This article proposes and validates the principle of a new magnetorheological elastomer (MRE) dynamic vibration absorber (DVA) for powertrain mount systems of automobiles. The MRE DVA consists of a vibration absorption unit and a passive vibration isolation unit. The vibration absorption unit composed of a magnetic conductor, a shearing sleeve, a bobbin core, an electromagnetic coil, and a circular cylindrical MRE is utilized to absorb the vibration energy, and the passive vibration isolation unit is used to support the powertrain. The finite element method is employed to validate the electromagnetic circuit of the MRE DVA and obtain the electromagnetic characteristics. The theoretical frequency-shift principle is analyzed via the established constitutive equations of the circular cylindrical MRE In order to demonstrate how the parameters of the MRE influence the vibration attenuation performance, the MRE DVA is applied to a powertrain mount system to replace the conventional passive mount. The frequency-shift property of the vibration absorption unit and the vibration attenuation performance of the MRE DVA on the powertrain mount system are experimentally tested. To validate and improve the vibration attenuation performance for the semi-active powertrain mount systems, an optimal variable step algorithm is proposed for the MRE DVA and numerical experiments are carried out.

Based on state observation, a rapid, stable, and effective control algorithm for magnetorheological elastomer (MRE)–based dynamic vibration absorbers (DVAs) applied to automobile powertrain mount systems is proposed and investigated in this article. The state-space model for powertrain mount systems with MRE-based DVAs is established using the rank criterion method for observable systems. According to the principle of system reconfiguration, a full state observation model using an adaptive Kalman filter with Sage–Husa noise estimator is developed. With the state vectors estimated by the Kalman filter, the phase difference between the displacement of the dynamic mass of the MRE-based DVA relative to the powertrain and the absolute displacement of the powertrain is updated continuously based on Simpson’s rule. By adjusting the applied current to the MRE-based DVA with fuzzy logic control corresponding to the cosine value of the phase difference, the natural frequency of the MRE-based DVA could track the excitation frequency of the powertrain well, which results in vibration attenuation of the powertrain mount system. With consideration of excitation noise, time delays, and parametric uncertainties, the simulation experiments of vibration attenuation performance of the MRE-based DVA for the powertrain mount systems when under time-varying excitation are carried out to verify the effectiveness and the stability of the proposed algorithm with fuzzy steps. The simulation results show that when using the proposed algorithm with fuzzy steps, the MRE-based DVA could attenuate the powertrain vibration rapidly and effectively, and the vibration attenuation performance will not be influenced by noise, time delays, and parametric uncertainties.

Magnetorheological elastomers (MREs), a smart composite, exhibit dual characteristics of both MR materials and particle reinforced composites, i.e., the viscoelasticity of MREs depends on external magnetic field as well as strain amplitude and excitation frequency. In this article, the principle of a frequency-, amplitude-, and magneto-dependent linear dynamic viscoelastic model for isotropic MREs is proposed and investigated. The viscoelasticity of MREs is divided into frequency-and amplitude-dependent mechanical viscoelasticity and frequency-, amplitude-, and magneto-dependent magnetic viscoelasticity. Based on the microstructures of ferrous particles and matrix, the relationships between mechanical shear modulus corresponding to the mechanical viscoelasticity and strain amplitude and excitation frequency are obtained. The relationships between magnetic shear modulus corresponding to the magnetic viscoelasticity with strain amplitude, excitation frequency, and further external magnetic field are derived using the magneto-elastic theory. The influence of magnetic saturation on the MR effect is also considered. The dynamic characteristics of a fabricated isotropic MRE sample under different strain amplitudes, excitation frequencies and external magnetic fields are tested. The parameters of the proposed model are identified with the experimental data and the theoretical expressions of shear storage modulus and shear loss modulus of the MRE sample are obtained. In the light of the theoretical expressions, the loss factors of the MRE sample under different loading conditions are analyzed and compared with the test results to evaluate the effectiveness of the proposed model.

A multi-objective robust optimization scheme for the powertrain mount system of an electric vehicle is proposed in this paper. A permanent magnet synchronous motor model is established by taking account of the effects of magnetic saturation and space harmonics, in which the d-q-axis inductance and the flux linkage excited by permanent magnet were obtained by finite element method. The rippled output torque of the permanent magnet synchronous motor mixed with harmonic components is obtained with the New European Driving Cycle as the running condition of the electric vehicle. A six degree-of-freedoms (DOFs) powertrain mount system is established and the response of the system is obtained with the rippled torque as the excitation input. A multi-objective optimization model of the powertrain mount system is built with the stiffness's of the mounts as the design variables, and with the goal of maximizing the decoupling rates and minimizing the dynamic reaction forces of the mounts acting on the car body. Genetic algorithm is used to conduct the global optimization and all the Pareto optimal solutions are found out based on the optimization theory, and the solution with the optimal robustness of dynamic reaction force is obtained by Latin hypercube sampling method. The results show that with the proposed multi-objective robust optimization scheme applied for the parameters optimization of the motor mount system, the decoupling rates increase obviously, the dynamic reaction force decreases apparently, and the optimization result shows good robustness. The optimization results can make the powertrain mount system of electric vehicles processing of optimal dynamic response characteristics correspondingly.

The principle of a magnetorheological elastomer (MRE) dynamic vibration absorber (DVA) is proposed and the corresponding configuration is designed in this paper. The MRE DVA is composed of a vibration absorbing unit and a passive vibration isolation unit. The vibration absorbing unit can be utilized to mitigate the kinetic energy acting on the primary system (i.e., the system of which the vibration will be mitigated) and the passive vibration isolation unit utilized to support the primary system. The vibration absorbing unit consists of magnetic conductor, shearing sleeve, bobbin core, electromagnetic coil winding, and vulcanized MRE between the shearing sleeve and the bobbin core. The magnetic field produced by the electromagnetic coil winding starts from the bobbin core, and passes through the magnetic conductor and the shearing sleeve, then goes through the MRE and forms a closed loop. The shear storage modulus of the MRE could be tuned continuously by varying the applied current, which results in natural frequency shift of the MRE DVA. The optimal parameters of the electromagnetic circuit of the MRE DVA are calculated based on Kirchoff’s law. The finite element method is employed to validate the electromagnetic circuit of the MRE DVA and to obtain the corresponding electromagnetic characteristics. The mathematical model of the MRE DVA is also derived. In order to analyze how the parameters of the MRE DVA influence the effectiveness of the vibration control and to validate the flexibility of the control systems, the MRE DVA is employed in a powertrain mount system to replace the conventional passive mount. A single-degree-of-freedom (SDOF) dynamic model for the semi-active powertrain mount system is established. A varied step optimum algorithm is adopted to realize the vibration control of the powertrain mount system based on the MRE DVA.