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

Abstract

The present invention relates to a kind of build-up tolerance Optimization Design based on genetic algorithm, the method is：Determine with the minimum process cost of assembly as optimization aim, set up the object function of build-up tolerance optimization；Determine the constraints of build-up tolerance；Tolerance type information is attached to VGC network, obtains the tolerance network of assembly, select to determine the dimensional tolerance of each assembly features and the span of geometric tolerances；Method using multiparameter concatenated coding carries out genetic coding；Determine fitness function；Determine selection opertor function；Determine the operational factor of genetic algorithm.The build-up tolerance Optimization Design based on genetic algorithm for the present invention, with its ability of searching optimum, stronger robustness and the concurrency calculating show powerful application potential to genetic algorithm wherein.

Description

Assembly tolerance optimization design method based on genetic algorithm

Technical Field

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

Background

In the prior art, the assembly dimensional tolerance and form and position tolerance of parts are generally determined according to the service performance requirement, the assembly function requirement, the quality guarantee, the processing material, the production condition, the manufacturing cost of a product and corresponding national, industrial or enterprise standards.

In the design stage, how to correctly and reasonably select the assembly tolerance value is a design problem which needs to be comprehensively considered, and the method has important significance for ensuring the assembly and the service performance of the product, improving the product quality, reducing the manufacturing cost and the like. Among the factors that affect the cost of machining parts, tolerances play a very important role. The smaller the design tolerance of the part is, the more the assembly function requirement can be guaranteed, but the processing cost is increased. When the accuracy is improved to a certain degree, the processing cost is drastically increased. How to design a reasonable assembly characteristic tolerance value to obtain the lowest processing cost under the condition of meeting the assembly function requirement is a problem which must be concerned when designing a product. The factors influencing the relation between the machining cost and the tolerance are many, and the relation between the machining cost and the tolerance of all the characteristics is difficult to accurately describe by using a unified mathematical model. For example, factors such as feature type, tooling equipment, chucking method, tooling process, operator, production lot, etc., may vary in tooling cost versus tolerance as long as one or more of them vary.

The constraint condition of the genetic algorithm is established according to the corresponding relation between the geometric tolerance and the dimensional tolerance, the comprehensive design of the dimensional tolerance and the geometric tolerance is realized, and the modeling of the tolerance and the processing cost is an important content in the tolerance optimization design. Tolerance optimization is a multi-parameter optimization design problem, and genetic algorithms show strong application potential in the global search capability, strong robustness and calculation parallelism of the genetic algorithms.

In view of the above-mentioned drawbacks, the present inventors have finally obtained the present creation through a long period of research and practice.

Disclosure of Invention

The present invention is directed to a method for designing an assembly tolerance optimization based on cost objective optimization, which overcomes the above-mentioned technical drawbacks.

In order to achieve the above object, the present invention provides an assembly tolerance optimization design method based on cost target optimization, the method comprising:

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; the function is described as follows:

in the formula, C_MAAs a function of the total processing cost of 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 ^jThe total number of position tolerances of;

the function is calculated by the following method,

step a1, setting a part representation function of the mechanical assembly;

a mechanical assembly is given as shown in the following formula:

in the formula:

MA_Σ-representing a mechanical assembly;

P_i-the i-th part that constitutes assembly MA;

n-the total number of parts making up assembly MA.

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

the total processing cost of the assembly is as follows:

in the formula:

C_MA-total processing cost function of assembly MA;

C(P_i) Part P in Assembly MA_iAs a function of the processing cost.

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

the processing cost of the parts is as follows:

in the formula:

f_i ^j-part P_iThe jth assembly feature of (a);

C(f_i ^j) -part P_iThe manufacturing cost function for the jth assembly feature of (1);

m-part P_iTotal number of assembled features.

Step a4, determining a machining cost function of the assembly features;

as follows:

in the formula:

feature f_i ^jThe machining cost-tolerance function of the a-th dimensional tolerance of (a);

feature f_i ^jThe machining cost-tolerance function of the b-th shape tolerance of (a);

feature f_i ^jThe machining cost-tolerance function of the c-th positional tolerance of (a);

g-characteristic f_i ^jThe total number of dimensional tolerances of;

h-characteristic f_i ^jThe total number of shape tolerances of (a);

s-feature f_i ^jTotal number of position tolerances.

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

obtaining an objective function for optimizing the assembly tolerance according to the formula (6);

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;

step e, determining a fitness function;

step f, determining a selection operator function;

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

Further, step b is a constraint condition of dimensional tolerance based on the requirement of assembly function,

T_CL≥T₁+T₂+…+T_p+…+T_n(7)

T_CLdenotes the dimensional tolerance of the closed loop, n denotes the number of component loops in the dimensional chain, T_pIndicating the dimensional tolerance of the p-th component ring; equation (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 ring.

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

dimensional tolerance constraints for features are established according to economic requirements, as shown in equation (8):

wherein,andrepresenting a dimensional tolerance level determined according to economic requirements for feature machining, andandare the tolerance values corresponding to them.

Further, the step b is a dimensional tolerance constraint condition based on the processing capacity,

the dimensional tolerance constraints based on machining capability can be expressed as:

wherein,andrespectively show the dimension tolerance grade guaranteed by the processing method adopted by the last processing procedure of the assembly characteristic,andrespectively representAndtolerance value corresponding to nominal dimension of the feature to be assembled, and T_dA design tolerance value of the assembly characteristic is represented; equation (9) indicates that the design value of the tolerance should not exceed the processing capability of the processing method.

Furthermore, the step b is a dimensional tolerance constraint condition based on the economic precision of cutting processing,

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

wherein,andand a tolerance value corresponding to the economic processing precision of the processing method selected by the characteristics is shown.

Further, form and position tolerance constraints based on machining capabilities are as follows,

wherein, T_gA value of some form tolerance of a feature is represented,anda tolerance value corresponding to the processing capability of the processing method is indicated.

Compared with the prior art, the invention has the beneficial effects that:

the assembly tolerance optimization design method based on the genetic algorithm shows strong application potential in the genetic algorithm by the global search capability, strong robustness and calculation parallelism of the genetic algorithm.

The invention takes the minimum processing cost as a target, respectively takes the processing capacity, the processing cost or the processing economic precision as the optimized tolerance obtained by constraint conditions, can meet the assembly function requirement of products, accords with the constraint conditions of mechanical processing, and can obtain good economic benefit; establishing constraint conditions of a genetic algorithm according to the corresponding relation between geometric tolerance and dimensional tolerance, and realizing the comprehensive design of the dimensional tolerance and the geometric tolerance; the method combines the research contents of assembly tolerance type design and tolerance network construction, and makes a beneficial search for realizing computer-aided tolerance design from assembly to size and form and position tolerance.

Drawings

FIG. 1 is a flow chart of an assembly tolerance optimization design method based on cost objective optimization according to the present invention;

FIG. 2a is a schematic view of a linkage assembly of the present invention;

FIG. 2b is a schematic view of the linkage assembly of the present invention;

fig. 2c is a tolerance diagram of the various structures of the linkage assembly of the present invention.

Detailed Description

The above and further features and advantages of the present invention are described in more detail below with reference to the accompanying drawings.

The invention takes the minimum processing cost as an optimization target, comprehensively considers the dimensional tolerance and the form and position tolerance, and establishes a new cost-tolerance model. The total machining cost of the assembly is made up of the machining costs of all the accessory parts, while the machining costs of the parts are made up of the machining costs of all their characteristic faces. Not every feature surface participates in the assembly of parts. Since the invention mainly considers the optimization design of the size of the assembly dimensional tolerance and the form and position tolerance, only the processing cost of the assembly characteristic surface is considered.

The method of the assembly tolerance optimization design method based on cost target optimization comprises the following steps:

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

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

given a mechanical assembly as shown in equation (1) below:

in the formula:

MA_∑-representing a mechanical assembly;

P_i-the i-th part that constitutes assembly MA;

n-the total number of parts making up assembly MA.

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

the total processing cost of the assembly is as follows:

in the formula:

C_MA-total processing cost function of assembly MA;

C(P_i) Part P in Assembly MA_iAs a function of the processing cost.

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

the processing cost of the parts is as follows:

in the formula:

f_i ^j-part P_iThe jth assembly feature of (a);

C(f_i ^j) -part P_iThe manufacturing cost function for the jth assembly feature of (1);

m-part P_iTotal number of assembled features.

Step a4, determining a machining cost function of the assembly features;

as follows:

in the formula:

feature f_i ^jA-th dimensional tolerance ofA difference function;

feature f_i ^jThe machining cost-tolerance function of the b-th shape tolerance of (a);

feature f_i ^jThe machining cost-tolerance function of the c-th positional tolerance of (a);

g-characteristic f_i ^jThe total number of dimensional tolerances of;

h-characteristic f_i ^jThe total number of shape tolerances of (a);

s-feature f_i ^jTotal number of position tolerances.

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

in the product design stage, the dimensional tolerance and form and position tolerance marked on the part drawing paper are formed by the final processing method of the feature. Therefore, the present invention determines the design tolerance considering only the machining cost of the last process of feature formation.

Step a6, taking the minimum machining cost of the assembly body as the optimization target, the objective function of the assembly tolerance optimization can be defined as:

and b, determining the constraint condition of the assembly tolerance.

In the invention, a plurality of constraint conditions are set according to the assembly function requirements of products, the processing capacities of various processing methods, the processing costs of different processing grades, the economic precision of various cutting processing and the corresponding relation between the dimensional tolerance and the form and position tolerance.

1) Dimensional tolerance constraints based on assembly function requirements

Dimensional tolerances are extracted from the sub-chains of the assembly tolerance network to obtain a chain of assembly dimensional tolerances corresponding to the sub-assemblies. The precision required by the assembly function is used as a closed ring of the dimensional tolerance chain, and the precision of other dimensions forming the tolerance chain is used as a combined ring. The precision of the closed ring depends on the precision of the component rings and is a result of the combined effect of the precision of the component rings. And describing the constraint relation between the required precision of the assembly function and the dimensional precision of each component ring in the tolerance chain by adopting an extreme value method, wherein the tolerance of the closed ring is equal to the sum of the tolerances of each component ring. In the assembly dimension chain, the closed ring represents the assembly function requirement of the product, is predetermined by a designer, and the precision of the closed ring reflects the requirement of assembly quality.

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

T_CL≥T₁+T₂+…+T_p+…+T_n(7)

T_CLdenotes the dimensional tolerance of the closed loop, n denotes the number of component loops in the dimensional chain, T_pThe dimensional tolerance of the p-th component ring is indicated. Equation (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 ring.

2) Dimensional tolerance constraints based on machining capabilities

The dimensional processing precision of the same assembly characteristic can be ensured to be different by adopting different processing methods. Therefore, when designing the dimensional tolerances of the assembled features, the machining capability of the last process step must be considered if the machining method is known. The dimensional tolerance constraints based on machining capability can be expressed as:

wherein,andrespectively show the dimension tolerance grade guaranteed by the processing method adopted by the last processing procedure of the assembly characteristic,andrespectively representAndtolerance value corresponding to nominal dimension of the feature to be assembled, and T_dThe design tolerance value of the assembly characteristic is indicated. Equation (8) indicates that the design value of the tolerance should not exceed the processing capability of the processing method. Using table 1, constraints on dimensional tolerances that can be guaranteed for various assembly features in different machining methods can be established.

TABLE 1 machining accuracy of conventional machining method for basic assembly feature plane

3) Dimensional tolerance constraints based on relative machining costs

When a feature is machined by a certain machining method, the machining cost rapidly varies with the variation of the tolerance level in some regions of the tolerance level-to-machining cost curve, and the machining cost tends to be constant when the tolerance level increases to a certain extent. It follows that when features are machined to different tolerance levels using the same machining process, there can be significant differences in machining costs.

Therefore, when designing the tolerance optimization, the dimensional tolerance constraints of the features can be established according to economic requirements within the processing capability of the processing method, as shown in equation (9).

Wherein,andrepresenting a dimensional tolerance level determined according to economic requirements for feature machining, andandare the tolerance values corresponding to them.

4) Dimensional tolerance constraint condition based on economic precision of cutting machining

The same feature can be obtained with different machining methods, and the machining accuracy that can be economically achieved with each machining method under normal production conditions is within a certain range. The economic accuracy of the face milling is IT6 to IT10, the economic accuracy of the face broaching is IT6 to IT9, and the economic accuracy of the face grinding is IT6 to IT 7. The economic machining accuracy of the machining method can be selected as a constraint of the tolerance optimization design, as shown in equation (10).

Wherein,andand a tolerance value corresponding to the economic processing precision of the processing method selected by the characteristics is shown.

5) Form and position tolerance constraint condition based on processing capacity

Like the dimensional tolerances, the different machining methods have different capabilities for machining form and location tolerances. Form and position tolerance constraints based on machining capabilities are established as shown.

Wherein, T_gA value of some form tolerance of a feature is represented,anda tolerance value corresponding to the processing capability of the processing method is indicated.

6) Geometric tolerance constraint condition based on dimensional accuracy

Dimensional tolerances designed on an independent basis only control the local physical dimensions of features and not directlyForm and position errors of the features. However, the dimensional tolerance band, while limiting the dimensional error of the feature, also indirectly controls the form and position error associated therewith. Similarly, form and position tolerances that follow independent principles only require that the feature being constrained be within a given form and position tolerance band, with the form and position errors being maximized regardless of the actual size of the feature. However, the limitation of the form and position tolerance band on the constrained features also limits the associated dimensional errors on the features. Therefore, the design of dimensional and geometric tolerances are subject to a relationship that is subject to constraints and compensates for each other. In general, the principles that should be followed to design the dimensional and geometric tolerances of the same feature are: t is_{Size of}＞T_{Position of}＞T_{Shape of}. Form and position tolerance constraints based on dimensional accuracy can be established accordingly as shown in equation (12).

Wherein, T_gIs the form and position tolerance value of the characteristic,andindicating a form and location tolerance level corresponding to a dimensional tolerance on the feature,andindicating and form tolerance gradeAndthe corresponding tolerance value.

During tolerance optimization design, the plurality of constraint conditions can be selected as constraint conditions of the genetic algorithm objective function according to the assembly function requirement of the product and the economic requirement of processing.

And c, adding the 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.

And d, carrying out genetic coding by adopting a multi-parameter cascade coding method.

The genetic coding is carried out by adopting a multi-parameter cascade coding method, each size tolerance and form and position tolerance are coded by a binary coding method, and then the codes are connected together according to a certain sequence to form a binary string chromosome representing all parameters. In this coding method, the binary code of the individual parameters (parameter substrings) cannot be changed again once the position of the total string of chromosomes has been determined, in order to avoid errors in the evolutionary computation.

The accuracy required to determine the size and form tolerance is 4 bits after the decimal point, based on GB/T1800.3-1998 Standard tolerance values and GB/T1184-1996 form tolerance values, thus the 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:

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

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.

TABLE 2 tolerance information for assembly characteristics

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

when coding, each tolerance parameter can have different value range, the invention adopts equal length coding technique, each parameter has different coding precision, 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:

the binary string chromosome, which consists of the tolerance variables in table 2, can be formalized as follows:

the encoding method can enable a tolerance optimized solution space and a search space of a genetic algorithm to have a one-to-one correspondence relationship.

Binary encoding chromosomes for a given tolerance variable:

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

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.

And e, determining a fitness function.

The GA algorithm determines that all the individuals in the current population are inherited to the next generation population according to the probability proportional to the individual fitnessThe probability that the individual with high fitness inherits the next generation is higher, and the probability that the individual with low fitness inherits the next generation is lower. In the tolerance optimization design, the minimum processing cost is used as an optimization objective function, and the probability that an individual with lower processing cost is selected to propagate a next generation individual is higher, so the level of the processing cost is used as a standard for evaluating the quality of the individual (solution). In order to enable good individuals with low processing costs to be stored and to continue to reproduce, the fitness function of the good individuals is constructed by using the reciprocal of the total processing cost of the good individuals, as shown in a formula (18). Wherein, F_k ^FitThe fitness value of the kth individual in the population.

And f, determining a selection operator function.

In this embodiment, an adaptive value proportion selection operator is selected for calculation.

And the proportion selection operator determines the genetic possibility according to the proportion of the individual fitness value in the total population fitness value, and the probability of inheritance to the next generation is higher when the proportion is higher.

The individual selection probability calculation formula is as follows:

wherein:

P_i-the selection probability of the ith individual;

n is the size of the population, representing the number of solutions for tolerance optimization design;

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

F_i ^Fit-fitness of the ith individual.

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.

And g, determining the operation parameters of the GA algorithm.

The operation parameters in the GA algorithm comprise a population size M, a termination evolution algebra T and a cross probability P_cProbability of mutation P_m。

M is the number of individuals contained in the population. If M takes a small value, the computation speed of the GA algorithm can be increased, but the individual diversity is reduced, which may cause premature aging, and if M takes a large value, the computation efficiency is reduced. M usually has a value range of 20-100;

t is a termination evolution algebra of a genetic algorithm and is generally 100-500;

P_cthe crossover probability is generally a large value, but if it is too large, the good pattern in the population is easily destroyed, and if it is too small, the rate of generating new individuals is slow. P_cThe value range is usually 0.4-0.99;

P_mis the mutation probability. Similar probability of co-crossing, P_mLarger values may destroy better patterns, and too small may be detrimental to the development of better new individuals and the suppression of premature events. P_mThe value of (b) is generally 0.0001 to 0.1.

The method of using genetic algorithm to optimize the design of assembly tolerances will now be described by taking the linkage assembly shown in fig. 2a as an example. After a three-dimensional model of the linkage assembly is established in the CAD system, the nominal dimensions of all the features on the linkage assembly are determined, and related tolerance design can be carried out on the basis. As shown in fig. 2b, in the assembly tolerance network of the linkage assembly, the assembly tolerances of the components such as the slide plate, the bracket, the coupling, the sliding bearing and the shaft can form a completely confined closed assembly tolerance subchain (for the sake of simplicity, one sliding bearing is omitted in the analysis). Next, tolerance optimization design is performed according to the functional requirements of the linkage assembly body. Wherein the dimensional tolerance grade is considered with the economic accuracy of machining of the assembly features, and the form and position tolerance grade is determined with the corresponding relationship between the form and position tolerance and the dimensional tolerance.

Determination of the dimensional tolerance range

In FIG. 2b, there are two pairs of holes for the shaft assembly, i.e. holes φ D on the bracket₃Shaft phi D on shaft coupling₄Nominal size is phi 50, and excircle phi D on shaft₈With a hole phi D in the slide bearing₇The nominal size is phi 38. Hole phi D₃Is S_icysThe basic characteristic surface can be processed by adopting a boring method, and the economic precision of the processing is IT 8-IT 10. Axis phi D₄Is S_ocysThe basic characteristic surface can be machined by a turning method, and the economic precision of the machining is IT 6-IT 9. According to the selection principle of the reference system, the hole phi D₃Axis phi D₄The base hole system is selected for matching. The fit between the bracket and the coupler requires an obvious gap, the bracket is easy to rotate, the economic precision of the processing is integrated, and the hole phi D is finally determined₃Axis phi D₄The composition of (a) is phi 50H8/e 7. The fit between the hole φ D7 and the outer circle φ D8 is a sliding fit, and is determined to be φ 38H8/f 7.

TABLE 3 linkage Assembly dimensional tolerance Range

Distance dimension D₁Nominal size of 19, based on the reference planeA is used as a processing standard, milling is adopted, the economic precision of the cutting processing of the basic assembly characteristic surface is checked, and the economic precision of the processing is IT 6-IT 10, namely T_D1∈ (IT 6-IT 10). distance dimension D₆Is 47, and is processed by a boring method by taking the reference surface C as a processing reference, and the economic precision of the processing is IT 8-IT 10, namely T_D6∈ (IT 8-IT 10) in the same manner, the accuracy ranges for all the dimensional tolerances of fig. 2(c) can be obtained as shown in table 3.

Determination of form and position tolerance type and range

Axis phi D₄Phi D of the hole₃Of the assembly constraint typeThe assembly tolerance function for which this constraint is obtained is:

according to the assembly function requirements of the bracket and the coupling and the selection and optimization rules of the assembly tolerance, a group of assembly tolerances between the assembly characteristic surfaces of the two parts can be determined as follows:

as can be seen from equation (21), the axis φ D needs to be aligned₄Phi D of the hole₃Setting tolerance requirements for cylindricity, i.e. setting tolerance T shown in FIG. 2c_G4And T_G3。

Design reference A surface and dimension D on sliding plate₁The plane in which the upper end dimension limit (see fig. 2c) is located constitutes a pair of geometric constraints, which are cross-referenced variable geometric constraints CVGC formed by two geometric features on the same part. Deducing the type of the corresponding cross-reference variable geometric constraint to be CC21, and deducing the type of the corresponding tolerance to be A of CC21T8, the type of geometric tolerance for which two feature planes correspond, is parallelism. Therefore, the dimension D is required₁The plane of the upper end dimensional limit of (a) puts requirements on parallelism of the reference A, as shown by the form and position tolerance T in FIG. 2c_G1。

After determining the type of form and location tolerance, a tolerance level range for the form and location tolerance can be determined based on the associated dimensional tolerance accuracy. In the above analysis, dimension D has been obtained₁The accuracy range of (A) is IT 6-IT 8, and the parallelism tolerance T can be obtained_G1The accuracy range of (D) is IT 7-IT 10. Similarly, the dimensional tolerance T on the support_G3And dimensional tolerance T on the coupling_G4The tolerance classes of (a) are H8 and e7, respectively, and the corresponding shape tolerance T is known from the corresponding relationship between the dimensional tolerance class and the roundness and cylindricity tolerance classes_G3And T_G4The tolerance levels of (A) are IT 8-IT 9 and IT 7-IT 8, respectively.

The ranges of precision for all form and position tolerances in fig. 2c obtained using the above method are shown in table 4.

TABLE 4 form and position tolerance range of linkage assembly

Linkage assembly body tolerance optimization objective function

And establishing a tolerance optimization objective function of the linkage assembly body. Wherein the processing cost-tolerance model for each type of feature is shown in table 5.

TABLE 5 model of processing costs for various types of features

Establishing a tolerance optimization objective function for the linkage assembly is as follows:

during assembly, the axes of the shaft and the shaft coupling of the linkage assembly body are required to be kept on the same straight line, and the height difference T is₀Not greater than 0.45mm, which is taken as a closed loop for assembling the dimensional chain, the constraints for establishing the objective function are as follows:

the constraints of the function are as follows:

determination of operating parameters

The population number M takes the value of 20, the genetic algebra T takes the value of 70, and the cross probability P_cValue 0.7, probability of variation P_mThe value is 0.08.

Assembly tolerance optimization results and analysis thereof

Common tolerance distribution methods include an analog tolerance method, an equal precision method, an equal influence method, an economic criterion method, and the like. The equal precision method is to take the same tolerance level for all the component ring sizes in the size chain, the equal influence method is to take the same influence on the tolerance of the closed ring by the dimensional tolerance of each component ring, and the equal tolerance rule is to take the same tolerance value for all the component ring sizes in the size chain. For a straight dimension chain, the equal tolerance method is equivalent to the equal influence method.

Table 6 shows the tolerance values obtained by the tolerance distribution methods such as the genetic algorithm, the equal precision method, the equal influence method, and the like, and the comparison of the processing costs thereof. The tolerance value obtained by the genetic algorithm is used for processing, and the total processing cost is only 35.1 percent of that of the equal influence method and 76.8 percent of that of the equal precision method.

TABLE 6 comparison of tolerance values for different tolerance assignment methods and their processing costs

The foregoing is merely a preferred embodiment of the invention, which is intended to be illustrative and not limiting. It will be understood by those skilled in the art that various changes, modifications and equivalents may be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

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.