Friction modeling and parameter identification for ultra-low-speed lifting motion of single-crystal silicon

In the Czochralski crystal growth process, a single-crystal silicon (SCS) ingot is pulled and rotated at an ultra-low speed during the entire process, which lasts around a hundred hours per batch. However, nonlinear friction disturbances can lead to speed jitter and creeping phenomena of an SCS lifting servo system, which can further affect the produced SCS’s quality. The classical LuGre friction model considers only the speed factor and, thus, cannot fully describe the friction characteristics of a complex SCS lifting servo system. To address this limitation, this paper proposes an improved LuGre friction model that considers the effects of weight variations and rotation of an SCS ingot. In addition, a parameter identification method is developed to estimate the friction model’s parameters. To overcome the problems in traditional optimization algorithms of easy falling into a local optimum and a slow convergence speed in multi-dimensional parameter space, this study divides the parameter identification into two stages: static and dynamic stages. Particularly, in the dynamic stage, an improved particle swarm optimization algorithm, which adopts a chaotic mapping and inertia weight nonlinear change strategy, is employed to improve the precision and convergence rate of the optimization process. The results of the experiments on an SCS lifting servo system demonstrate the high efficiency of the proposed method.