基于游动矢量球头立铣刀刃磨研究

Research on Ball End Mill Sharpening Based on Variational Vector

以“S”形等导程螺旋线建立球头立铣刀刃口曲线,以刃口曲线为磨削依据,提出以刃口曲线上磨削点的三个游动正交矢量为参考坐标系规划砂轮磨削轨迹的磨削方案。在此基础上,建立具有法前角的前刀面以及后刀面的磨削数学模型,通过求取磨削过程中任意时刻磨削点的游动正交矢量,利用偏心法求取球头立铣刀前刀面磨削深度。以磨削点的游动正交矢量、前刀面法向前角以及前刀面各磨削点对应深度来规划砂轮磨削前刀面的位姿,以磨削点的游动正交矢量、后刀面法向角度以及后刀面各磨削点对应宽度来规划砂轮磨削后刀面的位姿,最终遍历整个刃口曲线形成砂轮磨削铣刀的运动轨迹。利用五轴磨床对建立的铣刀模型进行实际加工,实验结果显示球头铣刀各结构参数误差均能保证在5%以内,验证了砂轮磨削轨迹模型的准确性,为球头立铣刀的磨削建立理论基础。

The cutting edge curve of the ball nose end mill was established by using the"s"shaped equal lead spiral,and the grinding edge curve was used as the grinding basis,and the grinding scheme of the grinding wheel grinding trajectory is planned with the three traveling orthogonal vectors of the grinding point on the cutting edge curve as the reference coordinate system.On this basis,the mathematical model of the rake face and the rake face with the normal rake angle is established,and the grinding depth of the rake face of the ball nose end mill is obtained by obtaining the traveling orthogonal vector of the grinding point at any time in the grinding process.The posture of grinding the rake face of the grinding wheel is planned by the traveling orthogonal vector of the grinding point,the rake angle of the rake face method and the corresponding depth of each grinding point of the rake face,and the posture of the rake face grinding is planned by the traveling orthogonal vector of the grinding point,the normal angle of the rake face and the corresponding width of each grinding point of the rake face,and finally the motion trajectory of the grinding wheel grinding milling cutter is formed by traversing the entire cutting edge curve.The experimental results show that the error of each structural parameter of the ball nose milling cutter can be guaranteed to be within 5%,which verifies the accuracy of the grinding trajectory model of the grinding wheel and establishes a theoretical basis for the grinding of the ball nose end mill.