中文摘要：

齿轮齿根过渡曲线是精确校核齿根弯曲强度和计算齿轮体积的重要计算依据，但是目前常用一个过渡圆弧近似的估算齿根过渡曲线，这就导致在用齿根过渡曲线做相关计算时引起较大的误差。通过分析范成法加工齿轮过程，建立了齿根过渡曲线的成形机理和数学模型，结合反转法和坐标变换推导出齿根过渡曲线的数学方程。把计算出的齿根过渡曲线与目前常用估算的齿根过渡曲线进行比较后，发现推导出的齿根过渡曲线与实际加工出的齿根过渡曲线相吻合，估算的齿根过渡曲线较多的去除了齿轮齿根部位的金属，与实际加工出来的齿根过渡曲线存在差异。

英文摘要：

Dedendum transition curve is a very important reference for checking precisely dedendum＇s flexural strength and correctly calculating gear＇s volume.However the dedendum transition curve currently is estimated by a transient circle arc ,which may lead to error in computing the curve.Based on analyzing process of machining gear by generating method,the compacting mechanism and a model for the dedendum transition curve are built to deduce a mathematical equation combining the reversal with coordinate transformation.The dedendum transition curve which is generated by equation fits the curve generated by estimating method after being compared with the curve estimated by a circle arc.There are differences between two kinds of curve ,the estimated curve actually remove metal near dedendum which should not be removed in fact.