Pascal蜗线型齿轮滚切插补算法对比

Comparison of Hobbing Interpolation Algorithms of Pascal Curve Gear

根据Pascal蜗线型齿轮滚切加工模型推导出Pascal蜗线型齿轮滚切插补算法,探讨了不同插补算法中程序段弧长和机床运动轴的变化规律.同时,为了对比程序段弧长的均匀性,提出了程序段弧长均匀度的概念.实例结果表明,在最小曲率半径处,工件等极角插补程序段弧长最长,工件等转角插补程序段弧长变换较为平稳,工件等弧长插补程序段弧长相等;3种插补算法程序段的弧长均匀度由小到大依次为工件等弧长插补、工件等转角插补和工件等极角插补;采用工件等极角插补算法时机床运动轴无一恒定,不便于控制,采用工件等转角插补算法的滚刀控制复杂,而工件等弧长插补算法较为实用.

According to the mathematical model for hobbing Pascal curve gear, interpolation algorithms of hobbing pascal curve gear were obtained. Developing regularity of different interpolation algorithms arc length of segment and machine motion axis were compared, the concept of the arc length of segment uniformity degree was proposed, thereby the uniformity of the arc length of segment could be judged. The ex periment shows that the stage equal polar angle interpolation arc length of segment is longest near the minimum curvature radius, the development rate of the stage equal rotational angle interpolation arc length of segment is more stable, and the stage equal arc length interpolation arc length of the segment is equal; The arc length of segment uniformity of the three algorithms were orderly increased, which were the stage equal polar angle interpolation, the stage equal rotational angle interpolation and the stage equal arc length interpolation; The stage equal polar angele interpolation machine motion axis motion was with variable velocity and was difficult to control, the stage equal rotational angle interpolation cutter control was complex, and the stage equal arc length interpolation was practical.