谐波齿轮负载侧隙和啮合力分布规律研究
Research on Distribution of Loading Backlash and Meshing Force of Harmonic Drive

为更真实地反映负载工况下谐波齿轮的啮合特性,提出了一种基于空载侧隙和周向线性啮合刚度的理论迭代算法,用于计算随负载变化的负载侧隙和啮合力分布。利用精确算法计算了装配状态下的空载侧隙;建立了三维实体单元的柔轮有限元模型,在柔轮齿上逐一施加啮合力,利用接触分析求解了双圆盘波发生器作用下反映柔轮齿廓啮合点周向刚度特性的啮合刚度矩阵;根据装配状态下的空载侧隙,迭代计算了在逐步增大的刚轮转动位移下的负载侧隙、啮合力及负载扭矩。由于理论算法无法考虑啮合刚度的非线性影响,为验证本文算法,利用有限元非线性接触分析方法,通过定义齿廓间的接触关系,数值求解了负载侧隙和啮合力。对比研究表明:在额定工况下,理论算法给出的啮合力分布与有限元分析结果基本吻合,但当负载较大时,理论算法的啮合刚度偏大,造成啮合力幅值偏高。
To investigate the meshing behavior of harmonic drives under transmission load, an iterative algorithm to calculate the distribution of meshing forces and loading backlashes under varied transmission torques is presented based on linear circumferential meshing stiffness and initial backlash. The initial backlash is calculated in assembly state with an exact algorithm. A 3D finite element model of the flexspline with solid elements is built under the action of a two？？disk wave generator, and the meshing stiffness matrix which reflects the circumferential stiffness characteristics of the engaged point on flexspline tooth is calculated by contact analysis under the meshing forces applied on each meshing point. The meshing forces, loading backlashes and transmission torques at gradually increased rotational displacements are iteratively calculated according to the initial backlash in assembly state. Because the effect of non？？linear meshing stiffness is neglected in the theoretical method, the contact relationship between tooth profiles is defined with non？？linear contact analysis of finite element method. And the loading backlashes and meshing forces are calculated in order to verify the iterative algorithm. Comparative studies show that the meshing force distribution obtained by this iterative algorithm is basically consistent with that by the finite element model, but the meshing force amplitude is higher when the load torque is large because bigger stiffness is used in the iterative algorithm