Position-independent geometric error compensation of a non-orthogonal five-axis machine tool using a simplified algebraic algorithm

Geometric errors are the key error sources that affect the machining quality of a five-axis machine tool. In the case of a non-orthogonal five-axis machine tool (NOFAMT), the modelling and compensation of geometric errors can be quite complex. This paper proposes a simplified modelling algorithm to derive the analytical expressions for the position-independent geometric error (PIGE) compensation of a NOFAMT without generating higher-order error terms. First, the geometric error modelling was conducted based on the homogeneous transformation matrix (HTM). Then, algebraic expressions for PIGE compensation were obtained according to the actual inverse kinematics and a simplified algorithm. By using the simplified algorithm, the efficiency of deriving algebraic expressions for geometric error compensation can be greatly enhanced. The PIGE compensation's numerical control (NC) codes can be directly computed using these algebraic expressions. Finally, the effectiveness and efficiency of the new algorithm were verified by numerical analysis and virtual machining. The detailed results were compared with those obtained using the differential method, and both sets of results showed the same trend.