环面蜗轮滚刀刃带宽受周向定位误差影响分析

环面蜗轮滚刀刃带面的刃带宽需控制在一定的范围内以保持刃口的强度和锋利性，圆周定位误差的存在使刃带宽发生变化。为了磨削出满足需要的刃带面，研究了周向定位误差对刃带宽的影响规律。根据微分几何和齿轮啮合原理，建立了求解含有周向定位误差的刃带宽的数学模型。研究了存在周向定位误差时，刃带宽沿环面蜗轮滚刀的轴向和齿高方向的变化规律。同时，在VERICUT中建立虚拟的四轴联动环面蜗杆磨床，对周向定位误差的影响进行仿真验证。研究结果表明:周向定位误差对环面蜗轮滚刀边齿齿顶处刃带宽的影响最大；刃带宽与周向定位误差具有很强的相关性，呈线性变化关系；对于特定的算例，当给定的刃带宽e=1.0 mm在±10%范围内变化时，周向定位误差允许的调整范围为-0.122°~0.054°。 

Influence of circumferential positioning error of an hourglass worm wheel hob on land width

Land surfaces of an hourglass worm wheel hob needs to be controlled within a range to ensure the strength and sharpness of cutting edges. Circumference positioning errors lead to the changes of the land width. In order to grind out the required land surfaces, this paper studies the influence of the circumferential positioning errors on the land width. A mathematical model for solving the land width with the circumferential positioning error is established. The variation of the land width along the axial direction and the tooth height direction of the hob is studied. Effects of the circumferential positioning errors on the land width are simulated based on a four-axis linkage virtual hourglass worm grinding machine in VERICUT. The results show that the circumferential positioning errors have the greatest influence on the land width of the side teeth of the hob. There is a strong correlation between the land width and the errors, showing a linear relationship. In an example, the allowable range of the circumferential positioning error is between -0.122° and 0.054° when the land width e=1.0 mm varies in the range of ±10%.