基于齿轮副整体误差的齿轮动力学模型及其动态特性

Comprehensive Dynamics Model and Dynamic Response Analysis of a Spur Gear Pair Based on Gear Pair Integrated Error

迄今提出的各种齿轮动力学模型,在处理齿轮误差的影响时,都回避因齿轮重合度大于1而分不清单双啮区的事实,由此得出的结果不能较全面反映实际情况。基于齿轮副整体误差概念,综合考虑齿轮啮合过程的时变啮合刚度、误差激励等非线性因素,建立一种新的考虑单、双啮过程的直齿轮动力学模型,能更精确地描述齿轮系统的动力学行为,解决现有模型存在的主要问题;应用变步长四阶Rounge-Kutta法获得新动力学模型的高精度数值解;定量研究不同工作条件下啮合刚度、加工误差对振动响应的影响,研究结果对于完整认识复杂的齿轮动态性能、进行动态优化设计具有重要的理论和实用价值。

The existing gear dynamics models,when dealing with the effect of gear error on gear dynamics,always omit distinguishing one pair of teeth from two pairs of teeth in contact during gear transmission since the contact ratio of gears is greater than one. Therefore,these models are unable to indicate the overall real conditions. Based on the concept of gear pair integrated error（GPIE） is proposed a new comprehensive dynamics model for spur gear pair,taking into account the number of teeth in contact,is built to overcome the drawbacks of existing models. Meanwhile,the nonlinear factors such as gear errors,time-varying mesh stiffness and load sharing are considered in the new model. Critically,the GPIE has the advantage to identify the number of teeth in contact in the whole gear rotation process,thus overcoming the limitations in conventional gear dynamics models. According to the actual GPIE curve from a gear integrated error tester,the simulations of a gear pair under various working conditions are conducted by the new model,and the gear dynamic behaviors are analyzed. The research results clarify some phenomena related to gear transmission,and can be used in dynamics design and noise control of gears.