六轴联动数控齿轮加工机床加工点啮合齿面的包络逼近原理

Envelope-Approximation Theory in Manufacture for Point-Contact Tooth Surface by Six-Axis CNC Hypoid Generator

提出了一种在六轴联动数控机床上加工点啮合齿面的新加工方法。该方法源于微分几何中通过空间曲线的Darboux-Frenet标架沿设计(理论)齿面上的一条指定接触迹线运动来描述曲面微分结构的思想,所展成的齿面与设计(理论)齿面沿指定的接触迹线有二阶切触且在接触迹线以外的区域与设计(理论)齿面之间具有指定(最小)误差,能完全控制齿面上每一个啮合点的啮合特性。利用六轴联动数控齿轮加工机床的万能运动功能,按被加工齿面预定的啮合特性确定刀具相对工件的运动。实例验证了方法的精确性和可行性。

A new generation method for point-contact tooth surface is proposed based on the six-axis movement of CNC machine.The new method is derived from the motion of Darboux-Frenet trihedron along a predesigned path of contact on the predesigned（theoretical） tooth surface.The generated tooth surface by the new method has tangency of second order with the predesigned（theoretical） surface along the predesigned path of contact and the predesigned（least） warping in regions that differ from the path of contact.This means that the new method can reliably control meshing characteristics at each contact point.In contrast,the previous method can only control meshing characteristics at a mean contact point and make correction by observing the contact-bearing condition to determine meshing characteristics at other contact points.Different from the previous CNC generation method translated from the cradle-style universal hypoid generator,the developed method directly suits the six-axis movement of CNC machine to identify the relative motion between the tool and the workpiece based on the predesigned meshing characteristics of the gear being generated.Numerical examples prove that the new manufacture method is accurate and feasible.