CN103903060A - Optimum design method for assembly tolerance - Google Patents

Abstract

The invention relates to an optimum design method for assembly tolerance. The method includes the steps of determining the dimensional tolerance according to an assembly tolerance chain, determining the constraint condition of the assembly tolerance, determining the type and the range of form and location tolerance, determining the minimum machining cost of an assembly as an optimization target, and setting up a target function for optimizing the assembly tolerance, wherein the target function is calculated through the steps of setting a part expression function of the mechanical assembly, determining a total machining cost expression function of the mechanical assembly, determining a machining cost function of each part in the assembly, determining a machining cost function of assembly characteristics, obtaining a total machining cost-tolerance function of the assembly and obtaining the target function for optimizing the assembly tolerance. The optimization tolerance obtained by enabling the minimum machining cost to serve as the target and enabling machining capacity or machining cost or machining economic accuracy to serve as the constraint condition can meet the assembly function requirements of products, the constraint condition of machining is met, and good economic benefits can be obtained.

Description

A kind of Optimization Design about build-up tolerance

Technical field

The present invention relates to a kind of Optimization Design of mechanical build-up tolerance, relate in particular to a kind of Optimization Design about build-up tolerance.

Background technology

Fitted position tolerance and the form and position tolerance of parts in prior art are generally to determine according to the usability demand of product, assembling function demand, quality assurance, rapidoprint, working condition, manufacturing cost and corresponding country, industry or company standard.

In the design phase, selecting build-up tolerance value how correctly, is reasonably a design problem that must consider, and it,, to ensureing assembling and the usability of product, improves the quality of products, and reduction manufacturing cost etc. all has great importance.Affecting in the factor of part processing cost, tolerance plays very important effect.The design tolerance of part is less, more can ensure its assembling function demand, but processing cost also increases thereupon.In the time that precision is brought up to a certain degree, processing cost can sharply increase.How, in the situation that meeting assembling function demand, design rational assembly features tolerance value, to obtain minimum processing cost, a problem must paying close attention to while being deisgn product.The factor that affects processing cost and tolerance relation is a lot, be difficult to a unified mathematical model accurately describe the relation of characteristic processing cost and tolerance.For example, the factors such as characteristic type, process equipment, chucking method, processing technology, operator, production lot, need only one of them or several change, and processing cost will be different from the relation of tolerance.

Many cost-tolerance models lay particular emphasis on the research of dimensional tolerence, and still, manufacturing cost is also subject to the impact of form tolerance and position of related features simultaneously, only has the model that three is considered to foundation, just closer to actual conditions.The present invention, taking minimum process cost as optimization aim, considers dimensional tolerence and form and position tolerance, sets up a new cost-tolerance models.

Set up the constraint condition of genetic algorithm according to the corresponding relation of form and position tolerance and dimensional tolerence, realize the comprehensive Design of dimensional tolerence and form and position tolerance, it is an important content in tolerance optimization design that tolerance and processing cost are carried out to modeling.Tolerance Optimization is the optimization design problem of a multiparameter, and genetic algorithm is with its ability of searching optimum, and stronger robustness and the concurrency of calculating have demonstrated powerful application potential therein.

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

Summary of the invention

The object of the present invention is to provide a kind of Optimization Design about build-up tolerance, in order to overcome above-mentioned technological deficiency.

For achieving the above object, the invention provides a kind of Optimization Design about build-up tolerance, this process is:

Step a, according to assembly tolerance chains, determines dimensional tolerence;

Step b, determines the constraint condition of build-up tolerance;

Step c, determines type and the scope of form and position tolerance;

Steps d, definite minimum process cost taking assembly, as optimization aim, is set up the objective function that build-up tolerance is optimized;

This function as shown in the formula described is:

$\min \left\{C_{\mathrm{MA}}\right\}=\min \left\{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\right[\underset{a=1}{\overset{g}{\mathrm{\Σ}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\Σ}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\Σ}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)\left]\right\}---\left(1\right)$

In formula, C _mAfor the total cost function of assembly MA;

for feature

the processing cost-tolerance function of a dimensional tolerence;

for feature

the processing cost-tolerance function of b form tolerance;

for feature

the processing cost-tolerance function of c position of related features; G is feature

dimensional tolerence sum; H is feature

form tolerance sum; S is feature

position of related features sum;

This function passes through following process computation and draws,

Steps d 1, sets the part representative function of mechanical assembly;

A given mechanical assembly is as shown in following formula:

${\mathrm{MA}}_{\mathrm{\Σ}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i=S_P(P_1,P_2,\·\·\·,P_i,\·\·\·{,P}_n)---\left(2\right)$

In formula:

MA _Σ---represent mechanical assembly;

P _i---i the part of composition assembly MA;

N---the part sum of composition assembly MA.

Steps d 2, determines the total cost representative function of mechanical assembly;

The total cost of assembly is as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}C\left(P_i\right)(i=1,\·\·\·,n)---\left(3\right)$

In formula:

C _mA---the total cost function of assembly MA;

C (P _i)---part P in assembly MA _iprocessing cost function.

Steps d 3, determines the processing cost function of each part in assembly;

The processing cost of part is as follows:

$C\left(P_i\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}C\left(f_i^j\right)---\left(4\right)$

In formula:

---part P _ij assembly features;

---part P _ithe processing cost function of j assembly features;

M---part P _iassembly features sum.

Steps d 4, determines the processing cost function of assembly features;

As follows:

$C\left(f_i^j\right)=\underset{a=1}{\overset{g}{\mathrm{\Σ}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\Σ}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\Σ}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)---\left(5\right)$

In formula:

---feature

the processing cost-tolerance function of a dimensional tolerence;

---feature

the processing cost-tolerance function of b form tolerance;

---feature

the processing cost-tolerance function of c position of related features;

G---feature

dimensional tolerence sum;

H---feature form tolerance sum;

S---feature position of related features sum.

Steps d 5, aggregative formula (3)～(5), show that the total cost-tolerance function of assembly can be expressed as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}[\underset{a=1}{\overset{g}{\mathrm{\Σ}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\Σ}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\Σ}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)]---\left(6\right)$

Draw according to above-mentioned formula (6) objective function that build-up tolerance is optimized;

Step e, appends to VGC network by tolerance type information, obtains the tolerance network of assembly, selects to determine the dimensional tolerence of each assembly features and the span of geometric tolerances;

Step f, adopts the method for multiparameter concatenated coding to carry out genetic coding;

Each dimensional tolerence and form and position tolerance are encoded with binary coding method, then these codings are formed to the binary string chromosome that represents whole parameters according to being necessarily linked in sequence together;

According to GB/T1800.3-1998 standard of tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, the precision of determining size and Geometrical Tolerance Principle is after radix point 4, tolerance decision variable T ∈ [T ^l, T ^u] should be divided at least (T ^u-T ^l) × 10 ⁴individual part, its binary string figure place (is used m _jrepresent) can calculate with following formula:

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

Chromosomal coded strings length is:

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

Wherein,

L---chromosomal coded strings length;

L _i---the code length of tolerance variable;

The sum of n---size and form and position tolerance variable;

Being accurate to the size of four and the maximum binary string code length of form and position tolerance variable after radix point is 14.Adopt fixed-length coding technology, the code length of each tolerance variable is decided to be 14, and a chromosome length with n tolerance parameter can be expressed as:

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

In the time encoding, each tolerance parameter can have different spans, adopts fixed-length coding technology, and each parameter has different encoding precision.If the span of a certain tolerance is [T ^l, T ^u], represent this tolerance with 14 binary coded characters, can generate 2 ¹⁴plant different codings, encoding precision (or code length) is:

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

Tolerance variable binary coding chromosome for given:

$a_1^1,a_2^1,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^1,a_1^2,a_2^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^j,a_2^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^n,a_2^n,\&CenterDot;\&CenterDot;\&CenterDot;{,a}_{14}^n$

The form of the binary string decoding functions of j tolerance variable is:

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

Wherein:

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

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

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

---m gene value of the binary coding string of j tolerance variable;

Step g, determines fitness function;

Step h, determines and selects operator function;

Step I, determines the operational factor of genetic algorithm.

Further, in described step e, adopt the inverse of individual total cost to construct its fitness function, shown in specific as follows stating,

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

In formula,

for k individual fitness value in population, C _mAfor the total cost function of assembly MA,

for feature

the processing cost-tolerance function of a dimensional tolerence;

for feature

the processing cost-tolerance function of b form tolerance;

for feature

the processing cost-tolerance function of c position of related features; G is feature

dimensional tolerence sum; H is feature

form tolerance sum; S is feature

position of related features sum.

Further, select adoption rate to select operator to calculate in described step f, wherein, ratio selects the concrete implementation of operator to be:

F1. calculate the fitness value of all individualities in colony;

F2. the fitness value summation to all individualities;

F3. calculate individual relative adaptation degree, individuality is genetic to follow-on selection probability;

F4. use simulation roulette wheel operation (i.e. random number between 0 and 1) to determine each individual selected number of times.

Further, wherein the selection probability calculation formula of individuality is as follows:

$P_i=\frac{F_i^{\mathrm{Fit}}}{\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{F}_k^{\mathrm{Fit}}}$

In formula,

P _ibe i individual selection probability;

N is the scale (number of the solution of tolerance optimization design) of population;

for the fitness of arbitrary individuality;

be i individual fitness.

Further, the operational factor in described step g comprises Population Size M, stops evolutionary generation T, crossover probability P _c, variation probability P _m;

M span is 20～100;

T is taken as 100～500;

P _cspan be 0.4～0.99;

P _mbe taken as 0.0001～0.1.

Beneficial effect of the present invention is compared with prior art:

Build-up tolerance Optimization Design of the present invention is taking minimum process cost as target, respectively with working ability, processing cost or processing economic accuracy for optimization tolerance that constraint condition was obtained, can meet the assembling function demand of product, meet the constraint condition of machining, can obtain good economic benefit; Set up the constraint condition of genetic algorithm according to the corresponding relation of form and position tolerance and dimensional tolerence, realized the comprehensive Design of dimensional tolerence and form and position tolerance; The method combines the research contents of build-up tolerance type design and tolerance network struction, for realizing from assembly to size and useful exploration has been done in the computer aided tolerance of form and position tolerance design.Genetic algorithm is with its ability of searching optimum, and stronger robustness and the concurrency of calculating have demonstrated powerful application potential therein.

Brief description of the drawings

Fig. 1 is the process flow diagram of the present invention about the Optimization Design of build-up tolerance;

Fig. 2 a is the present invention's assembly schematic diagram that links;

Fig. 2 b is the composition structural representation of assembly of the present invention;

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

Embodiment

Below in conjunction with accompanying drawing, technical characterictic and the advantage with other above-mentioned to the present invention are described in more detail.

The present invention, taking minimum process cost as optimization aim, considers dimensional tolerence and form and position tolerance, sets up a new cost-tolerance models.The total cost of assembly is made up of the processing cost of all accessories, and the processing cost of part is made up of the processing cost of its all characteristic faces.It is not the assembling that each characteristic face participates in part.Because the present invention mainly considers the optimal design of fitted position tolerance and form and position tolerance size, therefore only consider the processing cost of assembly features face.

The present invention is based on the process of build-up tolerance Optimization Design that cost objective optimizes as follows:

Step a, according to assembly tolerance chains, determines dimensional tolerence;

Step b, determines the constraint condition of build-up tolerance;

In the present invention, according to processing cost, the economic accuracy of various cut and the corresponding relation of dimensional tolerence and form and position tolerance of the working ability of the assembling function demand of product, various job operations, different processing grades, be provided with multiple constraint condition.

1) the dimensional tolerence constraint condition based on assembling function demand

From the subchain of build-up tolerance network, extract dimensional tolerence, to obtain the fitted position tolerance chain corresponding with sub-assemblies.Closed-loop by the precision of assembling function demand as dimensional tolerence chain, forms the precision of other sizes of tolerance chain as makeup ring.The precision of closed-loop depends on the precision of makeup ring, is the result of each makeup ring accuracy synthesis effect.Adopt extremum method to describe the restriction relation between assembling function demand precision and each makeup ring dimensional accuracy in tolerance chain, the tolerance of closed-loop equals each tolerance of unit ring sum.In dimensional chain for assembly, closed-loop embodies the assembling function demand of product, is predetermined by designer, and its precision has reflected the requirement of assembly quality.

In order to ensure the assembly quality of product, the dimensional tolerence constraint condition of foundation based on assembling function demand is as follows:

T _CL≥T ₁+T ₂+…+T _p+…+T _n (7)

T _cLthe dimensional tolerence that represents closed-loop, n represents the number of makeup ring in dimension chain, T _prepresent the dimensional tolerence of p makeup ring.Formula (7) represents that in dimension chain, each increasing encircles the dimensional tolerence that should be not more than closed-loop with the tolerance sum that subtracts ring.

2) the dimensional tolerence constraint condition based on working ability

The dimensioned precision that same assembly features adopts different job operations to ensure is different.Therefore while designing the dimensional tolerence of assembly features, if the job operation of known last procedure, the necessary working ability of considering this job operation.Dimensional tolerence constraint condition based on working ability can be expressed as:

$T_{{\mathrm{IT}}_{\max }^{\mathrm{pc}}}\&le;T_d\&le;T_{{\mathrm{IT}}_{\min }^{\mathrm{pc}}}---\left(8\right)$

Wherein, with

represent respectively the dimensional tolerence grade that job operation that last one manufacturing procedure of assembly features adopts can ensure,

with

represent respectively with

the tolerance value corresponding with assembly features nominal size, and T _drepresent the design tolerance value of assembly features.Formula (8) represents that the design load of tolerance should not exceed the working ability of job operation.Utilize table 1 can set up the constraint condition of the dimensional tolerence that various assembly features faces can ensure in different processing methods.

The machining precision of the basic assembly features face tradition of table 1 machining process

3) the dimensional tolerence constraint condition based on relative processing cost

In the time adopting a certain job operation machining feature, in some region of the grade of tolerance and processing cost curve, processing cost changes rapidly along with the variation of the grade of tolerance, and in the time that the grade of tolerance increases to a certain degree, processing cost is tending towards a constant.As can be seen here, when by same job operation during according to different grade of tolerance machining feature face, its processing cost may have larger difference.

Therefore, while carrying out tolerance optimization design, can, within the scope of the working ability of job operation, set up the dimensional tolerence constraint condition of feature according to economy demand, as shown in formula (9).

$T_{{\mathrm{IT}}_{\max }^{\mathrm{rpc}}}\&le;T_d\&le;T_{{\mathrm{IT}}_{\min }^{\mathrm{rpc}}},{\mathrm{IT}}_{\max }^{\mathrm{rpc}},{\mathrm{IT}}_{\min }^{\mathrm{rpc}}\&Element;({\mathrm{IT}}_{\max }^{\mathrm{pc}},{\mathrm{IT}}_{\min }^{\mathrm{pc}})---\left(9\right)$

Wherein,

with

represent according to the economy demand of feature machining and definite dimensional tolerence grade, and

with the tolerance value corresponding with them.

4) the dimensional tolerence constraint condition based on cut economic accuracy

Same feature can adopt different job operations to obtain, and the machining precision that various job operation can reach in economic mode under normal working condition is to have certain scope.The economic accuracy of slabbing processing is IT6～IT10, and the economic accuracy of surface broaching processing is IT6～IT9, and the economic accuracy of flat surface grinding processing is IT6～IT7.Economic accuracy of machining that can Choice and process method is as the constraint condition of tolerance optimization design, as shown in formula (10).

$T_{{\mathrm{IT}}_{\max }^{\mathrm{ea}}}\&le;T_d\&le;T_{{\mathrm{IT}}_{\min }^{\mathrm{ea}}}---\left(10\right)$

Wherein,

with

the tolerance value corresponding to economic accuracy of machining of the selected job operation of representation feature.

5) the form and position tolerance constraint condition based on working ability

Same size tolerance is the same, and the ability of different job operation processing form and position tolerances is not identical yet.The form and position tolerance constraint condition of foundation based on working ability as shown.

$T_{{\mathrm{IT}}_{\max }^{\mathrm{pc}}}\&le;T_g\&le;T_{{\mathrm{IT}}_{\min }^{\mathrm{pc}}}---\left(11\right)$

Wherein, T _gthe a certain form and position tolerance value of representation feature, with

represent the tolerance value corresponding with the working ability of job operation.

6) the form and position tolerance constraint condition based on dimensional accuracy

Adopt the local physical size of a dimensional tolerence controlling feature of independent principle design, and the direct morpheme error of controlling feature not.But tolerance zone, in the scale error of limited features, has also been controlled associated morpheme error indirectly.Same, observe the form and position tolerance of independent principle, only require that restrained feature is positioned at given form and position tolerance band, its morpheme error can reach maximal value, and irrelevant with the physical size of feature.But the restriction of form and position tolerance band to restrained feature, has equally also limited scale error relevant in feature.Therefore, the design of dimensional tolerence and geometric tolerances objectively exists the relation of mutual restriction, mutual compensation.Generally, designing the size of same feature and principle that geometric tolerances should be followed is: T _size> T _position> T _shape.Can set up accordingly form and position tolerance constraint condition based on dimensional accuracy as shown in formula (12).

$T_{{\mathrm{IT}}_{\max }^g}\&le;T_g\&le;T_{{\mathrm{IT}}_{\min }^g}---\left(12\right)$

Wherein, T _gfor the form and position tolerance value of feature,

with

represent the form and position tolerance grade corresponding with dimensional tolerence in feature,

with

represent and form and position tolerance grade with

corresponding tolerance value.

Step c, determines type and the scope of form and position tolerance;

Steps d, definite minimum process cost taking assembly, as optimization aim, is set up the objective function that build-up tolerance is optimized.

Steps d 1, sets the part representative function of mechanical assembly;

A given mechanical assembly is as shown in following formula (1):

${\mathrm{MA}}_{\mathrm{\&Sigma;}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i=S_P(P_1,P_2,\&CenterDot;\&CenterDot;\&CenterDot;,P_i,\&CenterDot;\&CenterDot;\&CenterDot;{,P}_n)---\left(1\right)$

In formula:

MA _Σ---represent mechanical assembly;

P _i---i the part of composition assembly MA;

N---the part sum of composition assembly MA.

Steps d 2, determines the total cost representative function of mechanical assembly;

The total cost of assembly is as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}C\left(P_i\right)(i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n)---\left(2\right)$

In formula:

C _mA---the total cost function of assembly MA;

C (P _i)---part P in assembly MA _iprocessing cost function.

Steps d 3, determines the processing cost function of each part in assembly;

The processing cost of part is as follows:

$C\left(P_i\right)=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}C\left(f_i^j\right)---\left(3\right)$

In formula:

---part P _ij assembly features;

---part P _ithe processing cost function of j assembly features;

M---part P _iassembly features sum.

Steps d 4, determines the processing cost function of assembly features;

As follows:

$C\left(f_i^j\right)=\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)---\left(4\right)$

In formula:

---feature the processing cost-tolerance function of a dimensional tolerence;

---feature

the processing cost-tolerance function of b form tolerance;

---feature

the processing cost-tolerance function of c position of related features;

G---feature

dimensional tolerence sum;

H---feature form tolerance sum;

S---feature

position of related features sum.

Steps d 5, aggregative formula (2)～(4), the total cost-tolerance function of assembly can be expressed as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}[\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)]---\left(5\right)$

At Design Stage, dimensional tolerence and the form and position tolerance of parts drawing subscript note are all to be formed by the last job operation of feature.Therefore, the present invention only consider feature shaping last procedure be processed into the original design tolerance of determining.

Steps d 6, taking the minimum process cost of assembly as optimization aim, the objective function of build-up tolerance optimization may be defined as:

$\min \left\{C_{\mathrm{MA}}\right\}=\min \left\{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\right[\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)\left]\right\}---\left(6\right)$

Step e, appends to VGC network by tolerance type information, obtains the tolerance network of assembly, selects to determine the dimensional tolerence of each assembly features and the span of geometric tolerances.

Step f, adopts the method for multiparameter concatenated coding to carry out genetic coding.

Adopt the method for multiparameter concatenated coding to carry out genetic coding, each dimensional tolerence and form and position tolerance are encoded with binary coding method, then these codings are formed to the binary string chromosome that represents whole parameters according to being necessarily linked in sequence together.In this coding method, the binary coding of parameters (parameter substring) once after the position of the total string of chromosome is determined, just can not change again, in order to avoid make mistakes in evolutionary computation.

The length of binary coding string depends on the desired solving precision of problem.According to GB/T1800.3-1998 standard of tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, the precision of determining size and Geometrical Tolerance Principle is after radix point 4, therefore tolerance decision variable T ∈ [T ^l, T ^u] should be divided at least (T ^u-T ^l) × 10 ⁴individual part, its binary string figure place (is used m _jrepresent) can calculate with following formula:

$2^{m_j-1}<(T^U-T^L)\&times;{10}^4\&le;2^{m_j}-1---\left(13\right)$

Chromosomal coded strings length is:

$L=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_i---\left(14\right)$

Wherein,

L---chromosomal coded strings length;

L _i---the code length of tolerance variable;

The sum of n---size and form and position tolerance variable.

The tolerance information of table 2 assembly features

According to the above analysis, being accurate to the size of four and the maximum binary string code length of form and position tolerance variable after radix point is 14.The present invention adopts fixed-length coding technology, and the code length of each tolerance variable is decided to be 14.A chromosome length with n tolerance parameter can be expressed as:

$L=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_i=14n---\left(15\right)$

In the time encoding, each tolerance parameter can have different spans, and the present invention adopts fixed-length coding technology, and each parameter has different encoding precision.If the span of a certain tolerance is [T ^l, T ^u], represent this tolerance with 14 binary coded characters, can generate 2 ¹⁴plant different codings, encoding precision (or code length) is:

$\mathrm{\&delta;}=\frac{T^L-T^U}{2^{14}-1}---\left(16\right)$

The binary string chromosome being made up of the tolerance variable in table 2 can formally be expressed as follows:

This coding method can make the solution space of Tolerance Optimization and the search volume of genetic algorithm have one-to-one relationship.

Tolerance variable binary coding chromosome for given:

$a_1^1,a_2^1,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^1,a_1^2,a_2^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^j,a_2^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^n,a_2^n,\&CenterDot;\&CenterDot;\&CenterDot;{,a}_{14}^n$

The form of the binary string decoding functions of j tolerance variable is:

$T_j=T_j^L+\left(\underset{m=1}{\overset{14}{\mathrm{\&Sigma;}}}{a}_m^j{2}^{m-1}\right)\frac{T_j^U-T_j^L}{2^{14}-1}---\left(17\right)$

Wherein:

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

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

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

---m gene value of the binary coding string of j tolerance variable.

Step g, determines fitness function.

GA algorithm decides all individual inheritances in current population to the chance in population of future generation by the probability being directly proportional to ideal adaptation degree, the individual inheritance that fitness is high is larger to follow-on probability, and the individual inheritance that fitness is low is lower to follow-on probability.In tolerance optimization design, using minimum process cost as the objective function of optimizing, the lower individuality of processing cost is selected, and to remove to breed individual probability of future generation larger, therefore using the height of processing cost as evaluating individual (solutions) fine or not standard.In order to make the defect individual that processing cost is lower can preserve and continue procreation, the present invention constructs its fitness function with the inverse of individual total cost, as shown in formula (18).Wherein,

for k individual fitness value in population.

$F_k^{\mathrm{Fit}}=\frac{1}{C_{\mathrm{MA}}}=\frac{1}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}[\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)]}---\left(18\right)$

Step h, determines and selects operator function.

In the present embodiment, select adaptive value ratio to select operator to calculate.

Ratio selects operator to determine according to the ratio of ideal adaptation Du Zhizhan colony adaptive value summation the possibility that it is hereditary, and ratio is larger, is genetic to follow-on possibility larger.

Individual selection probability calculation formula is as follows:

$P_i=\frac{F_i^{\mathrm{Fit}}}{\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{F}_k^{\mathrm{Fit}}}---\left(19\right)$

Wherein:

P _i---i individual selection probability;

The scale (number of the solution of tolerance optimization design) of n---population;

---the fitness of arbitrary individuality;

---i individual fitness.

Ratio selects the concrete implementation of operator to be:

F1. calculate the fitness value of all individualities in colony;

F2. the fitness value summation to all individualities;

F3. calculate individual relative adaptation degree, individuality is genetic to follow-on selection probability;

F4. use simulation roulette wheel operation (i.e. random number between 0 and 1) to determine each individual selected number of times.

Step I, determines the operational factor of GA algorithm.

Operational factor in GA algorithm comprises Population Size M, stops evolutionary generation T, crossover probability P _c, variation probability P _m.

M is the quantity of contained individuality in population.If M gets less value, can improve the arithmetic speed of GA algorithm, but reduce individual diversity, likely can cause precocious phenomenon, and in the time that M gets larger value, can reduce operation efficiency.The common span of M is 20～100;

T is the termination evolutionary generation of genetic algorithm, is generally taken as 100～500;

P _cfor crossover probability, generally get larger value, if but excessive, easily destroy the defect mode in population, the too small speed that can make to produce new individuality is slower.P _ccommon span is 0.4～0.99;

P _mfor variation probability.Similar with crossover probability, P _mwhile getting larger value, may destroy good pattern, too little the generation new individual and precocious phenomenon of inhibition preferably that is unfavorable for.P _mvalue be generally taken as 0.0001～0.1.

Now, taking the interlock assembly shown in Fig. 2 a as example, the method for build-up tolerance optimal design of the present invention is described.When setting up in CAD system after the three-dimensional model of interlock assembly, on it, the characteristic nominal size of institute is just determined thereupon, can carry out on this basis relevant tolerance design.

As shown in Figure 2 b, in the build-up tolerance network of interlock assembly, can be formed the build-up tolerance subchain (for simplification problem, omitting a sliding bearing when analysis) of the sealing of a Complete Bind by the build-up tolerance of the parts such as slide plate, support, shaft coupling, sliding bearing and axle.Carry out the optimal design of tolerance below, according to the functional requirement of interlock assembly.Wherein, consider dimensional tolerence grade with the processing economic accuracy of assembly features, determine form and position tolerance grade with the corresponding relation of form and position tolerance and dimensional tolerence.

Determining of dimensional tolerance range

In Fig. 2 b, there is the assembling of two pairs of holes and axle, i.e. hole φ D on support ₃with the axle φ D on shaft coupling ₄, nominal size is φ 50, the hole φ D on cylindrical φ 4 and sliding bearing on axle ₇, nominal size is φ 38.Hole φ D ₃for S _icysessential characteristic face, can adopt the method processing of bore hole, and the economic accuracy of processing is IT8～IT10.Axle φ D ₄for S _icysessential characteristic face, can adopt the method processing of turning, and the economic accuracy of processing is IT6～IT9.According to the selection principle of reference system, hole φ D ₃/ axle φ D ₄select basic hole system to coordinate.Cooperation between support and shaft coupling requires there is obvious gap, is easy to rotate, and the comprehensively economic accuracy of its processing, finally determines hole φ D ₃/ axle φ D ₄cooperation be φ 50H8/a7.Cooperation between hole φ D7 and cylindrical φ D8 belongs to and is slidably matched, and determines that it coordinates for φ 38H8/f7.

The table 3 assembly dimensional tolerance range that links

Apart from dimension D ₁nominal size be 19, using reference field A as machining benchmark, adopt Milling Process, consult the economic accuracy of basic assembly features face cut, the economic accuracy of known its processing is IT6～IT10, i.e. T _d1∈ (IT6～IT10).Apart from dimension D ₆nominal size be 47, taking reference field C as machining benchmark, adopt the method processing of bore hole, the economic accuracy of processing is IT8～IT10, i.e. T _d6∈ (IT8～IT10).Adopt identical method, the accuracy rating that can obtain all dimensional tolerences in Fig. 2 c is as shown in table 3.

Determining of Geometric Tolerance Types and scope

Axle φ D ₄with hole φ D ₃assembly constraint type be

obtaining the corresponding build-up tolerance function of this constraint is:

According to the choice and optimization rule of the assembling function demand of support and shaft coupling and build-up tolerance, can determine that one group of build-up tolerance between the assembly features face of two parts is:

From formula (21), need to be to axle φ D ₄with hole φ D ₃the Geometrical Tolerance Principle of cylindricity is proposed, i.e. form and position tolerance T shown in Fig. 2 c _g4and T _g3.

Design basis A face and dimension D on slide plate ₁upper end size limit (seeing the c) plane at the place geometrical constraint that partners of Fig. 2, is be made up of two geometric properties on Same Part mutual with reference to Variational Geometric Constraints CVGC.Reasoning its corresponding mutual be CC21 with reference to Variational Geometric Constraints type, the corresponding tolerance type of reasoning CC21 is AT8, the corresponding geometric tolerances type of two characteristic planes is the depth of parallelism.Therefore, need to be to dimension D ₁the plane at size limit place, upper end propose for the depth of parallelism requirement of benchmark A, form and position tolerance T as shown in Figure 2 c _g1.

Determining after the type of form and position tolerance, can the dimensional tolerence precision based on relevant determining the grade of tolerance scope of form and position tolerance.In above-mentioned analysis, obtain dimension D ₁accuracy rating be IT6～IT8, can obtain parallelism tolerance T _g1accuracy rating be IT7～IT10.In like manner, the dimensional tolerence T on support _g3with the dimensional tolerence T on shaft coupling _g4the grade of tolerance be respectively H8 and e7, by the known corresponding form tolerance T with it of the corresponding relation of dimensional tolerence grade and circularity and cylindricity tolerance grade _g3and T _g4the grade of tolerance be respectively IT8～IT9 and IT7～IT8.

The accuracy rating that obtains all form and position tolerances in Fig. 2 c with said method reasoning is as shown in table 4.

The table 4 assembly form and position tolerance scope that links

Interlock assembly Tolerance Optimization objective function

This section is set up the Tolerance Optimization objective function of interlock assembly.Wherein, the processing cost-tolerance Model of each category feature is as shown in table 5.

The processing cost model of the each category feature of table 5

The Tolerance Optimization objective function of setting up interlock assembly is as follows:

In the time assembling, require the axis of interlock assembly axis and shaft coupling to keep point-blank, its difference in height T ₀be not more than 0.45mm, the closed-loop using this as dimensional chain for assembly, set up bound for objective function as follows:

Determining of operational factor

Population number M value 20, genetic algebra T value 70, crossover probability P _cvalue 0.7, variation probability P _mvalue 0.08.

Build-up tolerance optimum results and analysis thereof

Conventional Tolerance Distribution Method have analogy tolerance method, etc. tolerance method, etc. precision method, etc. affect method and economic criteria method etc.Wherein, that all makeup ring sizes in dimension chain are got to the identical grade of tolerance etc. precision method, be exactly that each makeup ring dimensional tolerence has identical impact to closed-loop tolerance Deng the method for impact, and etc. tolerance rule be that all makeup ring sizes in dimension chain are got to equal tolerance value.For linear dimensional chain, the method that affects such as be equal to etc. tolerance method.

Table 6 listed respectively with genetic algorithm, etc. precision method and etc. affect every tolerance value and the processing cost comparison thereof that the Tolerance Distribution Method such as method obtain.Process with the tolerance value that genetic algorithm obtains, its total cost just waits and affects 35.1% of method, etc. 76.8% of precision method.

The tolerance value of the different Tolerance Distribution Method of table 6 and processing cost comparison thereof

The foregoing is only preferred embodiment of the present invention, is only illustrative for invention, and nonrestrictive.Those skilled in the art is understood, and in the spirit and scope that limit, can carry out many changes to it in invention claim, amendment, and even equivalence, but all will fall within the scope of protection of the present invention.

Claims (5)

1. about an Optimization Design for build-up tolerance, it is characterized in that, this process is:

Step a, according to assembly tolerance chains, determines dimensional tolerence;

Step b, determines the constraint condition of build-up tolerance;

Step c, determines type and the scope of form and position tolerance;

Steps d, definite minimum process cost taking assembly, as optimization aim, is set up the objective function that build-up tolerance is optimized;

This function as shown in the formula described is:

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

In formula, C _mAfor the total cost function of assembly MA;

for feature

the processing cost-tolerance function of a dimensional tolerence;

for feature

the processing cost-tolerance function of b form tolerance; for feature

the processing cost-tolerance function of c position of related features; G is feature

dimensional tolerence sum; H is feature

form tolerance sum; S is feature

position of related features sum;

This function passes through following process computation and draws,

Steps d 1, sets the part representative function of mechanical assembly;

A given mechanical assembly is as shown in following formula:

${\mathrm{MA}}_{\mathrm{\&Sigma;}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_i=S_P(P_1,P_2,\&CenterDot;\&CenterDot;\&CenterDot;,P_i,\&CenterDot;\&CenterDot;\&CenterDot;{,P}_n)---\left(2\right)$

In formula:

MA _∑---represent mechanical assembly;

P _i---i the part of composition assembly MA;

N---the part sum of composition assembly MA.

Steps d 2, determines the total cost representative function of mechanical assembly;

The total cost of assembly is as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}C\left(P_i\right)(i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n)---\left(3\right)$

In formula:

C _mA---the total cost function of assembly MA;

C (P _i)---part P in assembly MA _iprocessing cost function.

Steps d 3, determines the processing cost function of each part in assembly;

The processing cost of part is as follows:

$C\left(P_i\right)=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}C\left(f_i^j\right)---\left(4\right)$

In formula:

---part P _ij assembly features;

---part P _ithe processing cost function of j assembly features;

M---part P _iassembly features sum.

Steps d 4, determines the processing cost function of assembly features;

As follows:

$C\left(f_i^j\right)=\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)---\left(5\right)$

In formula:

---feature the processing cost-tolerance function of a dimensional tolerence;

---feature

the processing cost-tolerance function of b form tolerance;

---feature the processing cost-tolerance function of c position of related features;

G---feature

dimensional tolerence sum;

H---feature

form tolerance sum;

S---feature

position of related features sum.

Steps d 5, aggregative formula (3)～(5), show that the total cost-tolerance function of assembly can be expressed as follows:

$C_{\mathrm{MA}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}[\underset{a=1}{\overset{g}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TD}}^a\left(f_i^j\right)+\underset{b=1}{\overset{h}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TF}}^b\left(f_i^j\right)+\underset{c=1}{\overset{s}{\mathrm{\&Sigma;}}}{C}_{\mathrm{TP}}^c\left(f_i^j\right)]---\left(6\right)$

Draw according to above-mentioned formula (6) objective function that build-up tolerance is optimized;

Step e, appends to VGC network by tolerance type information, obtains the tolerance network of assembly, selects to determine the dimensional tolerence of each assembly features and the span of geometric tolerances;

Step f, adopts the method for multiparameter concatenated coding to carry out genetic coding;

Each dimensional tolerence and form and position tolerance are encoded with binary coding method, then these codings are formed to the binary string chromosome that represents whole parameters according to being necessarily linked in sequence together;

According to GB/T1800.3-1998 standard of tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, the precision of determining size and Geometrical Tolerance Principle is after radix point 4, tolerance decision variable T ∈ [T ^l, T ^u] should be divided at least (T ^u-T ^l) × 10 ⁴individual part, its binary string figure place (is used m _jrepresent) can calculate with following formula:

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

Chromosomal coded strings length is:

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

Wherein,

L---chromosomal coded strings length;

L _i---the code length of tolerance variable;

The sum of n---size and form and position tolerance variable;

Being accurate to the size of four and the maximum binary string code length of form and position tolerance variable after radix point is 14.Adopt fixed-length coding technology, the code length of each tolerance variable is decided to be 14, and a chromosome length with n tolerance parameter can be expressed as:

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

In the time encoding, each tolerance parameter can have different spans, adopts fixed-length coding technology, and each parameter has different encoding precision.If the span of a certain tolerance is [T ^l, T ^u], represent this tolerance with 14 binary coded characters, can generate 2 ¹⁴plant different codings, encoding precision (or code length) is:

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

Tolerance variable binary coding chromosome for given:

$a_1^1,a_2^1,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^1,a_1^2,a_2^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^2,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^j,a_2^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_{14}^j,\&CenterDot;\&CenterDot;\&CenterDot;,a_1^n,a_2^n,\&CenterDot;\&CenterDot;\&CenterDot;{,a}_{14}^n$

The form of the binary string decoding functions of j tolerance variable is:

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

Wherein:

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

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

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

---m gene value of the binary coding string of j tolerance variable;

Step g, determines fitness function;

Step h, determines and selects operator function;

Step I, determines the operational factor of genetic algorithm.

2. the build-up tolerance Optimization Design based on genetic algorithm according to claim 1, is characterized in that, adopts the inverse of individual total cost to construct its fitness function in described step e, shown in formula specific as follows,

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

In formula,

for k individual fitness value in population, C _mAfor the total cost function of assembly MA,

for feature the processing cost-tolerance function of a dimensional tolerence;

for feature

the processing cost-tolerance function of b form tolerance;

for feature

the processing cost-tolerance function of c position of related features; G is feature

dimensional tolerence sum; H is feature

form tolerance sum; S is feature

position of related features sum.

3. the build-up tolerance Optimization Design based on genetic algorithm according to claim 1 and 2, is characterized in that, selects adaptive value ratio to select operator to calculate in described step f, and wherein, ratio selects the concrete implementation of operator to be:

F1. calculate the fitness value of all individualities in colony;

F2. the fitness value summation to all individualities;

F3. calculate individual relative adaptation degree, individuality is genetic to follow-on selection probability;

F4. use simulation roulette wheel operation (i.e. random number between 0 and 1) to determine each individual selected number of times.

4. the build-up tolerance Optimization Design based on genetic algorithm according to claim 3, is characterized in that, wherein individual selection probability calculation formula is as follows:

$P_i=\frac{F_i^{\mathrm{Fit}}}{\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{F}_k^{\mathrm{Fit}}}$

In formula,

P _ibe i individual selection probability;

N is the scale (number of the solution of tolerance optimization design) of population;

for the fitness of arbitrary individuality;

be i individual fitness.

5. the build-up tolerance Optimization Design based on genetic algorithm according to claim 1 and 2, is characterized in that, the operational factor in described step g comprises Population Size M, stops evolutionary generation T, crossover probability P _c, variation probability P _m;

M span is 20～100;

T is taken as 100～500;

P _cspan be 0.4～0.99;

P _mbe taken as 0.0001～0.1.

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