基于双锥砂轮的环面蜗轮滚刀前刀面成形方法

多头环面蜗轮滚刀通常采用螺旋槽，以降低刀齿负前角的绝对值、并均衡每个刀齿左右两侧的前角，从而提高滚刀的切削性能。由于环面蜗轮滚刀螺旋线上各处的螺旋升角不同，所以各个刀齿左右两侧的前角均衡问题更为复杂，鲜有螺旋槽前刀面的精确成形方法的研究。基于环面蜗杆专用数控机床，提出采用双锥砂轮磨削螺旋槽环面蜗轮滚刀前刀面的方法，根据齿轮啮合理论，建立由双锥产形面展成平面二次包络环面蜗轮滚刀螺旋槽前刀面的数学模型，给出每个刀齿两侧在分度环面螺旋线上的前角计算公式。算例计算结果表明：如果采用直槽滚刀，对应的前角在-19.530 3°~19.530 4°；通过合理的参数选择，可使得螺旋槽滚刀对应的前角在-8.1°~7.3°，有效减小了刀齿负前角的绝对值。对环面蜗轮滚刀螺旋槽进行仿真加工，并且在仿真软件中对前角进行测量，测量结果与计算结果相吻合，证明本文方法的正确性。

Forming method of hourglass worm gear hob rake faces based on double-cone grinding wheel

For multi-thread hourglass worm gear hobs, spiral flutes are typically used to reduce the absolute value of the negative rake angle and to equalize the rake angles on the left and right sides of each tooth, which will improve the cutting performance of the hob. Because of the different spiral angle on the basic worm helical surface, the rake angle on both sides of each tooth is more difficult to balance. However, there are few researches on the precise forming method of the spiral flute rake face. Based on the NC machine tool for hourglass worm, a method for grinding the rake face of spiral flute with double-cone grinding wheel is proposed. According to the gear meshing theory, a mathematical model was established for the rake face of the planar double enveloping hourglass worm gear hob spiral flute formed by the double-cone grinding surface. The formula for calculating the rake angle on both sides of the tooth is given. The calculation results show that if the hob with straight flute is used, the rake angles are between -19.530 3° and 19.530 4°. Through proper parameter selection, the rake angles can be between -8.1° and 7.3° when the hob with spiral flute is used, which effectively reduces the absolute value of the negative rake angle of the tooth. The spiral flute of hourglass worm gear hob was simulated and the rake angle was measured in the simulation software. The measured results coincide with the calculated results and this proves the correctness of the method.