In order to extend the 2D-TRC (tool radius compensation) function of 3-axis CNC milling machines to ball end mills (BEMs), a new TRC named BEM-TRC is proposed to achieve successful milling of complex surfaces without over-cut. The implementation of the BEM-TRC for complex surfaces depicted in NURBS model is divided into three steps. The first one is to search the cutting point (CP) on a NURBS surface using equi-arc length interpolation in u or v direction. The second one is to accomplish BEM-TRC at the CP through offsetting the CP to the cutter center point (CCP) of a BEM along the normal vector at CP. The third one is to compute the cutter location point (CLP) of the BEM according to the BEM-CCP. The simulation and experiment verifies that the BEM-TRC is feasible and effective, and can avoid over-cut phenomenon successfully. The BEM-TRC extends the ability of the traditional 2D-TRC function, and makes 3-axis CNC milling machines to accomplish the milling process of complex NURBS surfaces.

为了将3轴CNC铣床的2D-TRC（刀具半径补偿）功能扩展到球头铣刀（BEM），提出了一种新的名为BEM-TRC的TRC，可以成功完成复杂曲面的铣削而不会过度切削。针对NURBS模型中描述的复杂曲面的BEM-TRC的实现分为三个步骤。第一个是使用u或v中的等弧长度插值在NURBS曲面上搜索切割点（CP）方向。第二个是通过沿着CP处的法向矢量将CP偏移到BEM的刀具中心点（CCP）上来在CP处完成BEM-TRC。第三个是根据BEM-CCP计算BEM的刀具定位点（CLP）。通过仿真和实验证明，BEM-TRC是可行和有效的，并且可以成功避免过切现象。BEM-TRC扩展了传统2D-TRC功能的能力，并制造了3轴CNC铣床来完成复杂NURBS曲面的铣削过程。