空气弹簧多变过程的有限元模拟
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摘要
由于当前的有限元软件无法计算空气多变过程,导致空气弹簧垂向刚度预测偏差较大。为了解决这个问题,该文提出了空气弹簧多变过程有限元模拟的解决方案。基于虚功原理,推导了充气结构的有限元方程;基于理想气体状态方程,通过引入多变指数得到多变过程的气体弹性常数,并使用ABAQUS软件的用户自定义单元二次开发程序接口UEL开发了多变空气单元。通过与实验对比,发现该文提出的多变空气单元可以精确预测空气弹簧在不同频率、不同载荷和不同附加气室情况下的垂向刚度,从而验证了该文方法的有效性。
The vertical stiffness of an air spring cannot be accurately predicted, because the existing finite element software cannot calculate the polytropic process of air. A solution for simulating the polytropic process of air springs was proposed in order to solve this problem. The finite element formulation was deduced based on virtual work, and the elasticity of air was deduced by introducing the polytropic index based on an ideal gas status equation. A pneumatic element was developed based on the user-defined element UEL, which is provided by ABAQUS software. Compared with the experimental results, we find the proposed method predicts the vertical stiffness of an air spring very precise under different frequencies, loads and additional reservoir volumes, which validates the proposed method.
The vertical stiffness of an air spring cannot be accurately predicted, because the existing finite element software cannot calculate the polytropic process of air. A solution for simulating the polytropic process of air springs was proposed in order to solve this problem. The finite element formulation was deduced based on virtual work, and the elasticity of air was deduced by introducing the polytropic index based on an ideal gas status equation. A pneumatic element was developed based on the user-defined element UEL, which is provided by ABAQUS software. Compared with the experimental results, we find the proposed method predicts the vertical stiffness of an air spring very precise under different frequencies, loads and additional reservoir volumes, which validates the proposed method.
引文
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[13]Wei Y T,Kaliske M,Huang Y J.Advanced mechanics of tire and rubber products,proceedings of 1st Tsinghua Tire Mechanics Workshop[M].Beijing:Tsinghua University Press,2013:195-238.
[14]Li X B,Wei Y T,He Y.Simulation on polytropic process of air springs[J].Engineering Computations,2016,33(7):1957-1968.
[15]朱明善.工程热力学[M].北京:清华大学出版社,1995:10-41.Zhu Mingshan.Engineering thermodynamics[M].Beijing:Tsinghua University Press,1995:10-41.(in Chinese)
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[2]Kunieda M.Foundation of air spring[J].Machine Design,1962,6(8):12-17.
[3]郭荣生.空气弹簧悬挂的设计与计算[M].青岛:交通部四方车辆研究所,1973:50―61.Guo Rongsheng.Design and calculation of air spring suspension[M].Qingdao:Sifang Rolling Stock Research Institute,The Ministry of Communications,1973:50―61.(in Chinese)
[4]Qing O,Yin S.The non-linear mechanical properties of an air spring[J].Mechanical Systems and Signal Processing,2003,17(3):705-711.
[5]Prasil L,Kracik V.Frydrych,D.Shape modeling of air bellows springs[J].Vysoke Tatry,Podbanske:Proceedings of Algorithm,2005:142-149.
[6]Li X,Li T.Research on vertical stiffness of belted air springs[J].Vehicle System Dynamics,2013,51(11):1655-1673.
[7]Li X B,He Y,Liu W Q,et al.Research on vertical stiffness of rolling lobe air spring[J].Journal of Rail and Rapid Transit,2015,230(4):1172-1183.
[8]Berry D T,Yang H T Y.Formulation and experimental verification of pneumatic and hydraulic finite elements[J].International Journal for Numerical Methods in Engineering,1996,39(7):1097-1114.
[9]Oman S,Nagode M.On the influence of the cord angle on air-spring fatigue life[J].Engineering Failure Analysis,2013,27(1):61-73.
[10]Dijk R,Keulen F,Sterk J C.Simulation of closed thin-walled structures partially filled with fluid[J].International Journal of Solids and Structures,2000,37(42):6063-6083.
[11]Sun J.Calculation of vertical stiffness of air spring with FEM[C]//Greece:4th ANSA&μETA International Conference,Thessaloniki,Greece:BETA CAE System USA,Inc,2011.
[12]Liu Z H,Li F,Huang Y H.Finite element analysis of vertical stiffness of air spring system[J].Journal of Southwest Jiaotong University,2006,41(6):700-704.
[13]Wei Y T,Kaliske M,Huang Y J.Advanced mechanics of tire and rubber products,proceedings of 1st Tsinghua Tire Mechanics Workshop[M].Beijing:Tsinghua University Press,2013:195-238.
[14]Li X B,Wei Y T,He Y.Simulation on polytropic process of air springs[J].Engineering Computations,2016,33(7):1957-1968.
[15]朱明善.工程热力学[M].北京:清华大学出版社,1995:10-41.Zhu Mingshan.Engineering thermodynamics[M].Beijing:Tsinghua University Press,1995:10-41.(in Chinese)
[16]Systèmes D.Abaqus theory manual[CP].Dessault Systémes,Providence,RI,2007,1.1.27-1-1.1.27-19.