Principle and Application of the Ball End Mill Tool Radius Compensation for NURBS Curve Swept Surfaces Based on 3-Axis CNC Milling Machines

Common 3-axis CNC milling machines are generally equipped with 2D tool radius compensation (2D-TRC), which can realize TRC function for the contours in three basic planes when flat end mills are used. The 2D-TRC function makes engineers to program according to the actual contour of a part, and avoids over-cut phenomenon. Unfortunately, the 2D-TRC is unsuitable for ball end mills (BEMs), especially in the situation of milling complex curves or surfaces. In this work, a new TRC named BEM-TRC is used for milling NURBS curve swept surfaces using BEMs based on 3-axis CNC milling machines. In BEM-TRC, the TRC of a BEM involves radial and axial compensation. The cutting point (CP), which is the tangent point between a BEM and a NURBS curve, is considered as a calculation basis point. After obtaining a CP on a NURBS curve using the equi-arc length bisection interpolation method, the cutter center point of a BEM is calculated through offsetting the CP the radius (r) distance of the BEM along its normal vector. Then the cutter location point of the BEM can be obtained according to the cutter center point. The CNC finishing program corresponding to the cutter location point can be obtained using Matlab software. The simulation based on VERICUT and machining based on a 3-axis milling machine verifies the effectiveness of the BEM-TRC. The over-cut phenomenon is avoided successfully when the BEM-TRC is used.