等几何法在雷诺方程中的应用
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摘要
针对有限元法和有限差分法求解雷诺方程精度和效率不高等问题,采用等几何法对雷诺方程进行了求解。建立了雷诺方程的等几何计算模型,给出了等几何求解流程和方法,在MATLAB中开发了等几何计算程序。数值算例求解得出油膜压力图以及不同阶次下压力积分相对误差图,分析了不同自由度和基函数阶次对求解结果的影响。结果表明:采用等几何法求解,大幅减少了表达油膜压力所需的自由度,求解精度和效率相对于有限元法显著提升,同时验证了求解过程中算法的稳定性和求解结果的正确性。
For the problem that solving Reynolds equation with the finite element method and finite difference method is of low accuracy and efficiency,the isogeometric method was used to solve the Reynolds equation. The isogeometric calculation model of Reynolds equation was established,the solving process and method were given,and the calculation procedure was developed in MATLAB.The numerical example gave the oil film pressure diagram and relative error diagrams of pressure integration under different degrees,analyzed the influence of different degrees of freedom and degrees of basis function on the solving results. The result showed that the using of isogeometric method significantly reduced the required degree of freedom to express the oil film pressure;the accuracy and efficiency,compared with the finite element method,significantly improved;at the same time,the stability of algorithm and correctness of the solving results were verified in the solving process.
For the problem that solving Reynolds equation with the finite element method and finite difference method is of low accuracy and efficiency,the isogeometric method was used to solve the Reynolds equation. The isogeometric calculation model of Reynolds equation was established,the solving process and method were given,and the calculation procedure was developed in MATLAB.The numerical example gave the oil film pressure diagram and relative error diagrams of pressure integration under different degrees,analyzed the influence of different degrees of freedom and degrees of basis function on the solving results. The result showed that the using of isogeometric method significantly reduced the required degree of freedom to express the oil film pressure;the accuracy and efficiency,compared with the finite element method,significantly improved;at the same time,the stability of algorithm and correctness of the solving results were verified in the solving process.
引文
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[2]喻丽华,谢庆生,李少波.钻削电主轴空气静压径向轴承润滑参数优化[J].机械设计与制造,2014(8):124-126.(Yu Li-hua,Xie Qing-sheng,Li Shao-bo.Optimization on the aerostatic journal bearing lubrication parameters for drill electric spindle[J].Machinery Design&Manufacture,2014(8):124-126.)
[3]魏思远,庞晓平,牛坤.具有通用膜厚方程径向轴承的动力学研究[J].机械设计,2014(7):59-64.(Wei Si-yuan,Pang Xiao-ping,Niu Kun.Study on hydrodynamic journal bearings based on general film thickness equation[J].Journal of Machine Design,2014(7):59-64.)
[4]Wannatong K,Chanchaona S,Sanitjai S.Simulation algorithm for piston ring dynamics[J].Simulation Modelling Practice and Theory,2008,16(1):127-146.
[5]Hughes T J R,Cottrell J A,Bazilevs Y.Isogeometric analysis:CAD,finite elements,NURBS,exact geometry and mesh refinement[J].Computer Methods in Applied Mechanics and Engineering,2005,194(39):4135-4195.
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[7]Patir N,Cheng H S.An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication[J].Journal of Lubrication Technology,1978,100(1):12-17.
[8]Patir N,Cheng H S.Application of Average Flow Model to Lubrication between Rough Sliding Surfaces[M].ASME,Lubrication Division,1978.
[9]张明喜,左兵权,黄正东.缸套-活塞系统中DAE与PDE联合求解方法[J].计算机应用与软件,2015,32(12):160-164.(Zhang Ming-xi,Zuo Bing-quan,Huang Zheng-dong.A combined solution for DAE and PDE of cylinder-piston system[J].Computer Application and Software,2015,32(12):160-164.)
[10]李建鸿,樊文欣,王跃.凹槽型织构化径向轴承的润滑性能[J].润滑与密封,2016,41(5):82-85.(Li Jian-hong,Fan Wen-xin,Wang Yue.Lubrication characteristics of groove surface textured journal bearing[J].Lubrication Engineering,2016(5):82-85.)