In order to improve the accuracy of the dynamic model of a flexible manipulator,deduced by the assumed mode method,the manipulator was simplified as a cantilever beam.By analyzing the influences of different boundary conditions on the lateral vibration of the Euler-Bernoulli cantilever beam,the shear boundary condition at the cantilever free end was specified as a specific mass and a tensile spring,and the bending moment boundary conditions were specified as specific torsion springs and rotational inertia components.The modal frequencies and vibration modes of the cantilever beam under various boundary conditions were calculated.The results show that the cantilever beam model attached with the specified boundary conditions can better describe the vibration of the flexible manipulator,and improve the accuracy of the dynamic model deduced by the assumed modal method.Considering the strong coupling between the modes of the flexible manipulator the method of equivalent density correction was further put forward.Finally,the iterative calculation method for taking into account the specified boundary conditions and the modified equivalent density was proposed.The ANSYS and Adams were used combinedly to simulate and analyse the vibration modes of a flexible manipulater with two links connected by driving joints and free joints,and the correctness of the calculation method was thus verified by the results.%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.
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