Investigation on multi-body dynamics based approach to the toolpath generation for ultraprecision machining of freeform surfaces

Abstract

This article presents an innovative approach to toolpath generation for ultraprecision machining of freeform optic surfaces based on the principle of Automatic Dynamics Analysis of Mechanical Systems. As components with freeform surfaces often have non-rotational symmetry, there are potential challenges facing their ultraprecision machining through single-point diamond turning, such as the projected points in complex large sag surfaces, which likely find it difficult to communicate with the control system and, thus, do not perform successfully. In ultraprecision machining, to achieve the highest performance in freeform surface resolution, the factors of dynamics, material and mechanical stiffness, frictions, tooling and accuracy of the servo component should be considered. The investigation is focused on an integrated approach and the associated scientific understanding of precision engineering design, ultraprecision machining and metrology of freeform surfaces as well as their application perspective. In this approach, the toolpath for very complex freeform surfaces can be generated using the Newton–Raphson method to solve the kinematics and dynamics equations of motion. The effect of friction and contact force are also investigated for accurate toolpath curve generation. Moreover, the Gear stiff (GSTIFF)/ Wielenga stiff (WSTIFF) integrator for solving the non-linear equations of motion is employed, and the result shows the time step size, playing a critical role in generating toolpath curves with a higher accuracy and resolution.