含非线性大变形构件的柔顺机构建模与分析
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摘要
柔顺机构的大范围运动引起柔性构件产生几何非线性大变形,使得机构的建模与分析变得困难。分别采用椭圆积分法和绝对节点坐标法(ANCF)建立柔顺机构的力学模型,获得了机构运动过程中柔性构件的变形和驱动力的变化规律。以一种固定—导向柔顺梁为例,仿真与实验结果验证了以上方法的有效性;以一种柔顺双稳态机构为例,仿真结果验证了ANCF法对复杂柔顺机构动力学特性分析的有效性;通过以上两种方法的建模与分析过程对比,ANCF法对柔顺机构建模与分析更具有适应性。
Geometrical nonlinear large deformations of flexible components caused by large scale motion of compliant mechanisms make it be difficult to model and analyze a compliant mechanism. Here, basic principles of the elliptic integral method(EIM) and the absolute nodal coordinate formulation(ANCF) were introduced, and two mechanical models of a compliant mechanism were established using EIM and ANCF, respectively to get variation laws of deformation and driving force of flexible components in motion process of the compliant mechanism. A fix-guided compliant mechanism was taken as an example, its simulation and test results verified the effectiveness of the above two methods. A dual-stable state compliant mechanism was taken as an example, and its simulation results verified the effectiveness of ANCF for dynamic characteristics analysis of complex compliant mechanisms. Through comparing modeling and analysis processes of the above two methods, it was shown that ANCF is more suitable for modeling and analysis of compliant mechanisms.
Geometrical nonlinear large deformations of flexible components caused by large scale motion of compliant mechanisms make it be difficult to model and analyze a compliant mechanism. Here, basic principles of the elliptic integral method(EIM) and the absolute nodal coordinate formulation(ANCF) were introduced, and two mechanical models of a compliant mechanism were established using EIM and ANCF, respectively to get variation laws of deformation and driving force of flexible components in motion process of the compliant mechanism. A fix-guided compliant mechanism was taken as an example, its simulation and test results verified the effectiveness of the above two methods. A dual-stable state compliant mechanism was taken as an example, and its simulation results verified the effectiveness of ANCF for dynamic characteristics analysis of complex compliant mechanisms. Through comparing modeling and analysis processes of the above two methods, it was shown that ANCF is more suitable for modeling and analysis of compliant mechanisms.
引文
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[10] 张爱梅.平面梁大挠度非线性问题的完备解与柔顺机构精确建模[D].西安:西安电子科技大学,2013:45-55.
[11] SHABANA A A,YAKOUB R Y.Three dimensional absolute nodal coordinate formulation for beam elements:theory[J].ASME Journal of Mechanical Design,2001,123:606-613.
[12] YAKOUB R Y,SHABANA A A.Three dimensional absolute nodal coordinate formulation for beam elements implementation and applications[J].ASME Journal of Mechanical Design,2001,123:614-621.
[13] OMAR M A,SHABANA A A.A two-dimensional shear deformable beam for large rotation and deformation problems[J].Journal of Sound and Vibration,2001,243(3):565-576.
[14] LIU Cheng,TIAN Qiang,HU Haiyan,et al.Simple formulations of imposing moments and evaluating joint reaction forces or rigid-flexible multibody systems[J].Nonlinear Dynamics,2012,69:127-147.
[15] SOPANEN J T,MIKKOLA A M.Description of elastic forces in absolute nodal coordinate formulation[J].Nonlinear Dynamics,2003,34:53-74.
[2] 张连杰,刘善增,朱真才.柔顺机构的研究进展[J].组合机床与自动化加工技术,2011(7):108-112.ZHANG Lianjie,LIU Shanzeng,ZHU Zhencai.Recent development of compliant mechanism[J].Journal of Modular Machine Tool & Automatic Manufacturing Technique,2011(7):108-112.
[3] 于靖军,郝广波,陈贵敏.柔性机构及其研究进展[J].机械工程学报,2015,51(13):53-68.YU Jingjun,HAO Guangbo,CHEN Guimin.State-of-art of Compliant Mechanisms and Their Applications[J].Journal of Mechanical Engineering,2015,51(13):53-68.
[4] HOWELL L L,MIDHA A.Parametric deflection approximations for end loaded large deflection beams in compliant mechanisms[J].ASME Tranaction Mechanical Design,1995,117(3):156-165.
[5] 王华伟,余跃庆,苏丽颖,等.柔顺机构动力学建模新方法[J].机械工程学报,2008,44(10):96-103.WANG Huawei,YU Yueqing,SU Liying,et al.New method for the dynamic modeling of compliant mechanism[J].Journal of Mechanical Engineering,2008,44(10):96-103.
[6] ZHANG Aimei,CHEN Guimin.A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms[J].Jourmal of Mechanisms and Robotics,2013(5):021006-1-10.
[7] HOLST G L,TEICHERT G H,JENSEN B D.Modeling and experiments of buckling modes and deflection of fixed-guided beams in compliant mechanisms[J].Journal of Mechanical Design,2001,133:051002-1-10.
[8] 王雯静,余跃庆.基于有限元法的柔顺机构动力学分析[J].机械工程学报,2010,46(9):79-86.WANG Wenjing,YU Yueqing.Dynamic analysis of compliant mechanisms based on finite element method[J].Journal of Mechanical Engineering,2010,46(9):79-86.
[9] BERZERI M,CAMPANELLI M,SHABANA A A.Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation[J].Multibody System Dynamics,2001(5):21-54.
[10] 张爱梅.平面梁大挠度非线性问题的完备解与柔顺机构精确建模[D].西安:西安电子科技大学,2013:45-55.
[11] SHABANA A A,YAKOUB R Y.Three dimensional absolute nodal coordinate formulation for beam elements:theory[J].ASME Journal of Mechanical Design,2001,123:606-613.
[12] YAKOUB R Y,SHABANA A A.Three dimensional absolute nodal coordinate formulation for beam elements implementation and applications[J].ASME Journal of Mechanical Design,2001,123:614-621.
[13] OMAR M A,SHABANA A A.A two-dimensional shear deformable beam for large rotation and deformation problems[J].Journal of Sound and Vibration,2001,243(3):565-576.
[14] LIU Cheng,TIAN Qiang,HU Haiyan,et al.Simple formulations of imposing moments and evaluating joint reaction forces or rigid-flexible multibody systems[J].Nonlinear Dynamics,2012,69:127-147.
[15] SOPANEN J T,MIKKOLA A M.Description of elastic forces in absolute nodal coordinate formulation[J].Nonlinear Dynamics,2003,34:53-74.