变位渐开线直齿圆柱齿轮传动过程接触应力分析

Analyses of Contact Stresses in Transmission Process of Involute Spur Cylindrical Modified Gear

为了便于变位齿轮精确传动设计,基于Hertz公式,计算变位渐开线直齿圆柱齿轮传动的最大接触应力,分析最大接触应力出现的位置,推导最大接触应力和节点啮合时接触应力的比值函数(称为应力比),将变位齿轮最大接触应力的计算式表达为应力比与节点应力的乘积。分析变位齿轮传动中应力比随小齿轮齿数和传动比变化的规律。结果表明:小齿轮齿数Z_(1)大于17时,随着Z_(1)增大,应力比减小;小齿轮齿数Z_(1)小于17时,随着Z_(1)增大,应力比增大;Z_(1)等于17时应力比最大;而传动比u增大,应力比会增大。如果齿轮接触强度的设计准则为最大接触应力比节点接触应力大8%或以上,则需要按最大接触应力进行精确设计。提供了需要进行精确接触强度计算的齿数和传动比的数值范围。在实例分析中采用有限元方法验证了推导的应力比计算式的正确性。

In order to facilitate the precise transmission design of the modified gear,the maximum contact stress of the involute cylindrical spur modified gear transmission was calculated based on Hertz formula,the position of the maximum contact stress was analyzed,and the ratio function(called the stress ratio)of maximum contact stress to the contact stress at gear node engagement was deduced,and maximum contact stress was expressed as the product of the stress ratio and the node stress.The rule of the stress ratio of modified gear varying with both the teeth number of small gear and the transmission ratio was analyzed.The results indicate that when the teeth number of small gear Z_(1) exceeds 17,the stress ratio decreases as Z_(1) increasing;and while Z_(1) is less than 17,it increases as Z_(1) increasing;with the transmission ratio u increasing,the stress ratio increases.The stress ratio arrives the maximum for Z_(1) being equal to 17.If the design criterion of the gear contact strength is that the maximum contact stress is 8%more than node contact stress,the accurate design is required according to the maximum contact stress.The ranges of both teeth number and transmission ratio are obtained for being required in precise contact strength calculations.The formula of the stress ratio is verified by the example analysis with the finite element method.