Theoretical modeling and performance analysis on the linear electromagnetic actuator with high nonlinear dynamic negative stiffness.

• A new linear solenoid elastic actuator (LSEA) with high stiffness is analyzed. • A new analytical model describing axial magnetic field distribution is proposed. • The proposed analytical model has advantages in accuracy and calculation speed. • A composite model with viscous and hysteres damping is developed. In order to improve the dynamic performance and load resistance of linear electromagnetic actuators, a novel linear solenoid elastic actuator with higher nonlinear negative stiffness and speed is proposed. In this paper, the nonlinear force–displacement relationship and transient performance of the actuator is analyzed and predicted. The analytical, numerical and finite element methods are used to establish and solve the electromagnetic–mechanical coupling model. First, the approximate analytical model of the electromagnetic force is derived by constructing an innovative axial magnetic field distribution model. Second, the transient dynamic model considering viscous and hysteretic damping is established and solved theoretically to obtain the performance indicators and system parameters. Finally, the transient displacements and performance indicators obtained from the analytical model, the numerical model, the finite element simulation and the experiment are compared. The maximum errors of the peak time, overshoot, setting time and stable displacement through the analytical model and experiment are 3.16 ms, 6.6 %, 76.3 ms and 0.16 mm, respectively. The theoretical and experimental results show the nonlinear effects of input currents on performance indicators and system parameters. The actuator can produce a displacement of 8.7 mm against a load of 20 g at a voltage of 8.8 V. The mass of the load is 2.94 times that of the actuator. Through the theoretical and experimental analysis, high negative stiffness provides better transient response and driving characteristics for linear electromagnetic actuators. This research provides a reference for the transient solution of nonlinear electromagnetic-dynamic coupling models and performance improvement of linear electromagnetic actuators. [ABSTRACT FROM AUTHOR]