Geometric error contribution modeling and sensitivity evaluating for each axis of five-axis machine tools based on POE theory and transforming differential changes between coordinate frames

Abstract

The influences of different axes on the accuracy of a machine tool vary due to their positions in the structure of the machine tool and their local errors. In this paper, geometric error contribution modeling and a sensitivity evaluation of the axes of a machine tool are proposed to obtain the influences of each axis and determine the crucial axes of the machine tool. First, the error vector components of the position-independent errors are obtained by product of exponential (POE) theory. Second, the error contributions of all axes are established based on transforming differential changes between coordinate frames by using the POE formula of the tool relative to each axis and the error vectors of the axes. Third, an error sensitivity matrix of each axis is established according to the formula of error contribution about the error vector of the axis. Fourth, two methods are proposed for an error sensitivity evaluation of the axes to determine the crucial axes: one method employs the weights of the error contributions of the axes, and the other method employs the error sensitivity coefficients of the axes. Finally, simulations and real cutting experiments are carried out with the SmartCNC500_DRTD five-axis machine tool to verify the effectiveness of the error contribution modeling and error sensitivity evaluation of the axis.