The Study on Mechanical Reliability Design Method and Its Application

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1 Avilble online t Energy Procedi 17 (2012 ) Interntionl Conference on Future Electricl Power nd Energy Systems The Study on Mechnicl Relibility Design Method nd Its Appliction Yng Yunfn School of Trnsporttion Science nd Engineering,Beihng University,Beijing, Chin Abstrct Bsed on the relibility test nd sttisticl nlysis of the filure dt, the bsic tsk of mechnicl relibility design is to propose mthemticl-mechnicl models nd methods for engineering prctice. In this wy the working stte nd life of the mechnicl product under the prescriptive working condition cn be predicted in the design stge. The connottion nd development of mechnicl relibility-bsed design is expounded by integrting modern mthemticl-mechnicl theories. A series of theories nd pproches, such s the mechnicl relibility-bsed design, dynmic relibility-bsed design, relibility-bsed optimiztion design, relibility-bsed sensitivity design, relibility-bsed robust design, re explined clerly nd systemticlly. Bsed on chrcteristics of mechnicl relibility design, s well s study on relibility design of mine hoist, tking mine hoist spindle bering s exmple, this pper discusses the ppliction of relibility design in mine hoist design Published by Elsevier by Elsevier Ltd. Selection Ltd. Selection nd/or peer-review nd/or peer-review under responsibility under responsibility of Hinn University. of [nme orgnizer] Open ccess under CC BY-NC-ND license. Keywords:Mechnicl Relibility; Design; Rolling Bering 1.Introduction The incresing development of science nd technology hs mde greter requirements of products, which should be of not only better performnce, but lso higher relibility. On the bsis of trditionl designs, the relibility design processes such prmeters s mteril properties, dimension of prts, lods, strength nd others to be rndom vribles tht comply with certin sttisticl lw. Besides, mthemticl probbility model nd its distribution will be formed ccording to this design rule. By virtue of probbility nd sttistics theories nd strength theory, the formul of probbility for prts dmge under given conditions is lso to be obtined nd thereby their dimension nd life under given relibility will be clculted, which both stisfies the opertion requirements nd helps with the formtion of optiml design prmeters[1], or the relibility of prts nd system cn be concluded ccording to the relibility design theory. Therefore, the design mentioned bove mkes up for the disdvntges of the conventionl designs nd reduces the distnce between design progrm nd production prctice Published by Elsevier Ltd. Selection nd/or peer-review under responsibility of Hinn University. Open ccess under CC BY-NC-ND license. doi: /j.egypro

2 468 Yng Yunfn / Energy Procedi 17 ( 2012 ) The Development Sttus of Relibility Optimiztion Design of Mechnicl Products The relibility-bsed optimiztion design hs become n importnt brnch of optimiztion design. Used in the mechnicl prts - ger, ger reducer. Chin hs been the relibility-bsed optimiztion design of ger trnsmission nd the relibility-bsed optimiztion design of plnetry ger trnsmission, etc. In the relibility of communiction problem, rdr, nd other spects of the mchines hve been put forwrd in Chin in the 1960s. With the rpid economic development nd reform nd opening in the lte 1970s propulsion system relibility of key components of use nd civil items. After yers of efforts, the relibility of militry components hs two orders of mgnitude. In the 1980s, group of reserchers nd technicl bckbone of the relibility of the orgniztion, estblished in Chin, further implementtion of stte ministries of relibility engineering hs begun. In 1990, Chin's civil nd militry products with qulittive lep, mny civil electricl products, hs mde such relibility of the product qulity hs reched new high. In the pst 30 yers, optimiztion design method, the rpid development of mechnicl products, especilly in the development of the relibility design of mechnicl products, technology nd prcticl in engineering prctice of mechnicl products. People think tht the optiml design of mechnicl products relibility is more resonble bsis, becuse in trditionl mechnicl products thn by s whole, the performnce of rndomness, in the future work. Tht is to sy, some prmeters of the simultion of mechnicl products s rndom vribles, in structure optimiztion design bsed on relibility, the relibility requirements of integrtion of mechnicl products for optimiztion design of the constrint conditions, or into our trget function optimiztion design, nmely, in certin relibility index weight, reduce the cost of mechnicl products, or by djusting the prmeters of mechnicl products, or under certin conditions, the mximum weight nd cost of mechnicl products by djusting the prmeters, the relibility of the prts. The min requirements of mechnicl products re not only sfe, relible nd economicl rtionlity. Therefore, the optimiztion design of mechnicl products, cn significntly improve the design qulity nd economic benefit, the relibility design of mechnicl products hs become n importnt problem in the empiricl reserch nd explortion in the domestic nd foreign current. However, due to mechnicl product relibility nlysis is relted to lrge mounts of invlidtion forms nd other relevnt problems of filure modes, relibility more difficult, more nd more complex, therefore, the relibility design of mechnicl products is becoming more difficult. In ddition, the optiml solution lgorithm ws used to optimize the design, is lso discussed. Therefore, the current level of relibility nd optiml design of mechnicl products is still in the erly stges of development [1]. 3.The Advntges of High Relibility Mechnicl Products 3.1. Improve the Usge Rte of Product To improve the relibility of mechnicl products, reduce downtime nd mintennce personnel, improve product utiliztion. Modern mchinery products work environment become more severe, nd from the lnd, se nd provide hrsh environment spce chllenge, high relibility, high sfety nd the chrcteristics of the system, system integrtion nd other needs to continue for long time without forcing the system must hve good relibility. 3.2.Prevent the Occurrence of Accidents nd Filures To improve the relibility of mechnicl products, it cn prevent ccidents nd filure, especilly in order to void ctstrophic ccidents. The 1986 chllenger spce-shuttle is Americ's sel filure, fter tke-off, explosion 76 seconds. The economic loss cused by 120 million dollrs. Modern high-tech product, becuse its strict function.

3 Yng Yunfn / Energy Procedi 17 (2012 ) Obvious Technology nd Economic Benefits Mechnicl relibility nd optiml design is bsed on probbility theory nd optimiztion design method, the ppliction of prticiption mechnism design, strength, nd the design, mteril selection nd life filure nlysis, nd mny other design vribles nd prmeters, nd provide cler technology. And the economy nd relibility index lso exists, the objective function optimiztion model nd the chrcteristics of probbility nd nonliner, non-convex nonliner, need to meet ll kinds of rndom constrints. Mechnicl product design method, ccording to the work product cn not only ensure the relibility nd sfety of the product, the function, the weight, smll volume, cost nd other prmeters re optimized, technicl nd economic benefits hve been mrkedly improved. 4.Relibility Optimiztion Design of Mechnicl Products This puts forwrd the problem of relibility optimiztion design. Relibility optimiztion design minly considers the following questions: With optimum design, cn ccording to different design requirements, choose different chrcteristic function s the objective function. Design vribles. The overll size of the structure nd size of components nd mechnicl properties, etc, re the most common design vribles of mechnicl components, is needed to optimize nd finl independent prmeters optimized design process. In the determintion of design prmeters of the rndomness nd distribution prmeters should be regrded s reflect the ctul conditions of the prts. Constrint conditions. Constrint conditions cn be restrictions not only on structurl prmeters, but lso on function of prts, this need refer to the conventionl optiml design, ccording to the specific circumstnces to determine. In the meeting reduce the requirement of relibility, or in the meeting of the totl cost of cost, the vlue of size, weight nd other indictors, the mximum relibility. Therefore, the relibility design of mechnicl products cn be divided into two types of the mthemticl model of optimum relibility design. Relibility s the objective function. Relibility s constrint condition 5.The Design Fetures of Mechnicl Prts 5.1.Stress nd Strength Are Rndom Vribles Becuse the stress tht prts cn support nd mterils strength re not certin vlues but rndom vribles with discreteness, distribution function is tken into ccount in mthemtics. It s becuse lods, strength, dimension nd opertion hve the chrcteristics of lterntiveness nd sttisticl property [2], nd thus probbility nd sttistics theories re needed to nlyze nd solve the problem. 5.2.Quntittive Description of Products Filure Probbility nd Relibility Cn Be Done As is known, the designed products hve certin filure probbility, which cn not be bove the permissible vlue stted in the technicl documents. However, the relibility design cn provide products filure probbility nd relibility quntitively.

4 470 Yng Yunfn / Energy Procedi 17 ( 2012 ) Vrious Relibility Indexes Cn Be Chosen The trditionl design hs only one evlution index for relibility, nmely, sfety coefficient. By contrst, the relibility design provides vrious nd pproprite indexes ccording to the specific conditions for different products, such s filure probbility, relibility, non filure working time on verge, firstfilure driving miles(for vehicles), mintinbility, vilbility nd so on. 5.4.The Effect of Environment Is Tken into Considertion Owing to the gret influence on stress of the following surroundings fctors such s temperture, impct, quke, moisture, mist, erosion, dust, nd brsion, relibility is considerbly ffected consequently. And thus tking environment into considertion cn reflect prts ctul opertion better 6.The Relibility Design Priciples of Mechnicl Products Compred with electric products, mechnicl products hve their own chrcteristics nd wys of design nd nlysis. To sum up, the relibility design of mechnicl products should stick to the principles s follows [3, 4]: 6.1.Combintion of Relibility Design nd Trditionl Design The trditionl sfety coefficient method which is intuitive, simple nd esy to mster nd hs smll worklod cn ensure the relibility of mechnicl prts under most circumstnces. But t present it is very difficult to crry out trditionl relibility design of mechnicl products in specil cses. For this reson, it seems resonble nd necessry to improve nd perfect the trditionl method with the help of probbility design. Moreover, the relibility probbility design imed to crucil prts cn be grdully performed 6.2.Integrtion of Qulity nd Quntity Design Quntity design refers to the quntity nlysis nd clcultion of relibility, but it cn not solve ll the problems concerned with relibility. Wht s more, t some times, it is inpproprite nd even impossible for relibility to expound quntitively. And thereby the relibility requires the integrtion of the qulity nd quntity. As for the prts which hve the qulity requirements nd re difficult to mke quntity clcultion, it is more resonble nd effective to conduct qulity design. Prctice hs proved tht the qulity design plys n importnt role in ssuring nd improving the relibility of mechnicl products. And thus during the process of relibility design, qulity nd quntity design should be integrted Prlleling of Mechnicl Relibility nd Durbility In brod sense, the relibility of mechnicl products includes relibility nd durbility. Therefore, mechnicl relibility design ccordingly comprises the two mentioned bove. Specificlly speking, relibility design is specific to occsionl fults, while durbility is specific to grdul fults, nd their fult mechnism re different. 6.4.Prlleling of System nd Prts Relibility Given tht mechnicl prts re of lower stndriztion nd universlity degree nd hve complex functionl sttus nd structure, the designers hve to mke comprehensive design of system nd prts. The prts strength is bsic gurntee of systemtic relibility nd prts re the most bsic unit of the whole system. In this cse, prts design should dd relibility design to the trditionl one. The im of systemtic

5 Yng Yunfn / Energy Procedi 17 (2012 ) relibility design is to chieve the coordintion nd optimiztion of technicl performnce, weight index, mnufcturing cost nd service life of the system, providing tht the system hs stisfied the estblished relibility index nd relized predetermined functions. 7.The Alliction of Relibility Design in Mine Hoist The key to the relibility design in mine hoist is how to chnge equipments t present nd prmeters concerned (for instnce the prts dimension, strength nd loding) into sttistics through experimentl dt nd finlly conclude its distribution. Furthermore, the relibility, dimension nd life service cn lso be clculted one fter one. The decelertor nd spindle structure in the hoist re equipped with rolling bering, whose life spn hs vitl impct on the opertion relibility of the hoist. Now tht the cycle times of rolling bering during the lese of life cn rech up to nd even exceed the cycle bse of mteril ftigue limit (bout 10 7 ). It is common to dopt limited life design in order to rtionlize the whole structure, reduce its dimension nd weight, nd t lst mke the best of mterils nd improve the bering cpcity of prts. On the condition tht cycles is10 6 nd relibility is 90%(nmely, with the help of equl lod of dynmic lod rting C, the rolling bering cn run 10 6 runs, nd in the menwhile 90% of the bering does not suffer from ftigue pitting filure [5] )the design nd choice of bering cpcity is executed. On the bsis of the previous nlysis, the relibility design of rolling bering in spindle structure is to be mde. The rolling bering stnds vice-vrying stress. The filure in the course of opertion results from the regulr chnges of the stress. Becuse of the long-term effect of the stress, the surfce metls fll down from both rolling body nd inner nd outer rcewys. Ftigue pitting comes into being nd lso leds to ftigue filure. It is proved tht the life spn of the originl nd device or equipments, of ll whose functions hve filed due to prtil ftigue filure or fult, is in line with Weibull distribution. So is tht of rolling bering. The filure probbility F cn be described s: In the bove, N F( N) 1 exp ( ) m N 6 N stnds for chrcteristic life; N for cycles, with 10 s the unit; m for the prmeter. Relibility cn be formulted s: After logrithm opertion on both sides: N m RN ( ) 1 FN ( ) exp[ ( ) ] (2) N N N R N (3) 1/ [ ln ( )] m Bsed upon the preceding nlysis, the rted life of rolling bering is L 10 (tht is, the filure probbility is 10%) when the relibility is 90%. Thus the rted life is L10 N0 N [ ln R(90)] N [ ln 0.9] (4) 1/ m 1/ m In the bove, N90 refers to the cycles when the relibility is 90%. (1)

6 472 Yng Yunfn / Energy Procedi 17 ( 2012 ) Divide (3) by (4), the result becomes: N ln RN ( ) ln 0.9 1/ m L10[ ] (5) Lrge quntities of sttistics indicte: the bll bering: 10 m the roller bering: 3 m the roller 9 2 bering of the cone: 4 m 3 For exmple, there is friction hoist JKD in mine. The life of its min bering (Model 3676) with 90% relibility is 1,000,000 rpm. And then the bering life with 93% relibility is: ln /4 N L10[( ) ] 756,000rpm ln Conclusion Through the study on mechnicl relibility design nd combintion with the structure of mine hoist, it is proposed tht the crucil procedure of relibility design s ppliction into mine hoist is s follows. The first is to scertin the sttistics of the relevnt prmeters, then to set up the filure mthemticl model, nd finlly the relibility design cn be operted. Besides, the rolling bering of mine hoist is regrded s the object of this study, menwhile bering s ftigue life s sttistics, from which the rule tht bering s life ccords with Weibull distribution is lerned. Next, bsed on the result tht the rted life of rooling bering is L 10 (tht is cycle) when the relibility is 90%, the bering s life (cycle) is clculted ccording to the given relibility. In word, it is extremely meningful for the improvement of hoist s relibility when the theoreticl knowledge bout mechnicl relibility design is pplied into the design of mine hoist prts. References [1] Zhng Xioqin, Mo Ci Song. Relibility Design Anlysis of Mechnicl Components [J] Journl of Moming College, [2] Liu Weixin. Relibility Design of Mchines.[M] Beijing: Tsinghu University Press, 1996 [3] Sun Wei, Go Linhu, Yo Xinmin et l. The Reserch on Relibility Design Methods of Mchine Products[J]. Mchinery Industry Stndrdiztion &Qulity, [4] Xing Yizhou, Chen Ge, Ding Liyu. The Relibility Design nd Tril of Mchine Product[J] Journl of Southwest Chin Norml University, [5] Ge Shirong. The Relibility Technology of Mine hoists[m].xuzhou: Chin University of Mining & Technology Press, 1994.

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Shanghai University of Electric Power (SUEP) Shnghi University of Electric Power (SUEP) Shnghi University of Electric Power, founded in 1951, is full-time institution of higher eduction, co-run by the centrl government nd Shnghi Municiplity, nd mnged