平面二次包络环面蜗杆传动齿面接触应力计算

The Contact Stress of the Planar Double Enveloping Hourglass Worm Gears

采用弹塑性接触有限元法求解了不同包容齿数下的齿间载荷分配系数,基于啮合原理计算了接触点的诱导法曲率半径并进行了回归分析,建立了单齿接触线长度和总接触线长度的简化计算模型。基于Hertz模型,推导出适用于平面二次包络环面蜗杆传动的承载最大齿对的接触应力计算公式和平均接触应力计算公式。建立了蜗杆副的有限元模型,分析了不同载荷作用下的齿间载荷分配及齿向应力分布规律。最后,通过实例对比了用于平面二包蜗轮副齿面接触应力分析的解析法及数值法。结果表明：解析法与数值法计算结果接近,前者计算值高于后者约10%~25%。

Load distribution factors among the teeth under different contact ratio were computed by the elastic-plasticity contact finite-element method,the normal curvature radius on the contact points were calculated by the theory of gear engagement,and simplified models of single and total length of contact line were established.Based on the Hertz model,contact stress analysis formula of the tooth which carries the maximum load was deduced,and contact stress formula of the teeth was deduced.The finite-element model of the worm gears was established,stress distribution status along the contact line and load distribution factor among the teeth were analyzed under different loads.At last,the contact stress analysis formula and finite-element method were compared by the example.The result showed that the results of the two method are very near,the result of the former higher than the later＇s about 10%~25%.