Sensitivity analysis using a variance-based method for a three-axis diamond turning machine

It is of great interest to determine which of the numerous sources of error in an ultra-precision diamond turning machine has the greatest influence on the machining inaccuracy. Global sensitivity analysis is a well-known mathematical technique that is able to quantify the contribution of each error source to the machining inaccuracy. The present study employs a variance-based sensitivity analysis method to comprehensively investigate the influence of each error source in a three-axis diamond turning machine on the machining inaccuracy. The procedure for establishing a volumetric error model based on multi-body system theory in conjunction with a homogeneous transformation matrix is first described in detail. The basic working principle and relevant estimation process of the Sobol method is then explained, and the Sobol method is employed to quantify the sensitivity index of each error source based on the volumetric error model. Finally, simulation testing is conducted to comprehensively investigate the main geometric error sources contributing to machining errors along the X, Y, and Z directions, and with respect to comprehensive volumetric errors. After the main geometric error sources are identified, some measures are taken to improve the identified error sources, and a flat surface cutting experiment is conducted to verify the effectiveness of the proposed sensitivity method. The results show that the proposed sensitivity method is effective for identifying the most crucial geometric errors, the form error of flat surface is improved by approximately 50% after modifying parts of these errors, and these errors should then be the subjects of careful scrutiny in the precision design, error compensation, and precision processing stages. The method is of significant guidance for on-machine and real-time online error compensation.