Robotic grinding relies on precise force control to ensure material removal precision and surface quality, particularly in thin-walled workpieces with varying stiffness. This paper introduces a novel electromagnetic variable stiffness actuator (EMVSA) designed to adjust the grinding force on variable-stiffness workpieces by modifying the actuator stiffness. The decoupling control of force and stiffness is achieved at the hardware level through the design of the EMVSA with Lorentz motor (LM) and electromagnetic variable stiffness spring (EVSS). The EVSS, with a ±15 mm displacement, addresses challenges in displacement and stiffness control for robotic grinding. Utilizing electromagnetic and finite element models of the EMVSA, optimization functions are established, followed by an analysis of physical constraints and parameter decoupling. A physically feasible united optimization method for 23 parameters ensures solution viability and comprehensiveness. A prototype of EMVSA is developed for performance evaluation. The output force constant of the LM has a 1.28% error compared to simulation results, and the EVSS stiffness coefficient shows a linearity of 0.9991, aligning with the theoretical design. Furthermore, an environmental stiffness estimation method is integrated with the active control of the EMVSA, and a robotic grinding platform incorporating the EMVSA is constructed. Compared with the series elastic actuator and EMVSA without variable stiffness control, the EMVSA with variable stiffness control reduces the average absolute error of material removal depth by 60.49% and 20.63%, respectively, and reduces the surface roughness by 59.12% and 31.96%, respectively. The results demonstrate the effectiveness and advantages of the developed EMVSA for robotic grinding.

In this paper, a fractional-order model of the gas film is proposed for the dynamic characteristics of an air bearing. Based on the dynamic characteristics common between gas film and viscoelastic body, the idea of the fractional-order equivalent modeling of the dynamic characteristics of the gas film is presented to improve the modeling accuracy. Four fractional-order gas film (FOGF) models are introduced based on generalization of traditional viscoelastic models. The analysis of the characteristics of the FOGF models shows that the FOGF model can capture more complex dynamic characteristics and fit the real dynamic data of the gas film better than traditional models. A genetic algorithm particle swarm optimization (GA-PSO) method is used for parameter identification of the proposed models. The experimental results tested on the air bearing motion platform show that the FOGF models are superior in accuracy to the traditional equivalent models for the gas film. In particular, the fractional-order Maxwell gas film (FOMGF) model has the best capture accuracy compared to the other FOGF models and traditional models.