CN109271653A - A kind of machine components matching method based on geometric tolerance and dimensional tolerance - Google Patents
A kind of machine components matching method based on geometric tolerance and dimensional tolerance Download PDFInfo
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Abstract
The invention discloses a kind of complex mechanical product matching method for comprehensively considering geometric tolerance and dimensional tolerance based on genetic algorithm, first pass through the coding method of Complex Dimensional Chain Analyses, the assembly problem of complex mechanical product is mapped in mathematical model, using assembly precision and assembly yield as the evaluation index of quality requirement, establish the apolegamy Integrated Optimization Model under multimass requires, utilize Efficient Characterization form of the geometric tolerance measured value in apolegamy, it establishes comprehensive geometric tolerance and dimensional tolerance is the mineral processing model of optimization aim, the fitness evaluation criterion of comprehensive Pareto intensity and closeness as genetic algorithm, and introduce priority of parts and quality requirement priority improves algorithm, this method not only realizes the apolegamy of complex mechanical product, improve assembly yield, it ensure that assembly precision, guarantee ruler The geometric tolerance of product is effectively reduced while very little tolerance assembly precision, the genetic algorithm for introducing apolegamy priority has better convergence rate.
Description
Technical field
The present invention relates to complex mechanical products to select assembly field, and in particular to one kind is based on geometric tolerance and dimensional tolerance
Machine components matching method.
Background technique
Complex mechanical product often has research and development are at high cost, product is constituted between complicated, components to have Complex Constraints relationship
The features such as.In assembling process, transmitting, the accumulation of itself quality and deviation on dimensional chain for assembly to be installed that replace the spare parts is common
Affect product quality.Match to guarantee that this complex mechanical product assembled by a large amount of multimass characteristic components possesses height
Precision is closed, if only can inevitably greatly increase production cost by the way that the accuracy of manufacture of part is continuously improved.And select assembly (referred to as
Apolegamy) accuracy of manufacture can not be increased under the premise of, the assembly using the powerful computing capability of computer to components to be assembled
Sequence is made overall planning, and when assembly then selects corresponding components to be matched, so that Product Precision is higher while remaining
Part is less.
Currently, domestic and foreign scholars mainly solve the problems, such as apolegamy in terms of group technology and intelligent algorithm two.Such as Kannan
Etc. having inquired into one-to-many parts selection matching grouping problem, proposing a kind of new packet mode can be effectively reduced the assembly of product
Tolerance, while reducing remaining number of parts again.It is searched for most based on Taguchi quality loss function using genetic algorithm again later
Excellent grouping, but this method is only applicable to part size Normal Distribution and each other little situation of distributional difference；
Quadratic loss function has been generalized to general convex loss function by Matsuura etc., and has been successfully established equation solution most optimal sorting
Group realizes and assumes that the probability density function of size distribution is the solution of logarithmic；Raj etc. is selected grouping using particle swarm algorithm
Method of completing the square is applied to tool there are three in the assembly of matching components, is not only effectively reduced remaining part, also improves calculating
Efficiency；Asha etc. considers that fit dimension is distributed different situations in high-precision assembly, is optimization mesh with minimum clearance fluctuation
Mark handles the assembly of piston, piston ring and cylinder using non-bad Sorting Genetic Algorithm；Liu Jiandong etc. establishes a kind of based on field mouthful
Quality loss evaluation rule of the theory towards asymmetric tolerance range, and asked using the apolegamy that genetic algorithm solves more dimensional chain for assembly
Topic；Place young tiger etc. remanufactures environment to engineering machinery and is analyzed, and constructs based on multivariate quality loss function and assembling deviation
The mathematical model of degree can effectively improve the utilization rate for reusing part and repair member while guaranteeing product assembly quality；Chen Jie
The characteristics of Deng complex product multimass characteristic is directed to, constructs and optimizes mould with the apolegamy that fit-up gap fluctuation is minimised as target
Type, and dynamic filing mechanism is introduced in particle swarm algorithm and shared mechanism solves model；Level etc. is appointed to construct
Unified apolegamy information model towards three-dimensional space under multimass requires, and power is used when solving using genetic algorithm
Pareto method effectively describes the primary-slave relation in multimass requirement production configuration between quality requirement；Wang Kang etc. proposes a kind of base
In the selection assembly method of strength Pareto evolutionary algorithm 2 (SPEA2), the result of final optimization pass with the boundary Pareto set representations,
Assembling quality can preferably be improved.
To sum up, the method based on grouping strategy is distributed dependent on the size of part, it is difficult to applied to disobeying specific distribution
And complicated assembly.Although intelligent algorithm can play good effect in single object optimization, complicated machinery is produced
Product often have the characteristics that quality requirement is more, dimension chain is complicated in assembly, cause intelligent algorithm difficult in multiple-objection optimization
To coordinate the optimization of multiple quality requirements simultaneously.Meanwhile the geometric tolerance of product is had ignored above with respect to the research of apolegamy, and
Actually other than size characteristic changes the i.e. influence of scale error, variation, that is, Form and position error of morpheme feature also influences whether whole
The final mass of a assembly.Therefore, it is necessary to a kind of Efficient Characterization forms of behavior tolerance measured value, using geometric tolerance as optimization
Target, complete the multiple-objection optimization that combines with dimensional tolerance of geometric tolerance and match.
Summary of the invention
The purpose of the present invention is to provide a kind of complex mechanical product apolegamys for comprehensively considering geometric tolerance and dimensional tolerance
Method, with overcome the deficiencies in the prior art.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
A kind of machine components matching method based on geometric tolerance and dimensional tolerance, comprising the following steps:
Step 1) establishes multiple-objection optimization mineral processing model:
According to the Efficient Characterization form of geometric tolerance measured value, comprehensive geometric tolerance and dimensional tolerance as optimization aim,
Using assembly yield and assembly precision as the evaluation index of quality requirement, that establishes that geometric tolerance combines with dimensional tolerance is answered
Miscellaneous engineering goods multiple-objection optimization mineral processing model；
Step 2), the apolegamy priority for calculating components and quality requirement:
The deviation of composite tolerance item fluctuates and the contribution degree in dimension chain is evaluated as the apolegamy priority of components
Index, and the apolegamy priority of each quality requirement is calculated on this basis；Simultaneously by the dimensional tolerance and geometric tolerance of product
As the quality requirement of assembly, the average loss combination dress that assembly precision deviates ideal value is calculated using Taguchi quality loss function
Make the evaluation index of quality requirement with success rate, establishes the multiple-objection optimization apolegamy mould for comprehensively considering geometric tolerance and dimensional tolerance
Type；
What step 3), the apolegamy priority obtained using step 2) again established step 1) after improving to genetic algorithm
Mineral processing model is solved: the characteristics of according to complex mechanical product dimensional chain for assembly, being used and is compiled by the gene of unit of components
Code mode, establishes the incidence relation between the multiple tolerance items of mapping association matrix description, assembly is mapped in mathematical model, utilizes
The apolegamy priority of components is adjusted genetic operator, with dominance relation bond quality of the individual in multiple optimization aims
It is required that priority calculate the Pareto intensity of individual, recycle k nearest neighbor algorithm to calculate closeness of the individual in population, finally
The fitness of comprehensive Pareto intensity and closeness as individual, completes machine components apolegamy.
Further, in step 1), the assembly sequence of components is characterized by mathematical method, establishes and is based on zero
The assembling scheme matrix X of part layering:
In formula (1), kLFor the number of components L in a set of assembly, L=1,2 ..., n；N is components species number；Table
Show the serial number of j-th of components L, j=1,2 ..., kLM；M is the part tricks for participating in apolegamy；When assembly, what each column represented
Component assembly is at an assembly.
Further, the building of mapping association matrix is carried out to assembling scheme matrix:
If the tolerance item number that part L includes is SL, then the mapping association matrix T of part L is establishedLAre as follows:
In formula,Indicate y-th of tolerance item measured value of x-th of part；SLThe tolerance item number for including for part L.
Further, the element in assembling scheme matrix XThe all-in allowance item actual measurement that i.e. corresponding j-th of part L has
ValueTolerance item measured value is calculated according to the deviation delivery rules of dimensional chain for assembly for assembling quality.
Further, the apolegamy priority obtained using step 2) again establishes step 1) after improving to genetic algorithm
Mineral processing model solved, specifically include:
(1) initial internal population pop is randomly generated, and constructs an empty external population out, scale is respectively Npop、
Nout, set up maximum evolutionary generation Z；
(2) according to components actual measurement Value Data and deviation transmitting data be calculated each components, quality requirement it is preferential
Grade FACTOR PL、Ps；
(3) pop ∪ out is calculated using the fitness evaluation criterion of comprehensive Pareto intensity and closeness concentrate the suitable of individual
Answer angle value Fit；
(4) selection operation is carried out using selection operator, updates internal collection pop using excellent individual；
(5) determine whether to meet termination condition, even current algebra is less than Z, collects into next step, otherwise output is internal
The corresponding assembly sequence of optimum individual in pop；
(6) individual in pop is intersected, mutation operation, mutation probability is adjusted according to priority of parts, excellent
First grade is higher, and probability is bigger；Finally filial generation is remained into external collection out, returns to (3) step.
Further, using assembly precision and assembly yield as the Optimized model of target:
Based on the assembly precision assessment models of field mouthful quality, to match the average damage that the assembly precision of product deviates ideal value
Losing is majorized function, guarantees the reliability and stability of assembly precision；Its expression is as follows:
In formula, yj,sFor s-th of quality requirement FR of jth part productsMeasured value；A is quality when quality requirement is unqualified
Loss, ymaxs、yminsRespectively tolerance design value maximum value and minimum value；TosFor design tolerance value；yo,sFor tolerance design center
Value, yo,s=(ymaxs+ymins)/2。
Further, using assembly yield as the important evaluation index of apolegamy quality, quality requirement FRsAssembly success
Rate are as follows:
η(FRs)=Ms/M (9)
In formula, M is once to match obtained product number of packages；MsOnce to match quality requirement FRsQualified product number of packages；
Single quality requirement FR can be obtainedsApolegamy Integrated Optimization Model are as follows:
In formula, X represents a matingplan；C is that constant (0≤c≤1) indicates influence journey of the assembly precision to assembling quality
Degree.
Further, the apolegamy Integrated Optimization Model based on single quality requirement can establish the multiple target choosing under multimass requires
With Integrated Optimization Model:
MinQ (X)=[Q1(X) Q2(X) … Qs(X)]
In formula, Q (X) is object vector；ysFor the corresponding closed-loop measured value of s-th of quality requirement；XmFor matingplan
Collection.
Further, the contribution of the group cyclization to closed-loop is combined according to the tolerance variations of each group cyclization in dimensional chain for assembly
Degree, determines the apolegamy priority of each components:
In dimension chain U, the contribution degree of i-th group of cyclization is definedAre as follows:
In formula, ΩsFor the group cyclization collection for synthesizing s-th of quality requirement (closed-loop)；Once to participate in all of apolegamy
Cyclization X is organized in componentsiThe standard deviation of tolerance item measured value；For XiDeviation on dimension chain U function direction transmits system
Number；
The apolegamy preferred number P of componentsLAre as follows:
In formula, ΩLFor the tolerance item collection for being under the jurisdiction of components L；
Using priority of parts to the mutation probability of components LIt is adjusted:
Further, the apolegamy priority factor P of quality requirement ssAre as follows:
In formula, AsWhen unqualified for quality requirement s, the mass loss threshold value of product；TosFor the design tolerance of quality requirement s
Value；
It is located at population P in genetic algorithm to be made of inside collection pop and external collection out, then the Pareto Strength co-mputation of individual X
It is as follows:
In formula, Pa(X) the Pareto intensity of individual X is indicated；ΩP-XFor other individuals in population P in addition to X；NsFor quality
It is required that number；PsPriority is matched for quality requirement；Qs(X) it indicates comprehensive quality loss, can be calculated by formula (10)；
Using the closeness of k nearest neighbor algorithm evaluation individual, individual X(a)Closeness Dis (X(a)) calculation formula are as follows:
In formula, ΩkaFor in population away from X(a)K nearest individual；K value be no more thanMaximum integer；NPFor population
The number of individuals of P；R is adjustment constant；
Comprehensively consider Pareto intensity and closeness, obtains individual X in population(a)Fitness Fit (X(a)) are as follows:
Fit(X(a))=Pa((X(a))+Dis(X(a)) (23)。
Compared with prior art, the invention has the following beneficial technical effects:
A kind of complex mechanical product apolegamy for comprehensively considering geometric tolerance and dimensional tolerance based on genetic algorithm of the present invention
Method first passes through the coding method of Complex Dimensional Chain Analyses, and the assembly problem of complex mechanical product is mapped in mathematical model, utilizes
The evaluation index of assembly precision and assembly yield as quality requirement establishes the apolegamy complex optimum mould under multimass requires
Type establishes comprehensive geometric tolerance and dimensional tolerance is optimization using Efficient Characterization form of the geometric tolerance measured value in apolegamy
The mineral processing model of target, the fitness evaluation criterion of comprehensive Pareto intensity and closeness as genetic algorithm, and introduce zero
Part priority and quality requirement priority improve algorithm, and this method not only realizes the choosing of complex mechanical product
Match, improve assembly yield, ensure that assembly precision, additionally it is possible under the premise of guaranteeing dimensional tolerance assembly precision, effectively
Reduce the geometric tolerance of product.Meanwhile the genetic algorithm for introducing apolegamy priority has better convergence rate.
Matching method towards geometric tolerance and dimensional tolerance simultaneously, can be in the premise for guaranteeing dimensional tolerance assembly precision
Under, the geometric tolerance of product is effectively reduced；
Compared with the coding method based on tolerance item combination interconnection constraint matrix, it is based on components combination mapping association matrix
Coding method have better versatility；
With traditional genetic algorithm ratio, the improved adaptive GA-IAGA for introducing apolegamy priority has better convergence rate；
The fitness evaluation criterion of comprehensive Pareto intensity and closeness has when genetic algorithm optimization target is more
Better applicability.
Further, overall merit is carried out using fitness, one side assurance function requires to be met, and reduces quality damage
It loses；On the other hand it ensure that population is able to maintain that higher diversity using closeness, so that searching algorithm avoids falling into part
Solution.
Detailed description of the invention
Fig. 1 is flow chart of the present invention；
Fig. 2 is crank link mechanism assembling schematic diagram；
Fig. 3 is Fig. 2 top view；
Fig. 4 is genetic algorithm flow chart；
Fig. 5 is the influence structural schematic diagram for matching priority to algorithm the convergence speed.
Specific embodiment
The invention will be described in further detail with reference to the accompanying drawing:
As shown in Figure 1, a kind of machine components matching method based on geometric tolerance and dimensional tolerance, comprising the following steps:
Step 1) establishes multiple-objection optimization mineral processing model
According to the Efficient Characterization form of geometric tolerance measured value, comprehensive geometric tolerance and dimensional tolerance as optimization aim,
Using assembly yield and assembly precision as the evaluation index of quality requirement, that establishes that geometric tolerance combines with dimensional tolerance is answered
Miscellaneous engineering goods multiple-objection optimization mineral processing model；
Specifically, the assembly sequence of components is characterized by mathematical method, the dress being layered based on components is established
With scheme matrix X:
In formula (1), kLFor the number of components L in a set of assembly, L=1,2 ..., n；N is components species number；Table
Show the serial number of j-th of components L, j=1,2 ..., kLM；M is the part tricks for participating in apolegamy.When assembly, what each column represented
Component assembly is at an assembly；
If the tolerance item number that part L includes is SL, then the mapping association matrix T of part L is establishedLAre as follows:
In formula,Indicate y-th of tolerance item measured value of x-th of part；SLThe tolerance item number for including for part L.
Element in assembling scheme matrix XThe all-in allowance item measured value that i.e. corresponding j-th of part L hasTolerance item measured value can be calculated according to the deviation delivery rules of dimensional chain for assembly for assembling quality；
Step 2), the apolegamy priority for calculating components and quality requirement
The deviation of composite tolerance item fluctuates and the contribution degree in dimension chain is evaluated as the apolegamy priority of components
Index, and the apolegamy priority of each quality requirement is calculated on this basis；Simultaneously by the dimensional tolerance and geometric tolerance of product
As the quality requirement of assembly, the average loss combination dress that assembly precision deviates ideal value is calculated using Taguchi quality loss function
Make the evaluation index of quality requirement with success rate, establishes the multiple-objection optimization apolegamy mould for comprehensively considering geometric tolerance and dimensional tolerance
Type；
Step 3), using genetic algorithm to model solution
The apolegamy mould that the apolegamy priority obtained using step 2) again establishes step 1) after improving to genetic algorithm
Type is solved, and is specifically included:
(1) according to complex mechanical product dimensional chain for assembly the characteristics of, uses the gene coding mode using components as unit,
And the incidence relation between the multiple tolerance items of mapping association matrix description is established, this engineering problem will be assembled and be mapped to mathematics
In model；
(2) genetic operator is adjusted using the apolegamy priority of components, the higher components of priority, intersect,
Mutation probability is bigger；
(3) priority that the dominance relation bond quality with individual on multiple optimization aims (quality requirement) requires calculates
The Pareto intensity of individual recycles k nearest neighbor algorithm to calculate closeness of the individual in population, final comprehensive Pareto intensity and
Fitness evaluation criterion of the closeness as individual.
Specifically, using genetic algorithm to model solution:
(1) initial internal population pop is randomly generated, and constructs an empty external population out, scale is respectively Npop、
Nout, set up maximum evolutionary generation Z；
(2) according to components actual measurement Value Data and deviation transmitting data be calculated each components, quality requirement it is preferential
Grade FACTOR PL、Ps；
(3) pop ∪ out is calculated using the fitness evaluation criterion of comprehensive Pareto intensity and closeness concentrate the suitable of individual
Answer angle value Fit；
(4) selection operation is carried out using selection operator, updates internal collection pop using excellent individual；
(5) determine whether to meet termination condition, even current algebra is less than Z, collects into next step, otherwise output is internal
The corresponding assembly sequence of optimum individual in pop；
(6) individual in pop is intersected, mutation operation, mutation probability is adjusted according to priority of parts, excellent
First grade is higher, and probability is bigger；Finally filial generation is remained into external collection out, returns to (3) step.
Below with reference to exemplary application and attached drawing, the present invention is described further:
1, in crank link mechanism geometric tolerance Efficient Characterization:
It uses 4GJS engine for in-line four cylinder gasoline engine, using full bearing crankshaft, there are 5 gear trunnions and 4 gears
The cooperation of rod journal, main bearing journal and main bearing shell and the cooperation of rod journal and connecting rod bearing shell are lubricated using pressures cycle,
Its assembling schematic diagram is as shown in Figure 2 and Figure 3, in figure, D1、D2Respectively indicate base bearing, connecting-rod bearing aperture；d1、d2It respectively indicates
Trunnion, rod journal diameter；τ1、τ2Respectively indicate main bearing shell, connecting rod bearing shell thickness, τ+With τ-Top bearing shell is respectively indicated under
Bearing shell；σ1、σ2Respectively indicate the fit clearance of main bearing hole and trunnion, the fit clearance of rod journal and pitman shaft bearing bore.
In view of if same group part fit clearance difference is larger, elastic different, will cause main shaft in crank link mechanism
Neck center is not overlapped, and when operating is hit larger.Therefore, in apolegamy other than guaranteeing fit clearance and meeting quality requirement, also
Need to reduce as far as possible the relative position degree tolerance at trunnion center everywhere in crankshaft, and in the pitman shaft bearing bore moved synchronously
Heart line O1′O2' and rod journal line of centres O1O2Between parallelism tolerance.
(1) calculating of trunnion center relative position degree tolerance.
From Fig. 2, Fig. 3 it is found that housing main bearing dead eye and main bearing journal there are five at, it is contemplated that in operational process
Lower main bearing shell can be contacted with trunnion in turn, therefore main bearing shell size takes upper and lower main shaft tilt sickness in the calculating of geometric tolerance
Average value, connecting rod bearing shell similarly, using the axis of housing main bearing dead eye as benchmark line, define trunnion center relative position degree tolerance
loExpression formula formula are as follows:
si=Di1-di1-τi1 (5)
In formula, n is the quantity of main bearing hole and trunnion cooperation；siDistance of each trunnion axle center to reference line；Di1For
Main bearing hole diameter at i-th；di1For trunnion diameter at i-th；τi1For the average value of half bearing thickness above and below main bearing shell at i-th；
(2) the parallelism tolerance P that rod journal, pitman shaft bearing bore cooperateoCalculating.
In formula, xo、yoRespectively rod journal, pitman shaft bearing bore center；τ2For half bearing thickness above and below connecting rod bearing shell
Average value；For the rod journal center of another group of synchronous cooperation, Similarly.
2, the mineral processing model based on assembly precision and assembly yield:
Complex mechanical product selects assembly for multi-objective optimization question, uses using assembly precision and assembly yield as mesh
Target Optimized model.
(1) the assembly precision assessment models based on field mouthful quality
According to the definition of field mouthful quality, qualitative character value distance objective value is closer, and mass loss is smaller；Conversely, quality is damaged
Mistake is bigger, and therefore, the average loss that the assembly precision to match product deviates ideal value guarantees assembly precision as majorized function
Reliability and stability；Its expression is as follows:
In formula, yj,sFor s-th of quality requirement FR of jth part productsMeasured value；A is quality when quality requirement is unqualified
Loss, is provided in instance analysis by engineering practical experience；ymaxs、yminsRespectively tolerance design value maximum value and minimum value；
TosFor design tolerance value；yo,sFor tolerance design central value, yo,s=(ymaxs+ymins)/2。
(2) the assembling quality evaluation model based on assembly yield
Under conditions of engineering goods are assembled and not exclusively exchanged, even if components to be assembled are all qualified, after assembly
It may be unsatisfactory for the actual requirement of closed-loop, lead to the generation of remaining part；Therefore, by assembly yield also as apolegamy quality
Important evaluation index, quality requirement FRsAssembly yield are as follows:
η(FRs)=Ms/M (9)
In formula, M is once to match obtained product number of packages；MsOnce to match quality requirement FRsQualified product number of packages.
Single quality requirement FR can be obtainedsApolegamy Integrated Optimization Model are as follows:
In formula, X represents a matingplan；C is that constant (0≤c≤1) indicates influence journey of the assembly precision to assembling quality
Degree.
(3) multiple target under multimass requires matches Integrated Optimization Model
Often there is the assembling function requirement of multiple needs while guarantee in the assembling process of complex mechanical product, it is referred to as more
Quality requirement can establish the multiple target apolegamy synthesis under multimass requires based on the apolegamy Integrated Optimization Model of single quality requirement
Optimized model:
MinQ (X)=[Q1(X) Q2(X) … Qs(X)]
In formula, Q (X) is object vector；ysFor the corresponding closed-loop measured value of s-th of quality requirement；XmFor matingplan
Collection.
3, based on the model solution of genetic algorithm
(1) the operator design based on priority of parts
The operator of genetic algorithm includes selection operator, crossover operator and mutation operator.Wherein, selection operator uses roulette
Method realize, i.e., selected individual probability is determined according to individual adaptation degree in proportion.
In view of the final quality requirement measured value of product is by forming each component tolerances item measured value institute of the product
It determines, it can be using the cyclic contribution degrees to closed-loop of group different in dimension chain as the evaluation criteria of priority of parts, contribution
Bigger part is spent, priority is higher；Combine the group cyclization to closing according to the tolerance variations of each group cyclization in dimensional chain for assembly
The contribution degree of ring determines the apolegamy priority of each components.
In dimension chain U, the contribution degree of i-th group of cyclization is definedAre as follows:
In formula, ΩsFor the group cyclization collection for synthesizing s-th of quality requirement (closed-loop)；Once to participate in all of apolegamy
Cyclization X is organized in componentsiThe standard deviation of tolerance item measured value；For XiDeviation on dimension chain U function direction transmits system
Number.
In view of same components may include multiple tolerance items, therefore the apolegamy preferred number P of componentsLAre as follows:
In formula, ΩLFor the tolerance item collection for being under the jurisdiction of components L.
For the execution efficiency for improving algorithm, it is contemplated that the tolerance item for being under the jurisdiction of same components should synchronize change in variation
Change, using priority of parts to the mutation probability of components LIt is adjusted as follows:
(2) the fitness evaluation criterion based on Pareto intensity and closeness
In the apolegamy that complex mechanical product multimass requires, there should be primary-slave relation between each quality requirement, and it is traditional
Way is to establish its significance level to the influence degree of final products performance according to each quality requirement.It is examined on the basis of herein
The final purpose for considering apolegamy is to guarantee that each quality requirement measured value of every set product is stable as far as possible in target design value
Near, therefore the bigger quality requirement of tolerance variations should give higher priority in apolegamy, to define quality requirement s's
Match priority factor PsAre as follows:
In formula, AsWhen unqualified for quality requirement s, the mass loss threshold value of product；TosFor the design tolerance of quality requirement s
Value.
During selection assembly optimization, interpretational criteria is the key that realize optimization.Traditional fitness evaluation method
Pareto regimen is often used, and the assembling quality requirement of complex mechanical product is more, and it is mutual not to be easy to appear individual in population
The case where domination, causes optimization efficiency low.It therefore, is ideal adaptation set forth herein a kind of combination Pareto intensity and closeness
The interpretational criteria of degree.It is located at population P in genetic algorithm to be made of inside collection pop and external collection out, then the Pareto of individual X is strong
Degree calculates as follows:
In formula, Pa(X) the Pareto intensity of individual X is indicated；ΩP-XFor other individuals in population P in addition to X；NsFor quality
It is required that number；PsPriority is matched for quality requirement；Qs(X) it indicates comprehensive quality loss, can be calculated by formula (10)；
Closeness describes the interparticle degree of crowding in group, characterizes the diversity of population, is commented using k nearest neighbor algorithm
The closeness of valence individual, individual X(a)Closeness Dis (X(a)) calculation formula are as follows:
In formula, ΩkaFor in population away from X(a)K nearest individual；K value be no more thanMaximum integer；NPFor population
The number of individuals of P；R is adjustment constant.
Comprehensively consider Pareto intensity and closeness, individual X in available population(a)Fitness Fit (X(a)) are as follows:
Fit(X(a))=Pa((X(a))+Dis(X(a)) (23)
Overall merit is carried out using fitness, one side assurance function requires to be met, and reduces mass loss；Another party
Face ensure that population is able to maintain that higher diversity using closeness, so that searching algorithm avoids falling into local solution；Algorithm stream
Journey figure is as shown in Figure 4.
The design public affairs that apolegamy analytical table 1 show 5 parts now are carried out to the part of 10 sets of crank link mechanisms to be assembled
Difference and priority of parts coefficient, table 2 show quality requirement and quality requirement priority factor, and table 3 show part
Characteristic size measured data.Specific comparing result is as shown in figure 5, influence structural representation of the apolegamy priority to algorithm the convergence speed
Figure.
1 machinery elements design Tolerance Data of table
If: the mass loss threshold value A of product is 100, p when assembly is unsatisfactory for requiringc=0.8, pm=0.8, c=0.5, r=
1, external population out and internal population pop scale are 30, Z=300.It finally obtained assembly sequence and is wanted in each quality
The mass loss asked is as shown in table 4.In table: cos (FRs) indicate the part product s-th of quality requirement loss, if such
The quantity more than one of quality requirement, then take its average value.As shown in table 5, different matching methods as a result, using the present invention knot
It closes geometric tolerance to be matched, obtained product qualification rate reaches 100%, it can be ensured that the qualified installation of each parts product.
Table 4 matches result
The result of the different matching methods of table 5
Claims (10)
1. a kind of machine components matching method based on geometric tolerance and dimensional tolerance, which comprises the following steps:
Step 1) establishes multiple-objection optimization mineral processing model:
According to the Efficient Characterization form of geometric tolerance measured value, comprehensive geometric tolerance and dimensional tolerance are as optimization aim, with dress
Evaluation index with success rate and assembly precision as quality requirement establishes the complicated machine that geometric tolerance is combined with dimensional tolerance
Tool product multiple-objection optimization mineral processing model；
Step 2), the apolegamy priority for calculating components and quality requirement:
The apolegamy priority evaluation index of the deviation fluctuation of composite tolerance item and the contribution degree in dimension chain as components,
And the apolegamy priority of each quality requirement is calculated on this basis；Simultaneously using the dimensional tolerance of product and geometric tolerance as dress
The quality requirement matched is combined using the average loss that Taguchi quality loss function calculates assembly precision deviation ideal value and is assembled successfully
Rate makees the evaluation index of quality requirement, establishes the multiple-objection optimization mineral processing model for comprehensively considering geometric tolerance and dimensional tolerance；
The apolegamy that step 3), the apolegamy priority obtained using step 2) again establish step 1) after improving to genetic algorithm
Model is solved: the characteristics of according to complex mechanical product dimensional chain for assembly, using the gene coding staff using components as unit
Formula establishes the incidence relation between the multiple tolerance items of mapping association matrix description, assembly is mapped in mathematical model, utilizes zero
The apolegamy priority of part is adjusted genetic operator, with dominance relation bond quality requirement of the individual in multiple optimization aims
Priority calculate the Pareto intensity of individual, recycle k nearest neighbor algorithm to calculate closeness of the individual in population, it is final comprehensive
The fitness of Pareto intensity and closeness as individual completes machine components apolegamy.
2. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 1, feature
It is, in step 1), the assembly sequence of components is characterized by mathematical method, establishes the assembly being layered based on components
Scheme matrix X:
In formula (1), kLFor the number of components L in a set of assembly, L=1,2 ..., n；N is components species number；Indicate the
The serial number of j components L, j=1,2 ..., kLM；M is the part tricks for participating in apolegamy；When assembly, the part of each column representative
It is assembled into an assembly.
3. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 2, feature
It is, the building of mapping association matrix is carried out to assembling scheme matrix:
If the tolerance item number that part L includes is SL, then the mapping association matrix T of part L is establishedLAre as follows:
In formula,Indicate y-th of tolerance item measured value of x-th of part；SLThe tolerance item number for including for part L.
4. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 3, feature
It is, the element in assembling scheme matrix XThe all-in allowance item measured value that i.e. corresponding j-th of part L has
Tolerance item measured value is calculated according to the deviation delivery rules of dimensional chain for assembly for assembling quality.
5. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 1, feature
Be, the apolegamy priority obtained using step 2) genetic algorithm is improved after again to step 1) establish mineral processing model into
Row solves, and specifically includes:
(1) initial internal population pop is randomly generated, and constructs an empty external population out, scale is respectively Npop、Nout,
Set up maximum evolutionary generation Z；
(2) the priority system of each components, quality requirement is calculated according to components actual measurement Value Data and deviation transmitting data
Number PL、Ps；
(3) fitness that pop ∪ out concentrates individual is calculated using the fitness evaluation criterion of comprehensive Pareto intensity and closeness
Value Fit；
(4) selection operation is carried out using selection operator, updates internal collection pop using excellent individual；
(5) determine whether to meet termination condition, even current algebra is less than Z, collects in pop into next step, otherwise output is internal
The corresponding assembly sequence of optimum individual；
(6) individual in pop is intersected, mutation operation, mutation probability is adjusted according to priority of parts, priority
Higher, probability is bigger；Finally filial generation is remained into external collection out, returns to (3) step.
6. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 5, feature
It is, using assembly precision and assembly yield as the Optimized model of target:
Based on the assembly precision assessment models of field mouthful quality, it is to match the average loss of the assembly precision deviation ideal value of product
Majorized function guarantees the reliability and stability of assembly precision；Its expression is as follows:
In formula, yj,sFor s-th of quality requirement FR of jth part productsMeasured value；A is mass loss when quality requirement is unqualified,
ymaxs、yminsRespectively tolerance design value maximum value and minimum value；TosFor design tolerance value；yo,sFor tolerance design central value,
yo,s=(ymaxs+ymins)/2。
7. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 5, feature
It is, using assembly yield as the important evaluation index of apolegamy quality, quality requirement FRsAssembly yield are as follows:
η(FRs)=Ms/M (9)
In formula, M is once to match obtained product number of packages；MsOnce to match quality requirement FRsQualified product number of packages；
Single quality requirement FR can be obtainedsApolegamy Integrated Optimization Model are as follows:
In formula, X represents a matingplan；C is constant, indicates influence degree of the assembly precision to assembling quality, 0≤c≤1.
8. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 5, feature
It is, the apolegamy Integrated Optimization Model based on single quality requirement can establish the multiple target apolegamy complex optimum mould under multimass requires
Type:
MinQ (X)=[Q1(X) Q2(X) … Qs(X)]
In formula, Q (X) is object vector；ysFor the corresponding closed-loop measured value of s-th of quality requirement；XmFor matingplan collection.
9. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 1, feature
It is, combines the group cyclization to the contribution degree of closed-loop according to the tolerance variations of each group cyclization in dimensional chain for assembly, determine each zero
The apolegamy priority of component:
In dimension chain U, the contribution degree of i-th group of cyclization is definedAre as follows:
In formula, ΩsFor the group cyclization collection for synthesizing s-th of quality requirement；It is formed in all components once to participate in apolegamy
Ring XiThe standard deviation of tolerance item measured value；For XiDeviation carry-over factor on dimension chain U function direction；
The apolegamy preferred number P of componentsLAre as follows:
In formula, ΩLFor the tolerance item collection for being under the jurisdiction of components L；
Using priority of parts to the mutation probability of components LIt is adjusted:
10. a kind of machine components matching method based on geometric tolerance and dimensional tolerance according to claim 1, feature
It is,
The apolegamy priority factor P of quality requirement ssAre as follows:
In formula, AsWhen unqualified for quality requirement s, the mass loss threshold value of product；TosFor the design tolerance value of quality requirement s；
It is located in genetic algorithm population P to be made of inside collection pop and external collection out, then the Pareto Strength co-mputation of individual X is such as
Under:
In formula, Pa(X) the Pareto intensity of individual X is indicated；ΩP-XFor other individuals in population P in addition to X；NsFor quality requirement
Number；PsPriority is matched for quality requirement；Qs(X) it indicates comprehensive quality loss, can be calculated by formula (10)；
Using the closeness of k nearest neighbor algorithm evaluation individual, individual X(a)Closeness Dis (X(a)) calculation formula are as follows:
In formula, ΩkaFor in population away from X(a)K nearest individual；K value be no more thanMaximum integer；NPFor of population P
Body number；R is adjustment constant；
Comprehensively consider Pareto intensity and closeness, obtains individual X in population(a)Fitness Fit (X(a)) are as follows:
Fit(X(a))=Pa((X(a))+Dis(X(a)) (23)。
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