Kinematics characterizing with dual quaternion and parametric modeling of geometric error terms based on measuring path planning of CNC machine tools.

Geometric error is a crucial factor influencing the spatial accuracy of CNC machine tools. A novel methodology for modeling, measuring, and identifying geometric errors in multi-axis machine tools is proposed in this paper. Firstly, a synthetic volumetric error model is established by utilizing dual quaternions for multi-axis CNC machine tools. To characterize the relative position relationship between the tool and the workpiece, the kinematics model automatically incorporates the complex coupling between position and orientation motion in an implicit way, enabling a concise and compact representation of the kinematics. Secondly, measure path planning includes candidate measurement positions which are screened to obtain the optimal position group by using observation indices and the modified Detmax method. Thirdly, a parametric modeling method based on exponential cosine fitting is proposed for representing both angular and linear errors, and an improved sparrow search algorithm and nested parameter uncertainty optimization are established to process curve fitting–based optimization of the geometric error term. The fitting of the exponential cosine model is quantified with model uncertainty, and the nested uncertainty optimization method is employed to improve geometric error terms with a poor fitting effect. Finally, the effectiveness is demonstrated through experimental comparisons. The geometric error of a single axis has an average decreased of 69.7%, and the compensation rate of roundness driven by two-axis synchronization is an average of 68.7%. This method offers the advantage of quantifying the minimum optimal number of measurements and positions, improving the efficiency of parametric modeling. [ABSTRACT FROM AUTHOR]