Abstract:

In accordance with  the force conditions of  cylinder sine oscillation tooth transmission,a  model of meshing force analysis  under theoretical conditions  was proposed  based  on  the hypothesis of stretch small distortion and distortion congruity.According  to Hertz theory and geometric relation of engagement pair,engagement stiffness models   of  the engagement pair were established, and  the calculation formulas of  the engagement stiffness  and the principal curvature of the contact point were deduced.The  torsional  vibration  model  of  cylinder sine oscillation tooth transmission were established by energy conservation principle,and the calculation formulas of equivalent torsional stiffness were given,forming a  complete set of  analysis and calculation methods of system stiffness matrix,and the presented methods  was  illustrated through an example.The fact is discovered,that the torsional vibration is a time-varying  system and the  system stiffness matrix shows the characteristics of cycle distribution,and the cycle calculation formula are found.Two simplified methods for solving natural frequency of the torsional vibration system were pointed out.The acquired results can be adopted as the analytical base for structure design and vibration analysis.

Key words: cylinder sine oscillation tooth transmission;meshing force；engagement stiffness;equivalent , torsional stiffness;system , stiffness matrix

摘要：

针对圆柱正弦活齿传动过程中的受力情况,基于弹性小变形和变形协调假设,提出了理论状态下啮合作用力分析模型；根据赫兹理论和啮合副的几何关系，建立了啮合副的啮合刚度模型，推导出接触点处主曲率和啮合副啮合刚度计算公式；依据能量不变原理建立了系统扭转振动模型，给出了等效扭转刚度计算公式，形成了一套完整的系统刚度矩阵计算分析方法;结合具体实例进行了分析,发现该扭转振动是一个时变系统且系统刚度矩阵呈现周期分布的特点，求出了周期计算公式，并提出了两种简化求解该扭转振动系统固有频率的方法。分析结果可作为圆柱正弦活齿传动机构的结构设计、振动分析的基础。

关键词: 圆柱正弦活齿传动, 啮合力, 啮合刚度, 等效扭转刚度, 系统刚度矩阵