Deterioration of form accuracy induced by servo dynamics errors and real-time compensation for slow tool servo diamond turning of complex-shaped optics

Abstract

Tool servo diamond turning is a promising method for generating complex-shaped optics. Considering the dynamic oscillation of the tool, servo dynamics are essential for the accuracy of the form generated with tool servo turning. Although static geometric errors and multiple compensation strategies for these errors have been studied extensively, the effects of dynamics errors of the servo axis on surface quality have received less attention. In this study, a dynamic surface generation model is established by considering the coupling effect between the servo axis dynamics and the cutting force. Using a micro-lens array (MLA) as an example, the components of the servo dynamics error of the servo motion, including dynamic deformation, resonant vibration, and trajectory tracking error, are characterised. The relationship between the servo dynamics error and the resulting form error is then theoretically identified with experimental verification. To compensate for the servo dynamics error in real-time, the concept of a cooperative tool servo (CTS) is proposed by incorporating a slow tool servo (STS) into a fast tool servo using a master-slave control strategy. Relative to using a STS for turning an MLA, the peak-to-valley (PV) servo motion error when using a CTS decreases from 4.8 μm to 0.3 μm experimentally, and the corresponding PV form error for one hexagonal lenslet decreases from 4 μm to 1.4 μm, demonstrating the effectiveness and superiority of a CTS for dynamics error compensation in the manufacturing of complex-shaped optics.