成形磨齿砂轮包络计算的双参数点矢量族法  

Envelope to a two-parameter family of point vectors method for surface swept by wheel during 5-axis gear form grinding

作　　者：李国龙[1] 林超[1] 李先广[1,2] 王攀攀[1] 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400044 [2]重庆机床(集团)有限责任公司,重庆400055

出　　处：《重庆大学学报（自然科学版）》2013年第4期11-18,共8页Journal of Chongqing University

基　　金：重庆市科技攻关资助项目(CSTC;2010AC0052);国家科技支撑计划资助项目(2012BAF13B09)

摘　　要：成形磨齿砂轮母线一般为多段直线、圆弧构成的组合曲线,砂轮扫掠体包络面的计算远比常规回转刀具复杂。双参数点矢量族包络法,将砂轮母线上离散点及其法向矢量定义为点矢量且每个点矢量唯一对应着一个虚拟球,点矢量的回转运动生成纬线圆,点矢量包络运动等效生成过球心的截圆,纬线圆与截圆的交点即为特征点;建立了特征点的解析计算模型,特征点由虚拟球几何参数及虚拟球心速度决定,虚拟球几何参数可直接采用点矢量信息计算;分析了典型五轴成形磨齿机的运动几何特性,进行了磨齿机惯性坐标架与活动坐标架的坐标变换,给出了基于磨齿数控代码的虚拟球心速度计算方法;通过1个计算实例验证了文中方法的有效性。该方法可用于五轴成形磨齿的几何仿真、精度评估及路径优化中。The wheel generating curve for gear grinding is always a composited curve which is composed of lines and arcs,and the calculation of the envelope surface is more complex than conventional rotary cutter.A method of envelope to a two-parametric family of point vectors is proposed,which defines the point and its normal vector on the wheel generating curve as a point vector.Each point vector corresponds to a virtual ball uniquely.The rotation of point vector forms latitude circle and the valid envelopment movement forms sectional circle.The intersection of latitude circle and sectional circle is grazing point.The analytical calculation model is established,in which the grazing point is determined by the geometry parameters of virtual ball and the velocity of virtual ball center,and the geometry parameters of virtual ball can be directly calculated from point vector.The kinematic geometry of 5-axis form gear grinder is analyzed.The coordinate transformation between fixed frame and moving frame is conducted,and the velocity of virtual ball center based on NC codes is obtained.An example is presented to demonstrate the effectiveness of the method which can be used for 5-axis gear grinding geometry simulation,accuracy evaluation and optimization of the wheel path.

关 键 词：扫掠体包络面 齿轮加工 成形磨削 砂轮 点矢量族 双参数运动 

分 类 号：TG701[金属学及工艺—刀具与模具]