滚齿加工齿轮齿根过渡曲线及其曲率半径的数值计算

Numerical Calculation for Gear Tooth Transition Curve and Its Curvature Radius in Hobbing

针对齿根过渡曲线及其曲率半径求解计算复杂的问题,给出一种实用的数值计算方法.以渐开线滚刀滚齿加工为研究对象,建立滚刀齿面的齿顶圆弧方程,利用滚齿加工数学模型,可计算获得精确的齿根过渡曲线的数值解.采用二次拉格朗日插值方法将诸多离散点构造成分段插值曲线以描述过渡曲线,可使过渡曲线曲率半径的计算得到简化.具体的算例表明,该方法具有精确、高效的特点.

To solve the complex problems of the calculations for gear tooth transition curve and its curvature ra- dius,a practical numerical calculation method is presented. As to the hobbing process with involute hob, the addendum arc equation of hob tooth surface is established, and the accurate numerical solution of tooth transi- tion curve can be calculated using the mathematical model of bobbing. The quadratic Lagrange interpolation method is introduced to construct the discrete points into the segmented interpolation curve, and further, to de- scribe the transition curve, thus simplifies the curvature radius calculation of the transition curve. The specific example shows that this method is accurate and efficient.