A tool path generation and contour error estimation method for four-axis serial machines

Although four-axis machines are widely used in welding, carving, and cutting revolving parts, much fewer four-axis tool path generation and contour error estimation researches have been studied when compared with five-axis ones. This paper proposes an off-line tool path generation and an on-line contour error estimation method for four-axis serial machines that are used for welding spatial intersecting curves on revolving parts. First, the kinematics module is derived, followed by proposing the tool path generation algorithm. The tool tip positions are represented by using a third order B-spline, while the tool orientations are represented by a third order polynomial-spline. Both splines, which form the C2 continuous tool path, are fitted to the curve length parameter of the tool tip positions. When compared with existing multi-axis trajectory generation methods, the proposed method is greatly simplified by mapping the tool pose commands from the Cartesian coordinate frame to the cylindrical coordinate frame. In the proposed contour error estimation method, the tool tip position contour error is estimated at first, followed by calculating the relative tool orientation contour error which is synchronized with the tool tip position contour error to one same pose on the desired trajectory. The proposed tool path generation and contour error estimation methods are experimentally verified on a four-axis welding machine controlled by an in-house developed CNC system. Experiment results show that the desired trajectory can be tracked continuously and steadily. The contour error can be estimated with high accuracy and reduced by 50% after performing on-line compensation.