基于椭圆的渐开线齿轮齿根过渡曲线研究

渐开线齿轮齿根过渡曲线是影响齿根弯曲应力的重要因素.为提高齿轮的弯曲强度,提出了采用椭圆曲线代替延伸渐开线的等距曲线,基于坐标转换原理,求出椭圆曲线方程.并采用30°切线法求出椭圆过渡曲线齿形系数和应力集中系数,与标准刀具加工的齿根曲线进行比较,结果表明采用椭圆过渡曲线可以使弯曲应力降低15％.根据齿形法线法,反求出获得该椭圆曲线的滚刀刀顶曲线,为滚刀刀顶设计和实际加工提供了理论依据.

Study of the Fillet Curve of Involute Gears Based on Ellipse

The fillet curve of involute gears is the important factor which affects the root bending stress.The goal is to improve tooth bend- ing stress substituting elliptic curve for equidistant curve of the prolate involute.Based on the principle of coordinate transform,the elliptic e- quation has been determined. The stress concentration factor and form factor of elliptical transition curve are calculated by the 30~ tangent method. Comparing with the fillet curve cutted by standard tool, the results show that bending stress of elliptical transition curve is reduced by 15%. It is using tooth profile normal method to obtain the hob cutter tip curve processing elliptical transition curve.The study lays a foun- dation for the design of hob cutter tip and actual manufacturing.