朱增宝 龚明针 王东雨

摘 要：为了研究模数变化对多模数渐开线直齿轮副齿面接触应力的影响规律，根据理论齿侧间隙为零原则，推导了多模数渐开线直齿轮副的啮合角计算公式;引入了渐开线齿廓参数，结合基于最小弹性势能的非均匀载荷分配模型和赫兹应力模型，提出了多模数直齿轮副齿面接触应力计算公式并对多模数渐开线直齿轮副接触应力进行分析。结果表明：齿面接触应力随模数比增大而减小;采用多模数啮合形式，能减小少齿数主动轮啮合起始点的接触应力;齿面最大接触应力位置在啮合起始点或单齿啮合内点。

关键词：多模数;渐开线直齿轮副;载荷分配;接触应力

Abstract：In order to study the effect of modulus change on the contact stress of multi-module involute spur gear pair，the formula was derived for calculating the meshing angle of the involute spur gear pair with multi-module based on the theory that the tooth side clearance was zero. By introducing the involute tooth profile parameters and applying the non-uniform load distribution model based on the minimum elastic potential energy and the Hertz stress model， a formula for calculating the contact stress on the tooth surface of the multi-module spur gear pair is presented and the contact stress of the multi-module spur gear pair is analyzed. The results show that the contact stress decreases with the increase of modulus ratio. Adopting multi-module meshing can reduce the contact stress of the initial meshing point of the driving wheel with few teeth. The position of the maximum contact stress of tooth surface is the initial meshing point or the inner point of single tooth meshing.

Key words：multi-module;involute spur gear pair; load distribution; contact stress

渐开线齿轮广泛应用于航空航天、船舶车辆和工程机械等领域，齿面接触应力是影响其接触疲劳破坏的主要因素[1]，同时也是衡量与评估齿面接触承载能力的重要条件。文献[2-3]使用赫兹接触理论来评估接触应力，假定载荷沿接触线均匀分配，并引入了几种载荷分配影响因素来校正接触应力的计算值[4-5]6。实际上，载荷分布取决于齿轮副接触点的啮合刚度，刚度在任何接触点都不同，这意味着每单位齿宽的载荷在接触线的任何点上也都不同[6]。有许多研究通过理论计算法、实验和有限元分析等多种方法确定了直齿轮副的载荷分配比[7-10]785。

以上研究都是针对主、从动轮模数相等的齿轮副。对于主、从动轮模数不相等，但满足法节相等啮合条件的齿轮副（简称多模数齿轮副）的齿面接触应力研究，目前鲜见相关报道。……