预置接触区长度系数的Spirac切齿调整计算方法

基于参考点处瞬时接触椭圆大体决定接触区长度的方法,提出一种切齿调整计算方法.根据奥利康刀倾半展成法(Spirac)切齿原理,建立摆线齿准双曲面齿轮的数学模型,得到了大轮齿面参考点处瞬时接触椭圆参数;在满足参考点位置、压力角和螺旋角的基础上,将刀倾角也作为迭代变量,并将接触区长度系数等于预置值作为新增的迭代条件,迭代求解切齿调整参数.最后以一对摆线齿准双曲面齿轮副为例,对比该方法与Spirac切齿调整计算结果,验证了该方法的准确性,并对不同预置接触区长度系数得到的齿面进行齿面接触分析.结果表明,该方法解决了反复调整刀倾角的问题,并通过精确控制大轮齿面接触区长度系数等于设计值,实现了对大轮齿面接触区长度的预控.

Spirac machine-tool setting calculation method by predetermined contact pattern length factor

Based on the method that the length of the instantaneous contact ellipse at the reference point almost decides the length of the contact pattern, a machine-tool setting calculation method was obtained. According to the Spirac cutting theory, a mathematical model of the epicycloids hypoid gear was built and the parameters of the instantaneous contact ellipse at the reference point of the gear tooth surface were obtained. By adding the cutter tilt angles to the machine setting iteration variables and taking the contact pattern length factors equaling to the predetermined values as the iteration conditions based on the required position of the reference point, the required pressure angle and the required spiral angle of the tooth surfaces at the point, the machine-tool setting parameters were solved. Finally, with a pair of epicycloids hypoid gear as an example, the result obtained from this method was compared with that from the Spirac to verify its accuracy, and the tooth contact analysis under different predetermined contact pattern length factors was accomplished. The results show that with this method, the problem of repeated adjustment of the cutter tilt is solved, and through precise control of different predetermined contact pattern length factors of the gear tooth surfaces equal to the design values, the pre-control of the contact pattern lengths of the gear tooth surfaces is achieved.