In this study, an impacting contact model of spur gear under lightly loaded condition is constructed by considering the pinion and the wheel as rigid body, in which the lubricant is modelled by a linear spring damper combination. The entire motion of the gear system is fell into three phases, i.e.,: meshing state, transient state and non-meshing state. An original numerical calculation method is proposed for this model, and its validation is confirmed by using the Co-simulation of Adams-Matlab/Simulink. Instead of using the Jacobian matrix, the proposed numerical method could effectively avoid the ill condition in the iteration on data resulting from the nonlinearity of gear backlash. The results in this study verified that the algorithm is useful not only can increase the accuracy, but also significantly decrease the calculation time of the entire system. And the original numerical calculation method is employed to illustrate and quantify the influences of the excitation frequency on the impacting contact model of spur gears.

中文翻译：

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一种原始的轻载条件下正齿轮碰撞接触模型的数值计算方法

在本研究中，将小齿轮和齿轮视为刚体，构建了轻载条件下正齿轮的碰撞接触模型，其中润滑剂由线性弹簧阻尼器组合建模。齿轮系统的整个运动分为三个阶段，即：啮合状态、瞬态和非啮合状态。针对该模型提出了独创的数值计算方法，并通过Adams-Matlab/Simulink联合仿真验证了其有效性。所提出的数值方法不是使用雅可比矩阵，而是可以有效地避免由于齿轮齿隙非线性导致的数据迭代中的病态。本研究的结果验证了该算法的实用性不仅可以提高准确率，同时也显着减少了整个系统的计算时间。并采用独创的数值计算方法来说明和量化激励频率对直齿轮碰撞接触模型的影响。