Contouring Control of a Five-Axis Machine Tool with Equivalent Errors

Abstract

In this study, the contouring control problem of a five-axis machine tool was examined. Due to the rotation axes, there are two coordinate systems involved in the five-axis machine tool, namely the workpiece coordinate system and machine coordinate system. The five-axis machine tool is required to follow a given desired path with tool orientation specified in the workpiece coordinate system. However, the system dynamics of the machine tool is described in the machine coordinates. Kinematic transformations exist between the two coordinate systems. One challenge of the problem is to design a controller in the machine coordinate system that will meet the requirements in the workpiece coordinate system. Another challenge is to minimize both the position contour error and tool orientation error. The method of equivalent errors is adopted to design the contouring controller. The desired path and tool orientation in the workpiece coordinate system are transformed into a five-dimensional hyper-curve in the machine coordinate system. A contouring controller was designed to follow the five-dimensional hyper-curve using the method of equivalent errors. Both numerical and experimental results validate the effectiveness of the proposed contouring control method.