Squareness error modeling for multi-axis machine tools via synthesizing the motion of the axes

This paper presents one novel model of squareness errors using the D-H matrix to improve the accuracy of integrated geometric errors of the machine tools. It considers the motion of the axis and reflects the geometric meaning of the squareness errors. Firstly, analysis of the existing squareness error models is proposed. It helps to find the improvements of the modeling. Secondly, squareness error modeling is represented by integrating the kinematic property of the axes. The influences of squareness errors are to change the translational direction of translational axes and to deflect the axial line of rotary axes. The squareness error model of translational axes is expressed as the translational homogeneous matrix along the real movement direction. And, the model of rotary axes is expressed as the rotational homogeneous matrix around the real axial line. The unit vector of the real direction is established based on the geometric definition of squareness errors. The models are available for different axes with the property of the axes. Finally, experiments are conducted on one SmartCNC500 five-axis machine tool. The virtual large squareness errors of translational axes and C-axis are simulated by the motion of axes. The positions of the target are measured by laser tracker when moving the axes. The comparisons of measured points and calculated points with the proposed model and one existing model are proposed. The results show that the novel models are precise.