Research on Fuzzy Synthetic Evaluation of Stamping Process Scheme

Research on Fuzzy Synthetic Evaluation of StampingProcess SchemeJI Tingwei GAO Jun' 2 , ZHAO Guoqun'( 1. School of Mater. Sci. and Eng. , Shandong Univ. ,Jinan 250061 , China E-mail :jtw@ mail. sdu. edu.cn ;2. Shandong University at Weihai , Weihai 264209 , China )creatire process needing time and experiences. The lead time is mainly spent on stam ping die design and manufacturing. As the ba-sis of die cdesign，process design is a non linearity and creative process , rwhich can be solved by using the fuzzy synthetic evaluation.In this paper , the potential of fuzzy synthetic evalucation for dealing with stamping process design was explored. The influencingfactor set，factor weight set , eraluation set，single factor fuzzy evaluation matrix，and fuzzy synthetic evaluation scheme werestuclied. Finally , the washer part , considering forming equipment , part dimensions and other factors , was selected to testify theevaluation process .Key words: stamping ; process scheme ; fuxzy symthetic eraluation1 IntroductionStamping process , which is widely used in various industries , plays great important roles in the field ofmetal forming. Stamping die design is based on the process design , which is the key point to produce stampingparts with high quality , high production rate , low cost , long life of die , and etc. Stamping process scheme isthe core of stamping process design.Synthetic evaluation is usually utilized to evaluate the objects or phenomena influenced by multi-factors.When the factors is fuzzified and extended to synthetic evaluation , the evaluation is defined as fuzzy synthetic e-valuation. Fuzzy set theory has been developed since 1965 , and was designed to supplement the interpretation oflinguistic or measured uncertainties for real- world phenomena. Fuzzy synthetic evaluation is designed to groupraw data into several different categories according to predetermined quality criteria , which can be normally de-scribed using a set of functions that are designed to reflect the absence of sharp boundaries between each pair ofadjacent criteria. Fuzzy synthetic evaluation comprises of establishing influencing factor set , factor weight set ,evaluation set , single factor fuzzy evaluation matrix , fuzzy synthetic evaluation , transforming the applied qualitystandards for evaluation ,and etd121.A well designed fuzzy process scheme evaluation may be capable of covering the uncertainties existing in thedesign processDuring the stamping process evaluation ,a series of influencing factors，which are the form-ing equipment，production volume , stamping part dimensions 1 prescribed part precision and etc 1 must be con-sidered. In this study , in order to determine the process scheme , the fuzzy synthetic evaluation was applied tothe stamping process design.2 Fuzzy Synthetic Evaluation Model of Stamping Process Design2.1 Construction of Factor Set , Weight Set and Evaluation SetIn order to study how to evaluate the stamping process scheme , the process scheme is broken down into theconstitutive factors. The factors influencing the process scheme design ,as are the forming equipment , stationarydimensions , production volume , stamping part dimensions , prescribed part precisions , and etc.，were selectedto establish the factor set. To define this concept ,let U=( u1u2 .. uUm ),where n=1 2 3.. .m. Each ele-ment in set U denotes the degree of an influencing factor as mentioned above.Stamping process fuzzy evaluation cannot be ascertained ators merely , each factorhas its own contributions to the stamping process design. Th中国煤化工h the factor weight setA=(a1 ra2 .. ram ), each factor should be given a weight coeMYHC N M H Gwledge and experiencesof the dominant experts. Here a; is subject to the requirementsof Za;=1 1a;20{ i=1 2.. ,m ).The fac-tors and weights can be integrated in the form of the hierarchy tree as shown in Fig. 1.The purpose of fuzzy synthetic evaluation is to get evaluation in evaluation set precisely , considering all in-一479-stamping schemeTforming equipmentstationary dimensionspart dimensionsdiamneterheightFig.1 The hierarchy treefluencing factors in the factor set. Let V=( V1 ,02 .. ,Un )be an evaluation set , where v( i=1 2.. m )rep-resents the possible stamping process scheme，which can be best ,better , good，bad ,worse and worst ,or com-pound stamping，single operation stamping , progressive punching ,and so on. The element of evaluation set rep-resents the possible results of scheme process design.2.2 The Process of Multi-stage Fuzzy Synthetic EvaluationSingle factor fuzzy evaluation is defined as the membership degree of one factor in order to evaluate the set .elements. rj , the element of R , denotes the degree of membershipof Uj in the factor set U. The evaluation re-sult of u; factor can be conveniently described in the form .+=+1+.+... +Timt n , where R; denotes the singlefactor fuzzy set，which can also be represented in the formof R;=( r;1 ri2 .. rin).Then , the single factor evaluation matrix , which is obtained by arranging R; , is defined by the matrixr11r12 .. rInr21r22.. r2nRmxn=. The fuzzy relationship matrix R; is defined on the factor set U and the evalua-m1tion set V ,so the relationship can be represent as R; =r;1_ri2Iinu;n(+(u;02)+- +(u; w,n),where(uoi=1 2.m ij=1 2.. m )is the memberof UX V4].However , only one factor is considered in the process of single factor evaluation , which cannot evaluate thestamping process design scheme influenced by numbers of factors. Accordingly , the fuzzy synthetic evaluationwas utilized to evaluate the stamping process design scheme.The fuzzy synthetic evaluation set can be determined via the formula B=A R=( b1 ,b2 .... ,bn ), WhereB is the vector representing the fuzzy synthetic evaluation index. In this study , from several fuzzy synthetic e-valuation models , the formula b;= V(a;\r;)(j=12 r m )was selected to be the memberof set B. Here ,b; denotes the membership degree of j member in evaluation set considering all the influencing factors. Afterfuzzy synthetic evaluation index produced , the finally fuzzy synthetic evaluation result can be obtained by severalmethods , which are max membership degree , weight average , fuzzy distribution , and etc.One- stage fuzzy synthetic evaluation described above can be applied to solve the simple problems. Howeverin practical engineering problems , there are a great number of influencing factors , which can be classified intoseveral clusters. Those engineering applications can be dealt with by using the multi- stage fuzzy synthetic evalua-tion ,which was developed based on the one- stage fuzzy synthetic evaluation. The two- stage fuzzy synthetic eval-「Ai R1uation is defined as the formB=A R=AAz R2=(by ,b2.. bp ),whereb,= V(a;ArzXk=1 2.. ,_A; R,p).The multi-stage fuzzy synthetic can be constructed in the form of the two -stage fuzzy synthetic evalua-tior[5].In this paper , how to evaluate the stamping process desi中国煤化工synthetic evaluation ismainly studied , the multi-stage fuzzy synthetic evaluation wa:YHCNMHG3 Algorithm Programming and Typical Testing Example3.1 Process and Algorithm ProgrammingThe goal of fuzzy synthetic evaluation is to optimize the stamping scheme. So the fuzzy synthetic evaluation- 48StartInput the stamping purte paranetcm &Esblish the fuxzryequipments snd stamping schememembership funetion byexperts experienceEstabEish the infuencing factor set ondthe factor weight setMembenshipSalet membenhip functionConvert the fnctor bythe memberabip functionsEstablish the single faeter fueyevaluation malrixNhs the nunber of factor orer?iesEstablish the fury evaluxion matrxUse the max-min compositio obainthe evolustion resulhtStopFig.2 The flow of stamping scheme fuzy synthetic evaluationshould rely on a great deal of reliable ,dynamic and real-time information so that the stamping scheme can be ad-justed in time. The fuzzy synthetic process of stamping scheme shows in Fig.2.Firstly ，the parameters of stamping part & equipment and stamping scheme were input into the program ,and the parameters were classified to establish the factor set. Secondly , the parameters were converted to the de-gree of membership by the fuzzy membership function , which was built by expert experience , and the degree ofmembership matrix to one factor was obtained until each factor fuzzy evaluation matrix was confirmed. Finally ,the max- min composition was used in the fuzzy synthetic evaluation to obtain the evaluation result for fuzzy eval-uation matrix and factor weight set. The fuzzy synthetic evaluation algorithm was programmed as shown in thefollowings :// one of the membership functionsTrapefur( double x ,double min ,double max )double mid mincha maxcha guail guai2 ,result ;mid=( min+ max )2 ;maxcha=( max-min )2 ;mincha =( max-min )4 ;guail = mid-mincha ;guai2 = mid + mincha ;i((0=max)max=min;temp[ i ]= max ;max=0 ;min=0 ;total+ = temp[ i];3.2 Typical Testing ExampleIn order to testify this fuzzy synthetic evaluation problem , the washer part was selected , as shown in Fig.When designing the process planning of the stamping part , the experts usually consider some factors experi-entially，which accord the design result properly. In this paper , the forming equipment , the stationary dimen-sions , production volume，washer part dimensions , and prescribed part precision were selected as the influencingfactors , in order to establishing the factors set U=( u1 ,u2 ,u3 ,ll4 ,u5), where u1 denotes the factor of theforming equipment and the stationary dimensions 1u2 denotes the production volume factor u3 denotes the wash-er plane dimension factor ,u4 denotes the washer thickness factor ,us denotes the washer precision factor. In or-der to evaluate the stamping process scheme , production volume is given as 20 000. The evaluation set is a col-lection of evaluation results for each factor in the factor set. Here ,V=( V1 r心U2 103 ) was adopted to evaluate theobject , where V1 ,U2 and V3 represents the degree of single-operation stamping , compound stamping , progres-sive stamping respectively .The product volume factor was selected as an exampleto show how to convert the variable of stamping scheme in-、35to the degree of membership. The meaning of product vol-ume to single-operation stamping was defined by the mem-bership function whose form is shown in Fig.4. So the de-gree of product volume to single- operation stamping was0.150. Each element of fuzzy evaluation matrix was ob-目tained by the same method. Finally ,the process design pa-rameters were converted to establish fuzzy evaluation matrixFig.3 Washer part for testingRsx3 , as shown in Fig.5.1.0Fl(E) Ed(国Vew() HebilD0.08里Fuzzy synthetic evaluation matrix;0.60.180 0.550 0.320其0.4-0.150 0.470 0.380发0.,0.150.200 0.350 0.4505000 10000 15 00020000 25 000中国煤化工Product volumeFig.4 Product volume to single- operation membership functionMYHC N M H Gzzy evaluation matrixEach weight cofficient was given based on its functions , which was given by the experts as shown in Fig.6.The fuzzy synthetic evaluation set B was established by max- min fuzzy synthetic evaluation model and couldbe calculated and normalized by the program ,as in Fig. 7.- 48DG口FileED E(国) WewV Heptl)Fuery syothetie evabuston motbxe0.180 0.550 0.3200.150 0.70 0.3000.210 0.350 0.440Weightsel: {0.090 0.090 0.180 0.180 0.460 }0.200 0.350 0.4500.100 0.500 D.400Weightseh 10.090 0.090 0.180 0.180 0.460 1RrsulE[0.173 .42 D.385 1Fig.6 The weight coefficientFig. 7 The result of stamping scheme fuzzy synthetic evaluationKnown from the data of the fuzzy synthetic evaluation set B , the number 0. 442 corresponds to the evalua-tion result compound stamping'4 ConclusionsIn developing a new stamping part , a large proportion of the lead time is spent on the design and manufac-ture of stamping dies. Any reduction of the lead- time required for the design and evaluation of the design schemeis the critical factor. With CAD ,AI ,CAE , and other advanced technologies applied to the stamping forming ,the evaluation of process design scheme has entered a new era. In this paper , fuzzy synthetic evaluation appliedto evaluate the stamping process scheme was present. Based on the analysis of the stamping process design , in-fluencing factors was extracted. The evaluation set and weight set were established by domain experts. Thefuzzy synthetic evaluation matrix was obtained by the domain experts and the max min fuzzy model. It has beenproved that the application of fuzzy synthetic evaluation to stamping process design has the significance that canaccomplish the effective analysis in the shortest time and enhance the efficiency to use the expert experience.In this paper , some simplifications have been premised and proved validate ,a lot of questions still need fur-ther investigation.AcknowledgementsThis study was supported by National Science Foundation for Distinguished Young Scholars of China( 50425517 ) and Foundation for Outstanding Young Scientists of Shandong Province, P. R. China( 2005BS05005 ).References[1] W. Chen,J.C. Yang ,Z. Q. Lin. Application of Integrated Formability Analysis in Designing Die- face of Automobile PanelDrawing Dies. Journal of Materials Processing Technology ,2002 ,121 :293-300 .[2] C. E. Bozdag , C. Kahraman ,D. Ruan. Fuzzy Group Decision Making for Selection Among Computer Integrated Manufactur-ing Systems. Computer in Industry ,2003 ,51 :13-29.[3] H.Z. Wu,F. Wang ,X. 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