Modeling and simulation of the nonlinear dynamic response typical in gear transmissions usually require extensive input from tooth contact analysis combined with data derived from numerical techniques that in turn comprise a time and resource-consuming procedure. In this work, an efficient SDOF model that captures meshing nonlinearities in a non-implicit manner is presented. An extensive geometric analysis designates the underlying physical mechanisms prevailing in tooth meshing enabling incorporation of the effects of backlash, varying mesh stiffness and corner contact. By this analysis, an accurate repositioning method is proposed for involute teeth contact reversal, while a general approximation function for gear pair mesh stiffness including load dependence is formulated and successfully fitted to analytical data. Consequently, distinction between single and double tooth contact is captured through a modified parametric s-curve, including the effect of corner contact. A SDOF dynamical model is formulated for a given pinion rotational velocity and solved numerically. Both static and dynamic results are compared to data available in the literature, showing high agreement with more complex methods, while maintaining the advantages of minimum required pre-calculations and low computational cost.

齿轮传动中典型的非线性动态响应的建模和仿真通常需要来自齿接触分析的大量输入，并结合从数值技术中得出的数据，而数值技术又包括时间和资源消耗过程。在这项工作中，提出了一种有效的SDOF模型，该模型以非隐式方式捕获网格非线性。广泛的几何分析指定了在齿啮合中占主导地位的潜在物理机制，从而能够考虑到反冲，变化的啮合刚度和角接触的影响。通过这种分析，提出了一种精确的重新定位方法，用于渐开线齿的接触反转，同时制定了包括载荷相关性的齿轮副啮合刚度的通用逼近函数，并将其成功地拟合到分析数据中。所以，单齿和双齿接触之间的区别是通过修改后的参数s曲线获得的，包括角接触的影响。针对给定的小齿轮转速制定SDOF动力学模型，并进行数值求解。将静态和动态结果与文献中的可用数据进行比较，显示出与更复杂的方法高度吻合，同时保持了所需的最少预先计算量和低计算成本的优势。