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.

中文翻译：

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高非线性动态负刚度线性电磁作动器理论建模与性能分析


为了提高线性电磁执行器的动态性能和抗负载能力，提出了一种具有更高非线性负刚度和速度的新型线性电磁弹性执行器。本文对作动器的非线性力-位移关系和瞬态性能进行了分析和预测。采用解析法、数值法和有限元法建立并求解电磁-机械耦合模型。首先，通过构建创新的轴向磁场分布模型，推导出电磁力的近似解析模型。其次，建立考虑粘性阻尼和滞回阻尼的瞬态动力学模型，并进行理论求解，得到性能指标和系统参数。最后，对解析模型、数值模型、有限元模拟和实验得到的瞬态位移和性能指标进行了比较。通过分析模型和实验，峰值时间、超调量、整定时间和稳定位移的最大误差分别为3.16 ms、6.6%、76.3 ms和0.16 mm。理论和实验结果表明输入电流对性能指标和系统参数的非线性影响。执行器在 8.8 V 电压下可对 20 g 负载产生 8.7 mm 的位移。负载质量是执行器质量的 2.94 倍。通过理论和实验分析，高负刚度为线性电磁执行器提供了更好的瞬态响应和驱动特性。 该研究为非线性电磁动力耦合模型的瞬态求解和线性电磁执行器的性能提升提供参考。