CN103903060B - A kind of Optimization Design on build-up tolerance - Google Patents
A kind of Optimization Design on build-up tolerance Download PDFInfo
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Abstract
The present invention relates to a kind of Optimization Design on build-up tolerance, according to assembly tolerance chains, dimensional tolerance is determined；Determine the constraints of build-up tolerance；Determine the type and scope of form and position tolerance；It is determined that using the minimum process cost of assembly as optimization aim, the object function of build-up tolerance optimization is established；The function is calculated by following processes, sets the part representative function of mechanical assemblies；Determine the total cost representative function of mechanical assemblies；Determine the processing cost function of each part in assembly；Determine the processing cost function of assembly features；Draw the total cost tolerance function of assembly；Draw the object function of build-up tolerance optimization.The present invention is using minimum process cost as target, the optimization tolerance obtained respectively using working ability, processing cost or processing economic accuracy by constraints, the assembling function demand of product is disclosure satisfy that, meets the constraints of machining, good economic benefit can be obtained.
Description
Technical field
The present invention relates to a kind of Optimization Design of Automatic manual transmission tolerance, more particularly to it is a kind of on the excellent of build-up tolerance
Change design method.
Background technology
The fitted position tolerance and form and position tolerance of parts in the prior art, usually according to the performance need of product
Ask, assembling function demand, quality assurance, rapidoprint, working condition, manufacturing cost and corresponding country, industry or enterprise
Industry standard determines.
In the design phase, how correctly, reasonably select build-up tolerance value is the design problem that must be considered,
It improves product quality, reduces manufacturing cost etc. and all have great importance to ensureing assembling and the performance of product.In shadow
In the factor for ringing part processing cost, tolerance plays very important effect.The design tolerance of part is smaller, can more ensure its dress
With functional requirement, but processing cost also increases therewith.When precision improves to a certain extent, processing cost can increased dramatically.
How in the case where meeting assembling function demand, rational assembly features tolerance value is designed, to obtain minimum be processed into
This, the problem that must be paid close attention to when being deisgn product.The factor for influenceing processing cost and tolerance relation is a lot, it is difficult to one
Unified mathematical modeling accurately describes the relation of the processing cost of all features and tolerance.For example, characteristic type, processing are set
The factors such as standby, chucking method, processing technology, operator, production batch, as long as one of those or several change,
Processing cost will be different from the relation of tolerance.
Many cost-tolerance models lay particular emphasis on the research of dimensional tolerance, and still, manufacturing cost is also simultaneously by form tolerance
With the influence of position of related features, three is only considered to the model of foundation, just closer to actual conditions.The present invention is with minimum
Processing cost is optimization aim, considers dimensional tolerance and form and position tolerance, establishes a new cost-tolerance models.
Corresponding relation according to form and position tolerance and dimensional tolerance establishes the constraints of genetic algorithm, realize dimensional tolerance and
The comprehensive Design of form and position tolerance, it is an important content in tolerance optimization design that tolerance and processing cost, which are modeled,.It is public
Difference optimization is the optimization design problem of a multi-parameter, and genetic algorithm is with its ability of searching optimum, stronger robustness and calculating
Concurrency show powerful application potential wherein.
In view of drawbacks described above, creator of the present invention obtains this creation finally by prolonged research and practice.
The content of the invention
It is an object of the invention to provide a kind of Optimization Design on build-up tolerance, to overcome above-mentioned technology to lack
Fall into.
To achieve the above object, the present invention provides a kind of Optimization Design on build-up tolerance, it is characterised in that should
Method is：
Step a, according to assembly tolerance chains, determine dimensional tolerance；
Step b, determine the constraints of build-up tolerance；
Step c, determine the type and scope of form and position tolerance；
Step d, it is determined that using the minimum process cost of assembly as optimization aim, establish the target letter of build-up tolerance optimization
Number；
The function is as described in following formula：
In formula, CMAFor assembly MA total cost function；It is characterizedA-th of dimensional tolerance plus
Work cost-tolerance function；It is characterizedB-th of form tolerance processing cost-tolerance function；It is characterizedC-th of position of related features processing cost-tolerance function；G is characterizedDimensional tolerance sum；H is characterizedShape
Tolerance sum；S is characterizedPosition of related features sum；
The function is calculated by following methods,
Step d1, set the part representative function of mechanical assemblies；
A mechanical assemblies are given as shown in following formula：
In formula：
MA∑--- represent mechanical assemblies；
Pi--- composition assembly MA i-th of part；
N --- composition assembly MA part sum；
Step d2, determine the total cost representative function of mechanical assemblies；
The total cost of assembly is as follows：
In formula：
CMA--- assembly MA total cost function；
C(Pi) --- part P in assembly MAiProcessing cost function；
Step d3, determine the processing cost function of each part in assembly；
The processing cost of part is as follows：
In formula：
--- part PiJ-th of assembly features；
--- part PiJ-th of assembly features processing cost function；
M --- part PiAssembly features sum；
Step d4, determine the processing cost function of assembly features；
It is as follows：
In formula：
--- featureA-th of dimensional tolerance processing cost-tolerance function；
--- featureB-th of form tolerance processing cost-tolerance function；
--- featureC-th of position of related features processing cost-tolerance function；
G --- featureDimensional tolerance sum；
H --- featureForm tolerance sum；
S --- featurePosition of related features sum；
Step d5, aggregative formula (3)~(5), drawing total cost-tolerance function of assembly can represent as follows：
The object function of build-up tolerance optimization is drawn according to above-mentioned formula (6)；
Step e, tolerance type information is attached to VGC networks, obtains the tolerance network of assembly, selection determines each assembling
The dimensional tolerance of feature and the span of geometric tolerances；
Step f, genetic coding is carried out using the method for multi-parameter concatenated coding；
Each dimensional tolerance and form and position tolerance are encoded with binary coding method, then by these codings according to one
Surely the composition together that is linked in sequence represents the binary string chromosome of whole parameters；
According to GB/T1800.3-1998 standards of tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, determine size and
The precision of Geometrical Tolerance Principle is tolerance decision variable T ∈ [T 4 after decimal pointL, TU] at least (T should be divided intoU-TL)×
104Individual part, its binary system displacement number mjRepresent, calculated with below equation：
Then the coding string length of chromosome is：
Wherein,
The coding string length of L --- chromosome；
li--- the code length of tolerance variable；
The sum of n --- size and form and position tolerance variable；
It is 14 to be accurate to the maximum binary string code length of the size of four and form and position tolerance variable after decimal point, is adopted
With fixed-length coding technology, the code length of each tolerance variable is set to 14, then a chromosome with n tolerance parameter
Length can be expressed as：
When being encoded, each tolerance parameter can have different spans, using fixed-length coding technology, then often
Individual parameter has different encoding precisions, if the span of a certain tolerance is [TL, TU], with 14 binary coded characters come
The tolerance is represented, then can generate 214The different coding of kind, encoding precision or code length are：
For given tolerance variable binary coding chromosome：
The form of the binary string decoding functions of j-th of tolerance variable is：
Wherein：
Tj--- the value of j-th of tolerance variable in chromosome；
--- the value lower limit of j-th of tolerance variable；
--- the value upper limit of j-th of tolerance variable；
--- m-th of gene value of the binary coding string of j-th of tolerance variable；
Step g, determines fitness function；
Step h, determine selection opertor function；
Step i, determine the operational factor of genetic algorithm.
Its fitness function is constructed using the inverse of the total cost of individual in the step e, shown in formula specific as follows,
In formula,For the fitness value of k-th of individual in population, CMAFor assembly MA total cost function,It is characterizedA-th of dimensional tolerance processing cost-tolerance function；It is characterizedB-th of shape it is public
Processing cost-tolerance function of difference；It is characterizedC-th of position of related features processing cost-tolerance function；G is spy
SignDimensional tolerance sum；H is characterizedForm tolerance sum；S is characterizedPosition of related features sum.
Calculated in the step f from adaptive value ratio selection opertor, wherein, the specific execution of ratio selection opertor
Process is：
F1. all individual fitness values in colony are calculated；
F2. all individual fitness values are summed；
F3. the relative adaptability degrees of individual are calculated, i.e., individual is genetic to follow-on select probability；
F4. the random number between 0 and 1 is taken to determine the selected number of each individual using simulation roulette wheel operation.
Wherein individual select probability calculation formula is as follows：
In formula,
P′iFor the select probability of i-th of individual；
N ' is the scale of population, represents the number of the solution of tolerance optimization design；
For the fitness value of k-th of individual in population；
For the fitness of i-th of individual.
Operational factor in the step g includes Population Size M, terminates evolutionary generation T ', crossover probability Pc, mutation probability
Pm；
M spans are 20~100；
T ' is taken as 100~500；
PcSpan be 0.4~0.99；
PmIt is taken as 0.0001~0.1.
Compared with prior art the beneficial effects of the present invention are：
Build-up tolerance Optimization Design of the present invention using minimum process cost as target, respectively with working ability, be processed into
This processes the optimization tolerance that economic accuracy is obtained by constraints, disclosure satisfy that the assembling function demand of product, meets machine
The constraints of tool processing, can obtain good economic benefit；Established according to the corresponding relation of form and position tolerance and dimensional tolerance
The constraints of genetic algorithm, realize the comprehensive Design of dimensional tolerance and form and position tolerance；This method combines build-up tolerance class
Type design and tolerance network struction research contents, for realize from assembly to size and form and position tolerance computer aided tolerance
Beneficial exploration has been made in design.Genetic algorithm is with its ability of searching optimum, and stronger robustness and the concurrency that calculates are wherein
Show powerful application potential.
Brief description of the drawings
Fig. 1 is flow chart of the present invention on the Optimization Design of build-up tolerance；
Fig. 2 a are present invention linkage assembly schematic diagram；
Fig. 2 b are the composition structural representation of assembly of the present invention；
Fig. 2 c are the tolerance schematic diagram of each structure of assembly of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the forgoing and additional technical features and advantages are described in more detail.
The present invention considers dimensional tolerance and form and position tolerance using minimum process cost as optimization aim, establishes one newly
Cost-tolerance models.The total cost of assembly is made up of the processing cost of all accessories, and part is processed into
This is then made up of the processing cost of its all characteristic face.It is not the assembling that each characteristic face is involved in part.Due to this hair
The bright main optimization design for considering fitted position tolerance and form and position tolerance size, therefore only consider being processed into for assembly features face
This.
Build-up tolerance Optimization Design of the present invention based on cost objective optimization is as follows：
Step a, according to assembly tolerance chains, determine dimensional tolerance；
Step b, determine the constraints of build-up tolerance；
In the present invention, according to the assembling function demand of product, the working ability of various processing methods, different processing grades
Processing cost, the economic accuracy and the corresponding relation of dimensional tolerance and form and position tolerance of various machinings, be provided with a variety of
Constraints.
1) the dimensional tolerance constraints based on assembling function demand
Dimensional tolerance is extracted from the subchain of build-up tolerance network, to obtain fitted position tolerance corresponding with sub-assemblies
Chain.By the use of the precision of assembling function demand as the closed-loop of dimensional tolerance chain, the precision conduct of the other sizes of tolerance chain is formed
Form ring.The precision of closed-loop depends on the precision of composition ring, is the result of each group cyclization accuracy synthesis effect.Using extremum method
To describe the tolerance of restriction relation, then closed-loop in tolerance chain between assembling function demand precision and each group cyclization dimensional accuracy
Equal to each tolerance of unit ring sum.In dimensional chain for assembly, closed-loop embodies the assembling function demand of product, is pre- by designer
First determine, its precision reflects the requirement of assembling quality.
In order to ensure the assembling quality of product, the following institute of dimensional tolerance constraints based on assembling function demand is established
Show：
TCL≥T1+T2+…+Tp+…+Tn (7)
TCLThe dimensional tolerance of closed-loop is represented, n represents to form the number of ring, T in dimension chainpRepresent to form ring p-th
Dimensional tolerance.Formula (7) represents that each tolerance sum for increasing ring and subtracting ring should be not more than the dimensional tolerance of closed-loop in dimension chain.
2) the dimensional tolerance constraints based on working ability
The dimensioned precision that same assembly features can guarantee that using different processing methods is different.Therefore design
During the dimensional tolerance of assembly features, if it is known that the processing method of last procedure, then must take into consideration adding for the processing method
Work ability.Dimensional tolerance constraints based on working ability can be expressed as：
Wherein,WithRepresent that the processing method that last one of the manufacturing procedure of assembly features uses can protect respectively
The dimensional tolerance grade of card,WithRepresent respectivelyWithThe tolerance value corresponding with assembly features nominal size,
And TdThen represent the design tolerance value of assembly features.Formula (8) represents that the processing of processing method is not to be exceeded in the design load of tolerance
Ability.The constraint bar for the dimensional tolerance that various assembly features faces can guarantee that in different processing methods can be established using table 1
Part.
The machining accuracy of the basic assembly features face Conventional machining methods of table 1
3) the dimensional tolerance constraints based on relative processing cost
When using a certain processing method machining feature, in the grade of tolerance and some regions of processing cost curve, processing
Cost changes rapidly with the change of the grade of tolerance, and when the grade of tolerance increases to a certain extent, processing cost then tends to
One constant.As can be seen here, when with same processing method according to different grade of tolerance machining feature faces, its processing cost can
Larger difference can be had.
, can be in the range of the working ability of processing method, according to economy demand when therefore carrying out tolerance optimization design
The dimensional tolerance constraints of feature is established, as shown in formula (9).
Wherein,WithThe dimensional tolerance grade determined according to the economy demand of feature machining is represented, and
WithIt is the tolerance value corresponding with them.
4) the dimensional tolerance constraints based on machining economic accuracy
Same feature can be obtained using different processing methods, and various processing methods are under normal working condition
The machining accuracy that can reach in an economical manner is that have certain scope.Slabbing processing economic accuracy be IT6~
IT10, the economic accuracy of surface broaching processing is IT6~IT9, and the economic accuracy of flat surface grinding processing is IT6~IT7.It can select
Constraints of the economic accuracy of machining as tolerance optimization design of processing method is selected, as shown in formula (10).
Wherein,WithRepresent tolerance value corresponding to the economic accuracy of machining of the processing method selected by feature.
5) the form and position tolerance constraints based on working ability
The same with dimensional tolerance, the ability of different processing method processing form and position tolerances also differs.Establish based on processing
The form and position tolerance constraints of ability is as shown.
Wherein, TgThe a certain form and position tolerance value of feature is represented,WithRepresent corresponding with the working ability of processing method
Tolerance value.
6) the form and position tolerance constraints based on dimensional accuracy
Using the local actual size of the dimensional tolerance controlling feature of independent principle design, without direct controlling feature
Form and position error.But tolerance zone is when the scale error of limited features, the also associated morpheme of indirect control
Error.Likewise, in accordance with the form and position tolerance of independent principle, restrained feature is only required in given shape position tolerance area,
Its Form and position error can reach maximum, and unrelated with the actual size of feature.But shape position tolerance area is to restrained feature
Limitation, equally also limit scale error related in feature.Therefore, the design of dimensional tolerance and geometric tolerances is objectively present
The relation for mutually restricting, mutually compensating for.Generally, the principle that the size of same feature and geometric tolerances should follow is designed
It is：
TSize＞ TPosition＞ TShape.It can establish accordingly shown in the form and position tolerance constraints such as formula (12) based on dimensional accuracy.
Wherein, TgThe form and position tolerance value being characterized,WithRepresent the morpheme corresponding with the dimensional tolerance in feature
The grade of tolerance,WithRepresent and form and position tolerance gradeWithCorresponding tolerance value.
Step c, determine the type and scope of form and position tolerance；
Step d, it is determined that using the minimum process cost of assembly as optimization aim, establish the target letter of build-up tolerance optimization
Number.
Step d1, set the part representative function of mechanical assemblies；
Give shown in for example following formula (1) of a mechanical assemblies：
In formula：
MA∑--- represent mechanical assemblies；
Pi--- composition assembly MA i-th of part；
N --- composition assembly MA part sum；
Step d2, determine the total cost representative function of mechanical assemblies；
The total cost of assembly is as follows：
In formula：
CMA--- assembly MA total cost function；
C(Pi) --- part P in assembly MAiProcessing cost function；
Step d3, determine the processing cost function of each part in assembly；
The processing cost of part is as follows：
In formula：
--- part PiJ-th of assembly features；
--- part PiJ-th of assembly features processing cost function；
M --- part PiAssembly features sum；
Step d4, determine the processing cost function of assembly features；
It is as follows：
In formula：
--- featureA-th of dimensional tolerance processing cost-tolerance function；
--- featureB-th of form tolerance processing cost-tolerance function；
--- featureC-th of position of related features processing cost-tolerance function；
G --- featureDimensional tolerance sum；
H --- featureForm tolerance sum；
S --- featurePosition of related features sum；
Step d5, aggregative formula (2)~(4), total cost-tolerance function of assembly can represent as follows：
In Design Stage, the dimensional tolerance and form and position tolerance of parts drawing subscript note are added by the last of feature
What work method was formed.Therefore, the present invention only considers that being processed into for last procedure of feature shaping determines design tolerance originally.
Step d6, using the minimum process cost of assembly as optimization aim, the object function definable of build-up tolerance optimization
For：
Step e, tolerance type information is attached to VGC networks, obtains the tolerance network of assembly, selection determines each assembling
The dimensional tolerance of feature and the span of geometric tolerances.
Step f, genetic coding is carried out using the method for multi-parameter concatenated coding.
Genetic coding is carried out using the method for multi-parameter concatenated coding, by each dimensional tolerance and form and position tolerance with binary system
Coding method is encoded, then these are encoded to the binary system that whole parameters are represented according to the composition together that is necessarily linked in sequence
String chromosome.In this coding method, the binary codings of parameters is parameter substring in the position that chromosome is always gone here and there one
Denier cannot change again after determining, in order to avoid malfunctioned in evolutionary computation.
The solving precision that the length of binary coding string is depended on required by problem.According to GB/T1800.3-1998 standards
Tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, the precision for determining size and Geometrical Tolerance Principle is 4 after decimal point
Position, therefore tolerance decision variable T ∈ [TL, TU] at least (T should be divided intoU-TL)×104Individual part, its binary system displacement number are used
mjExpression is calculated with below equation：
Then the coding string length of chromosome is：
Wherein,
The coding string length of L --- chromosome；
li--- the code length of tolerance variable；
The sum of n --- size and form and position tolerance variable.
The tolerance information of the assembly features of table 2
According to the above analysis, it is accurate to the maximum binary string of the size of four and form and position tolerance variable coding after decimal point
Length is 14.The present invention uses fixed-length coding technology, and the code length of each tolerance variable is set to 14；Then one has
The chromosome length of n tolerance parameter can be expressed as：
When being encoded, each tolerance parameter can have different spans, and the present invention uses fixed-length coding skill
Art, then each parameter has different encoding precisions, if the span of a certain tolerance is [TL, TU], with 14 binary codings
Symbol represents the tolerance, then can generate 214The different coding of kind, encoding precision or code length are：
The expression that the binary string chromosome being made up of the tolerance variable in table 2 can formalize is as follows：
This coding method can make the solution space of Tolerance Optimization and the search space of genetic algorithm that there is one-to-one corresponding to close
System.
For given tolerance variable binary coding chromosome：
The form of the binary string decoding functions of j-th of tolerance variable is：
Wherein：
Tj--- the value of j-th of tolerance variable in chromosome；
--- the value lower limit of j-th of tolerance variable；
--- the value upper limit of j-th of tolerance variable；
--- m-th of gene value of the binary coding string of j-th of tolerance variable.
Step g, determines fitness function.
GA algorithms are determined in current population all individual inheritances to the next generation by the probability directly proportional to individual adaptation degree
Chance in population, the high individual inheritance of fitness is larger to follow-on probability, and the low individual inheritance of fitness is to next
The probability in generation is then relatively low.It is relatively low using minimum process cost as the object function optimized, processing cost in tolerance optimization design
Individual be chosen to breed individual of future generation probability it is larger therefore the height of processing cost is good as evaluation individual (solution)
Bad standard.In order that the relatively low defect individual of processing cost can preserve and continue to multiply, present invention individual it is total
The inverse of processing cost constructs its fitness function, as shown in formula (18).Wherein,For the adaptation of k-th of individual in population
Angle value.
Step h, determine selection opertor function.
In the present embodiment, calculated from adaptive value ratio selection opertor.
The ratio that ratio selection opertor accounts for colony's adaptive value summation according to ideal adaptation angle value determines its hereditary possibility,
Ratio is bigger, and it is bigger to be genetic to follow-on possibility.
The select probability calculation formula of individual is as follows：
Wherein：
--- the select probability of i-th of individual；
The scale of n ' --- population, represent the number of the solution of tolerance optimization design；
--- the fitness value of k-th of individual in population；
--- the fitness of i-th of individual.
The specific implementation procedure of ratio selection opertor is：
F1. all individual fitness values in colony are calculated；
F2. all individual fitness values are summed；
F3. the relative adaptability degrees of individual are calculated, i.e., individual is genetic to follow-on select probability；
F4. the random number between 0 and 1 is taken to determine the selected number of each individual using simulation roulette wheel operation.
Step i, determine the operational factor of GA algorithms.
Operational factor in GA algorithms includes Population Size M, terminates evolutionary generation T ', crossover probability Pc, mutation probability Pm。
M is contained individual quantity in population.If M takes less value, the arithmetic speed of GA algorithms can be improved, but is dropped
The diversity of low individual, it is possible to precocious phenomenon can be caused, and when M takes larger value, then it can reduce operation efficiency.M leads to
Normal span is 20~100；
T ' is the termination evolutionary generation of genetic algorithm, is typically taken as 100~500；
PcFor crossover probability, typically take larger value, if but excessive, the defect mode being easily destroyed in population, it is too small then
The speed of generation new individual can be made slower.PcCommon span is 0.4~0.99；
PmFor mutation probability.It is similar with crossover probability, PmWhen taking larger value, preferable pattern may be destroyed, too it is small then not
Beneficial to the preferable new individual of generation and suppress precocious phenomenon.PmValue be typically taken as 0.0001~0.1.
Now by taking the linkage assembly shown in Fig. 2 a as an example, to illustrate the method for the build-up tolerance optimization design of the present invention.When
After the threedimensional model that linkage assembly is set up in CAD system, the nominal size of all features just determines therewith thereon, herein
On the basis of can carry out correlation tolerance design.
As shown in Figure 2 b, linkage assembly build-up tolerance network in, by slide plate, support, shaft coupling, sliding bearing and
The build-up tolerance subchain that the build-up tolerance of the parts such as axle may be constructed the closing of a Complete Bind (in order to simplify problem, is analyzed
When omit a sliding bearing).Below, the optimization design of tolerance is carried out according to the functional requirement of linkage assembly.Wherein, with dress
Processing economic accuracy with feature considers dimensional tolerance grade, and shape is determined with the corresponding relation of form and position tolerance and dimensional tolerance
The position grade of tolerance.
The determination of dimensional tolerance range
In figure 2b, there is the assembling of two device to hole and axle, i.e., the hole φ D on support3With the axle φ D on shaft coupling4, nominal chi
Very little is φ 50, the cylindrical φ D on axle8With the hole φ D on sliding bearing7, nominal size is φ 38.Hole φ D3For SicysSubstantially it is special
Sign face, the method for bore hole can be used to process, the economic accuracy of processing is IT8~IT10.Axle φ D4For SocysEssential characteristic face, can
Processed using the method for turning, the economic accuracy of processing is IT6~IT9.According to the selection principle of reference system, hole φ D3/ axle φ D4
From hole base system of fits.Cooperation requirement between support and shaft coupling has obvious gap, is easy to rotate, the warp of its comprehensive processing
Ji precision, it is final to determine hole φ D3/ axle φ D4With being combined into φ 50H8/e7.Cooperation between hole φ D7 and cylindrical φ D8 belongs to sliding
It is dynamic to coordinate, determine that it is matched somebody with somebody and be combined into φ 38H8/f7.
The linkage assembly dimensional tolerance range of table 3
Apart from dimension D1Nominal size be 19, using reference plane A as machining benchmark, using Milling Process, consult substantially
The economic accuracy of assembly features face machining, it is known that its economic accuracy processed is IT6~IT10, i.e. TD1∈ (IT6~
IT10).Apart from dimension D6Nominal size be 47, using reference plane C as machining benchmark, using bore hole method process, processing
Economic accuracy is IT8~IT10, i.e. TD6∈ (IT8~IT10).Using identical method, all dimensional tolerances in Fig. 2 c can be obtained
Accuracy rating is as shown in table 3.
The determination of Geometric Tolerance Types and scope
Axle φ D4With hole φ D3Assembly constraint type beObtain corresponding to the constraint
Build-up tolerance function is：
According to selection and the principle of optimality of the assembling function demand and build-up tolerance of support and shaft coupling, it may be determined that two 0
One group of build-up tolerance between the assembly features face of part is：
Understood by formula (21), it is necessary to axle φ D4With hole φ D3The Geometrical Tolerance Principle of cylindricity is proposed, i.e., shown in Fig. 2 c
Form and position tolerance TG4And TG3。
Design basis A faces and dimension D on slide plate1Upper end size limit (see Fig. 2 c) where plane partner it is several
What is constrained, and is mutually to refer to Variational Geometric Constraints CVGC by what two geometric properties on Same Part were formed.Reasoning is corresponding to it
With reference to Variational Geometric Constraints type be mutually CC21, the tolerance type corresponding to reasoning CC21 is AT8, i.e. two characteristic planes it is right
The geometric tolerances type answered is the depth of parallelism.Therefore, it is necessary to dimension D1Upper end size limit where plane be proposed for base
Quasi- A depth of parallelism requirement, form and position tolerance T as shown in Figure 2 cG1。
It is determined that after the type of form and position tolerance, tolerance of form and position tolerance etc. can be determined based on the dimensional tolerance precision of correlation
Level scope.In above-mentioned analysis, dimension D has been obtained1Accuracy rating be IT6~IT8, parallelism tolerance T can be obtainedG1Essence
Degree scope is IT7~IT10.Similarly, the dimensional tolerance T on supportG3With the dimensional tolerance T on shaft couplingG4The grade of tolerance point
Not Wei H8 and e7, understand that corresponding shape is public by the corresponding relation of dimensional tolerance grade and circularity and cylindricity tolerance grade
Poor TG3And TG4The grade of tolerance be respectively IT8~IT9 and IT7~IT8.
In aforementioned manners reasoning obtain all form and position tolerances in Fig. 2 c accuracy rating it is as shown in table 4.
The linkage assembly form and position tolerance scope of table 4
Link assembly Tolerance Optimization object function
This section establishes the Tolerance Optimization object function of linkage assembly.Wherein, processing cost-tolerance Model of each category feature
As shown in table 5.
The processing cost model of 5 each category feature of table
The Tolerance Optimization object function for establishing linkage assembly is as follows：
When being assembled, it is desirable to which the axis of link assembly axis and shaft coupling is kept point-blank, its height
Poor T0No more than 0.45mm, in this, as the closed-loop of dimensional chain for assembly, it is as follows to establish bound for objective function：
The determination of operational factor
Population number M values 20, genetic algebra T ' values 70, crossover probability PcValue 0.7, mutation probability PmValue 0.08.
Build-up tolerance optimum results and its analysis
Conventional Tolerance Distribution Method have analogy tolerance method, etc. tolerance method, equally accurate method, etc. influence method and economic criteria method
Deng.Wherein, equally accurate method is to take the identical grade of tolerance to all composition ring sizes in dimension chain, and it is exactly each group to wait influence method
Cyclic dimensional tolerance has identical influence to closed-loop tolerance, and it is to all composition ring sizes in dimension chain to wait tolerance rule
Take equal tolerance value.For linear dimensional chain, the influence method such as it is equal to etc. tolerance method.
Table 6 lists with genetic algorithm, equally accurate method and waits the items obtained by the Tolerance Distribution Methods such as influence method respectively
Tolerance value and its processing cost compare.The tolerance value obtained with genetic algorithm is processed, and its total cost, which simply waits, to be influenceed
The 35.1% of method, the 76.8% of equally accurate method.
The tolerance value and its processing cost of 6 different Tolerance Distribution Methods of table compare
Presently preferred embodiments of the present invention is the foregoing is only, is merely illustrative for invention, and it is nonrestrictive.
Those skilled in the art understands, can carry out many changes to it in the spirit and scope that invention claim is limited, and changes,
It is even equivalent, but fall within protection scope of the present invention.
Claims (5)
1. a kind of Optimization Design on build-up tolerance, it is characterised in that this method is：
Step a, according to assembly tolerance chains, determine dimensional tolerance；
Step b, determine the constraints of build-up tolerance；
Step c, determine the type and scope of form and position tolerance；
Step d, it is determined that using the minimum process cost of assembly as optimization aim, establish the object function of build-up tolerance optimization；
The function is as described in following formula：
<mrow>
<mi>min</mi>
<mo>{</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
</mrow>
</msub>
<mo>}</mo>
<mo>=</mo>
<mi>min</mi>
<mo>{</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mo>&lsqb;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>g</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>D</mi>
</mrow>
<mi>a</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>h</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>F</mi>
</mrow>
<mi>b</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>s</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>P</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, CMAFor assembly MA total cost function；It is characterized fi jA-th dimensional tolerance be processed into
Sheet-tolerance function；It is characterized fi jB-th of form tolerance processing cost-tolerance function；It is characterized fi j's
Processing cost-tolerance function of c-th of position of related features；G is characterized fi jDimensional tolerance sum；H is characterized fi jForm tolerance
Sum；S is characterized fi jPosition of related features sum；
The function is calculated by following methods,
Step d1, set the part representative function of mechanical assemblies；
A mechanical assemblies are given as shown in following formula：
<mrow>
<msub>
<mi>MA</mi>
<mi>&Sigma;</mi>
</msub>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mi>P</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
<mn>...</mn>
<mo>,</mo>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msub>
<mi>P</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
MAΣ--- represent mechanical assemblies；
Pi--- composition assembly MA i-th of part；
N --- composition assembly MA part sum；
Step d2, determine the total cost representative function of mechanical assemblies；
The total cost of assembly is as follows：
<mrow>
<msub>
<mi>C</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
CMA--- assembly MA total cost function；
C(Pi) --- part P in assembly MAiProcessing cost function；
Step d3, determine the processing cost function of each part in assembly；
The processing cost of part is as follows：
<mrow>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
fi j--- part PiJ-th of assembly features；
C(fi j) --- part PiJ-th of assembly features processing cost function；
M --- part PiAssembly features sum；
Step d4, determine the processing cost function of assembly features；
It is as follows：
<mrow>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>g</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>D</mi>
</mrow>
<mi>a</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>h</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>F</mi>
</mrow>
<mi>b</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>s</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>P</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
--- feature fi jA-th of dimensional tolerance processing cost-tolerance function；
--- feature fi jB-th of form tolerance processing cost-tolerance function；
--- feature fi jC-th of position of related features processing cost-tolerance function；
G --- feature fi jDimensional tolerance sum；
H --- feature fi jForm tolerance sum；
S --- feature fi jPosition of related features sum；
Step d5, aggregative formula (3)~(5), drawing total cost-tolerance function of assembly can represent as follows：
<mrow>
<msub>
<mi>C</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mo>&lsqb;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>g</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>D</mi>
</mrow>
<mi>a</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>h</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>F</mi>
</mrow>
<mi>b</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>s</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>P</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
The object function of build-up tolerance optimization is drawn according to above-mentioned formula (6)；
Step e, tolerance type information is attached to VGC networks, obtains the tolerance network of assembly, selection determines each assembly features
Dimensional tolerance and geometric tolerances span；
Step f, genetic coding is carried out using the method for multi-parameter concatenated coding；
Each dimensional tolerance and form and position tolerance are encoded with binary coding method, then encoded these according to certain suitable
Sequence, which links together, forms the binary string chromosome of the whole parameters of expression；
According to GB/T1800.3-1998 standards of tolerance numerical value and GB/T1184-1996 form and position tolerance numerical value, size and morpheme are determined
The precision of tolerance is tolerance decision variable T ∈ [T 4 after decimal pointL, TU] at least (T should be divided intoU-TL)×104It is individual
Part, its binary system displacement number mjRepresent, calculated with below equation：
<mrow>
<msup>
<mn>2</mn>
<mrow>
<msub>
<mi>m</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo><</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>T</mi>
<mi>U</mi>
</msup>
<mo>-</mo>
<msup>
<mi>T</mi>
<mi>L</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<msup>
<mn>10</mn>
<mn>4</mn>
</msup>
<mo>&le;</mo>
<msup>
<mn>2</mn>
<msub>
<mi>m</mi>
<mi>j</mi>
</msub>
</msup>
<mo>-</mo>
<mn>1</mn>
</mrow>
Then the coding string length of chromosome is：
<mrow>
<mi>L</mi>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>l</mi>
<mi>i</mi>
</msub>
</mrow>
Wherein,
The coding string length of L --- chromosome；
li--- the code length of tolerance variable；
The sum of n --- size and form and position tolerance variable；
It is 14 to be accurate to the maximum binary string code length of the size of four and form and position tolerance variable after decimal point, using etc.
Long codes technology, the code length of each tolerance variable are set to 14, then a chromosome length with n tolerance parameter
It can be expressed as：
<mrow>
<mi>L</mi>
<mo>=</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>l</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>14</mn>
<mi>n</mi>
</mrow>
When being encoded, each tolerance parameter can have different spans, using fixed-length coding technology, then each to join
Number has different encoding precisions, if the span of a certain tolerance is [TL, TU], represented with 14 binary coded characters
The tolerance, then it can generate 214The different coding of kind, encoding precision or code length are：
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mi>T</mi>
<mi>L</mi>
</msup>
<mo>-</mo>
<msup>
<mi>T</mi>
<mi>U</mi>
</msup>
</mrow>
<mrow>
<msup>
<mn>2</mn>
<mn>14</mn>
</msup>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
For given tolerance variable binary coding chromosome：
<mrow>
<msubsup>
<mi>a</mi>
<mn>1</mn>
<mn>1</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mn>1</mn>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>14</mn>
<mn>1</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>14</mn>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>1</mn>
<mi>j</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mi>j</mi>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>14</mn>
<mi>j</mi>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>1</mn>
<mi>n</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mi>n</mi>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>a</mi>
<mn>14</mn>
<mi>n</mi>
</msubsup>
</mrow>
The form of the binary string decoding functions of j-th of tolerance variable is：
<mrow>
<msub>
<mi>T</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mi>L</mi>
</msubsup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mn>14</mn>
</munderover>
<msubsup>
<mi>a</mi>
<mi>m</mi>
<mi>j</mi>
</msubsup>
<msup>
<mn>2</mn>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mi>U</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mi>L</mi>
</msubsup>
</mrow>
<mrow>
<msup>
<mn>2</mn>
<mn>14</mn>
</msup>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
Wherein：
Tj--- the value of j-th of tolerance variable in chromosome；
--- the value lower limit of j-th of tolerance variable；
--- the value upper limit of j-th of tolerance variable；
--- m-th of gene value of the binary coding string of j-th of tolerance variable；
Step g, determines fitness function；
Step h, determine selection opertor function；
Step i, determine the operational factor of genetic algorithm.
A kind of 2. Optimization Design on build-up tolerance according to claim 1, it is characterised in that the step e
The inverse of the middle total cost using individual constructs its fitness function, shown in formula specific as follows,
<mrow>
<msubsup>
<mi>F</mi>
<mi>k</mi>
<mrow>
<mi>F</mi>
<mi>i</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>C</mi>
<mrow>
<mi>M</mi>
<mi>A</mi>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mo>&lsqb;</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>g</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>D</mi>
</mrow>
<mi>a</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>h</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>F</mi>
</mrow>
<mi>b</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>s</mi>
</munderover>
<msubsup>
<mi>C</mi>
<mrow>
<mi>T</mi>
<mi>P</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>i</mi>
<mi>j</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
</mrow>
In formula,For the fitness value of k-th of individual in population, CMAFor assembly MA total cost function,For
Feature fi jA-th of dimensional tolerance processing cost-tolerance function；It is characterized fi jB-th of form tolerance processing
Cost-tolerance function；It is characterized fi jC-th of position of related features processing cost-tolerance function；G is characterized fi jChi
Very little tolerance sum；H is characterized fi jForm tolerance sum；S is characterized fi jPosition of related features sum.
A kind of 3. Optimization Design on build-up tolerance according to claim 1 or 2, it is characterised in that the step
Calculated in rapid f from adaptive value ratio selection opertor, wherein, the specific implementation procedure of ratio selection opertor is：
F1. all individual fitness values in colony are calculated；
F2. all individual fitness values are summed；
F3. the relative adaptability degrees of individual are calculated, i.e., individual is genetic to follow-on select probability；
F4. the random number between 0 and 1 is taken to determine the selected number of each individual using simulation roulette wheel operation.
A kind of 4. Optimization Design on build-up tolerance according to claim 3, it is characterised in that wherein individual
Select probability calculation formula is as follows：
<mrow>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>F</mi>
<mi>i</mi>
<mrow>
<mi>F</mi>
<mi>i</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mrow>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msup>
<mi>n</mi>
<mo>&prime;</mo>
</msup>
</munderover>
<msubsup>
<mi>F</mi>
<mi>k</mi>
<mrow>
<mi>F</mi>
<mi>i</mi>
<mi>t</mi>
</mrow>
</msubsup>
</mrow>
</mfrac>
</mrow>
In formula,
Pi' it is i-th of individual select probability；
N ' is the scale of population, represents the number of the solution of tolerance optimization design；
For the fitness value of k-th of individual in population；
Fi FitFor the fitness of i-th of individual.
A kind of 5. Optimization Design on build-up tolerance according to claim 1 or 2, it is characterised in that the step
Operational factor in rapid g includes Population Size M, terminates evolutionary generation T ', crossover probability Pc, mutation probability Pm；
M spans are 20~100；
T ' is taken as 100~500；
PcSpan be 0.4~0.99；
PmIt is taken as 0.0001~0.1.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101982821A (en) * | 2010-10-26 | 2011-03-02 | 西安交通大学 | Method for reasoning assembly tolerance standard and tolerance zone type of complex assembly body |
| CN102622495A (en) * | 2012-04-13 | 2012-08-01 | 北京航空航天大学 | Tolerance optimization allocation method based on tolerance grade and genetic algorithm |
| CN102662356A (en) * | 2012-03-30 | 2012-09-12 | 宁波腾工精密机械制造有限公司 | Tolerance optimization method of feed mechanism |
-
2013
- 2013-12-27 CN CN201310756985.6A patent/CN103903060B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101982821A (en) * | 2010-10-26 | 2011-03-02 | 西安交通大学 | Method for reasoning assembly tolerance standard and tolerance zone type of complex assembly body |
| CN102662356A (en) * | 2012-03-30 | 2012-09-12 | 宁波腾工精密机械制造有限公司 | Tolerance optimization method of feed mechanism |
| CN102622495A (en) * | 2012-04-13 | 2012-08-01 | 北京航空航天大学 | Tolerance optimization allocation method based on tolerance grade and genetic algorithm |
Non-Patent Citations (2)
| Title |
|---|
| 基于遗传算法的形位公差优化设计;乐英;《煤矿机械》;20051205(第12期);全文 * |
| 基于遗传算法的配合尺寸公差优化设计;王伯平 等;《农业机械学报》;20040801;第35卷(第4期);全文 * |
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