: machines, devices, aggregates or assembly units, including the base product and its modifications of the same or similar functional purpose and products with similar or similar kinematics, scheme of working movements, layout and other features. Examples of such an approach to standardizing product parameters are inter-industry unification carried out for trucks, wheeled and tracked vehicles, agricultural and road-cleaning equipment. The creation of structurally unified rows in the production of household appliances, such as washing machines, refrigerators, food processors, has become especially widespread. and etc.
There are cases when it is expedient to use mixed series, in which the number of members of the series increases in the range of the highest frequency of use of products. Thus, the increased demand of consumers of products with characteristics in specific ranges of values is taken into account. Therefore, when developing and putting products into production, marketing is carried out in order to establish the distribution density of the applicability of products with different meanings main parameters. For example, in general engineering, about 90% of all used gear modules are in the range of 1 - 6 mm. The maximum applicability value falls on wheels with a module of 2-4 mm. Taking into account the applicability, the standard provides for the largest number of gradations in the range of 2-4 mm in a number of modules.
The smallest and largest values of the main parameter, as well as the frequency of the series, are set after a feasibility study, taking into account the current need and the future increase in demand. In addition, the achievements of science and technology and the possible prospects for improving the quality of this type of product while reducing the cost of production are taken into account.
Theory Workshop Tasks Information
Any product is characterized by certain parameters (geometrical dimensions, power, productivity, speed, strength, etc.). Product parameters are divided into main, main and secondary.
Main parameters is a set of all parameters that characterize the operational (consumer) qualities of the product.
Main parameter name such a parameter from among the main ones, which most fully characterizes the product; remains unchanged for a long time and can only change with the introduction of more advanced products.
Secondary parameters depend on various improvements and are characterized by instability.
Consider, for example, an automobile filling station (ARS). It is characterized by many parameters; tank capacity, filling time, emptying time, length of the degassed (disinfected) strip, the number of simultaneously processed objects of equipment, etc. All these parameters are basic and are included in the description of the main technical data.
But among these parameters there is the main one, which most fully characterizes the product, remains unchanged with any improvements to this sample. Such a parameter in our example is the capacity of the tank. The remaining parameters are auxiliary, because they depend on various conditions, possible improvements and are unstable.
However, there are many consumers in the country who need road tankers of various capacities. And what, for each customer to produce tanks of the capacity that he needs? But this is not economically viable.
A similar task is faced in many areas: what power to produce electric motors, what diameters to produce pipes, bolts, etc. To resolve this issue, you need to know:
extreme values of the main parameters based on the needs of the country;
pattern of change in the interval between neighboring values of the main parameter.
That is, you need to build row values of the main parameter, called parametric series, consisting of a series of preferred numbers.
Suppose that for the manufacture of any machines it is desirable to use bolts of seven diameters: 24, 25, 26, 27, 28, 29, and 30 mm. In this case, threading bolts and nuts, as well as drilling holes for bolts, will require seven sets of threading tools and drills. If you use only three sizes of bolts (24, 27 and 30 mm), then you will need only three sets metal cutting tools; the number of changeovers of equipment for the manufacture of bolts and nuts and for drilling holes for bolts will be reduced, the variety of spare parts will decrease and, consequently, the repair of machines will be simplified.
AT this example one row of sizes has been replaced by another, more rational row. Since the numbers of the second row create more favorable conditions for the design, manufacture and operation of the product, they are preferred.
Similar examples could be given with the need for a wide variety of tanker capacities, electric motor capacities, pipe diameters, etc. But from a large number of the variety of these figures, it is necessary to choose the preferred numbers, which in their totality would constitute a parametric series.
Naturally, for the main parameters of various products, different series of preferred numbers are needed. And here questions arise: how to build one or another series of preferred numbers, how many parametric series should be.
In this regard, it is necessary to build these parametric series and standardize them. Then, having calculated the main parameter of the product, it is necessary to take it from among the preferred numbers of one or another parametric series. The system of parametric series and preferred numbers is the basis of state standardization and its theoretical basis.
The meaning of this system lies in the possibility of using only those values of parameters and sizes that are included in the system of preferred numbers and are subject to a strictly defined mathematical dependence, and not any values obtained as a result of calculations or taken in the order of a volitional decision. The use of preferred numbers allows a wide unification of sizes and parameters both within and between industries.
The series of preferred numbers may be expressed as arithmetic or geometric progressions.
Elementary arithmetic or geometric progressions can be represented by the following examples:
0,3-0,6-0,9-1,2-1,5…
25-50-75-100-125…
An arithmetic series is characterized by the fact that in it the difference between any two successive numbers of the series is always constant. In the examples given, this difference is respectively 1; 0.3 and 25. The use of an arithmetic progression does not require rounding of numbers. The arithmetic series is simple.
A significant disadvantage of such a series is its relative unevenness. With a constant absolute difference, the relative difference between the terms sharply decreases as the series increases. So, the relative difference between the members of the arithmetic series 1, 2, 3 ... 10 for the numbers 1 and 2 is 200%, and for the numbers 9 and 10 only 11%. In the arithmetic series 25, 50, 75, ..., 475, 500 for the numbers 25 and 50 the difference is 200%, and for 475 and 500 - only 5%. This property of a simple arithmetic series limits the possibility of its use, although in some cases it finds application in standardization practice.
The most convenient are geometric series, since in this case the relative difference between any adjacent numbers of the series is the same. This important property is explained by the fact that a geometric progression is a series of numbers in which the ratio of two adjacent terms is always constant for a given series and is equal to the denominator of the progression:
1-2-4-8-16-32…
1-1,1-1,21-1,331…
10-100-1000-10000…
So, in a series of geometric progression 1,2,4..32, the serial number (i) of the digit 32 will be 5 (the serial number for unity is 0). Then Ni =2 5 =32.
Geometric progressions have important properties of great practical importance.
In connection with the listed properties of a geometric progression, dependencies determined from the products of members or their integer degrees will always obey the laws of the series. So, if a series determines linear dimensions, then the areas or volumes formed from these linear quantities obey its laws.
Thus, series of preferred numbers are best expressed as a geometric progression. But what numbers to take as the denominator of the progression?
It turned out that for the purposes of standardization, the preferred series of numbers, including the number 1 and having a denominator, turned out to be the most convenient.
Now the State Standard of the Russian Federation has established four main rows of preferred numbers (R5, R1O, R20 and R40) and an additional row of preferred numbers (R80), the use of which is allowed in separate, only technically justified cases. All these series are decimal series with rounded numbers of geometric progressions with denominators.
As you can see, the square root of the denominator of the progression of the previous row is equal to the denominator of the progression of the next row:
1,25; =1,12; =1,06; =1,03.
The table shows the preferred numbers of the four main parametric series. The number of numbers in the decimal series is 5; tenth -10; twentieth - 20; the fortieth - 40 and the eightieth - 80. Moreover, each subsequent row includes all the numbers of the previous rows, i.e. the tenth row includes all the numbers of the fifth row, the twentieth - all the numbers of the fifth and tenth rows, etc.
The preferred number series is unlimited in both directions. Numbers over 10 are obtained by multiplying the values set in the range 1…10 by 10; 100; 1000, etc., and numbers less than 1 - by 0.1; 0.01; 0.001 etc.
Starting from the tenth row, among the preferred numbers is the number 3.15, which is approximately ?. Therefore, the circumferences and areas of circles whose diameters are standardized parameters should be expressed in preferred numbers. This also applies to circumferential speeds, cylindrical and spherical surfaces and volumes.
Thus, the parametric series of preferred numbers presented in the table are the basis for the development of parametric standards for machines, equipment and instruments. These standards specify a number of preferred numbers for the main parameter that determines the operational and technological capabilities cars. So, for example, it was established that the accuracy classes of measuring instruments (pressure gauges, thermometers, etc.) should be selected and assigned from the fifth parametric series, i.e. must be 1; 1.6; 2.5; 4.0: 6.0 where n=1, 0, -1, -2, etc.). The diameters of the cases of manometers and vacuum gauges are assumed to be 160 mm and 250 mm.
Having chosen a number of preferred numbers for the main parameter, select rows for auxiliary parameters and other standardized sizes. In this case, the row R5 should be preferred to the row R10; R10-row R20, R20-row R40.
It should be noted that now, on the recommendation of the International Organization for Standardization (ISO), more rounded values of the preferred numbers R "(1st rounding) and R" (2nd rounding) have already been developed. With regard to R', the caveat is given that they should be avoided in all respects if possible.
For the 5th row, R "5 (1.5 and 6) are provided; for the 10th row - R10 (3.2) and R "10 (1.2; 1.5; 3; 6). For the 20th row, R20 values (1.1; 2.2; 3.2; 3.6) and R20 values (1.2; 3; 3.5; 5.5; bi7) are given.
The versatility of parametric series of preferred numbers allows them to be widely used in all industries. So, the rated power of electric motors and generators is set according to the R10 series and in the range from 100 to 1000 kW. This power range is: 100 - 125 -160 -200 -250 - 320 -400-500-630-800 - 1000.
The upper measurement limits for pressure gauges are set to the R5 series: 1 - 1.6 - 2.5 - 4 - 6 - 10 - 16 - 25 - 40 - 60 - 100 - 160 - 250 - 400 -600 - kgf / cm.
However, despite the universality of the given series, the International Organization for Standardization (ISO) decided that it was necessary to develop a system of preferred numbers for linear dimensions in mechanical engineering. This is due to the fact that the largest number of numerical values used in technology falls on the share of linear dimensions measured in units of length of the first degree (mm, cm, m, km), It is the linear dimensions, in most cases, that determine the requirements for the interchangeability of parts, which must have the same nominal dimensions and tolerances. The tolerances are in some cases very small and such values can be obtained by dividing the numbers in the decimal interval of the R5 - R40 series by 10, 100, 1000, etc. But at the same time, especially when defining landing dimensions, it may turn out that the preferred numbers in the rows R5 - R40 will not be rounded enough.
Therefore, for linear dimensions, the series Ra5, Ral0, Ra20, Ra40 have been developed with a large rounding of numbers (the letter “a” means that the series contains rounded numbers).
The series of linear dimensions (Ra5 - Ra40) are developed on the basis of the series R5 - R40 for all decimal intervals from 0.001 to 20000 mm. So the preferred numbers in the R5 series are:
For an interval of 0.001 linear size: 0.001; 0.002; 0.003; 0.004; 0.006 (i.e. size 0.0016 in row R5 is rounded up to 0.002, and size 0.0025 in row R5 is rounded up to 0.003).
R5… 10=1.5849=1.6
R10… 10=1.2589=1.25
R20… 10=1.1220=1.12
R40… 10=1.0593=1.06
R80… 10=1.0292=1.03
(difference +1.26% to -1.01%)
For an interval of 0.01 linear size: 0.010; 0.016; 0.025; 0.040; 0.060 (here, the size 0.063 in row R5 is rounded up to 0.060).
For an interval of 0.1 linear size: 0.1: 0.16; 0.25; 0.40; 0.60 (here, too, the size 0.63 in the R5 series is rounded up to 0.60).
For interval 1.0 and 10 linear dimensions, dimensions 6.3 and 63 are rounded up to 6.0 and 60, etc.
Similar roundings within the specified intervals are also available in the series Ra10, Ra20 and Ra40.
Thus, the main parametric series of preferred numbers are the series R5 - R40, and for linear dimensions, the series Ra5 - Ra40. Based on these series, parametric standards are developed for certain types of machines, instruments, parts, which indicate the preferred series of numbers that must correspond certain parameter these products. However, in practice there may be cases when, in order to establish parameters, especially those dependent on natural conditions, a more complex pattern or the use of an arithmetic progression is required. Such deviations must be justified in each individual case.
The use of series of preferred numbers is used not only in standardization, but also in the design of any machines, mechanisms, devices and products, their parts and assemblies, in the development of size ranges of machines, equipment and devices for which there are no parametric standards.
Returning again to our example, when deciding what capacity of a tank truck the industry should produce, it is necessary to choose a parametric series.
The R5 series is rarer. It reduces the number of standard sizes and it is difficult to select a tanker of the required capacity,
We have to take a tank of obviously larger capacity, and this is due to an increase in the carrying capacity of the car, which is not justified by the calculated need.
It is not advisable to use higher rows R20 and even more so R40 because they significantly increase the number of standard sizes. Therefore, in most cases, parametric series are used in mechanical engineering, based on a number of preferred R10 numbers. The same row is also used in the construction of the preferred row of tanker containers. The industry produces tank trucks with a capacity of 1000, 1250, 1600, 2000, 2500 liters.
But in the general case, the choice of a parametric series in each individual case is a typical optimization problem. It should be chosen in such a way that the total costs for the manufacture of products of a given series are the smallest for a given efficiency of these products in operation.
So, the essence of parametric standardization lies in the fact that the parameters and dimensions of products are not set arbitrarily, but adhering to certain, clearly justified series of preferred numbers. Therefore, the theoretical basis of modern standardization is preferred number system (Fig. 1510)10).
yes, any parameters of the product (capacity, speed, speed, power, pressure, dimensions) are guided by a certain scientifically based number of preferential numbers, then the product will be consistent with other types of products associated with it: electric motors - with technological equipment, lifting devices; lifting devices - with trucks; trucks - with transport containers; transport packaging - with consumer packaging, etc.
. Product Parameter- this is a quantitative characteristic of the properties of the product or its states, which determine the purpose of the product and the conditions for its use. Product parameters are given in regulatory documents.
According to the characteristic properties of products, the most important product parameters are distinguished:
o dimensional parameters (size of clothes and shoes, capacity of dishes);
o weight parameters (mass of certain types of sports equipment);
o parameters characterizing the performance of machines and devices (fan performance, vehicle speed);
o energy parameters (engine power).
In 1953, the International Organization for Standardization (ISO) adopted. International recommendations for prevailing numbers. ISO / R3, which became the basis for the development of parametric standards in many countries of the swi and tu. Recommendations other than a number. I entered 5 rows I am 10,. I am 20,. I am 40 which are also called rows. Renard. There are two additional rows. YaYA 80 and. Yako, which are used only in individual, technically justified cases.
. Rows of preferred numbers must meet the following requirements:
o be a rational system of gradations that meets the needs of the production and operation of products;
o be infinite, both in the direction of small and large numbers, i.e. allow the establishment of an unlimited number of parameters or sizes in the direction of both increasing their value and decreasing;
o include all consecutive tenfold or fractional values of each number in the series and one;
o be simple so that they are easy to remember.
The prevailing numbers have certain mathematical patterns. So, when determining the dimensions and parameters of products wide application found series of numbers that are built on the basis of arithmetic or geometric progression.
simple series of preferred numbers are built on the basis of an arithmetic progression - such a sequence of numbers in which the difference between the next and previous members remains constant, that is:
a p= a 1 + d (n - 1)
where a1- the first member of the progression;
d- progression difference;
P- number of the taken member.
The positive point is that the arithmetic series is simple, does not require rounding of numbers, but its significant drawback is the relative unevenness in these series is that they are simple, do not require rounded numbers. But a significant drawback is the relative unevenness. With a constant absolute difference between the members of the series, the relative unevenness sharply decreases. So, the relative difference between the members of the arithmetic series 1, 2 10 for the numbers 1 and 2 is 100%, and for the numbers 9-10 only 11%. If the change in the relative difference for the members of this series is depicted graphically, then we obtain a dependence according to which, with an increase in the absolute values of the members of the arithmetic series, the relative difference decreases.
Series of preferred numbers based on arithmetic progression are little used in parametric standards. They are used, for example, in standards for shoe sizes, bearing diameters when used, diameters of metric threads, and gear modules.
In most cases, geometric series of numbers are most suitable for standardizing parameters. However, there are infinitely many geometric series, so we have to choose from them those that will have certain advances over others.
. Geometric progression - this is a series of numbers in which each subsequent number, which is obtained by multiplying the previous one by the same number, which is called the denominator of the progression
up= a 1 o q p-1
The geometric progression has a number of useful properties:
1 is relatively the difference between any adjacent members of the series constant. Any member of the progression is greater than the previous one by 100%.
2. The product or fraction of any members of a progression is a member of that progression. This property is used when linking the parameters to be standardized within the same series, the overwhelming number of them.
Geometric progressions allow you to coordinate with each other the parameters that are connected not only by linear, but also by quadratic, cubic and other dependencies. Also in. Ancient. In the Roman Empire, the diameters of the wheels of the aqueducts were chosen according to a geometric progression. In. France in 1805, the size of the typographic font was also established in accordance with geometric progression.
The history of the formation of the series of preferred numbers is associated with the name of an officer of the French engineering corps. Charles. Renard, who in 1877-1879 laid the scientific foundations for the use of preferred numbers for constructs. Given the advantage of a geometric progression,. Renard built the length as a basis and built a series, taking such a denominator of the progression, which provides somewhere
The parameters and dimensions of mass-produced products are set in accordance with the main series of preferred numbers. But the use of derived series is allowed. They are obtained from the main series by selecting ru 2 -, 3 -, 4th or n-th member of the main or additional series. For example, R R 5/2 is a derivative series obtained from every 2nd member of the main series R 5 . Derived series are used when none of the main series meets the specified requirements and gradations of numerical characteristics are introduced, which depend on the parameters and sizes, formed on the basis of the main series.
Introduction in all industries of a single procedure for establishing numerical values
parameters and sizes for standardization objects, as well as the transition from one numerical parameter value to another using a system of prevailing numbers (parametric series) allows you to reduce the number of standard sizes, save materials, coordinate and connect with each other different kinds products, materials, semi-finished products, vehicles
production equipment.
The development of parametric standards for standardization objects is carried out in stages:
o choice of nomenclature of parameters;
o selection of the range of the parametric series;
o choice of gradation of the parametric series.
. parametric series- this is a set of numerical values of parameters, built in a certain range based on the accepted system of gradations.
To determine the parametric series, its two characteristics should be taken into account: the range of the series and the gradation. The range of a series is an interval limited by the extreme values of the members of the series. The gradation of the parametric p series is called a mathematical pattern that determines the nature of the intervals between the members of the series in a certain range. The choice of the optimal gradation of the parametric series is reduced to finding such a series of transient numbers that best meets the requirements of the national economy of the country.
The use of a system of prevailing numbers with different rows allows for the possibility of combining them. Most of the parametric series included in the current parametric standards is based on the RR 10 series. This gives reason to believe that the Rio series is now the most appropriate for constructing parametric series for machines and equipment.
. Derived series - rows that are formed from the main or additional through the selection of n-x members.
Parametric series R40 (with rounded values of the prevailing numbers) - 1.0; 1.06; 1.12; 1.18; 1.25; 1.32; 1.40; 1.50; 1.60, 1 1.06.
METHODOLOGICAL INSTRUCTIONS
UNIFICATION OF PRODUCTS
CONSTRUCTION OF PARAMETRIC
AND DIMENSIONAL RANGE OF PARTS
AND ASSEMBLY UNITS
GENERAL ENGINEERING
APPLICATIONS
RD 50-632-87
Date of introduction 01.07.88
These guidelines apply to parts and assembly units of general machine-building use (hereinafter referred to as products) and regulate the methodological provisions and the content of work on the construction of parametric and standard-size series of these objects during their unification and standardization.
Guidelines do not apply to products designed and manufactured by order of the Ministry of Defense.
The Guidelines can be used in whole or in part to build parametric and standard-size series of parts and assembly units for special applications, as well as various final products (machines, equipment, instruments, etc.; hereinafter referred to as equipment). However, in these cases, one should consider the need to refine the objective functions and constraints for optimization and the advisability of using other optimization methods.
Methodological guidelines are developed in accordance with the requirements of a set of documents on methods for optimizing product quality and the requirements of standards.
1 . GENERAL PROVISIONS
1.1. The main indicators of the product are determined by a set of basic parameters, among which the main one is chosen.
The definition of the term "main parameter" is according to GOST 23945.0-80.
The main parameter should determine or be closely related to the main indicator of the functional purpose of the product, be stable and be linked to other main parameters and economic indicators of the product. The main parameter should not depend on the technology and quality of the product, the materials used, types of equipment, etc.
As a rule, the main parameter of the product should be one.
The set of basic parameters should be minimal, providing the definition key indicators products.
1.2. Parametric series of products according to GOST 23945.0-80 - an ordered set of numerical values of a product parameter.
A parametric series is built for products of a certain class, subclass, type or type, which should be clearly defined in the name of the series, which allows you to establish the area of \u200b\u200bits distribution.
1.3. Parametric series are built according to the main parameter of the product (series of the main parameter), as well as for each individual main parameter (series of main parameters).
1.4. After constructing a series of the main parameter and series of the main parameters of the product, a standard-size series is built.
Product size range according to GOST 23945.0-80 - an ordered set of sets of numerical values of the main parameters characterizing the standard sizes of products, the numerical values of the main parameters of which are in the parametric series.
For example, a series of the main parameter of flat spur gears with a straight tooth is built according to the modulus values. The size range of wheels of the specified type contains, for each value of the modulus, a specific set of values of the main parameters - the number of teeth, the length of the tooth, the diameter of the mounting hole.
1.5. The construction of parametric and standard series should be carried out with their optimization.
1.6. Optimization is carried out according to the criterion of minimum reduced economic costs or maximum profit.
In some cases (providing special safety requirements, environmental protection, social requirements, etc.), optimization is allowed according to non-economic criteria.
1.7. The optimal parametric (or standard) series of products is a parametric (or standard) series containing a set of values (or sets of values) of a parameter that determines a number of products that satisfies a given need for products of a modern technical level with the lowest reduced national economic costs (or the highest profit) for stages of the product life cycle.
1.8. Before constructing the optimal series, a rational technical level of the product must be determined or the corresponding requirements for the level of parameter values must be entered directly into the optimization mathematical model (into the objective function or into restrictions).
The methodology for establishing rational values of the main specific indicators of the technical level of parts and assembly units of general machine-building use (OMP) is given in the recommended Appendix 1.
The methodology for establishing rational values of the specific indicators of the technical level of unified gears is given in the recommended Appendix 2.
1.9. The numerical values of the parameter in the row should, as a rule, correspond to the numerical values of one or more rows of preferred numbers according to GOST 8032-84 or normal linear dimensions according to GOST 6636-69. Numerical values of parameters that can only take on certain discrete values (number of gear teeth, etc.) are chosen closest to the respective preferred numbers.
In technically justified cases (with modular design, etc.), deviation from the system of preferred numbers is allowed.
1.10. The structure of the series in the form of a stepped geometric progression or its special case - a geometric progression, is preferable.
In technically justified cases (application of the principles of building structures, modular design, etc.), structures in the form of arithmetic, stepped arithmetic progressions and etc.
1.11. After constructing the optimal row, if there are technical justifications, adjustments can be made to it (for example, one of the standard sizes of the design series can be replaced by a mass-produced standard size with a value close to the calculated value of the parameter, some additional standard size can be introduced to replace it during repairs earlier manufactured and in-service products, etc.).
When significant changes are introduced, a comparative calculation of national economic expenditures for the original and corrected series should be made and a final decision should be made taking into account the magnitude of the losses caused by the adjustment of the calculated series.
1.12. Sometimes, due to the specifics of the product, as its main or one of the main parameters, a characteristic can be taken that directly depends on the quality of manufacture and operation of the materials used, etc., i.e. the value of the parameter may change to some extent during manufacture or operation (for example, power is taken as the main parameter of an internal combustion engine). Usually, this situation occurs when the power characteristic is chosen as the main parameter. In such cases, in order to ensure that the components in which the value of the main parameter is increased due to improvements are not considered as non-standard (non-unified), the tolerance (usually positive) for the growth of the parameter should be indicated in the document regulating the parametric series.
1.13. The construction of parametric series of products is carried out during their unification and standardization on the scale of the entire national economy, several of its industries (intersectoral level), one industry (industry level), economic region (regional level), production association or enterprise (enterprise level).
The end result of constructing optimal parametric series, as a rule, should be the creation of specialized industries with the provision of cooperative deliveries at the appropriate level (intersectoral, sectoral, regional).
1.14. Depending on the task of choosing a product range or its creation, parametric series are constructed as follows:
selection of standard sizes from the existing nomenclature (non-unified, unified or standard sizes - creation of restrictive standards or lists);
construction of regular series of new standard sizes based on the generalization of data on existing non-standardized ones;
construction of regular series of standard sizes of new, previously unmanufactured products.
1.15. The following sequence of work steps is advisable when constructing parametric and standard series:
the choice of types of unified (standardized) products and the establishment of the nomenclature of the main and basic parameters;
collection of data on the applicability of products, assessment of their uniformity and representativeness;
analysis of applicability data and setting the ranges of parameter changes within which the series will be built;
establishing a rational technical level of products, a number of which should be built (when building a new range of standard sizes);
construction of an optimal parametric series (a series of the main parameter and, if necessary, series of the main parameters);
building an optimal size range;
determination of the economic effect from the manufacture and operation of products from a series.
The methodology for collecting and analyzing applicability data and establishing ranges for changing parameters is described in detail in.
1.16. The task of optimizing a parametric (standard) series includes a mathematical optimization model consisting of an objective function and constraints, and an optimization method.
The objective function is a mathematical description of the dependence of the optimization goal (in accordance with the accepted criterion) on various influencing factors and product indicators at all or main stages of the life cycle.
Constraints to the optimization problem are additional technical or technical and economic requirements that are not included in the objective function (due to the technical difficulties of optimization, etc.) and are usually formulated in the form of inequalities.
It is advisable to formulate requirements for the technical level of products in the form of restrictions on the optimization problem.
The restriction is also an indication of the choice of the numerical values of the parameter from the preferred numbers.
1.17. The construction of parametric and standard series and their optimization is carried out for some future period. Therefore, the initial data on the range of construction of the series, the value of indicators of the technical level and quality level, the needs for various standard sizes must be adjusted taking into account the relevant planning targets and forecasts. The efficiency of the constructed series to a large extent depends on the degree of conformity of the received forecast data real situation future period for which the series is built.
1.18. When developing a series, the lead period and the period of validity of the document regulating the series should be determined. The lead period is understood as the period of time between the work on constructing a series with the implementation of the forecasts also indicated in paragraph 1.17 and the moment the constructed series is put into operation. The period of validity of the document regulating the series should be taken depending on the expected magnitude of changes in the technical level of products and demand for them. In most cases, it is advisable to proceed from a period of 5 to 10 years.
For parts and assembly units for which relative stability of indicators is assumed, it is advisable to take the period of validity of the series equal to 10 years.
After accepting the lead period and the validity period of the series, it is advisable to build the series according to the forecast data on the technical level and demand, determined for the middle of the validity period, i.e. according to forecasts for a period of time equal to the sum of the lead period and half the period of the series.
To check the stability of the solution obtained and the possibility of the series being valid during the accepted period, it is necessary to make additional calculations of the optimal series according to the forecast data for the initial year of the period and the year preceding the final year of the period. In the event that the constructed series do not differ (or the differences are insignificant) from the series constructed for the middle of the period, it should be considered that, in accordance with the available forecast, the validity period of the series is taken correctly. If there are significant differences, the duration of the series should be shortened.
If the period of validity of the series exceeds 5 years, it is necessary to check its optimality every 4–5 years using new corrected forecast data.
2 . SELECTION OF MAIN AND MAIN PARAMETERS
2.1. To solve the problems of constructing rows, the main parameters are selected that characterize the overall dimensions, the main dimensions of the working surfaces, the main dimensions of interchangeability for parts and assembly units of the WMD and special applications.
2.2. As the main parameter for parts and assembly units of WMD and special applications, one chooses from among the main parameters, as a rule, a dimensional indicator that most fully characterizes the bearing capacity or other operational property and size.
The nomenclature of the main and main parameters of parts and assembly units is given in the mandatory Appendix 3.
2.3. In some cases, when the product is multifunctional, it can be characterized by two (or more) main parameters. In this case, a first-order dimension series is built - according to the totality of the main parameters and a second-order dimension series, which also includes sets of basic parameters.
3 . TECHNICAL AND TECHNICAL AND ECONOMIC FACTORS TO BE TAKEN INTO ACCOUNT WHEN CONSTRUCTING A SERIES OF DETAILS AND COMPONENT PARTS, AND WAYS TO ACCOUNT FACTORS
3.1. The choice of technical and techno-economic factors to be taken into account when constructing series should be made on the basis of the need to establish national economic costs in the areas of the life cycle of products.
The life cycle of a product is a cycle consisting of the stages of design, production, manufacture, transportation, use of the product in the design of equipment and operation of the product.
At the stage of application, such important factors for taking into account when optimizing the series appear as the influence of the dimensions of the component on the dimensions and mass of other components structurally related to it, as well as on the indicators of material and energy consumption of the product as a whole.
To optimize their product lines life cycle should be conditionally considered as including the stages of operation of products of the same type, installed instead of equipment that has failed during the service life of the equipment completed with this product.
3.2. For parts and assembly units, the factors most significantly influencing the construction of rows are the factors of the production (manufacturing), the scope of application in the design of equipment and the scope of operation (including the change of equipment that has failed during its service life). The factors of these areas, as a rule, are to be taken into account when constructing the optimal rows of parts and assembly units.
3.3. When constructing parametric series for calculating numerical values various factors according to the standard sizes of the row, the value of the main parameter is changed, and the values of the main parameters or the ratio of the values of the main parameters and the main one are usually assumed to be constant for the entire series or its individual sections. The values of the main parameters are taken as average or corresponding to the standard size, the need for which is greatest.
3.4. When determining production costs for parts, as a rule, the main parameter, the most important basic parameters, the cost per unit mass of material, the processing accuracy and the annual production program should be taken into account.
3.5. Production costs for parts and assemblies should be expressed as the cost of these component parts.
To determine the cost of a part and a simple assembly unit (drive couplings, hydraulic cylinders, etc.) when constructing series, a multifactor one-term power dependence of the form is used:
(3.1)
where A i- main parameter (size) i-th standard size, mm;
R- the main parameter, which, together with the main parameter, characterizes the overall size (entered if the main parameter does not determine the overall size, for example, for gears, the main parameter is the module, then the parameter R- number of teeth); if the main parameter determines the overall size, R = 1;
L- the main parameter (size), characterizing the overall size of the part in a plane perpendicular to the plane of measurement of the main parameter (size), mm;
p- cost per unit mass of material, rub./kg;
t- an indicator characterizing the manufacturing accuracy and expressed in points proportional to the tolerance value for the main parameter (for example, for sleeves of plain bearings - proportional to the tolerance for the hole diameter, for gears - a tolerance corresponding to the degree of accuracy of the teeth) or another main parameter;
N i- annual production program i-th standard size for the acquisition of newly manufactured equipment and for the replacement of equipment that fails or is forced to be replaced during repairs of equipment in operation, pcs .;
K i, u, ?, ?, X, at, n- coefficient and exponents, constant for parts and assembly units of the same type. The table below shows the calculated values t in points for various degrees of accuracy of cylindrical holes and degrees of accuracy of cylindrical gears.
Manufacturing accuracy index
To determine the coefficient and exponents, a regression analysis of the cost model is performed (see section 4 of the methodology) based on the collected data on the applicability of manufactured similar parts or assembly units.
The calculated values of the coefficient and exponents can be used in the construction of rows of parts and assembly units of this type with different ratios of sizes, different materials and processing accuracy.
For example, regression equations for the cost of spur gears are obtained
(3.2)
where t, z- modulus and number of teeth of the wheel;
L- hub length, mm,
and plain bearing bushings without shoulder
where d- diameter of the inner hole, mm;
D - outside diameter, mm,
L- sleeve length, mm.
It should be noted that the exponents t and N must be negative.
A simplified dependency can also be used:
C i" = K 1 A i u N i n, (3.4)
where for parts and assembly units of WMD the constants usually have numerical values n = -0,03 ... -0,25, u = 1,4 ... 2,5.
Based on the OMP reducers, an equation of the type (3.4) is obtained:
C i" = KA t i 0,98 N -0,10 , (3.5)
where A t i- center distance of the low-speed stage i-th standard size of a reducer, mm;
values K are equal: for cylindrical gearboxes with helical and chevron wheels - 3.1? 3.2, for worm and conical - 3.3? 3.4, for gear planetary - 4.0.
To determine the cost of complex assembly units, a multi-factor one-term exponential dependence of types (3.1), (3.4) is preferable. Models of another type can also be applied - linear polynomial, etc.
3.6. When determining the costs that arise in the application when designing equipment, it is necessary to take into account the costs of changing the dimensions and mass of mating and structurally related parts and assembly units due to the use of the nearest larger part or assembly unit from a row, instead of the required one by calculation.
Structurally related parts - parts that are not directly in contact with the part under consideration, but whose dimensions and mass change when the size and mass of the part under consideration change. For example, the housing and housing cover are structurally related parts for the gears of the gearbox.
Accounting should be done by setting costs C ? G resist to the difference in the increment in the mass of mating and associated parts and assembly units for the standard size of the series in question and the non-standardized standard sizes it replaces, or, in the absence of sufficient data on the replaced standard sizes, to the difference in the increment in the mass of mated and associated parts and assembly units for the standard size of the series in question and one from the most dense rows according to GOST 6636-69 or GOST 8032-84 (for parts - R80):
where? c - the average cost of 1 kg of mated and connected parts (on average 0.30 ... 0.50 rubles / kg);
?G- the average value of the increase in the mass of mated and connected parts per 1 kg of the mass of a unified part (is it advisable to determine? G based on the recommended ratios of the dimensions of the elements of the parts); for plain bearings? G= 7 ... 8 kg/kg, for rolling bearings 2 ... 3 kg/kg, for spur gears 0.7 ... 1.5 kg/kg;
G" i; G" iR 80, l - masses i-th standard size and replacing it 1, 2, ..., l-th standard size of the R80 series;
N" i; N" iR 80,l- annual graduation programs i-th and replacing it standard sizes for the acquisition of newly manufactured equipment.
For assembly units, the standard sizes of the rows R40 or R20 (Ra40 or Ra20) are used as compared.
For mobile machines (transport, road, hoisting and transport, etc.), additional costs for fuel (or electricity, etc.) should be taken into account for transporting an overestimation of the mass of mated and associated parts. In this case, in (3.4) instead of? with the expression (? c + ? t), where? m - the cost of fuel (or electricity, etc.) consumption per 1 kg of additional transported mass for the average annual mileage (travel path) of vehicles equipped with the considered unified parts from the series.
3.7. Operating costs for parts and assembly units when comparing rows of different density should be determined by calculating the cost of manufacturing these products to replace those that fail over the average or standard service life of the equipment completed with these products.
3.8. For parts and assembly units that are forcibly replaced in the course of scheduled preventive maintenance (SPM), when determining operating costs, only such changes in durability should be taken into account that lead to an increase in the service life of the product by one or more repair cycles (i.e., in two or more times).
Studies have shown that in cases of incomplete operational information, when it is known that a part or assembly unit of the type in question is replaced for the service life of the equipment completed with it, but the service life T n part or assembly unit (number of replacements) is not known, it is advisable to strive to increase the resource when creating a unified series T u 2 times.
3.9. For parts that are replaced as they fail (belts, chains, wear parts, etc.), when constructing rows, the expected value of the change in durability is taken into account without taking into account the duration of repair cycles.
3.10. In order to obtain more accurate results of calculating the optimal series, it is necessary to take into account, among the operational factors, the increase in the durability of a part of the annual program for the production of each standard size of load-bearing parts and assembly units, associated with the use of the nearest larger standard size from the series (instead of the calculated one) and with the variation of actual loads within the nominal load range , served by each standard size .
3.11. The total annual graduation program in j year i-th standard size of parts and assembly units required for completing newly manufactured equipment and for replacing, according to the PPR system, these products that fail during the life of the equipment, should be determined taking into account the factor specified in paragraph 3.10, according to the equation:
where N"- the total annual production program of all standard sizes for the acquisition of newly manufactured equipment, pieces;
N"i- annual program (in fractions of a unit) of output i-th standard size for the acquisition of newly manufactured equipment;
determined N" using a theoretical differential distribution function constructed from usability data adjusted for the planning period;
brackets mean that only the integer part of the expression enclosed in them is taken into account;
µ j ,? ; µ j-one,? - are determined by dependence (3.8), but instead of That put 2 T y (in accordance with the instructions in paragraph 3.8);
N" i,? - annual program (in fractions of a unit) of the output part i-th standard size, which has a durability two or more times higher than the nominal due to the use at loads less than the nominal.
In the case of calculating operating costs without taking into account the factor specified in clause 3.8, it is assumed N i ,? = 0.
3.12. If there are appropriate initial data and calculated dependencies, it is advisable in the operating costs when constructing rows to take into account the increase in the level of reliability (reliability) of bearing parts and assembly units in connection with the operation of a part of the output of each standard size at reduced loads that are within the nominal range of loads served by each standard size from row. This increase depends on the density of the row and leads to a decrease in the number of failures of parts and assembly units during overhaul periods.
Increased reliability can lead to a real reduction in the need for replacement due to outages.
A method for calculating the reduction in the need for replacement rolling bearings due to the increase in reliability under operating conditions at reduced loads is given in the recommended appendix 4.
3.13. Definition N" i is produced according to the distribution of annual production programs of standard sizes, obtained using applicability data. For a very common case, when the distribution of programs corresponds to or is close to the log-normal law, the value N"i is determined using the tables of the probability integral given in the courses of probability theory and mathematical statistics. In accordance with the recommendations, the boundaries of the unification range are usually taken based on the coverage of 90 - 93% of the total production program for all standard sizes. In the normalized form, the values of the boundaries are ± 1.80?.
As an example, let's define N"i for the fifth size of the R40 series. The number of sizes in a row is:
(3.9)
where BUT 0 and BUTm- parameter values at the boundaries of the unification range;
q is the denominator of the series.
Let's pretend that m= 100. Consequently, the difference between neighboring values of the parameter in the normalized form is 3.60/100 = 0.036?. We determine the boundaries of the interval corresponding to the fifth standard size in the normalized form: 0.036 4 = 0.144 and 0.36 5 = 0.180. The corresponding values of Ф( t) according to the table of the integral of probabilities are 0.0572 and 0.0714. Having determined the difference between the values of Ф( t), we get N" 5 = 0,0142.
3.14. To improve the accuracy of accounting for operating costs for assembly units, if it is possible to obtain the relevant initial data, in addition to the factors specified in paragraphs. 3.5 - 3.9, it is also advisable to take into account other operational factors (for example, a change in the complexity of the repair depending on the density of the row, i.e. on the repeatability of the size, etc.).
3.15. For gearboxes, the determination of operating costs for maintenance can be made using a power-law regression dependence on the repeatability of each standard size at one consumer enterprise, obtained by converting the regression dependences given in:
(3.10)
where A t is the center distance of the low-speed stage, mm;
N- annual program for the production of gearboxes, pcs.;
K e- equal for single-stage cylindrical gearboxes - 6.8, for two-stage cylindrical gearboxes - 10.6; for three-stage - 11.8; for conical - 7.6; worm - 8.3? 9.2; planetary - 16.5? 15.1;
l- repeatability at one consumer enterprise.
3.16. Due to the very large variety of types of products for special applications and the fundamental differences in their purpose and operation in each specific case of constructing product lines a certain kind Based on the analysis of their functional purpose and potential conditions for their use, it is necessary to determine a set of factors and indicators that change when one standard size is replaced by another and affect the technical and economic indicators of manufacturing and operation of the standard size.
3.17. When constructing standard size series, during which sets of all the main parameters (dimensions) of products are determined, in addition to the factors indicated above, as a rule, additional factors related to the specifics of the product design, technical level, production technology, as well as the specifics of operating conditions should be taken into account .
4 . OBJECTIVE FUNCTIONS AND CONSTRAINTS FOR CONSTRUCTING SERIES
4.1. To build optimal series, it is necessary to develop target functions that take into account the costs of various technical and technical and economic factors in different areas of the product life cycle, as well as the distribution of demand values (outputs) in various standard sizes.
The objective function of the optimal parametric series is the dependence to be minimized
where P i is a cost function that takes into account various life cycle costs i-th standard size of the row under construction;
t- number of sizes in a row.
Considering that when constructing a parametric series, mainly dependencies are used P i, we will conventionally call them objective functions.
4.2. For parts and assembly units, it is advisable to represent the generalized expression of the objective function for the case of conditionally accepting the average for the forecast period of constant annual output for the acquisition of newly manufactured equipment in the form:
(4.2)
where FROM"i- is determined by (3.1 ), (3.4 ); FROM ? G resist - according to (3.6);
g - average term service (before decommissioning) of equipment completed with the considered components.
4.3. Due to the fact that the optimal parametric and standard series, as a rule, should be a geometric progression from the preferred numbers according to GOST 8032-84 or from normal linear dimensions according to GOST 6636-69, it is advisable to build such series by comparing the costs by sections of the R5 series , R10, R20, R40 (or Ra5, Ra10, Ra20, Ra40). Since each standard size from a series of preferred numbers corresponds to two standard sizes from an adjacent more concentrated series, the comparison of costs P i, Irare per standard size of any row with costs Pi, August + Pi, II thick for two standard sizes of a denser row, it is advisable to produce in the form of a calculated inequality:
Pi,Irare Pi, August + Pi, IIst. (4.3)
After substituting in (4.3) the corresponding objective functions and carrying out reductions and transformations, calculated inequalities are obtained for cases of full or partial accounting for influencing factors, depending on the type of product, and a parametric series is built.
4.4. When constructing parametric series of parts and assembly units:
a) if their durability is assumed to be equal to or greater than the durability of the equipment they complete, and the effect of dimensional change from the use of the nearest larger part or assembly unit from a row, instead of the calculated one, on the change in dimensions of mating and surrounding parts and assembly units is negligible (for example, pulleys belt drives at low wear rates, drive clutches in open gears at low speeds, etc.), take into account only manufacturing costs and the calculated inequality has the form:
(4.4)
where - the ratio of the annual programs for the production of larger and smaller sizes of the more concentrated of the compared series, expressed as shares of the total annual program for all sizes, taken as a unit;
q- the denominator of the progression of a more condensed series;
n, u- indicators of the degree of multifactor power-law dependence of the cost of the type (3.1) or (3.4);
b) when taking into account all the main influencing factors in the areas of production, application in the design of products and operation, including taking into account the change in durability within the annual program of each size due to the use at various loads in the service range, for the acquisition of stationary and mobile equipment apply the inequality:
where K 1 , K 2 - coefficients of multifactorial power equations for determining the cost of the type (3.1), (3.4) and mass (depending on the main and main parameters and the density of the material -?); it is expedient to use in the mass model a part of the dependence of the cost price of the type (3.1 ), (3.4 ) without R, t, N, i.e. part characterizing the volume of a part or assembly unit - G = K 2 A u R ? (L/A) ? ? h or G = K 2 Au?h;
in order to establish the error caused by such use, it is necessary to determine the relative errors of the calculated mass values compared with the actual ones according to the applicability data; P = p x t v(see paragraph 3.3), when using equation (3.4) R = 1; H= ? With? G? h g (see item 3.4); h- exponent at? close to 1;
c) in a case similar to b), but without taking into account the change in durability within each standard size from the series, inequality (4.5) is applied, but B ? in both parts of the inequality are replaced by the expression
(4.6)
d) in a case similar to b), but under conditions where it is assumed that the average durability of parts and assembly units from a series will be equal to or greater than the average durability of the equipment they complete, apply the inequality (4.5) when AT ? = 1.
4.5. For complex assembly units (gearboxes, gearboxes, etc.) and some special parts, as a rule, in each specific case of constructing parametric series, it is necessary to study the influencing factors and assess the feasibility of developing and including additional influencing factors in the objective function and the calculated inequality of mathematical models factors.
4.6. The calculated inequalities given in paragraph 4.4, it is also advisable to develop for constructing parametric series and in cases of selecting standard sizes for the optimal series from the available nomenclature by excluding some standard sizes with a corresponding expansion of the scope of the remaining ones.
4.7. To build standard size series, objective functions are developed that include, in addition to the factors discussed above, also others related to the input parameters.
It is advisable to include factors that reflect the specific features of the conditions of use in the design of equipment and operating conditions. In cases of complex dependencies with a large number of parameters, optimization should be carried out in stages, as indicated in Section 5, by building separate objective functions.
In the recommended Appendix 6, an objective function is given for optimizing a number of gear ratios of gear boxes of metal-cutting machine tools. Optimizing a number of gear ratios is the first preliminary stage optimization of the standard size range of gearbox gears.
4.8. When constructing parametric and standard size series of equipment, it is necessary to include in the objective function the scope and structures of work to be performed by the standard sizes of the series under construction. At the same time, the features of equipment and types of work should be taken into account from the standpoint of varying degrees of replacement of standard sizes.
4.9. It is advisable to distinguish the following types of substitutability:
one-sided - a replacement size can only have a larger (in certain types products - only a smaller) value of the main parameter than the size being replaced (for example, rolling and sliding bearings, gearboxes, gears, etc.);
double-sided - a replacement size can have both a larger and a smaller value of the main parameter; Bilateral interchangeability is possessed by equipment and components that perform such functions that can be divided according to the main parameter while maintaining the technical equivalence of the result of operation, while economic indicators may be different (for example, one pump of greater productivity or two of less);
mixed - for one type of work, the replacement standard size should have only greater value the main parameter, and according to others - it can have both more and less.
In addition, interchangeability should be classified according to the degree to which the level of all technical requirements for the work performed is met as follows:
full - the replacement standard size performs the functions of the replaced one, fulfilling all the technical requirements for work at the same level;
partial - the replacement size does not fully perform the functions of the replacement, or performs all the functions, but the level of all or part of the technical requirements is not met, in such cases it may be necessary to perform additional work, or the product will be of a lower technical level.
4.10. A number of important technical or techno-economic requirements or conditions are not included in the objective function to avoid its excessive complexity or due to the difficulty of combining with the factors and conditions contained in the objective function.
Such requirements or conditions are formulated separately in the form of inequalities - restrictions to the optimization problem of the series.
4.11. As shown above, the use of unified or standard products from the built series leads to an overestimation of the dimensions and weight of the product (as well as other products structurally related to it) in cases where the nearest larger standard size from the series is used instead of the required one according to the calculation (or the previously used special one).
In most cases, due to some increase in the specific indicators of the technical level of parts and assembly units, a certain reduction in the size and mass of unified standard sizes in a row can be achieved compared to unified standard sizes, the specific technical level indicators of which are taken on the basis of the widely used principle of average or most frequently encountered in to be replaced by a unified set of corresponding original components. The proposed approach ensures the elimination or minimization of these losses from the use of the nearest larger part or assembly unit from the series and leads to a corresponding increase in the technical level of equipment completed with new standard sizes from the series.
4.12. Based on the analysis of large data sets on specific parts and assembly units, the practical possibility and technical and economic feasibility of switching in many cases to the manufacture of parts and assembly units in a series of higher-strength materials with more perfect species hardening, which provides the required increase in the values of specific indicators of the technical level.
Given that the main goal of building an optimized series of standard and unified products is the organization of their highly specialized industries, the implementation of these improvements in material and technological processes should be considered as real, progressive and cost-effective.
4.13. For load-bearing parts and assembly units, when constructing their rows, in addition to the restriction on the numerical values of the parameters (choosing them from the rows of preferred numbers), two technical restrictions should be formulated that ensure the solution of the problem posed in paragraph 4.11:
the total mass of the annual program for the production of all standard sizes of components from the built range, satisfying the planned needs, should not be more than the total program for the production of all standard sizes of original components to be replaced, satisfying the same needs,
(4.7)
the total resource (or loads) of the annual program for the production of all standard sizes from the series that satisfies the planned need should not be less than the total resource (or loads) of the annual program for the production of all standard sizes of original components to be replaced that satisfies the same needs,
where? p , y, ?p ,0, y- permissible specific load of unified parts and original parts made of j-th material;
G 0,i,k , N 0,i,k- weight and annual production program k-th original part from the first to l th parts to be replaced i th unified.
4.14. A simplified approximate use of inequalities is allowed by solving them up to the complete solution of the series optimization problem. In this case, inequality (4.7 ) is preliminarily solved. For the solution, some constant most probable values are taken R, L/A, ?at and take a series of values as successive values of the preferred numbers R20 (or R10) within the range determined to build a series from the analysis of the array of initial data. In case of explicit dissatisfaction, inequalities (4.7) shift the range by one value from the series R20 (or R10) towards smaller values and again check the inequality. The solution of the inequality is continued until it is satisfied. The resulting series of parameter values from the series R20 (R10) within the range that satisfies inequality (4.7) is introduced into inequality (4.8) and solved with respect to? p , y. Next, set the type of material and the type of hardening, providing the value obtained? p , y.
4.15. If it is impossible to fully satisfy both inequalities (4.7) and (4.8), a decision should be made on the priority of one or the other, depending on the specific technical and economic problems to be solved.
4.16. General requirements for the formation of mathematical optimization models.
4.17. Basic models for optimizing the parametric series of measuring instruments and automation - according to RD 50-397-83.
5 . REQUIREMENTS FOR METHODS FOR CONSTRUCTION OF PARAMETRIC AND SIZE SERIES
5.1. The methods used to build parametric and standard series must meet the following requirements:
allow, according to the nomenclature and nature of the initial data required for the implementation settlement procedure, build rows at the initial stages of designing unified WMD products, ensure, as a rule (except for the special cases specified in paragraph 1.6), the construction of optimal rows with the lowest economic costs (or the highest economic profit) provided that the established technical level of products adopted restrictions on the structure of the series and the numerical values of the parameters specified in section 1;
ensure the construction of optimal series with the structure of the objective functions given or described in section 4;
carried out with the help of computational operations, practically implemented manually or on modern computers;
provide objective results.
5.2. Methods for constructing type-size series should, as a rule, provide the possibility of simultaneous optimization of all or the most important group of main parameters for the entire range of values of the main parameter.
5.3. In cases of a large number of main parameters, which causes computational difficulties, it is allowed to divide the main parameters into groups and build series by successive optimization of groups of parameters.
5.4. To reduce losses in cases of constructing standard-size series with a large number of basic parameters and in the presence of uncertainty in the initial information, a two-stage construction of the series can be applied:
at the initial stages of design, less accurate, but simpler approximate methods for constructing series are used with consideration of a large number of options;
at the final stages of design, when the necessary information is accumulated, more accurate and complex methods are used with a small number of options considered.
5.5. A rationally applied optimization method should provide a selection problem, taking into account the types of product substitutability specified in Section 4.
5.6. Rest General requirements to the methods used to optimize the series, - .
5.7. Classification and applicability of optimization methods - according to RD 50-220-80.
6 . METHODS FOR CONSTRUCTION OF PARAMETER AND SIZE SERIES OF PARTS AND ASSEMBLY UNITS
6.1. The method of constructing parametric series by transfer points (the method of transition points) is designed to construct optimal parametric series (series of the main parameter) of parts and assembly units, the distribution of demand for which can be approximated by continuous dependencies (functions) of a single-vertex (unimodal) type.
The application of this method does not provide for the mandatory use of previously produced standard sizes; it is possible to build an optimal parametric series with a rational structure based on the analysis of data on previously manufactured standard sizes.
The construction of series by this method is most expedient when carrying out work on the unification, standardization of parts and assembly units in the context of the development of new ranges of equipment, machine systems, etc., when replacing models of manufactured equipment at enterprises and in industries with a multi-product unit or serial nature of production ( machine tool building, heavy engineering, various sub-sectors of mechanical engineering for light and food industries, sub-sectors of road construction engineering, etc.). The method is also intended for use in optimizing the series of parts and assembly units in accordance with state and industry standards, especially when creating specialized production facilities for these products.
By the presence and type of the mathematical procedure for searching for an extremum ( optimal solution) the method of transition points refers to particular methods of mathematical programming.
6.1.1. The main parameter of parts and assembly units in most cases has a distribution close to logarithmically normal. With a logarithmically normal distribution, the application of the transition point method is the least laborious. The method can be applied both for manual calculation and using a computer.
6.1.2. When constructing series by the transition point method, the criteria, objective functions, calculated inequalities and restrictions given in sections 1 and 4 are used.
The method is based on the laws of rational structures of the series of the main parameter of parts and assembly units. It is applicable not only for optimizing the series of the main parameter, but also for the series of other main parameters.
6.1.3. The procedure for constructing the optimal parametric series by the transition point method is as follows.
Based on the data on the distribution of the parameter being optimized, the boundaries of the rational range of unification are determined. According to the literature data, it is expedient to cover 90–93% of the total output of all standard sizes of a unified product by unification, which corresponds to the values of the boundaries of approximately ±1.80 with a logarithmically normal distribution law.
Determine by (3.9) the number of sizes of the Ra40 (R40) series in the unification range.
Further, using the tables of the probability integral (see paragraph 3.13) or according to pre-calculated tables of values ? i and N" i, I determine the value? the smallest of the Ra40 series (as a rule, corresponds to the last two sizes of the series with highest values parameter) and N" i, I for the smaller size of the respective pair.
Then, the most suitable inequality for the case under consideration is solved, from among those indicated in section 4, in which the costs for the standard size of the Ra20 series and two standard sizes of the Ra40 series are compared.
If the inequality sign shows that the cost per size of the Ra20 series is less, then it is assumed that the sizes of the Ra40 series do not belong to the optimal series and one should proceed to a similar comparison of the largest size of the Ra10 series and the corresponding two sizes of the Ra20 series. If the sign of the first inequality shows that the costs for the standard sizes of the Ra40 series are less, then determine? largest (usually corresponds to the smallest two sizes of the Ra40 series) and the corresponding value N" i, I . Solve the inequality for the corresponding size of the Ra20 series and two sizes of the Ra40 series. If the inequality sign again indicates greater efficiency (lower costs) of the sizes of the Ra40 series, then this is proof that the optimal series consists of the sizes of the Ra40 series over the entire range and no further calculations are required. Finally, if the last inequality showed a greater efficiency of the Ra20 series size, it can be considered established that a part of the Ra40 series belongs to the optimal one. To find the transition point in the optimal row from the Ra40 row to the Ra20 row, the inequality is solved for the sizes Ra20 and Ra40 located in the middle of the common range. Next, the inequality is solved for the middle of that half of the range, at the edges of which there are inequalities with opposite signs, then for that of the quarters, at the edges of which the inequalities have opposite signs etc. until two inequalities are obtained for neighboring sizes, having opposite signs. Between these sizes is the transition point. Thus, it is established that the sizes of the Ra40 series from the largest to the size at the transition point belong to the optimal series.
The construction of the series ends with the establishment of the density of that part of the optimal series, which belongs to the smallest standard sizes of the unification range.
6.1.4. Subject to the accepted restrictions, the method of transition points and calculated inequalities make it possible to build rows of parts and assembly units, the manufacture and operation of which is carried out with national economic costs 10–25% less than the costs of rows of parts and assembly units built according to previously accepted methods, due to introduction into the calculation of factors previously not taken into account, clarification and development of methods for accounting for other factors. In addition, the procedure of the method ensures the obligatory construction of a series with a rational structure - geometric or step-geometric, thickening in the direction from lower parameter values to larger ones, which, in turn, allows to reduce costs for a number of technical and technical and economic factors (reduction and rationalization range of workpieces and reduction of losses due to overestimation of allowances, reduction of the range of processing and measuring tool etc.), which are not taken into account, due to difficulties in determining, in the objective functions and calculated inequalities given in Section 4.
The method of transition points can also be used in the construction of standard series by successive optimization of the series of each of the parameters.
The method of transition points is used to construct the optimal series of the main parameter of rolling bearings in GOST 5721-75 (light series of diameters), GOST 8419-75 (especially light series of diameters 1) and housings of plain bearings in GOST 11521-82.
An example of constructing a parametric series by the method of transition points is given in Appendix 6.
6.2. The method of constructing parametric and standard size series with the exception of standard sizes is designed to build a series of parts and assembly units in industries and associations with a mass production of individual standard sizes, the production programs of which significantly exceed the production programs of other standard sizes of parts or assembly units of the same type (for example, agricultural engineering, some sub-sectors of mechanical engineering for light and food industries, chemical and petroleum engineering, instrument making, etc.) when upgrading and replacing individual models of manufactured equipment in conditions where the task is to maintain the design and dimensions of the most mass-produced standard sizes produced at specialized industries, as well as when setting the task of minimal processing of the most mass-produced models of equipment and the least restructuring of mass production.
6.2.1. The method procedure is as follows. Based on the collected applicability (actual manufacturing) data, a histogram of the distribution of production programs for the standard sizes of the product in question is built (with appropriate adjustments for the expected growth of production programs). Define the boundaries of the unification range as indicated in section 3. According to the histogram, the most mass-produced and specialized manufactured sizes are selected, which are taken as the initial basic sizes of the row under construction.
6.2.2. Based on the requirements for equipment in which parts and assembly units from the series under construction will be used, the technical level of the basic standard sizes is checked. If it is expedient to increase their technical level, calculations are performed using the methods described in section 2. At the same time, the task is to minimize changes in the design, overall and connecting dimensions. The established technical level is accepted for all sizes, or, if appropriate, it is differentiated for different sizes.
6.2.3. Compile estimated inequalities of the type (4.3 - 4.5) to compare the costs for the life of the completed equipment for annual production programs for each of the selected base i-x standard sizes and the nearest smaller one manufactured ( i- 1)th standard size - on one side and along i-th size when replacing them ( i- 1)-th standard size, taking into account the change in cost from a change in the release program, the cost of overestimating the mass of mating parts from the use i-th size instead of ( i- 1)-th and taking into account the costs of technical training production of mating parts modified due to the specified change in standard sizes (technical preparation costs can be provisionally attributed to the first year of production):
where N i , i-1 - total annual release program i-th and ( i- 1) standard sizes, pcs.;
K m.p. - cost increase factor due to the cost of technical preparation of production. It is desirable to determine K etc. according to the actual data, in their absence, you can use the following indicative values:
|
Annual release program, pcs. |
|||
Rest conventions correspond to those adopted in Section 3.
Quantities N i ,j , N i -1,j determined by equation (3.7).
In the event that the costs of the combined standard size turn out to be less, they constitute a similar inequality for replacement cases i-th standard size of two standard sizes - ( i- 1)th and ( i- 2) th.
In this case, a term is added to the left side of inequality (6.1 ) that characterizes the costs of ( i- 2)-th standard size, and on the right side in the first member in the numerator write the total program for three standard sizes, the other two members of the right side of the inequality (6.1) are written separately for ( i- 1)th and ( i- 2)-th standard sizes. If, in this case, the costs for the combined standard size turn out to be less, then the inequality for the combination of four standard sizes is similarly made. If, when analyzing the second inequality, it turns out that the costs for a standard size that combines only i-th and ( i- 1)-th standard sizes, then in this area they are finally taken in the optimal row i-th size and exclude ( i- 1) th. Similarly, an analysis is carried out for all accepted as basic mass sizes. In areas that remain after that not covered by the analysis, a similar analysis is performed, starting with the largest of the unconsidered standard sizes in this area.
6.2.4. As a result of a consistent consideration of costs by standard sizes in all parts of the unification range, an optimal series is formed. If necessary, in areas with a large vacuum, the expediency of introducing additional (previously not produced) standard sizes into the optimal range can be made in a similar way.
6.2.5. If, in the above analysis, only standard sizes with different values of the main parameter are considered, but there are also versions with different values of the main parameters with the same value of the main parameter, then as a result of the analysis, a series is obtained that can conditionally be classified as parametric (the series of the main parameter). If there are no standard sizes with different values of the main parameters with the same value of the main one, then the constructed series is standard, since its construction determines all the necessary standard sizes both for the main and for all the main parameters and further analysis is not required.
used in this method the method of comparing costs for actually manufactured and combined standard sizes is similar to the method described in the work.
6.3. The method of constructing standard size series by transition points using a generalizing parameter is designed to build standard size ranges of load-bearing parts and assembly units, when a set of numerical values of the main parameters of any size (with a specific material and method of hardening) corresponds to a certain calculated value of the transferred load. For example, knowing the modulus, the number of teeth, the length of the gear tooth, the material of the wheel and the type of hardening, it is possible to determine the transferred load according to the criteria of bending strength and contact strength.
6.3.1. At the first stage, for each numerical value of the main parameter, a number of sets of numerical values of the main parameters in their real combinations are determined using the transition point method.
6.3.2. Due to significant computational difficulties in joint optimization of sets of numerical values of several parameters, especially when taking into account complex multimodal functions that characterize the corresponding objective functions, optimization is performed using one generalized parameter - bearing capacity, which, as noted above, characterizes specific sets of basic parameters.
6.3.3. To optimize the size range in terms of bearing capacity, the transition point method described above is used.
6.3.4. After optimization, the resulting series of bearing capacities is replaced by the corresponding series of sets of numerical values of the main parameters, which is the optimal size range.
6.4. In cases where, for technical reasons, it turns out to be appropriate to select parameter values when optimizing a series not from preferred numbers and normal linear dimensions, but from any natural numbers or from a continuous numerical sequence, i.e. without restrictions on the numerical basis, it is advisable to use programming methods (dynamic programming, etc.) for constructing parametric and standard series, which are detailed in the methods.
6.5. Due to the large variety of various special products, their functions, types of work, the different nature of the interchangeability of product sizes, the variety of types of their parameters, there is currently no most rational single method for optimizing their parametric and standard series.
Taking into account the specific features of products, influencing factors, structures of objective functions and types of restrictions, described in sections 3 and 4, to solve a specific problem, one should choose a method corresponding to the characteristics of the problem, effective and mathematically correct.
6.6. In cases of building series of products for special applications, when it is difficult or inappropriate to use the methods set out in paragraphs. 6.1 - 6.3 apply the following methods:
for parametric series
with more options, double-sided interchangeability, intersecting areas of work of various sizes, etc. - method of dynamic programming;
in the absence of an analytical function of operating costs caused by some discrepancy between any standard size from a series of specific operating or consumption conditions compared to a specially designed product (sometimes this function is called a function of adaptation losses) - an adaptive series optimization method or a method of statistical decisions. In both methods, it is conditionally assumed that the losses from adaptation are proportional to the square of the value, which is the ratio of the difference between the required parameter and the parameter value from the series to the required parameter value;
for standard series
branch-and-bound type method.
METHODOLOGY FOR ESTABLISHING RATIONAL VALUES OF THE MAIN SPECIFIC INDICATORS OF THE TECHNICAL LEVEL OF PARTS AND ASSEMBLY UNITS OF GENERAL ENGINEERING APPLICATION (OMP)
1. For most parts and assembly units of WMD, the main indicator of the technical level is the specific bearing capacity.
2. For WMD parts, the value of the specific bearing capacity should be taken as the value of the allowable stress (according to the main type of load the part is designed to carry) or other similar characteristic, and for assembly units - the ratio of the bearing capacity to the mass of the assembly unit or other important relative characteristic.
3. In order to establish a rational value of the main quality indicators of unified WMD products and build their series at manufacturing enterprises and organizations operating products subject to unification, the following materials and data are collected:
drawings of products indicating the cost and annual production program in the current or previous year;
average life (or durability) data T n WMD products before replacement, methods of replacement (forced during the next repair or as the limit state is reached), the most common cause of failure or forced replacement (destruction criterion; for example, fatigue fracture, contact fatigue, abrasive wear, etc.) ;
average life data T m until the write-off of the equipment completed with the WMD products in question.
4. The data specified in paragraph 3 are collected on all standard sizes of the WMD product, which are supposed to be replaced in the future with unified ones, or on a sufficiently complete and representative sample. It is desirable to obtain data for at least 100 - 200 standard sizes. If it is impossible to obtain the specified sample size or with a small number of replaced standard sizes, a corresponding decrease in the sample size is allowed, however, this increases the calculation error.
5. The data obtained and the data of the drawings for products of the same type are summarized in a table of applicability, which indicates: the designation of the product according to the drawing, the main and main parameters, mass, type of heat treatment, hardness, annual production program, cost, causes of failure, durability or service life of the WMD product, service life until the write-off of the equipment completed with this WMD product (the last two types of data - if available).
6. On the basis of applicability data on unofficial WMD products, which are supposed to be replaced by unified ones, a theoretical distribution of the values of the main parameter is built, which is closest to the empirical one (see).
7. According to the operation data, the ratio of durability (service life) of WMD products subjected to unification is determined - T n and durability (service life before decommissioning) of the equipment completed with these products - . If it was possible to establish the actual average value of the ratio and determine the desired average value of durability (service life) for unified WMD products - , based on the feasibility of providing
When operational information is insufficient, when it is known that T P< T m, but the ratio is not established T P: T m, and it is known that the replacement of standardized WMD products is carried out during repairs at certain intervals (a system of scheduled preventive repairs), it is advisable to take what is established by calculations for a large number of types of equipment in various branches of engineering. In this case, as will be shown below, there is no need to set the actual numerical value
8. Having determined according to the data of the sample (according to information about the material used, the type of hardening, hardness, etc.) for each i th standard size of the part, the value of the allowable stress? add.P i(or other similar characteristic), set the weighted average values of the allowable voltage:
(1)
and main parameter
(2)
where G Pi, A Pi, NPi- weight, main parameter and annual production program i-th size.
9. From the ratios between , , , obtained from expressions for calculating the strength and durability of parts of the corresponding type (ratios for gears and gears are given in Appendix 2), determine, since , , are defined earlier, as indicated in paragraphs. 7, 8.
where , - allowable contact stress with the number of stress cycles 10 6 for non-standardized and unified wheels.
In case of insufficient operational information, when they accept (see clause 7), instead of numerical values and in the expression for calculation, a ratio of 1: 2 is substituted.
If the inequality turns out to be practically unattainable or impractical due to too large values of , one should take this from possible values, which will provide an increase in comparison with by a multiple of the overhaul cycle.
10. If, after establishing the values according to the relations of the type (3), it will be possible to choose the material and the type of its hardening, providing more high value appropriate to determine the possibility overall decrease values of the main parameter in the row under construction compared with the values for parts to be replaced by unified ones (in the absence of technical restrictions on reduction, for example, in terms of rigidity, etc.). To do this, use the relationship between the values of the main parameter and the allowable stresses obtained from the equations for calculating parts of this type for strength and durability.
For example, for cylindrical gears, when contact fatigue is taken into account, the relation has the form
(4)
In this case, all values of the main parameter in the theoretical distribution are reduced (see paragraph 6) by a number of times equal to
The final value of the reduction in the values of the main parameter is set after checking according to the technical criteria that limit the reduction in size (for example, for gears - the minimum number of teeth without undercut, the strength of the hub, etc.).
11. If, according to the operation data, it is established that in most cases of the use of WMD products subject to unification, there is a ratio, then when establishing the technical level during unification (building a series), it is advisable, if possible, to choose a material, type of heat treatment, hardness, etc., based on ensuring the same ratio for unified WMD products while simultaneously rationally reducing the size in the manner specified in clause 10.
12. If it is possible to collect the relevant initial data, instead of the construction indicated in clause 6 according to the applicability data for the distribution of the values of the main parameter, it is more advisable to first build the distribution of the required load values and then, according to this distribution, build the distribution of the values of the main parameter, based on the WMD established for unified products permissible loads or other specific load characteristics. This approach allows in some cases to obtain additional savings from downsizing.
ESTABLISHMENT OF RATIONAL VALUES OF SPECIFIC INDICATORS OF THE TECHNICAL LEVEL OF UNIFIED GEARS
1. According to the data collected in the production of the tables of applicability of manufactured gears using the formulas GOST 21354-75 “Cylindrical involute gears. Strength calculation "calculate a table of endurance limits for various materials and for each i-th standard size and corresponding material, type of heat treatment and hardness. The values of the endurance limit are determined from the table for the leading type of destruction (for example, for the case of destruction due to contact fatigue - ) and the base number of cycles N ho , which are entered into the table.
2. Calculate the endurance limit for the number of cycles 10 6 (this number of cycles is convenient, since it corresponds to the inclined branch of the fatigue curves according to contact stress and in bending for various steels and types of heat treatment)
(1)
3. For everyone i-th standard size is determined in accordance with the instructions of GOST 21354 -75 coefficient values S NP, Z R P i, Z V P i, KL P i, KXH P i.
4. Calculate for each wheel the allowable stress at N = 10 6
(2)
5. Set the weighted average value of the allowable stress for the entire sample of wheels
(3)
where N i- the number of wheel sizes (in the sample) with the same material, heat treatment and hardness;
The total net weight of wheels made of the same material, with the same heat treatment and hardness.
6. According to the ratios given in the table of this appendix, the allowable stress is determined at N= 10 6 cycles for unified wheels, for example
Ratios for establishing a rational technical level of unified gears and wheels
|
Part or complex type, main parameter |
Strength calculation criterion |
The relationship between allowable stresses and |
|
|
durability |
main parameters (dimensions) |
||
|
Cylindrical gears (pairs of wheels), the main parameter is the center distance a ? |
|||
|
bending fatigue |
|||
|
Cylindrical gears, the main parameter is the module m |
Contact stress fatigue |
||
|
bending fatigue |
|||
Note. n= 6 for wheels with tooth surface hardness HB? 350 and wheels with a ground transitional surface regardless of hardness, n= 9 for wheels with an unpolished transitional surface with HB > 350.
7. Based on the type of equipment for which the wheels are unified, certain indicators of the quality of the wheels are assigned, taking into account also the operating conditions (they are taken on average the same for unified wheels and for the non-unified wheels they replace), and determine the numerical values of the coefficients S HU, Z RU, Z V Y, K LU, K XNU.
8. Count
(5)
10. Using formulas like ( 1 ) recalculate the values of the endurance limit with the base number of cycles from the table (p. 6) into the values of the endurance limit with the number of cycles N\u003d 10 6 and set for unified wheels the material, heat treatment and hardness, providing the next larger values in comparison with those obtained by calculation and
11. The given technique does not take into account cases when the destruction occurs from maximum loads or low-cycle fatigue. However, with the correct calculation of the wheels and their correct operation, as a rule, loads should not occur that exceed the loads taken into account in the cyclogram, and, accordingly, for these reasons, a significant number of failures should not occur.
12. Given in paragraphs. 1 - 10, the technique is based on the calculated dependences of the fatigue strength of the gear material corresponding to the "pre-baseline" zone (the inclined branch of the fatigue curve). However, when the desired values of the durability of unified wheels are established, it is quite likely that they will fall into the “out of base” zone. Calculations have established that in this case the obtained values of the allowable stresses required for unified wheels turn out to be somewhat overestimated, but the relative value of this overestimation, as a rule, does not exceed 5–7%.
APPENDIX 3
Mandatory
NOMENCLATURE OF MAIN AND BASIC PARAMETERS OF PARTS AND ASSEMBLY UNITS OF WMD
Table 1
Mechanical gear parts
|
product name |
Main and main parameters |
||||||||||
|
dl 2 number |
u nom |
Number of grooves |
Groove section |
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|
Asterisks |
|||||||||||
|
for flat belts |
|||||||||||
|
for V-belts |
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|
Gear cylindrical power transmissions |
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|
Cylindrical gear wheels |
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|
Bevel gears |
|||||||||||
|
Worm gears |
|||||||||||
table 2
Rolling and sliding bearings
Table 3
Details of rolling and plain bearing units
|
product name |
Main and main parameters |
||||
|
hole diameter |
outside bore diameter |
outer diameter (overall) |
length (for bushings), center distance between mounting bolts (for housings) |
distance from the shaft to the base of the paws |
|
|
Flanged rolling bearing housings |
|||||
|
Foot Mounted Rolling Bearing Housings |
|||||
|
Covers deaf |
|||||
|
Covers with a hole |
|||||
|
Spacer bushings in the body |
|||||
|
Bushings remote on the shaft |
|||||
|
Plain bearing housings with foot mounting |
|||||
|
Plain bearing housings, flanged version |
|||||
Table 4
Fasteners
|
product name |
Main and main parameters |
|||||
|
outside diameter |
thread diameter |
inner diameter |
length (thickness) |
head diameter |
head height |
|
|
Rivets |
||||||
Table 5
Reducers, couplings, variators
|
product name |
Main and main parameters |
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|
M nom |
M naib |
regulation range |
u nom |
D bunk |
dl 2nom |
|||||
|
Gearboxes |
cylindrical |
|||||||||
|
conical |
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|
conical-cylindrical |
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|
planetary |
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|
worm |
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|
worm-cylindrical |
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|
jagged |
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|
cam |
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|
flanged |
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|
elastic with toroidal shell |
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|
Variators |
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Table 6
Hydraulic, pneumatic and lubrication equipment
|
product name |
Main and main parameters |
|||||||||
|
P nom |
n nom |
V nom |
Q nom |
|||||||
|
cylinders |
||||||||||
|
Equipment |
||||||||||
|
Hydraulic accumulators |
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Symbols adopted in Table. one - 6
XX - main parameter;
X - main parameter;
a? - center distance, mm;
aΔt - interaxal distance of the low-speed stage of the gearbox, mm;
b(AT) - crown width, mm;
D- diameter (pulley, cylinder), outer diameter of the coupling, mm;
Dy- conditional passage, mm;
d- rod diameter, mm;
dl 2nom - nominal diameter the base of the dividing cone (dividing diameter) of the wheel of the bevel gear pair, mm;
Filtration fineness, microns;
L- piston stroke, mm;
t- module, mm;
M t - torque on the low-speed shaft of the gearbox, N m (kgf m);
M nom - rated torque, N m;
M naib - maximum torque, N m;
n nom - nominal number of revolutions, s -1;
r c - carrier radius, mm;
u nom - nominal gear ratio;
t- chain pitch, mm;
z- number of teeth;
R nom - nominal pressure, MPa;
V nom - nominal volume, cm 3;
V 0 - working volume, cm 3;
Q nom - nominal flow (flow rate), dm 3 / s (l / min).
METHOD FOR CALCULATION OF REDUCING THE NEED FOR ROLLING BEARINGS DUE TO GROWTH OF FAILURE-FAULT UNDER OPERATION CONDITIONS AT LOW LOADS
1. Based on the well-known position that the probability of non-failure operation of rolling bearings is well described by the Weibull equation and taking into account the constants of the international standard ISO 281/1-77, the equation for the probability of non-failure operation of a bearing in j year from start of operation
(1)
where T d, abs - service life before scheduled replacement in years.
The equation is derived from the acceptance condition T d = 1 at rated load.
2. Quantity N over.un. i bearings in question i-th standard size (in fractions of the total demand, taken as a unit) required per year to replace suddenly failed bearings, it is advisable to determine using the average value of uptime for the year. The specified value is calculated as the arithmetic mean of the probabilities of failure-free operation during the first and last years overhaul cycle. The probabilities for each of these years are in turn determined as the average of the cases of operation at rated and lowest loads within the range served by this bearing size. With this in mind, the number of suddenly failed bearings is equal to
3. In accordance with GOST 18855-82
where FROM din, i- dynamic load capacity of the bearing i-th standard size;
-th size.Taking into account the condition adopted in paragraph 1, assuming that
FROM din, i = R i.
The greatest durability obtained at the lowest load, i.e. at Pi = FROM din i-1 equals
(8)
where? = 3 for ball bearings;
3.33 for roller bearings.
Thus, by introducing into the objective function and the calculated inequality, taking into account the change in demand from a change in the level of reliability, we can compare the gains when comparing costs by standard sizes of rows of different density.
OBJECTIVE FUNCTION FOR OPTIMIZING A SERIES OF TRANSMISSION RATIO OF GEAR GEARS OF GEARBOXES OF METAL-CUTTING MACHINES [ 3 ]
To optimize the size range of spur gears for gear boxes of metal-cutting machine tools, an objective function has been developed for preliminary optimization of one of the main parameters - a number of gear ratios.
The objective function compares the costs of manufacturing a gearbox (costs decrease with a decrease in the density of the rows of spindle speeds, i.e. with a decrease in the number of gears in the gearbox) and the cost of processing on a machine tool (costs for a tool decrease as they approach optimal cutting speeds, i.e. e. with an increase in the density of rows of spindle speeds)
where P- total costs before the first overhaul machine;
FROM st - the cost of manufacturing and operating the machine itself until the first overhaul;
FROM in - operating costs cutting tool before the first overhaul of the machine;
for lathes;
FROM current repair - expenses for the current repair of the gearbox;
FROM cor - the cost of the gearbox;
BUT sp - center distance of the intermediate shaft and spindle, which mainly determines the dimensions of the box;
The range of spindle speed changes associated with the kinematic complexity of the box;
N- an annual program for the production of gearboxes;
FROM h - the cost of a machine part without a gearbox (does not depend on the number of gearbox gears);
O - the denominator of the most condensed series of spindle speeds, ? 0 = 1.06;
i- whole natural number;
V opt - optimal cutting speed with economic tool life for the most frequently machined material;
Cutting condition indicator for turning;
FROM? - constant, depending on the material being processed, the material of the cutter, etc.;
K- coefficient taking into account the influence on the cutting speed of the angle in the plan, the material being processed and the size of the tool;
t- depth of cut;
S- submission;
An indicator of relative durability? = 1/m.
t mash - machine processing time;
t non-machine - non-machine processing time;
S in - the cost of operating the cutting tool for the period of its durability;
K 3 - machine load factor;
The service life of the machine before the first overhaul in years;
Ф - the total annual fund of the machine's operating time in minutes.
As a result of calculations for the given objective function, it was found that under the accepted conditions, the total minimum costs are obtained in the manufacture of gearboxes with the number of gears determined by the given ratio n nb: n nm and? = 1.12 - 1.26.
APPSE 6
Reference
CONSTRUCTION OF THE OPTIMAL PARAMETER SERIES (SERIES OF THE MAIN PARAMETER) OF PAIRS OF BEVEL GEARS BY THE METHOD OF TRANSITION POINTS
According to the data of one of the sub-sectors of mechanical engineering on manufactured non-standardized pairs of bevel gears, an optimal parametric series was constructed using the transition point method (see section 5) using the calculated inequalities indicated in section 3. For the main parameter of the pair, the diameter of the initial circle of the larger wheel is taken. Statistical analysis of applicability data showed that the distribution of the values of the main parameter of manufactured pairs is satisfactorily described by the logarithmic-normal law. The rational range of unification, covering about 93% of all pairs, i.e. ±1.80?, equals 40 - 400 mm.
According to the actual data, the statistical calculation of the equation (3.4) of these guidelines and the mass equation determined the constants u = 1,65; n = -0,2; K" 1 = 0,07; K" 2=0.001; ? G = 6 kg/kg; ? c = 0.5 rub. The average service life of complete machines g = 6 years, and the average service life of pairs of bevel wheels T d = 2 years. The total annual requirement is 1000 pairs of wheels. To construct the optimal series, the calculated inequality (4.5 ) is used for R = 1.
By calculation according to the formula (3.8) of these guidelines, the following values \u200b\u200bare obtained?:
1 = ? 2 = 0; ? 3 = ? 4 = 1; ? 5 = ? 6 = 2.
B = 8,81; H = 93,06.
The calculation of the series began, in accordance with the provisions of Section 5, with the determination of the effectiveness of the Ra40 series compared to the Ra20 series.
The number of sizes of the Ra40 series in the unification range according to (3.9) of these guidelines is
According to the table of values of the integral of probabilities for a series with 40 standard sizes, it is determined for the last two (largest) standard sizes N" 40.40, I = 0.01; N" 40.40, II = 0.0085 and? 40.40 = 0.85. Indexes at? denote the number of the largest member of the pair under consideration and the number of members in the series, the indices y N- number of the larger standard size, number of standard sizes, index of standard sizes of the considered pair (smaller - I, larger - II).
As we can see, the member of the Ra20 series turned out to be more effective. Based on the theoretical analysis underlying the transition point method, we can state that not a single member of the Ra40 series belongs to the optimal one.
The inequality has been solved again according to new data
Thus, it was found that the sizes of the Ra20 series are also not included in the optimal series.
The solution of the corresponding inequality led to the values
The inequality sign shows that the sizes of the Ra10 series are included in the optimal series. Putting the greatest inequality? 2.10 = 1.66 and N 2.10,I =0.04 to check whether the entire series Ra10 belongs to the optimal one and solve the inequality, we get
Thus, the optimal series consists of 10 sizes of the Ra10 series: 50 - 63 - 80 - 100 - 125 - 160 - 200 - 250 - 320 - 400 mm.
BIBLIOGRAPHY
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INFORMATION DATA
1 . DEVELOPED AND INTRODUCED by the All-Union Research Institute for Normalization in Mechanical Engineering (VNIINMASH)
Deputy Director Ph.D. B.N. Volkov
Topic leader, sector V.Ya. Kremyansky
CONTRACTOR V.Ya. Kremyansky
2 . APPROVED AND INTRODUCED BY Decree of the USSR State Committee for Standards dated March 25, 1987 No. 951.
3 . INTRODUCED FOR THE FIRST TIME
4 . REFERENCE REGULATIONS AND TECHNICAL DOCUMENTS:
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Number of paragraph, subparagraph, enumeration, application |
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GOST 23945.0-80 |
1.1 ; 1.2 ; 1.4 |
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GOST 1643-81 |
1.9 ; 3.5 ; 4.3 |
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GOST 6636-69 |
1.9 ; 3.6 ; 4.3 |
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GOST 8032-84 |
1.9 ; 3.6 ; 6.1.4 |
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GOST 8419-75 |
6.1.4 |
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GOST 11521-82 |
3.5 ; 6.1.4 |
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GOST 5721-75 |
6.1.4 |
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GOST 25347-82 |
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1. General Provisions. 1 2. Selection of main and main parameters. 4 3. Technical and techno-economic factors to be taken into account when constructing a series of parts and components, and ways to account for factors. 5 4. Objective functions and restrictions for constructing series. 10 5. Requirements for methods for constructing parametric and standard series. 14 6. Methods for constructing parametric and standard series of parts and assembly units. 15 Appendix 1 Methodology for establishing rational values of the main specific indicators of the technical level of parts and assembly units of general machine-building use (OMP) 19 Appendix 2 Establishment of rational values of specific indicators of the technical level of unified gears. 22 Annex 3 Nomenclature of the main and main parameters of parts and assembly units of WMD.. 23 Annex 4 Method for calculating the reduction in the need for rolling bearings due to the increase in reliability under operating conditions with reduced loads. 26 Appendix 5 Objective function for optimizing a number of gear ratios of gear boxes of machine tools. 27 Appendix 6 Construction of the optimal parametric series (series of the main parameter) of pairs of bevel gears by the method of transition points. 28 |
Scientific and technical principles and methods of standardization
Machine quality and its evaluation
Quality created products is a set of properties that determine their suitability to satisfy certain needs in accordance with the purpose.
When assessing the quality of products, regulated indicators are distinguished, established regulatory documentation; nominal, from which the allowable deviations are counted; limit - maximum and minimum. As a result of comparing the values of the quality indicators of the evaluated products with their base values, a relative characteristic is obtained, called the level of product quality.
Currently, certification of industrial products is widely carried out, confirming the compliance of a product with certain standards or conditions.
Quality indicators according to the characterized properties can be divided into the following groups:
- appointments: a) classification (power, gear ratio, etc.); b) operational (productivity, efficiency, etc.); c) constructive (overall dimensions, weight, coefficient of assembly, etc.),
– reliability (durability, non-failure operation, maintainability, storability);
– ergonomics (hygienic, anthropometric, physiological, psychophysiological, psychological);
- aesthetics (rationality of form, color, composition integrity, information expressiveness, etc.),
– manufacturability (labor intensity, metal intensity, cost price);
– standardization and unification (coefficients of applicability and repeatability);
– transportability (costs for transportation and preparatory and final works);
– patent law (on patent protection and patent purity of the product);
– environmental (emissions of harmful particles and gases, etc.);
– security;
- economic (costs for the development, manufacture and operation of products).
The final stage of the product evaluation is the certification of its quality.
The organization of standardization work gives high efficiency in production due to the observance of fundamental principles.
Research principle provides, along with a generalization of domestic and foreign experience carrying out theoretical, experimental and development work to develop a draft standard.
The principle of progressiveness and optimization of standards is that the developed standards should not only correspond to the world level of science, technology and industry, but also take into account the development trends of the object being standardized.
The principle of consistency and interconnection of standards is that in order to achieve highest quality products, systems of standards are developed that cover all stages of product creation, at which quality indicators are formed: design development, manufacturing and operation.
The foundation the principle of interconnection- a method of complex standardization, the essence of which is the purposeful, systematic establishment and application of interrelated requirements for a standardized object, its components, materials, processes, calculation methods, etc.
The principle of functional interchangeability of standardized products allows to ensure the interchangeability of products in terms of operational indicators, which is important for complex standardization.
The principle of preference- one of the most important general principles standardization - consists in systematizing the parameters and dimensions of machines, their parts and parts using parametric series compiled on the basis of a system of preferred numbers.
The principle of ensuring patent purity standards lies in the fact that standardized products - the object of delivery to the foreign market - must not only be competitive, but must not violate the patents in force in the countries of import. Valid patents provide their owners with the exclusive right to use the patented object (design, technological process, test method, etc.) for a certain period of time.
Standardization in the process of creating machines involves the use of two main methods: unification and aggregation. There are also methods derived from them: sectioning, compounding, modification etc. The use of these methods makes it possible to quickly and in large quantities manufacture various machines, reduce the cost of their repair and operation, and also expand the range of spare and replaceable parts and assemblies. The methods are based on the continuity of design and technological solutions, as well as on the use of parametric and standard series of machines that allow you to set optimal parameters and sizes.
Modern mechanical engineering, including construction and road building, is characterized by a wide and growing range of products: machines, equipment, mechanisms and instruments. New technologies require an increase in the number of types and sizes of products.
To determine the rational number of manufactured products and standard sizes, i.e. reducing their unreasonably large range, standards are being developed for parametric series (series of basic parameters) . For example, standards for parametric series of construction and road machines have been developed and are in effect.
Parameter- a value that characterizes any property of a machine or any other product. The set of parameters determines the technical characteristics of the machine: productivity, main dimensions, design, etc.
A sequential series of numerical values of any parameter, built in a certain range of its values based on the accepted gradation system, is called parametric series. As a rule, a machine is characterized by a large number of different parameters, however, for any machine, the parameters characterizing them are usually divided into main, main and auxiliary.
Main parameter to the greatest extent characterizes the beneficial effect of the functioning of the product and to a minimum extent depends on the technology of its manufacture and use. As the main parameter, an indicator is chosen that determines the fundamental possibility of the machine to work in these technological conditions. In addition, this parameter should determine to the greatest extent the technical and economic indicators of the machine in the field of its creation and operation.
main parameters characterize the most significant, defining constructive and technological operational properties, show the feasibility of using a machine or mechanism. As a rule, the main parameters are distinguished from among the main ones.
For certain types of products, auxiliary parameters associated with the development and implementation of scientific and technological achievements, leading to the improvement of structures, the use of more durable materials, etc. These may include: specific gravity, specific consumption of fuel, electricity, oil, efficiency, etc. For road construction machines, the main parameters are: power, force developed by the working body, dimensions of the working bodies, productivity,
The nomenclature of the main and main parameters should be minimal (so as not to limit the possibility of systematic improvement of structures), but at the same time sufficiently complete in terms of operational requirements and modern level development of this class of machines. The nomenclature of the main and basic parameters must remain unchanged with structural modifications and technical improvements of machines, and also be identical for machines of related types or groups (for example, cargo cranes, cars, tractors). According to the main (or main) parameters, parametric series are built. Determining the range of parameter values should be technically and economically justified based on practical needs. The numerical values of the main parameters of the series must correspond to the preferred numbers and the preferred number series.
The law of series formation, which determines the nature of the change in the intervals between the members of this series, is called the gradation of the parametric series.
A kind of parametric series - standard size(size) series, the main parameters of which are the dimensions of the product. Based on the standard series, constructive series of specific models of machines (mechanisms) of the same design and the same functional purpose are created.
When designing parametric series, they proceed from the fact that a rational series should contain the most advantageous number of standard sizes of products, ensuring minimal production and operation costs.
Lecture 12(4.6. Unification in mechanical engineering and the methodology for its implementation; 4.7. Intersectoral unification of machines; 4.8. Assessment of the level of standardization and unification; 5. BASICS OF ARTISTIC DESIGN, ERGONOMICS AND LABOR SAFETY; 5.1. Artistic design as a stage in the process of creating a machine)
