Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach
Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach
复制标题
DOI：
10.1007/s12206-018-0704-9
复制
发表时间：
2018-08
影响因子：
1.6
通讯作者：
M. Rezaei;M. Poursina;S. H. Jazi;F. H. Aboutalebi
中科院分区：
文献类型：
--
作者：
M. Rezaei;M. Poursina;S. H. Jazi;F. H. Aboutalebi
时变啮合刚度是引起齿轮传动系统振动和动力激励的重要原因。本研究将斜齿行星齿轮系与斜齿行星齿轮系的解析公式结合起来，计算斜齿行星齿轮系的时变啮合刚度。为此，在第一步中，推导出直齿圆柱齿轮副的解析方程。然后将斜齿划分为若干独立的薄直齿切片，提取斜齿轮副的啮合刚度。最后，将这些方程推广到斜齿行星齿轮系统。当螺旋角小于15 °时，本文的分析结果与有限元法的计算结果吻合较好。计算了行星架固定、太阳轮固定、齿圈固定等不同情况下斜齿行星齿轮系统的啮合刚度。这些结果表明，在每种情况下的啮合频率比的值在旋转角方向上缩放啮合刚度形状。换句话说，啮合频率比参数决定了行星轮每转一圈的啮合周期数。
Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.