考虑不同边界条件悬臂梁的模态研究

发布时间：2018-03-26 20:21

本文选题：柔性机械臂　切入点：悬臂梁模型　出处：《振动与冲击》2017年19期

【摘要】：为了提高假设模态法建立动力学模型的精确性,研究了将柔性机械臂简化为更精确的悬臂梁模型的问题。通过分析不同边界条件对Euler-Bernoulli悬臂梁横向振动的影响规律,将悬臂梁自由端的剪力边界条件具体化为集中质量和拉伸弹簧,弯矩边界条件具体化为扭转弹簧和转动惯性元件,得到了各种边界条件下悬臂梁的模态频率和模态振型的变化规律。结果表明添加边界条件的悬臂梁模型可以更好地表示柔性机械臂的模态振动,因此可以提高假设模态法建立的动力学模型的精确性。针对柔性机械臂之间模态振动耦合较强,添加边界条件无法表示柔性机械臂模态频率的变化规律,提出了修正当量密度的方法。最后给出了边界条件和修正当量密度的迭代计算方法,并用ANSYS和ADAMS联合仿真分析了由驱动关节和自由关节连接的二连杆柔性机械臂模型对应的模态振动,验证了计算方法的正确性。
[Abstract]:In order to improve the accuracy of the dynamic model established by the hypothetical modal method, the problem of simplifying the flexible manipulator into a more accurate cantilever model is studied. The influence of different boundary conditions on the transverse vibration of the Euler-Bernoulli cantilever beam is analyzed. The shear boundary conditions at the free end of the cantilever beam are concretely converted into concentrated mass and tension springs, and the moment boundary conditions are concretely transformed into torsional springs and rotational inertia elements. The modal frequencies and modal modes of the cantilever beam are obtained under various boundary conditions. The results show that the cantilever model with boundary conditions can better represent the modal vibration of the flexible manipulator. Therefore, the accuracy of the dynamic model established by the hypothetical modal method can be improved. In view of the strong coupling of modal vibration between flexible manipulators, the addition of boundary conditions cannot represent the variation of modal frequencies of flexible manipulators. The method of modifying equivalent density is presented. Finally, the boundary conditions and iterative calculation method of modified equivalent density are given. The modal vibration corresponding to the two-link flexible manipulator model connected by the driving joint and the free joint is simulated by ANSYS and ADAMS, and the correctness of the calculation method is verified.
【作者单位】：山东理工大学机械工程学院;
【基金】：国家自然科学基金(61303006) 山东省优秀中青年科学家科研奖励基金项目(BS2012ZZ009)
【分类号】：TH165

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