Development of a novel decoupled dual-axial elliptical vibration-assisted cutting stage utilizing the stiffness matrix model and screw theory

Abstract Elliptical vibration-assisted cutting (EVC) is an advanced machining process that creates micro-nanostructures. However, the current device faces low efficiency and motion accuracy problems. To solve this problem, this paper develops a high-precision dual-axial EVC stage utilizing a stiffness matrix model and screw theory. The stage integrates a compliant mechanism with two stacked piezoelectric actuators. The compliant mechanism is made up of the bridge-type amplification mechanism and the double parallelogram mechanism, with a mirror-symmetric layout. The input/output stiffness, amplification ratio, and the natural frequency of the compliant mechanism are analyzed via a mathematical model. The mechanism design is optimized by applying an improved differential evolution algorithm, which deals with a nonlinear optimization problem within the given performance constraints. The effectiveness of the optimized compliant mechanism is validated via the finite element simulation. An open-loop test shows that the developed dual-axial EVC stage has low coupling and high natural frequencies. To enhance the motion accuracy, a closed-loop control system is designed to obtain high tracking accuracy for a sinusoidal trajectory with a frequency of 100 Hz and an amplitude of 10 μm. The tracking errors are within ±0.9% and ±0.8%, demonstrating the superior performance of the dual-axial EVC stage.