含间隙的斜齿轮副扭振分析与试验研究

建立了科齿轮副的间隙型非线性扭振模型，其中考虑了斜齿轮副的啮合综合误差，齿侧间隙和时变啮合刚度。采用三维有限元法计算了斜齿轮副啮合刚度，用三次样条插值拟合得到时变啮合刚度函数。用数值积分方法对系统的非线性动力学微分方程进行了求解，获得了斜齿轮副在外转矩作用下受静态传动误差激励的非线性稳态强迫响应，并对系统的动态响应进行了测试，试验和理论计算结果了一致性证实了本文所提出模型和解法的正确性。

Theoretical and Experimental Investigations of Torsional Vibration in a Helical Gear Pair with Baclklash

A nonlinear dynamic model of a helical gear pair with backlash and time-varying gear meshing stiffness, as excited by the static transmission error under a mean torque load, is established in this paper. The meshing stiffness is calculated by employing 3-dimensional FEM and its function is formed by cubic spline interpolation and approximation of the discrete mesh points in a mesh period. Further more, a numerical integration algorithm with adaptive step size control has been applied to solve the governed equation aiming to obtain the steady state forced response for the internal sinusoidal excitations. By using a dynamics test rig of the helical gear pair, the vibration acceleration of gear teeth is measured and spectral characteristics of dynamic response are obtained. A good agreement between the numerical and experimental results indicates that the presented method is practical and efficient.