Position-dependent system dynamics modeling for diamond turning of microlens arrays

The increasing demand for micro-lens arrays (MLAs) in advanced optical applications necessitates ultra-precision machining techniques capable of achieving sub-micron form accuracy and nanometric surface quality. This study introduces a novel position-dependent system dynamics modeling approach for ultra-precision diamond turning of MLAs. A electromechanical model of the coreless permanent magnet linear motor (CPMLM) driving the slow tool servo (STS) system is developed to characterize position-dependent nonlinearities arising from electromagnetic field variations. The proposed model establishes a position-dependent transfer function that accurately predicts dynamic tracking errors across different machining positions. Experimental validation confirms strong agreement between the modeled and actual system responses, with frequency-domain deviations below 0.3 dB across the 0–200 Hz bandwidth. Leveraging this predictive capability, an iterative compensation strategy incorporating segmented trajectory optimization is introduced to systematically reduce tracking errors. Comparative machining experiments demonstrate that the proposed method achieves a 63.6 % reduction in tracking errors and a 56.1 % improvement in MLA surface form accuracy, effectively mitigating position-dependent machining inconsistencies. These findings provide a robust framework for enhancing the precision and stability of ultra-precision machining systems, offering practical advancements for high-performance optical component fabrication.