A general approach for error modeling of machine tools

• An novel, generalized and systematic approach for error modeling is proposed.
• It allows two kinds of source errors to be separated for design and compensation.
• It has clear physical meanings and is linearized with high computational efficiency.
• The influence of "compensatable source errors" can be eliminated by compensation.
• The "uncompensatable ones" should be minimized in manufacture and assembly processes.

This paper presents a general and systematic approach for geometric error modeling of machine tools due to the geometric errors arising from manufacturing and assembly. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within machine tool kinematic chains using homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the error intensities of a machine tool; (3) combination of these two models for error separation. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the machine tool to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement by suitable measures, i.e. component tolerancing in design, manufacturing and assembly processes, and error compensation. Two typical multi-axis machine tools are taken as examples to illustrate the generality and effectiveness of this approach.