弧齿锥齿轮齿面误差的最少参数修正法

Least Parametrical Modification Method of Spiral Bevel Gear Tooth Surface Errors

研究弧齿锥齿轮小轮齿面误差与调整参数误差之间的敏感性关系,基于SFT加工法得出对齿面误差影响较大的调整参数,提出齿面误差最少参数修正法。建立刀倾法加工的弧齿锥齿轮齿面数学模型,推导弧齿锥齿轮小轮的理论齿面方程和误差齿面方程,推导机床调整参数误差作用下的齿面任一点加工误差的解析表达式,提出机床调整参数误差对齿面误差的影响系数概念,依此判断各项机床调整参数误差对齿面误差的影响程度。通过理论齿面和误差齿面的比较,确定各项机床调整参数误差作用下的全齿面法向误差的变化规律。由解析法和数值法相互验证,确定弧齿锥齿轮加工过程中对齿面误差影响较大的调整参数误差项。利用函数法建立机床调整参数变化量与齿面法向误差的关系,采用序列二次规划法,求得机床调整参数修正量最优解。通过实例验证,提出的反调修正方法可以有效降低齿面误差。

The sensitivity relationship between the machine adjustment parameter errors and surface errors of the hypoid gears was researched herein,and the major impact of the machine adjustment parameter errors were determined based on the method of SFT（spiral format title）,and a least parametrical modification method of tooth surface errors was proposed.The tooth surface mathematical model of a spiral bevel gear by SFT was established,and the equations of theoretical tooth bearing and error tooth were established,the analytical expression of tooth surface processing errors caused by the machine adjustment parameter errors was derived,and the concept of error influence coefficient was proposed,and the impact of surface errors caused by machine adjustment parameter errors can be obtained according to the error influence coefficient.Through comparison of theoretical tooth bearing and error tooth,the effect law of tooth surface node processing errors and the whole tooth surface normal errors were determined.The major impacts of the machine adjustment parameter errors were determined by analytical and numerical method.The relationship between the machine adjustment parameter errors and surface errors was determined by the functional method,and the optimal solution of the machine adjustment parameter was solved by using the sequential quadratic programming method.The correct method proposed can effectively reduce the tooth surface error by means of experimental verification.