多项式函数结合对数螺旋线方程的织构型线优化
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摘要
目的为提高一种新型动静压转台承载能力,对其动压楔形织构型线进行优化设计。方法首先求解动压楔形织构承载性能,并将其承载能力作为优化目标。以多项式函数结合对数螺旋线方程表达织构型线,并以多项式系数作为设计变量建立优化模型。选用布谷鸟搜索算法求解该优化模型,并探究不同结构参数下的最优解变化规律。最后,比较本方法得到的最优织构和最优单一螺旋角织构的润滑性能。结果综合考虑计算精度和时间,选取半径的二次多项式函数表达织构型线螺旋角。最优织构型线形状的变化规律为:随半径增大,先顺时针弯折,再逆时针弯折,其螺旋角先增大,再减小。摩擦副膜厚越大,最优型线顺时针弯折趋势越明显,最小螺旋角和终止螺旋角越小,最大动压承载力越小。织构个数越多,型线上各点螺旋角越小,最大动压承载力越大。结论该优化设计方法突破了规则几何形状的限制,并在表达更多可能织构型线的基础上减少了设计变量个数。相比最优单一螺旋角织构,该最优型线下的织构有更优良的润滑性能,证明了该设计方案的应用价值。
The work aims to optimize and design the hydrodynamic texture outline of novel hybrid rotary table to improve its load-carrying capacity. Firstly, the load-carrying property of the texture was calculated and the load-carrying capacity(LCC) was set as the objective function. The texture outline was expressed for logarithmic spiral equation based on polynomial function and the coefficients of the polynomial function were determined as design variables to set up the optimization model. Cuckoo Search was applied to solve the optimization model and the law of the optimal solution under various structural parameters was discussed. Finally, lubrication performance of textures with optimal outline and optimal spiral angle was compared. In consideration of computational accuracy and time, quadratic polynomial function of radius was selected as spiral angle. Optimal texture outline bended clockwise and then anticlockwise with the increase of radius, and the spiral angle increased and then declined. With the increasing film thickness, the clockwise bending tendency was more obvious, the minimal angle and fi-nal angle were smaller and the maximal hydrodynamic LCC(HLCC) was smaller. With the increasing number of textures, spiral angle on each point of the outline was smaller while the maximal HLCC was larger. The optimization and design method breaks through the limitation of regular shapes and reduces the number of design variable on the basis of more texture outlines further. Compared with the optimal texture of single spiral angle, the texture under the optimal outline has more lubrication performance and verifies the application value of the design scheme.
The work aims to optimize and design the hydrodynamic texture outline of novel hybrid rotary table to improve its load-carrying capacity. Firstly, the load-carrying property of the texture was calculated and the load-carrying capacity(LCC) was set as the objective function. The texture outline was expressed for logarithmic spiral equation based on polynomial function and the coefficients of the polynomial function were determined as design variables to set up the optimization model. Cuckoo Search was applied to solve the optimization model and the law of the optimal solution under various structural parameters was discussed. Finally, lubrication performance of textures with optimal outline and optimal spiral angle was compared. In consideration of computational accuracy and time, quadratic polynomial function of radius was selected as spiral angle. Optimal texture outline bended clockwise and then anticlockwise with the increase of radius, and the spiral angle increased and then declined. With the increasing film thickness, the clockwise bending tendency was more obvious, the minimal angle and fi-nal angle were smaller and the maximal hydrodynamic LCC(HLCC) was smaller. With the increasing number of textures, spiral angle on each point of the outline was smaller while the maximal HLCC was larger. The optimization and design method breaks through the limitation of regular shapes and reduces the number of design variable on the basis of more texture outlines further. Compared with the optimal texture of single spiral angle, the texture under the optimal outline has more lubrication performance and verifies the application value of the design scheme.
引文
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[20]马艺元,宋卫平,宁爱平,等.混沌云模型多目标布谷鸟搜索算法[J].计算机应用, 2017, 37(4):1088-1092.MAYi-yuan,SONGWei-ping,NINGAi-ping,etal.Cuckoo search algorithm for multi-objective optimization basedonchaoscloudmodel[J].Journalofcomputer applications, 2017, 37(4):1088-1092.
[21]吴国芳.云环境中基于布谷鸟搜索算法的度目标任务调度方案[J].计算机应用研究, 2015, 32(9):2674-2677.WUGuo-fang.Multi-objectivetaskschedulingscheme basedoncuckoosearchalgorithmincloudenvironment[J].Applicationresearchofcomputers,2015,32(9):2674-2677.
[22]陈淑江.螺旋油楔滑动轴承润滑机理的理论与实验研究[D].济南:山东大学, 2007.CHENShu-jiang.Theoreticalandexperimentalstudyon lubrication mechanism of a spiral oil wedge journal bearing[D]. Jinan:Shandong University, 2007.
[2]NARENDRA S, SATISH C S, JAIN S C, et al. Performanceofmembranecompensatedmultirecesshydrostatic/hybridflexiblejournalbearingsystemconsidering variousrecessshapes[J].Tribologyinternational,2004,37:11-24.
[3]张艳芹,陈瑶,范立国,等.四种油腔形状重型静压轴承承载性能理论分析[J].哈尔滨理工大学学报,2013,18(2):68-71.ZHANGYan-qin,CHENYao,FANLi-guo,etal.Theoreticalanalysisofbearingperformanceoffourshapesof recessinheavyhydrostaticbearing[J].JournalofHarbin University of Science and Technology, 2013, 18(2):68-71.
[4]GENFu,ALEXANDRINAU.Anoptimumdesignapproachfortexturedthrustbearingwithelliptical-shape dimplesusingCFDandDOEincludingcavitation[J].Journalofengineeringforgasturbines&power,2016,139(9):092502.
[5]叶红玲,文聘,张颜明,等.基于多层可行方向法液体静压转台优化设计[J].工程力学, 2014, 31(2):249-256.YEHong-ling,WENPin,ZHANGYan-ming,etal.De-signoptimizationofhydrostaticworktablebasedon multi-layermethodoffeasibledirection[J].Engineering mechanics, 2014, 31(2):249-256.
[6]孟曙光,熊万里,王少力,等.有限体积法和正交试验法相结合的动静压轴承结构优化设计[J].中国机械工程, 2016, 27(9):1234-1242.MENG Shu-guang, XIONG Wan-li, WANG Shao-li, et al.Structureoptimizationdesignofhydrostatic-dynamic journalcombinedfinitevolumemethodwithorthogonal experimentaldesignmethod[J].Chinamechanicalengineering, 2016, 27(9):1234-1242.
[7]HASHIMOTOH,OCHIAIM.Optimizationofgroove geometry for thrust air bearing to maximize bearing stiffness[J]. Tribology, 2008, 130(3):031101-1.
[8]FESANGHARY M, KHONSARI M M. On the optimum groove shapes for load-carrying capacity enhancement in parallelflatsurfacebearings:Theoryandexperiment[J].Tribology international, 2013, 67(4):254-262.
[9]庞晓平,陈进,王家序.采用通用膜厚方程的动压径向轴承形状优化[J].西安交通大学学报,2009,43(1):57-61.PANG Xiao-ping, CHEN Jin, WANG Jia-xu. Shape optimizationforhydrodynamicjournalbearingsbasedon generalfilmthicknessequation[J].JournalofXi?an Jiaotong University, 2009, 43(1):57-61.
[10]BONNEAUD,HUITRICJ,TOURNERIEB.Finiteelement analysis of grooved gas thrust bearings and grooved gasfaceseals[J].ASMEjournaloftribology,1993,115:348-354.
[11]ZHUQ,ZHANGWJ.Anumericalprocedurebasedon theboundaryelementmethodanalysisoftheArchimedeanspiralgroovedthrustoilbearing[J].ASMEjournal of tribology, 2000, 122(3):565-572.
[12]郝木明,庄媛,章大海,等.考虑空化效应的螺旋槽油膜密封特性数值研究[J].中国石油大学学报,2015,39(3):132-137.HAOMu-ming,ZHUANGYuan,ZHANGDa-hai,etal.Numerical study on sealing performance of spiral groove liquidfilmseal consideringeffectsof cavitation[J].JournalofChinaUniversityofPetroleum,2015,39(3):132-137.
[13]陈源,彭旭东,李纪云,等.螺旋槽结构参数对干气密封动态特性的影响研究[J].摩擦学学报,2016,36(4):397-405.CHEN Yuan, PENG Xu-dong, LI Ji-yun, et al. The influence of structure parameters of spiral groove on dynamic characteristicsofdrygasseal[J].Tribology,2016,36(4):397-405.
[14]YANGXin-she,SUASHDE.Cuckoosearchvialévy flights[C]//Worldcongressonnature&biologicallyinspired computing. USA:IEEE Publications, 2009:210-214.
[15]张永芳,刘成,李莎,等.基于混合遗传算法的径向滑动轴承表面织构优化[J].交通运输工程学报,2017,17(3):90-98.ZHANGYong-fang,LIUCheng,LISha,etal.Surface textureoptimizationofjournalbearingbasedonhybrid geneticalgorithm[J].Journaloftrafficandtransportation engineering, 2017, 17(3):90-98.
[16]ZHANG Hui, HUA Meng, DONG Guo-zhong, et al. OptimizationoftextureshapebasedonGeneticAlgorithm underunidirectionalsliding[J].Tribologyinternational,2017, 115:222-232.
[17]GANDOMI A H, YANG X S, ALAVI A H. Cuckoo search algorithm:Ametaheuristicapproachtosolvestructural optimizationproblems[J].Engineeringwithcomputers,2013, 29(1):17-35.
[18]CIVICIOGLUP,BESDOKE.Aconceptualcomparison oftheCuckoo-search,particleswarmoptimization,differential evolution and artificial bee colony algorithms[J].Artificial intelligence review, 2013, 39(4):315-346.
[19]YANG Xin-she, DED S. Cuckoo search:Recent advances andapplications[J].Neuralcomputing&applications,2014, 24(1):169-174.
[20]马艺元,宋卫平,宁爱平,等.混沌云模型多目标布谷鸟搜索算法[J].计算机应用, 2017, 37(4):1088-1092.MAYi-yuan,SONGWei-ping,NINGAi-ping,etal.Cuckoo search algorithm for multi-objective optimization basedonchaoscloudmodel[J].Journalofcomputer applications, 2017, 37(4):1088-1092.
[21]吴国芳.云环境中基于布谷鸟搜索算法的度目标任务调度方案[J].计算机应用研究, 2015, 32(9):2674-2677.WUGuo-fang.Multi-objectivetaskschedulingscheme basedoncuckoosearchalgorithmincloudenvironment[J].Applicationresearchofcomputers,2015,32(9):2674-2677.
[22]陈淑江.螺旋油楔滑动轴承润滑机理的理论与实验研究[D].济南:山东大学, 2007.CHENShu-jiang.Theoreticalandexperimentalstudyon lubrication mechanism of a spiral oil wedge journal bearing[D]. Jinan:Shandong University, 2007.