CN103902759B - A kind of build-up tolerance Optimization Design based on genetic algorithm - Google Patents

Abstract

The invention relates to an assembly tolerance optimization design method based on a genetic algorithm. The method includes: determining the minimum processing cost of an assembly as the optimization target, and establishing an assembly tolerance optimization objective function; determining the constraint conditions of the assembly tolerance; Attach to the VGC network to obtain the tolerance network of the assembly, select and determine the value range of the dimensional tolerance and geometric tolerance of each assembly feature; use the method of multi-parameter cascade coding for genetic coding; determine the fitness function; determine the selection operator function ; Determine the operating parameters of the genetic algorithm. The assembly tolerance optimization design method based on the genetic algorithm of the present invention, the genetic algorithm shows strong application potential because of its global search ability, strong robustness and parallelism of calculation.

Description

An Optimal Design Method for Assembly Tolerance Based on Genetic Algorithm

technical field

The invention relates to a method for optimizing design of mechanical assembly tolerance, in particular to a method for optimizing design of assembly tolerance based on genetic algorithm.

Background technique

The assembly size tolerance and geometric tolerance of parts in the prior art are generally determined according to the product’s performance requirements, assembly function requirements, quality assurance, processing materials, production conditions, manufacturing costs, and corresponding national, industry, or enterprise standards. of.

In the design stage, how to correctly and reasonably select the assembly tolerance value is a design problem that must be considered comprehensively. It is of great significance to ensure the assembly and performance of the product, improve product quality, and reduce manufacturing costs. Among the factors that affect the cost of machining a part, tolerances play a very important role. The smaller the design tolerance of the part, the better the assembly function requirements can be guaranteed, but the processing cost will also increase. When the accuracy is improved to a certain extent, the processing cost will increase sharply. How to design a reasonable assembly feature tolerance value to obtain the lowest processing cost while meeting the assembly function requirements is a problem that must be paid attention to when designing products. There are many factors affecting the relationship between processing cost and tolerance, and it is difficult to use a unified mathematical model to accurately describe the relationship between processing cost and tolerance of all features. For example, feature type, processing equipment, clamping method, processing technology, operator, production batch and other factors, as long as one or several of them change, the relationship between processing cost and tolerance will be different.

Based on the relationship between shape tolerance and size tolerance, the constraints of genetic algorithm are established to realize the comprehensive design of size tolerance and shape tolerance. Modeling tolerance and processing cost is an important content in tolerance optimization design. Tolerance optimization is a multi-parameter optimization design problem. Genetic algorithm shows a strong application potential in it because of its global search ability, strong robustness and parallel computing.

In view of the above-mentioned defects, the author of the present invention has finally obtained this creation through long-term research and practice.

Contents of the invention

The object of the present invention is to provide an assembly tolerance optimization design method based on cost target optimization to overcome the above-mentioned technical defects.

In order to achieve the above object, the present invention provides a method for optimal design of assembly tolerance based on cost target optimization, the method is:

Step a, determine the minimum processing cost of the assembly as the optimization goal, and establish the objective function of assembly tolerance optimization; the function is described as follows:

In the formula, C _MA is the total processing cost function of assembly MA; is the processing cost-tolerance function of the ath dimensional tolerance of feature f _i ^j ; is the processing cost-tolerance function of the bth shape tolerance of feature f _i ^j ; is the processing cost-tolerance function of the cth position tolerance of feature f _i ^j ; g is the total number of size tolerances of feature f _i ^j ; h is the total number of shape tolerances of feature f _i ^j ; s is the total number of position tolerances of feature f _i ^j ;

This function is calculated by the following method,

Step a1, setting the part representation function of the mechanical assembly;

Given a mechanical assembly as shown in the following formula:

In the formula:

MA _Σ - represents the mechanical assembly;

P _i ——the i-th part of the assembly MA;

n—the total number of parts that make up the assembly MA.

Step a2, determining the representation function of the total processing cost of the mechanical assembly;

The total machining cost for the assembly is as follows:

In the formula:

C _MA - total machining cost function of assembly MA;

C(P _i )——the processing cost function of part P _i in assembly MA.

Step a3, determining the machining cost function of each part in the assembly;

The machining cost of the part is as follows:

In the formula:

f _i ^{j ——the} jth assembly feature of part P _i ;

C(f _i ^j )——the processing cost function of the jth assembly feature of part P _i ;

m—the total number of assembly features of part P _i .

Step a4, determining the processing cost function of the assembly feature;

As follows:

In the formula:

——machining cost-tolerance function of the a-th dimensional tolerance of feature f _i ^j ;

——the machining cost-tolerance function of the bth shape tolerance of feature f _i ^j ;

——machining cost-tolerance function of the c-th position tolerance of feature f _i ^j ;

g—the total number of dimensional tolerances of feature f _i ^j ;

h—the total number of shape tolerances of feature f _i ^j ;

s - the total number of position tolerances for feature f _i ^j .

Step a5, combining formulas (3) to (5), the total processing cost-tolerance function of the assembly can be expressed as follows:

Obtain the objective function of assembly tolerance optimization according to above-mentioned formula (6);

Step b, determining constraints on assembly tolerances;

Step c, attaching the tolerance type information to the VGC network to obtain the tolerance network of the assembly, and selecting and determining the value range of the dimensional tolerance and geometric tolerance of each assembly feature;

Step d, adopting the method of multi-parameter cascade coding to carry out genetic coding;

Step e, determining the fitness function;

Step f, determine the selection operator function;

Step g, determining the operating parameters of the genetic algorithm.

Further, the above-mentioned step b is the constraint condition of the dimensional tolerance based on the functional requirements of the assembly,

T _CL ≥T ₁ +T ₂ +…+T _p +…+T _n (7)

T _CL represents the dimensional tolerance of the closed loop, n represents the number of constituent rings in the dimensional chain, T _p represents the dimensional tolerance of the p-th constituent ring; formula (7) represents the sum of the tolerances of each increasing and decreasing ring in the dimensional chain It should not be greater than the dimensional tolerance of the closed ring.

Further, in the above step b, the dimensional tolerance constraint condition based on the relative processing cost,

The dimensional tolerance constraints of the features are established according to the economic requirements, as shown in formula (8):

in, with Indicates the dimensional tolerance level determined according to the economic requirements of feature processing, while with are the tolerance values corresponding to them.

Further, the above-mentioned step b is a dimensional tolerance constraint condition based on processing capability,

The dimensional tolerance constraints based on processing capability can be expressed as:

in, with Respectively represent the dimensional tolerance level that can be guaranteed by the processing method adopted in the last processing procedure of the assembly feature, with Respectively with The tolerance value corresponding to the nominal size of the assembly feature, and T _d represents the design tolerance value of the assembly feature; formula (9) indicates that the design value of the tolerance should not exceed the processing capacity of the processing method.

Further, in the above step b, the dimensional tolerance constraints based on the economic precision of the cutting process,

The economic machining accuracy of the machining method is selected as the constraint condition of the tolerance optimization design, as shown in formula (10),

in, with Indicates the tolerance value corresponding to the economical machining accuracy of the machining method selected by the feature.

Further, the shape and position tolerance constraints based on processing capability are as follows,

Among them, T _g represents a certain shape and position tolerance value of the feature, with Indicates the tolerance value corresponding to the processing capability of the processing method.

Compared with prior art, the beneficial effects of the present invention are:

The assembly tolerance optimization design method based on the genetic algorithm of the present invention, the genetic algorithm shows strong application potential because of its global search ability, strong robustness and parallelism of calculation.

The invention takes the minimum processing cost as the goal, and the optimized tolerance obtained by taking the processing capacity, processing cost or processing economic precision as the constraint conditions respectively can meet the assembly function requirements of the product, meet the constraint conditions of mechanical processing, and can obtain good economic benefits ; According to the corresponding relationship between shape tolerance and size tolerance, the constraints of genetic algorithm are established, and the comprehensive design of size tolerance and shape tolerance is realized; this method combines the research content of assembly tolerance type design and tolerance network construction, to realize The computer-aided tolerance design from body to dimension and shape and position tolerance has been beneficially explored.

Description of drawings

Fig. 1 is the flowchart of the assembly tolerance optimization design method based on cost target optimization of the present invention;

Figure 2a is a schematic diagram of the linkage assembly of the present invention;

Figure 2b is a schematic diagram of the composition and structure of the linkage assembly of the present invention;

Fig. 2c is a schematic diagram of the tolerance of each structure of the linkage assembly of the present invention.

detailed description

The above and other technical features and advantages of the present invention will be described in more detail below in conjunction with the accompanying drawings.

The invention takes the minimum processing cost as the optimization goal, comprehensively considers the size tolerance and shape tolerance, and establishes a new cost-tolerance model. The total tooling cost of an assembly consists of the tooling costs of all attached parts, and the tooling cost of a part consists of the tooling costs of all its feature faces. Not every feature face participates in the assembly of the part. Since the present invention mainly considers the optimization design of assembly size tolerance and shape tolerance size, only the processing cost of the assembly feature surface is considered.

The method of the assembly tolerance optimization design method based on cost target optimization of the present invention is as follows:

Step a, determine the minimum processing cost of the assembly as the optimization goal, and establish the objective function of assembly tolerance optimization.

Step a1, setting the part representation function of the mechanical assembly;

Given a mechanical assembly as shown in the following formula (1):

In the formula:

MA _∑ —— indicates mechanical assembly;

P _i ——the i-th part of the assembly MA;

n—the total number of parts that make up the assembly MA.

Step a2, determining the representation function of the total processing cost of the mechanical assembly;

The total machining cost for the assembly is as follows:

In the formula:

C _MA - total machining cost function of assembly MA;

C(P _i )——the processing cost function of part P _i in assembly MA.

Step a3, determining the machining cost function of each part in the assembly;

The machining cost of the part is as follows:

In the formula:

f _i ^{j ——the} jth assembly feature of part P _i ;

C(f _i ^j )——the processing cost function of the jth assembly feature of part P _i ;

m—the total number of assembly features of part P _i .

Step a4, determining the processing cost function of the assembly feature;

As follows:

In the formula:

——machining cost-tolerance function of the a-th dimensional tolerance of feature f _i ^j ;

——the machining cost-tolerance function of the bth shape tolerance of feature f _i ^j ;

——machining cost-tolerance function of the c-th position tolerance of feature f _i ^j ;

g—the total number of dimensional tolerances of feature f _i ^j ;

h—the total number of shape tolerances of feature f _i ^j ;

s - the total number of position tolerances for feature f _i ^j .

Step a5, combining formulas (2) to (4), the total processing cost-tolerance function of the assembly can be expressed as follows:

In the product design stage, the dimensional tolerances and shape tolerances marked on the component drawings are formed by the final processing method of the features. Therefore, the present invention only considers the machining cost of the final operation of feature formation to determine the design tolerance.

Step a6, taking the minimum processing cost of the assembly as the optimization goal, the objective function of assembly tolerance optimization can be defined as:

Step b, determining the constraint conditions of the assembly tolerance.

In the present invention, various constraints are set according to the assembly function requirements of the product, the processing capabilities of various processing methods, the processing costs of different processing levels, the economic precision of various cutting processes, and the correspondence between dimensional tolerances and shape tolerances. condition.

1) Dimensional tolerance constraints based on assembly functional requirements

Dimensional tolerances are extracted from subchains of the assembly tolerance network to obtain assembly dimensional tolerance chains corresponding to subassemblies. The accuracy required by the assembly function is used as the closed loop of the dimensional tolerance chain, and the accuracy of other dimensions that constitute the tolerance chain is used as the constituent ring. The accuracy of the closed loop depends on the accuracy of the constituent rings, which is the result of the combined effect of the accuracy of each constituent ring. The extremum method is used to describe the constraint relationship between the assembly function requirement accuracy and the dimensional accuracy of each component ring in the tolerance chain, then the tolerance of the closed loop is equal to the sum of the tolerances of each component ring. In the assembly size chain, the closed loop reflects the assembly function requirements of the product, which is predetermined by the designer, and its accuracy reflects the assembly quality requirements.

In order to ensure the assembly quality of the product, the dimensional tolerance constraints based on the assembly function requirements are established as follows:

T _CL ≥T ₁ +T ₂ +…+T _p +…+T _n (7)

T _CL represents the dimensional tolerance of the closed loop, n represents the number of constituent rings in the dimensional chain, and T _p represents the dimensional tolerance of the pth constituent ring. Formula (7) indicates that the sum of the tolerances of the increasing and decreasing rings in the dimensional chain should not be greater than the dimensional tolerance of the closed loop.

2) Dimensional tolerance constraints based on processing capabilities

The dimensional machining accuracy that can be guaranteed by different processing methods for the same assembly feature is different. Therefore, when designing the dimensional tolerances of assembly features, if the processing method of the last process is known, the processing capability of the processing method must be considered. The dimensional tolerance constraints based on processing capability can be expressed as:

in, with Respectively represent the dimensional tolerance level that can be guaranteed by the processing method adopted in the last processing procedure of the assembly feature, with Respectively with The tolerance value corresponding to the nominal size of the assembly feature, and T _d represents the design tolerance value of the assembly feature. Formula (8) indicates that the design value of the tolerance should not exceed the processing capacity of the processing method. Table 1 can be used to establish the constraints on the dimensional tolerances that can be guaranteed by various assembly feature surfaces in different processing methods.

Table 1 Machining accuracy of traditional machining methods for basic assembly feature surfaces

3) Dimensional tolerance constraints based on relative processing costs

When using a certain processing method to process features, in some areas of the tolerance level and processing cost curve, the processing cost changes rapidly with the change of the tolerance level, and when the tolerance level increases to a certain extent, the processing cost tends to a constant. It can be seen that when the same processing method is used to process the feature surface according to different tolerance levels, the processing cost may be quite different.

Therefore, when performing tolerance optimization design, within the range of processing capacity of the processing method, the dimensional tolerance constraints of features can be established according to economic requirements, as shown in formula (9).

in, with Indicates the dimensional tolerance level determined according to the economic requirements of feature processing, while with are the tolerance values corresponding to them.

4) Dimensional tolerance constraints based on economical precision of machining

The same feature can be obtained by different processing methods, and the processing accuracy that various processing methods can achieve economically under normal production conditions has a certain range. The economic precision of plane milling is IT6~IT10, the economic precision of plane broaching is IT6～IT9, and the economic precision of plane grinding is IT6～IT7. The economic machining accuracy of the machining method can be selected as the constraint condition for the tolerance optimization design, as shown in formula (10).

in, with Indicates the tolerance value corresponding to the economical machining accuracy of the machining method selected by the feature.

5) Geometric tolerance constraints based on processing capabilities

Like dimensional tolerances, different processing methods have different abilities to process shape and position tolerances. The geometrical tolerance constraints based on processing capability are established as shown.

Among them, T _g represents a certain shape and position tolerance value of the feature, with Indicates the tolerance value corresponding to the processing capability of the processing method.

6) Geometric tolerance constraints based on dimensional accuracy

The dimensional tolerance designed by the independent principle only controls the local actual size of the feature, and does not directly control the shape and position error of the feature. However, when the dimensional tolerance zone limits the dimensional error of the feature, it also indirectly controls the related shape and position error. Similarly, the shape and position tolerance that obeys the principle of independence only requires that the constrained feature is located within a given shape and position tolerance zone, and its shape and position error can reach the maximum value, regardless of the actual size of the feature. However, the restriction of the geometric tolerance zone on the constrained features also limits the related dimensional errors on the features. Therefore, the design of dimensional tolerance and geometric tolerance objectively has a relationship of mutual restriction and mutual compensation. In general, the principle to be followed in designing the size and geometric tolerance of the same feature is: T _size > T _position > T _shape . Based on this, the geometric tolerance constraints based on dimensional accuracy can be established, as shown in formula (12).

Among them, T _g is the shape and position tolerance value of the feature, with Indicates the geometric tolerance class corresponding to the dimensional tolerance on the feature, with Representation and Geometric Tolerance Class with The corresponding tolerance value.

In the tolerance optimization design, according to the assembly function requirements of the product and the economic requirements of processing, the above-mentioned constraints can be selected as the constraints of the genetic algorithm objective function.

In step c, add the tolerance type information to the VGC network to obtain the tolerance network of the assembly, and select and determine the value range of the dimensional tolerance and geometric tolerance of each assembly feature.

In step d, genetic coding is carried out by using a multi-parameter cascade coding method.

The method of multi-parameter cascading coding is used for genetic coding, and each size tolerance and shape tolerance is coded by binary coding method, and then these codes are connected together in a certain order to form a binary string chromosome representing all parameters. In this coding method, the binary code (parameter substring) of each parameter cannot be changed once the position of the total chromosome string is determined, so as to avoid errors in evolutionary calculations.

The length of the binary coded string depends on the resolution required by the problem. According to GB/T1800.3-1998 standard tolerance value and GB/T1184-1996 shape and position tolerance value, the precision required to determine the size and shape and position tolerance is 4 decimal places, so the tolerance decision variable T∈[T ^L , T ^U ] It should be divided into at least (T ^U -T ^L )×10 ⁴ parts, where T ^L represents the lower limit of the tolerance decision-making variable, T ^U represents the upper limit of the tolerance decision-making variable, and the binary string digits of the tolerance decision-making variable is represented by m _j means calculated with the following formula:

Then the length of the coding string of the chromosome is:

in,

L - the length of the coding string of the chromosome;

l _i ——code length of tolerance variable;

n—the total number of dimensional and geometric tolerance variables.

Table 2 Tolerance information of assembly features

According to the above analysis, the maximum binary string encoding length of the size and shape and position tolerance variables accurate to four digits after the decimal point is 14 digits. The present invention adopts equal-length coding technology, and the coding length of each tolerance variable is set to 14 bits. Then a chromosome length with n tolerance parameters can be expressed as:

When coding, each tolerance parameter can have different value ranges. The present invention adopts equal-length coding technology, so each parameter has different coding precision. Suppose the value range of a certain tolerance is [T ^L , T ^U ], using 14-bit binary coding symbols to represent the tolerance, then 2 ¹⁴ different codings can be generated, and the coding precision is:

The binary string chromosome composed of the tolerance variables in Table 2 can be expressed formally as follows:

This encoding method can make the solution space of tolerance optimization and the search space of genetic algorithm have one-to-one correspondence.

For a given tolerance variable binary coded chromosomes:

The binary string decoding function of the jth tolerance variable has the form:

in:

T _j - the value of the jth tolerance variable in the chromosome;

- the lower limit of the value of the jth tolerance variable;

- the upper limit of the value of the jth tolerance variable;

——The value of the mth gene of the binary coded string of the jth tolerance variable.

Step e, determining the fitness function.

The GA algorithm determines the chance of all individuals in the current population being inherited to the next generation population according to the probability proportional to the individual fitness. Generation one is less likely. In the tolerance optimization design, the minimum processing cost is used as the optimization objective function, and the individual with a lower processing cost has a higher probability of being selected to reproduce the next generation of individuals, so the processing cost is used as the criterion for evaluating the quality of the individual (solution). . In order to preserve and continue to reproduce excellent individuals with lower processing costs, the present invention uses the reciprocal of the individual's total processing costs to construct its fitness function, as shown in formula (18). Among them, F _k ^Fit is the fitness value of the kth individual in the population.

Step f, determine the selection operator function.

In this embodiment, the fitness value ratio selection operator is selected for calculation.

The proportion selection operator determines the possibility of heredity according to the proportion of the individual fitness value to the total fitness value of the group. The larger the proportion, the greater the possibility of inheritance to the next generation.

The formula for calculating the selection probability of an individual is as follows:

in:

P _i ——the selection probability of the i-th individual;

n—the size of the population, which represents the number of solutions of the tolerance optimization design;

F _k ^Fit - the fitness value of the kth individual in the population;

F _i ^{Fit ——the} fitness of the i-th individual.

The specific execution process of the ratio selection operator is:

f1. Calculate the fitness value of all individuals in the group;

f2. Sum the fitness values of all individuals;

f3. Calculate the relative fitness of the individual, that is, the selection probability of the individual being inherited to the next generation;

f4. Use the simulated roulette operation to take a random number between 0 and 1 to determine the number of times each individual is selected.

Step g, determine the running parameters of the GA algorithm.

The operating parameters in the GA algorithm include the population size M, the terminal evolution algebra T, the crossover probability P _c , and the mutation probability P _m .

M is the number of individuals contained in the population. If M takes a smaller value, the calculation speed of the GA algorithm can be improved, but the diversity of individuals is reduced, which may cause premature phenomenon, and when M takes a larger value, the calculation efficiency will be reduced. M usually ranges from 20 to 100;

T is the termination evolution algebra of the genetic algorithm, which is generally taken as 100-500;

P _c is the crossover probability, which generally takes a larger value, but if it is too large, it is easy to destroy the good model in the population, and if it is too small, it will slow down the generation of new individuals. P _c usually ranges from 0.4 to 0.99;

P _m is the mutation probability. Similar to the crossover probability, when P _m takes a larger value, it may destroy a better model, and if it is too small, it is not conducive to producing better new individuals and inhibiting the premature phenomenon. The value of P _m is generally taken as 0.0001-0.1.

Now take the linkage assembly shown in Figure 2a as an example to illustrate the method of using genetic algorithm to optimize the design of assembly tolerance. After the three-dimensional model of the linkage assembly is established in the CAD system, the nominal dimensions of all the features on it will be determined accordingly, and the relevant tolerance design can be carried out on this basis. As shown in Figure 2b, in the assembly tolerance network of the linkage assembly, the assembly tolerances of parts such as slide plates, brackets, couplings, sliding bearings and shafts can form a fully constrained closed assembly tolerance sub-chain (in order to simplify the problem , a sliding bearing is omitted from the analysis). Next, optimize the tolerance design according to the functional requirements of the linkage assembly. Among them, the dimensional tolerance level is considered with the machining economic precision of the assembly features, and the shape and position tolerance level is determined by the corresponding relationship between the shape and position tolerance and the size tolerance.

Determination of dimensional tolerance range

In Figure 2b, there are two pairs of holes and shaft assembly, that is, the hole φD ₃ on the bracket and the shaft φD ₄ on the coupling, the nominal size is φ50, the outer circle φD ₈ on the shaft and the hole φD on the sliding bearing ₇ , the nominal size is φ38. Hole φD ₃ is the basic feature surface of Si _icys , which can be processed by boring method, and the economic precision of processing is IT8～IT10. Axis φD ₄ is the basic feature surface of S _ocys , which can be processed by turning, and the economic precision of processing is IT6~IT9. According to the selection principle of the datum system, the hole φD ₃ /shaft φD ₄ chooses the base hole system fit. The cooperation between the bracket and the coupling requires obvious clearance, easy to rotate, and considering the economical precision of its machining, the matching of hole φD ₃ / shaft φD ₄ is finally determined as φ50H8/e7. The fit between the hole φD7 and the outer circle φD8 is a sliding fit, and its fit is determined to be φ38H8/f7.

Table 3 Linkage assembly size tolerance range

The nominal dimension of the distance dimension D ₁ is 19, and the datum plane A is used as the processing datum, and the milling process is adopted, and the economic precision of the cutting process of the basic assembly feature surface is checked, and the economic precision of the machining is IT6~IT10, that is, T _D1 ∈ (IT6 ~IT10). The nominal dimension of the distance dimension D ₆ is 47, and the datum plane C is used as the machining reference, and the boring method is used for machining. The economic precision of machining is IT8~IT10, that is, T _D6 ∈(IT8~IT10). Using the same method, the accuracy ranges of all dimensional tolerances in Figure 2(c) are shown in Table 3.

Determination of type and range of form and position tolerance

The assembly constraint type of shaft φD ₄ and hole φD ₃ is The assembly tolerance function corresponding to this constraint is:

According to the assembly function requirements of the bracket and the coupling and the selection and optimization rules of the assembly tolerance, a set of assembly tolerances between the assembly feature surfaces of the two parts can be determined as:

It can be known from formula (21) that the shape and position tolerance requirements of the axis φD ₄ and the hole φD ₃ need to be put forward, that is, the shape and position tolerances T _G4 and T _G3 shown in Fig. 2c.

The design reference surface A on the skateboard and the plane where the upper dimension limit of dimension D1 (see _Fig . 2c) form a pair of geometric constraints, which is a cross-reference variable geometric constraint CVGC composed of two geometric features on the same part. It is inferred that the corresponding cross-reference change geometric constraint type is CC21, and the tolerance type corresponding to CC21 is AT8, that is, the geometric tolerance type corresponding to the two feature planes is parallelism. Therefore, it is necessary to put forward parallelism requirements for the datum A on the plane where the upper limit of the dimension D ₁ is located, as shown in Figure 2c for the geometrical tolerance T _G1 .

After determining the type of geometric tolerance, the tolerance grade range of geometric tolerance can be determined based on the relevant dimensional tolerance accuracy. In the above analysis, the accuracy range _of the dimension D1 has been obtained from IT6 to IT8, and the accuracy range of the parallelism tolerance T _G1 can be obtained from IT7 to IT10. Similarly, the tolerance grades of the dimensional tolerance T _G3 on the bracket and the dimensional tolerance T _G4 on the coupling are H8 and e7 respectively, and the corresponding relationship between the dimensional tolerance grade and the roundness and cylindricity tolerance grades shows the corresponding shape The tolerance grades of tolerance T _G3 and T _G4 are IT8~IT9 and IT7~IT8 respectively.

Table 4 shows the accuracy ranges of all shape and position tolerances in Figure 2c obtained by reasoning with the above method.

Table 4 Linkage assembly form and position tolerance range

Tolerance optimization objective function of linkage assembly

To establish the tolerance optimization objective function of the linkage assembly. Among them, the processing cost-tolerance models of various features are shown in Table 5.

Table 5 Processing cost model of various features

The objective function of tolerance optimization for establishing a linkage assembly is as follows:

When assembling, it is required that the central axis of the linkage assembly and the axis of the coupling remain on a straight line, and the height difference T ₀ is not greater than 0.45mm. This is used as a closed loop of the assembly dimension chain. The constraints for establishing the objective function are as follows Shown:

The constraints of the function are as follows:

Determination of operating parameters

The population number M takes a value of 20, the genetic algebra T takes a value of 70, the crossover probability P _c takes a value of 0.7, and the mutation probability P _m takes a value of 0.08.

Assembly Tolerance Optimization Results and Analysis

Commonly used tolerance allocation methods include analog tolerance method, equal tolerance method, equal precision method, equal influence method, and economic criterion method. Among them, the equal precision method is to take the same tolerance level for the dimensions of all the component rings in the dimensional chain, the equal influence method is that the dimensional tolerances of each component ring have the same impact on the tolerance of the closed loop, and the equal tolerance method is for all components in the dimensional chain Ring dimensions take equal tolerance values. For linear dimension chains, the equal tolerance method is equivalent to the equal influence method.

Table 6 lists the tolerance values obtained by using genetic algorithm, equal precision method and equal influence method and other tolerance distribution methods and their processing cost comparisons. The total processing cost is only 35.1% of the equal-influence method and 76.8% of the equal-precision method by using the tolerance value obtained by the genetic algorithm to process.

Table 6 Tolerance value and processing cost comparison of different tolerance allocation methods

The above descriptions are only preferred embodiments of the present invention, and are only illustrative rather than restrictive to the present invention. Those skilled in the art understand that many changes, modifications, and even equivalents can be made within the spirit and scope defined by the claims of the invention, but all will fall within the protection scope of the present invention.

Claims (5)

1. An assembly tolerance optimization design method based on genetic algorithm is characterized by comprising the following steps:

step a, determining an objective function which takes the minimum processing cost of an assembly body as an optimization objective and establishes assembly tolerance optimization;

b, determining a constraint condition of assembly tolerance;

c, adding tolerance type information to the VGC network to obtain a tolerance network of the assembly body, and selecting and determining the value range of the dimensional tolerance and the geometric tolerance of each assembly feature;

step d, adopting a multi-parameter cascade coding method to carry out genetic coding;

coding each size tolerance and form and position tolerance by a binary coding method, and then connecting the codes together according to a certain sequence to form a binary string chromosome representing all parameters;

according to GB/T1800.3-1998 standard tolerance value and GB/T1184-1996 geometric tolerance value, the accuracy of the requirement for determining the size and geometric tolerance is 4 decimal places, and a tolerance decision variable T ∈ [ T ∈ ]^L，T^U]Should be divided into at least (T)^U-T^L)×10⁴A moiety of which T^LRepresents the lower value limit, T, of the tolerance decision variable^URepresenting the upper limit of tolerance decision variable, the binary string bit number of the tolerance decision variable is m_jThe expression is calculated by the following formula:

$2^{m_j-1}<(T^U-T^L)\&times;{10}^4\&le;2^{m_j}-1$

the length of the code string for the chromosome is then:

$L=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_i$

wherein,

l-coding string length of chromosome;

l_i-the encoded length of the tolerance variable;

n-the total number of dimensional and form and position tolerance variables;

the maximum binary string encoding length of the size and form and position tolerance variables of four digits after the decimal point is accurate is 14 digits, and by adopting an equal length encoding technology, the encoding length of each tolerance variable is 14 digits, so that the length of a chromosome with n tolerance parameters can be represented as follows:

$L=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_i=14n$

when encoding, each tolerance parameter can have different value ranges, and each parameter has different encoding precision by adopting an equal length encoding technology, and the value range of a certain tolerance is set as [ T ]^L，T^U]By representing the tolerance with a 14-bit binary code symbol, a2 can be generated¹⁴Different codes are adopted, and the coding precision is as follows:

$\mathrm{\&delta;}=\frac{T^U-T^L}{2^{14}-1}$

binary encoding chromosomes for a given tolerance variable:

$a_1^1,a_2^1,...,a_{14}^1,a_1^2,a_2^2,...,a_{14}^2,...,a_1^j,a_2^j,...,a_{14}^j,...,a_1^n,a_2^n,...,a_{14}^n$

the binary string decoding function for the jth tolerance variable is of the form:

$T_j=T_j^L+\left(\underset{m=1}{\overset{14}{\mathrm{\&Sigma;}}}{a}_m^j{2}^{m-1}\right)\frac{T_j^U-T_j^L}{2^{14}-1}$

wherein:

T_j-the value of the jth tolerance variable in the chromosome;

-a value lower limit of the jth tolerance variable;

-an upper value limit for the jth tolerance variable;

-the mth gene value of the binary encoded string of the jth tolerance variable;

step e, determining a fitness function;

step f, determining a selection operator function;

and g, determining the operation parameters of the genetic algorithm.

2. The method for optimizing the assembly tolerance according to the genetic algorithm, according to claim 1, wherein the fitness function is constructed in step e by using the reciprocal of the total processing cost of the individual, as shown in the following formula,

$F_k^{Fit}=\frac{1}{C_{MA}}=\frac{1}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\&lsqb;\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{TD}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{TF}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{TP}^c\left(f_i^j\right)\&rsqb;}$

in the formula,is the fitness value of the kth individual in the population, C_MAAs a function of the total processing cost of the assembly MA,is characterized by_i ^jThe machining cost-tolerance function of the a-th dimensional tolerance of (a);is characterized by_i ^jThe machining cost-tolerance function of the b-th shape tolerance of (a);is characterized by_i ^jThe machining cost-tolerance function of the c-th positional tolerance of (a); g is a characteristic f_i ^jThe total number of dimensional tolerances of; h is a characteristic f_i ^jThe total number of shape tolerances of (a); s is a characteristic f_i ^jTotal number of position tolerances.

3. The assembly tolerance optimization design method based on the genetic algorithm as claimed in claim 1 or 2, wherein the adaptive value proportion selection operator is selected for calculation in the step f, wherein the specific implementation process of the proportion selection operator is as follows:

f1. calculating fitness values of all individuals in the population;

f2. summing fitness values of all individuals;

f3. calculating the relative fitness of the individual, namely the selection probability of the individual being inherited to the next generation;

f4. the number of times each individual is selected is determined using a simulated betting round operation taking a random number between 0 and 1.

4. The genetic algorithm-based assembly tolerance optimization design method according to claim 3, wherein the individual selection probability calculation formula is as follows:

in the formula,

P_ia selection probability for the ith individual;

n is the size of the population and represents the number of solutions for tolerance optimization design;

the fitness value of the kth individual in the population;

F_i ^Fitthe fitness of the ith individual.

5. The assembly tolerance optimization design method based on genetic algorithm as claimed in claim 1 or 2, wherein the operation parameters in the step g comprise population size M, termination evolution algebra T and cross probability P_cProbability of mutation P_m；

The value range of M is 20-100;

t is 100-500;

P_cthe value range of (a) is 0.4-0.99;

P_mthe amount is 0.0001 to 0.1.