Prediction of surface generation in ultra-precision raster milling of optical freeform surfaces using an Integrated Kinematics Error Model

Due to the geometrical complexity of optical freeform surfaces, it is still difficult to predict the form errors for ultra-precision multi-axis raster milling of these surfaces with sub-micrometer form accuracy. This paper presents an Integrated Kinematics Error Model (IKEM) for the analysis of form error for ultra-precision raster milling of optical freeform surfaces. It attempts to address the challenges of previous kinematics models which are either too conceptual or too theoretical in which the error components are difficult to determine. As an alternate approach, the components of the machine motion errors are analyzed and the homogenous transformation matrix is employed to build a kinematic machining error model step by step. Considering the difficulties and inconveniences of measuring separate error components, IKEM is proposed on the theory of multi-body kinematics and the surface generation mechanism in ultra-precision machining. A series of experiments have been conducted to further validate the proposed model. The successful development of IKEM makes it more convenient for machining error budgets, and can also be generalized and applicable for other multi-axis machining systems.