CN102662356A - Tolerance optimization method of feed mechanism - Google Patents
Tolerance optimization method of feed mechanism Download PDFInfo
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- CN102662356A CN102662356A CN2012100895845A CN201210089584A CN102662356A CN 102662356 A CN102662356 A CN 102662356A CN 2012100895845 A CN2012100895845 A CN 2012100895845A CN 201210089584 A CN201210089584 A CN 201210089584A CN 102662356 A CN102662356 A CN 102662356A
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Abstract
The invention discloses a tolerance optimization method of a feed mechanism. The method comprises the following steps: A, establishing a feed mechanism tolerance-processing cost function model: C(t)=a0e<-a1t>, wherein the C(t) expresses processing cost of a corresponding tolerance t and a0 and a1 are weighting coefficients of different processing cost evaluation functions; B, employing a random simulation algorithm to calculate a correlated statistic characteristic of a feed mechanism quality characteristic according to design parameters of all components of the feed mechanism and initial tolerance data; and C, employing a genetic algorithm to output an optimized tolerance of the design parameters according to the correlated statistic characteristic of the feed mechanism quality characteristic. According to the invention, correlated knowledge of tolerance robustness is employed and a quality-cost balance relation is utilized as a quality maxim for a tolerance robustness optimization design; therefore, it can be ensured that the quality of the feed mechanism has good robustness and processing cost of the mechanism can be effectively reduced, thereby reaching an optimum balance between the product quality and the cost and thus further improving product market competitiveness.
Description
Technical field
The present invention relates to a kind of quality control optimization method that is used for the feed mechanism of mechanical design field, especially relate to a kind of Tolerance Optimization method of feed mechanism.
Background technology
In the actual machine project engineering; For the design of various mechanical parts, such as feed mechanism, because the influence of foozle; There are certain variation in the actual value of each rod member of feed mechanism and design load; And there is certain influence in the fluctuation meeting of these design parameters to feed mechanism determinacy results of optimum design, especially may reduce the quality of feed mechanism output characteristics, and then influences the serviceability of whole plant equipment.Feed mechanism with cold headers is an example; For improving the quality of feed mechanism output characteristics; Usually need the machining tolerance of strict each rod member length parameter of control feed mechanism,, will increase manufacturing cost greatly but too control machining tolerance to reduce the fluctuation of its member length parameter.Otherwise looser tolerance no doubt can lower manufacturing cost, but the thing followed is the robustness that has reduced mechanism's quality.
Summary of the invention
Technical matters to be solved by this invention is to overcome the defective of traditional design method; Solve workmanship that the control of feed mechanism tolerance brings and the contradiction between the cost, a kind of Tolerance Optimization method that had not only guaranteed the feed mechanism quality but also can effectively reduce its processing cost is provided.
It is with the equilibrium relation of the quality-cost criterion as the tolerance robust optimized that the present invention solves the problems of the technologies described above the know-why that is adopted; Foundation is based on the mathematical model of the feed mechanism tolerance robust optimized of quality-cost model; Adopt Method of Stochastic that probability problem in the model is analyzed, and combine widely used genetic algorithm to come the solution procedure of Optimization Model is compared and improves.(purpose of this method is the optimization tolerance that will obtain design parameter or design variable, and this optimization tolerance can obtain a better quality-cost balance, and this balance is the effect of this optimization tolerance, and to optimize tolerance just passable so this method is write)
Technical scheme of the present invention is: a kind of feed mechanism Tolerance Optimization method comprises the steps:
A, set up feed mechanism tolerance and processing cost function model
Wherein C (t) representes the processing cost of corresponding tolerance t, wherein a
0, a
1Weighting coefficient for different processing cost valuation functions;
B, according to the design parameter of each member of feed mechanism and the ASSOCIATE STATISTICS characteristic of initial tolerances The data stochastic simulation algorithm computation feed mechanism mass property;
C, adopt the optimization tolerance of genetic algorithm output design parameter according to the ASSOCIATE STATISTICS characteristic of feed mechanism mass property.
Tolerance-processing cost the model that adopts is function model practical and that have the exponential type of stronger ubiquity, promptly
Wherein C (t) representes the processing cost of corresponding tolerance t, wherein a
0, a
1Be the weighting coefficient of different processing cost valuation functions, actual processing factors such as the concrete size characteristic of its value and workpiece, material, machined parameters is relevant.
The applying step of the ASSOCIATE STATISTICS characteristic of said stochastic simulation algorithm computation feed mechanism mass property is:
(1) confirms feed mechanism mass function y=f (x
1, x
2..., x
9) in the probability distribution of each stochastic variable, wherein stochastic variable x
i(i=1,2 ..., 9) and be the design parameter of each member of feed mechanism.The mass function of feed mechanism is meant each member of feed mechanism crudy of (comprising the long and position of bar), and promptly nominal size+mismachining tolerance is a stochastic variable.
(2) distribution probability according to each stochastic variable produces stochastic variable sample X
1, X
2..., X
9
In the sample value substitution feed mechanism mass function of each stochastic variable that (3) will produce, and calculate a sample value Y who obtains the feed mechanism mass property
1=f (X
1, X
2..., X
9), thereby constituted single test.Repeat above-mentioned steps N time, i.e. frequency in sampling N, promptly obtaining a pool-size is the feed mechanism mass property sample Y of N
1, Y
2..., Y
N
(4), calculate the ASSOCIATE STATISTICS characteristic of feed mechanism mass property according to feed mechanism mass property sample total.
The probability distribution of said each stochastic variable is normal distribution.This regularity of distribution derives from member manufacturing statistics data analysis in enormous quantities.
Adopt mathematical statistics method to calculate the ASSOCIATE STATISTICS characteristic of feed mechanism mass property.
The ASSOCIATE STATISTICS characteristic of said feed mechanism mass property comprises sample average, sample variance and reliable probability.
Adopt the method for the optimum tolerance of genetic algorithm output design parameter to be:
Set up each member designs parameter machining tolerance f of feed mechanism
1(T) and total processing cost valuation functions f
2(T), its ratio is objective function, is expressed as
Wherein
Here,
The rocking bar that is respectively feed mechanism realizes that the actual value and the design load of maximum pendulum angle, the output of ε outgoing mechanism need the accuracy requirement of satisfying, T=(t
1, t
2..., t
9)
T, t
iIt is the machining tolerance value of i parameter;
Total processing cost valuation functions for feed mechanism.
Processing request according to feed mechanism is set constraint condition, according to the optimum tolerance value of the maximum output of objective function.
Being expressed as of said genetic algorithm:
In the formula:
N
0, N
TBe respectively the initial number of times and final number of times of stochastic simulation;
Tanh () is a hyperbolic tangent function, and t, T are respectively current genetic algebra and maximum genetic algebra;
η, δ is for changing controlled variable, wherein η＞1,0＜δ＜1.
Said genetic algorithms use MATLAB software.
In above-mentioned feed mechanism tolerance Robust Optimal Design model; Relate to the reliability problem in objective function and the constraint function is carried out probability analysis; For guaranteeing the accuracy of feed mechanism reliability probability analysis, the present invention adopts Method of Stochastic to carry out the probability analysis of tolerance Robust Optimal Design model.
For obtaining best feed mechanism tolerance Robust Optimal Design result, adopt the genetic algorithm of being used widely that Optimization Model is found the solution.Be optimized when finding the solution using genetic algorithm; According to the description of tolerance Robust Optimal Design model and the characteristics of objective function; Fitness function is the objective function of preference pattern directly; Because this objective function need carry out the reliable probability analysis, thereby this method invention is applied to the evaluation procedure to its fitness function with Method of Stochastic.
In order to make genetic algorithm and stochastic simulation algorithm be applied to tolerance Robust Optimal Design process better, this method invention is used both combinations and has been carried out significant improvement.According to the application characteristic separately of two kinds of algorithms, has the thought that dynamic accuracy adapts to function for reducing assessing the cost of tolerance design problem, adopting; Promptly set up the relational expression of stochastic simulation number of times and genetic algebra; Along with the continuous increase of genetic algebra, the simulation number of times also increases thereupon, thereby its precision that adapts to function also improves thereupon; The calculation features that meets genetic algorithm has so also just guaranteed the computational accuracy of genetic algorithm.
Through above-mentioned improvement, make the total degree of stochastic simulation reduce to reduce assessing the cost of problem, improve and resolve efficient, also guaranteed to resolve result's precision effectively, guarantee to resolve result's accuracy.
For these practical problemss of feed mechanism,, adopt the quality criterion of the equilibrium relation of quality-cost as the tolerance Robust Optimal Design in conjunction with the sane relevant knowledge of tolerance.The quality that so both can guarantee feed mechanism possesses good robustness, has reduced the processing cost of mechanism again effectively, so that reach optimum balance between the quality of product and the cost, thereby can further improve the competitiveness of product in market.
Description of drawings
Fig. 1 is the illustraton of model of feed mechanism among the embodiment.
Fig. 2 is a computation optimization process flow diagram among the embodiment.
Fig. 3 is genetic algorithm converges figure among the embodiment.
Fig. 4 adopts initial tolerances to calculate the result of calculation sectional drawing of the statistical characteristics of feed mechanism mass property among the embodiment.
Fig. 5 adopts among the embodiment to optimize the result of calculation sectional drawing that tolerance is calculated the statistical characteristics of feed mechanism mass property.
Embodiment
A feed mechanism tolerance robust optimized embodiment of this method invention is described below:
Present embodiment is certain the model cold headers feeding Mechanism Design parameter that provides according to enterprise, and its tolerance is carried out Robust Optimal Design.
(1) the feed mechanism model can be reduced to the combination in series of two groups of linkage assemblys, and its simplified model sketch is as shown in Figure 1, and wherein, rod member OA is a crank, corresponding to the feeding eccentric wheel structure; Rocking bar BCD is corresponding to the feeding rocker structure, and wherein the length of BD is for regulating parameter (can less than BC length) to satisfy the requirement of different feed lengths; Rocking bar EF is corresponding to the ratchet rocker structure, and its maximum pendulum angle that in a work period, can reach has determined the length of feeding.
(2) in the initial tolerances scheme, the determinacy design load and the manufacturing tolerance of each rod member design variable of feed mechanism is respectively (mm of unit): L
OA=53 ± 0.25, L
AC=860 ± 0.25, L
BC=155 ± 0.25, L
DE=595 ± 0.25, L
EF=103 ± 0.25, according to rectangular coordinate system shown in Figure 1, the position coordinates of B and tolerance thereof are (875 ± 0.25,103 ± 0.25), and the position coordinates of F and tolerance are (1405 ± 0.25,327 ± 0.25).
Linkage assembly OACB (seeing accompanying drawing 1) belongs to crank and rocker mechanism, and need satisfy the OA rod member is the bar elongate member of crank mechanism, and requirement and the body function that also will satisfy the minimum transmission angle of linkage assembly simultaneously requires the lowest reliable probability demands that satisfies.Therefore the constraint condition of feed mechanism tolerance Robust Optimal Design is:
In the formula:
α is the least reliability probability that mechanism need satisfy functional requirement;
L
OA, L
OB, L
AC, L
BCDeng being that each bar of feed mechanism is long, see accompanying drawing 1;
γ
MinThe minimum transmission angle that need satisfy for linkage assembly OACB;
t
i, t
Min, t
MaxBe i rod member length machining tolerance and range of choice thereof, i=1,2 ..., 9.
(3) according to the application principle and the improvement strategy thereof of foregoing stochastic simulation and genetic algorithm, in MATLAB software, work out computation optimization program, its computation optimization flow process such as accompanying drawing 2.
By above-mentioned constraint condition calculating processing tolerance f
1(T) and total processing cost valuation functions f
2(T) ratio
Its ratio is objective function;
Adopt the mode of stochastic simulation to calculate the ASSOCIATE STATISTICS characteristic of corresponding feed mechanism mass property again, comprise sample average, sample variance and reliable probability etc.;
Adopt following genetic algorithm to carry out the calculating of optimum tolerance:
In the formula:
N
0, N
TBe respectively the initial number of times and final number of times of stochastic simulation;
Tanh () is a hyperbolic tangent function, and t, T are respectively current genetic algebra and maximum genetic algebra;
η, δ is for changing controlled variable, wherein η＞1,0＜δ＜1.
According to enterprise practical processing conditions and engineering experience, the boundary condition of machining tolerance in genetic algorithm of setting design parameter is [0.03 0.3]; The initial number of times of getting stochastic simulation is respectively 100 and 1000 with final number of times, and controlled variable η, δ are taken as 7 and 0.7; Getting population size during genetic algorithm optimization is 20, adopts the real coding form, and maximum genetic algebra is 40, and crossover probability is 0.8, and the variation probability is 0.05.Press the job requirement of cold headers feed mechanism, the design load of fetching and delivering material mechanism output maximum pendulum angle is 40 °, and accuracy requirement is ± 0.15 °, and the least reliability probability that mechanism's quality need satisfy is 0.95.
(4) genetic algorithm searches out globally optimal solution when evolving to for the 10th generation, shown in accompanying drawing 3.
(5) it is as shown in table 1 to find the solution the prioritization scheme of acquisition.
With the value of initial tolerances shown in the table 1 with optimize tolerance value respectively in the MATLAB program of substitution stochastic simulation algorithm to calculate the statistical characteristics of feed mechanism mass property, both result of calculation shows respectively like accompanying drawing 4 with shown in the accompanying drawing 5.
(6) utilize tolerance processing cost function to calculate the processing cost value of two kinds of schemes respectively, and the initial tolerances scheme is compared with optimizing the tolerance scheme, the result is as shown in table 2.
(7) result of implementation analysis: as shown in table 2, in the design proposal of initial tolerances, its required processing cost is less, but this design proposal makes that the reliability of feed mechanism is relatively poor, is 90%, and the reliable probability that does not reach regulation requires (95%).And in optimizing the Tolerance Design scheme, though its processing cost slightly increases, increasing degree is little; Be merely 3.4%; But the reliability likelihood ratio initial tolerances scheme of this scheme has improved 8.7%, can reach 97.8%, thereby the equilibrium relation of feed mechanism quality and cost has improved (0.135-0.128)/0.128=5.47%; Both have reached optimum balance, have farthest guaranteed the quality robustness and the economy of mechanism.Simultaneously variance yields shows that the feed mechanism mass property fluctuation situation of optimizing in the tolerance scheme also improved 20%, makes feed mechanism under the enchancement factor influence, still can work well, has guaranteed mechanism stability and reliability.[annotate: the calculating of correlative value is by (initial tolerances-optimization tolerance)/initial tolerances in the table]
Each design parameter Tolerance Optimization of table 1 is table as a result
| Parameter | L OA | L AC | L BC | L DE | L EF | x B | y B | x F | y F |
| Initial value | ±0.25 | ±0.25 | ±0.25 | ±0.25 | ±0.25 | ±0.25 | ±0.25 | ±0.25 | ±0.25 |
| Optimal value | ±0.18 | ±0.28 | ±0.16 | ±0.15 | ±0.25 | ±0.23 | ±0.26 | ±0.22 | ±0.23 |
Table 2 initial tolerances and quality-cost result contrast table of optimizing tolerance
| Average | Variance | Reliable probability | Processing cost | Ratio (equilibrium relation) | |
| Initial tolerances | 40.01 | 0.005 | 0.90 | 7.01 | 0.128 |
| Optimize tolerance | 40.01 | 0.004 | 0.978 | 7.25 | 0.135 |
| Correlative value | / | 20％↓ | 8.7％↑ | 3.4％↑ | 5.5％↑ |
Claims (8)
1. a feed mechanism Tolerance Optimization method comprises the steps:
A, set up feed mechanism tolerance and processing cost function model
Wherein C (t) representes the processing cost of corresponding tolerance t, wherein a
0, a
1Weighting coefficient for different processing cost valuation functions;
B, according to the design parameter of each member of feed mechanism and the ASSOCIATE STATISTICS characteristic of initial tolerances The data stochastic simulation algorithm computation feed mechanism mass property;
C, adopt the optimization tolerance of genetic algorithm output design parameter according to the ASSOCIATE STATISTICS characteristic of feed mechanism mass property.
2. feed mechanism Tolerance Optimization method according to claim 1 is characterized in that, the applying step of the ASSOCIATE STATISTICS characteristic of said stochastic simulation algorithm computation feed mechanism mass property is:
(1) confirms feed mechanism mass function y=f (x
1, x
2..., x
9) in the probability distribution of each stochastic variable, wherein stochastic variable x
i(i=1,2 ..., 9) and be the design parameter of each member of feed mechanism;
(2) distribution probability according to each stochastic variable produces stochastic variable sample X
1, X
2..., X
9
In the sample value substitution feed mechanism mass function of each stochastic variable that (3) will produce, and calculate a sample value Y who obtains the feed mechanism mass property
1=f (X
1, X
2..., X
9), repeat substitution N time, obtaining a pool-size is the feed mechanism mass property sample Y of N
1, Y
2..., Y
N
(4), calculate the ASSOCIATE STATISTICS characteristic of feed mechanism mass property according to feed mechanism mass property sample total.
3. feed mechanism Tolerance Optimization method according to claim 2 is characterized in that the probability distribution of said each stochastic variable is normal distribution.
4. feed mechanism Tolerance Optimization method according to claim 2 is characterized in that, adopts the method for the optimum tolerance of genetic algorithm output design parameter to be:
(1) sets up each member designs parameter machining tolerance f of feed mechanism
1(T) and total processing cost valuation functions f
2(T) ratio
Be objective function, wherein
The rocking bar that is respectively feed mechanism realizes that the actual value and the design load of maximum pendulum angle, the output of ε outgoing mechanism need the accuracy requirement of satisfying, T=(t
1, t
2..., t
9)
T, t
iIt is the machining tolerance value of i parameter;
(2) set constraint condition according to the processing request of feed mechanism, according to the optimum tolerance value of the maximum output of objective function.
5. feed mechanism Tolerance Optimization method according to claim 4 is characterized in that said genetic algorithm is expressed as:
In the formula:
N
0, N
TBe respectively the initial number of times and final number of times of stochastic simulation;
Tanh () is a hyperbolic tangent function, and t, T are respectively current genetic algebra and maximum genetic algebra;
η, δ is for changing controlled variable, wherein η＞1,0＜δ＜1.
6. feed mechanism Tolerance Optimization method according to claim 1 is characterized in that, said genetic algorithms use MATLAB software.
7. feed mechanism Tolerance Optimization method according to claim 2 is characterized in that, adopts mathematical statistics method to calculate the ASSOCIATE STATISTICS characteristic of feed mechanism mass property.
8. feed mechanism Tolerance Optimization method according to claim 2 is characterized in that the ASSOCIATE STATISTICS characteristic of said feed mechanism mass property comprises sample average, sample variance and reliable probability.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103810324A (en) * | 2013-12-27 | 2014-05-21 | 西京学院 | Assembly tolerance optimum design method based on cost objective optimization |
| CN104090494A (en) * | 2014-07-02 | 2014-10-08 | 北京航空航天大学 | Self-organization match working machining method based on task reliability |
| CN103903060B (en) * | 2013-12-27 | 2017-11-10 | 西京学院 | A kind of Optimization Design on build-up tolerance |
| CN107871034A (en) * | 2017-09-22 | 2018-04-03 | 湖北汽车工业学院 | Tolerance assignment multi-objective optimization design of power method based on mutative scale learning aid algorithm |
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| CN102129242A (en) * | 2011-04-12 | 2011-07-20 | 上海大学 | Product quality control method during batch processing production process based on two-layer hybrid intelligent optimization |
| CN102360403A (en) * | 2011-10-26 | 2012-02-22 | 中冶南方工程技术有限公司 | Method for optimally designing structure of sliding shaft sleeve based on Kriging model |
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2012
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US6657798B1 (en) * | 2003-02-10 | 2003-12-02 | Electo Optical Sciences, Inc. | Method for optimizing the number of good assemblies manufacturable from a number of parts |
| CN102129242A (en) * | 2011-04-12 | 2011-07-20 | 上海大学 | Product quality control method during batch processing production process based on two-layer hybrid intelligent optimization |
| CN102360403A (en) * | 2011-10-26 | 2012-02-22 | 中冶南方工程技术有限公司 | Method for optimally designing structure of sliding shaft sleeve based on Kriging model |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103810324A (en) * | 2013-12-27 | 2014-05-21 | 西京学院 | Assembly tolerance optimum design method based on cost objective optimization |
| CN103810324B (en) * | 2013-12-27 | 2016-08-24 | 西京学院 | A kind of build-up tolerance Optimization Design optimized based on cost objective |
| CN103903060B (en) * | 2013-12-27 | 2017-11-10 | 西京学院 | A kind of Optimization Design on build-up tolerance |
| CN104090494A (en) * | 2014-07-02 | 2014-10-08 | 北京航空航天大学 | Self-organization match working machining method based on task reliability |
| CN104090494B (en) * | 2014-07-02 | 2016-12-07 | 北京航空航天大学 | The self-organizing of a kind of task based access control reliability is joined and is made processing method |
| CN107871034A (en) * | 2017-09-22 | 2018-04-03 | 湖北汽车工业学院 | Tolerance assignment multi-objective optimization design of power method based on mutative scale learning aid algorithm |
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Application publication date: 20120912 |