修形人字齿轮成形磨最大砂轮直径精确计算

Accurate Calculation of the Maximum Grinding Wheel Diameter for the Form Grinding of Modification Herringbone Gears

提出了一种修形人字齿轮成形磨削时,最大砂轮直径的精确计算方法。建立齿廓为3段抛物线修形的修形曲面,根据砂轮和工件的啮合方程,推导了砂轮接触线方程。将砂轮接触线绕着工件轴线做螺旋运动,同时考虑砂轮中心距变动,实现了人字齿轮的双向修形。根据砂轮磨削齿面终止点时的几何条件,计算砂轮最大直径,并分析了齿轮基本参数、修形参数和工艺参数对砂轮最大直径的影响规律。通过数值算例仿真表明,齿面修形对砂轮最大直径影响较小,磨削深度对砂轮最大直径影响较大,齿数和螺旋角均对砂轮最大直径有明显的影响。

An accurate calculation method of the maximum grinding wheel diameter for the form grinding of modification herringbone gears is proposed. A modified surface with three-section parabolic tooth profile is established. According to the meshing equation of the grinding wheel and the workpiece,the contact line equation of the grinding wheel is derived. The contact line of the grinding wheel is moved spirally around the axis of the workpiece,and considering the change of the center distance of the grinding wheel,a double modification of the herringbone gear is realized. According to the geometric conditions,when the grinding wheel is grinding the end point of the tooth surface,the maximum diameter of the grinding wheel is calculated,and the influence of the basic parameters,modification parameters and process parameters of the gear on the maximum diameter of the grinding wheel is analyzed. Numerical example simulation shows that tooth surface modification has little effect on the maximum diameter of the grinding wheel,and grinding depths have a greater influence on the maximum diameter of the grinding wheel. Both the number of teeth and the helix angle have an obvious effect on the maximum diameter of the grinding wheel.