螺旋面截形尖点矢量离散法及其在双圆弧滚刀过渡曲面最小化中的应用

Method of Discreting Cusp Vectors of Helicoid and Its Application in Minimization of the Relief Grinding of Double Circular-arc Gear Hob

在具有尖点廓形的螺旋曲面成形加工中,计算出的刀具截形常常产生曲线自交叉现象,导致刀具加工出的螺旋曲面在尖点处生成较大的过渡曲面。为此,提出尖点矢量离散法,将点及其法向矢量定义为一个点矢量,对两相交曲线在尖点处形成的首尾两个点矢量进行离散,使尖点处更多的几何信息带入到廓形计算中,提高了计算精度。给出过渡曲面最小化算法,用工件截形离散尖点矢量及两侧四个点矢量计算刀具廓形点,消除自交叉后得到刀具尖点及附近四个点;用刀具点反算工件廓形点,得到过渡曲线;通过所建立的过渡曲面大小评价标准,以过渡曲线最小为目标在一定范围内进行刀具安装角优化。将该方法应用于双圆弧齿轮滚刀的铲磨加工中,通过实际加工验证,表明该方法可有效降低过渡曲面的大小,适用于具有尖点廓形的螺旋曲面成形加工的计算优化。

Self-intersect curve is often existent in the profile of forming cutter computed by the helicoid with cusp,which leads to form the big size of transition surface at the location of cusp of the helicoid processed by the cutter.Therefore,a method of discreting the cusp vector is proposed.It firstly defines a point and its normal vector as ＂point vector＂,and discrete the two point vectors formed by the two intersection curves at the location of cusp,which brings more information of the cusp into the computation process of profile for the accuracy improvement.Then,an algorithm for the minimization of transition surface is put forward.The discrete cusp vectors and the four point vectors on the cusp sides are used to compute the points which forming the profile of cutter.The cusp of the cutter and other four nearby points are obtained after the self-intersect is eliminated,which are used in the inverse calculation to gain the transition surface.The evaluation standard of transition surface is developed to optimize the installation angle of cutter within a certain range aiming at the minimization of transition surface.At last,the method is applied in the relief grinding for the double circular-arc gear hob.The actual processing result verifies that the method is helpful to reduce the size of transition surface effectively and also applicable to optimize the forming processing of helicoid with cusp.