Dynamic and steady-state performance analysis of a linear solenoid parallel elastic actuator (LSPEA) with nonlinear stiffness

Abstract

Abstract In order to predict and evaluate the response time and displacement of a large-stroke, high-speed micro-LSPEA under different currents and springs, numerical and analytical methods are used to obtain the dynamic and steady-state performance indicators of the nonlinear system. Firstly, the analytic functions of the electromagnetic force and the magnetic field distribution were presented. The nonlinear vibration equation was obtained by dynamic modeling. The averaging method and the KBM method were employed to obtain analytical solutions of the undamped system. The equivalent linearization of the damped nonlinear system was performed to obtain the approximate analytical solutions of performance indicators. Finally, the displacement of the actuator equipped with different springs was measured experimentally. Meanwhile, the transient network was constructed by Simulink software to solve the nonlinear equation numerically. The displacement curves and performance indicators obtained by experiment, numerical and analytical methods are compared. The maximum errors of the peak time, overshoot and steady displacement through experiment and simulation are 8.4 ms, 4.36% and 0.59 mm, respectively. The solution result of the vibration equation considering stiffness nonlinearity can reflect the dynamic and steady-state performance of the LSPEA within a certain error, which is helpful for the solution of nonlinear systems caused by multi-physics coupling.