中文摘要：

根据塑性成形体积不变原则，提出一种新型的花键轴增量式滚轧成形坯料直径的计算公式，该公式计算简单且相对误差小于0．1％。其主要思想为：初步计算单齿圆周角范围内的齿形面积，进一步根据分度圆半径与中线圆半径的比较结果进行补偿，从而获得精确的单齿面积、花键轴及其坯料的截面积。此外，对该计算公式进行了不同坯料直径下的花键轴增量式滚轧成形有限元分析验证，结果表明，由该计算公式获得的坯料直径符合工艺要求，成形的花键轴齿廓清晰、齿形填充饱满。

英文摘要：

According to the principle of constant volume during plastic forming process, a novel and simple method of diameter calculation of billet before incremental rolling for spline shaft was proposed with relative error below O. 1%. The main thought of this method can he summarized as follows： calculating the tooth area within the single tooth angle initially, and then making the compensation based on the comparisons between the radius of pitch circle and the middle line circle, finally the exact single tooth area, the sectional area of spline shaft and billet can be obtained. In addition, the finite element analysis and validation on this method were conducted under different billet diameters. The results show that the diameter calculated by this method can be satisfied with the application requirement well.