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The quasi-static model, without considering the inertia effect, is usually used to design and evaluate magnetorheological energy absorbers (MREAs). Although the quasi-static model is generally acceptable to describe the behavior of MREA operated at low velocity and low frequency, it is not sufficient to predict that under high-speed impact conditions. For this situation, we develop an analytical model inclusive of fluid Inertia as well as Minor losses based on the Bingham-plastic model (called BPIM model). In particular, instead of using area-averaged acceleration (assuming fluid acceleration uniformly distributes over the flow cross-sectional area), we directly take the non-averaged acceleration to analyze fluid inertia. Then, the governing equation is obtained from Navier–Stokes equations and continuity equation, in which the time-related term representing inertia effect is no longer neglected. In addition, the expression of damping force is derived by solving the initial-value problems obtained from the governing equation, boundary conditions and initial conditions using the method of separation of variables. Further, the influence of inertia effect and minor losses on MREA force is quantitatively analyzed. Besides, the MREA coupled with disc springs as the storage element is presented, and the nonlinear model of disc spring is employed. To validate the theoretical model, two identical MREAs are fabricated, and a high-speed drop tower is set up to test the two MREAs placed in parallel. It is shown that the BPIM model is capable of well predicting the dynamic behavior of the MREA.

Magnetorheological energy absorbers (MREAs) have manifested their superiority as a controllable damper. An ideal feature for MREA is to remain a constant damping force within a certain impact displacement (referred to as plateau behavior) in the transient impact process. Realizing this plateau behavior by introducing the structure of drain hole is able to effectively reduce harmfulness from the overshoot to the buffered object. In this study, a radial flow mode MREA with a center drain hole configuration is proposed, in order to achieve an approximate plateau as well as to expand the dynamic range. The Power-Law model is employed to analyze the impact behaviors of the MREA due to its smooth shear stress-shear rate curve and simple mathematical form. Five parameters (i.e., plateau angle, radial flow velocity ratio, minor losses ratio, dynamic range ratio, and peak force ratio) are defined to characterize the effects of the drain hole quantitatively and comprehensively. The diameter of center drain hole is specially focused on because of its significant influences on the parameters. Two types of MREAs with/without drain holes are fabricated and tested using a drop tower facility with a 600 kg mass. The experimental results show that the plateau angle of MREA with drain hole is reduced by 56.1% compared to that without hole, and also demonstrate that the Power-Law based model is capable of well predicting the dynamic behavior of the MREA.

Theoretical models are of great significance in the development of magnetorheological energy absorbers (MREAs). There are two types of models, i.e., quasi-steady and dynamic models, depending on whether considering the inertia effect. It is necessary to perform comparative analysis between different models to determine the superiority of a model regarding a specific type of MREA. In our previous work, we proposed a dynamic model by using non-averaged acceleration (NA-BPIM model). This study focuses on giving a comprehensive comparative analysis for the NA-BPIM model with a quasi-steady and another dynamic model (considering inertia effect using area-averaged acceleration, AA-BPIM) for MREA under impact conditions. In order to evaluate the superiority of the models, the comparative analysis is qualitatively and quantitatively performed from the following three aspects: (1) the accuracy of theoretical model to predict MREA peak force, (2) the global agreement of dynamic force curves between model and experiment results and (3) the accuracy of theoretical model to predict the dynamic range. Specifically, the quantitative evaluations are conducted by means of the relative error, RE PF , for MREA peak force, the mean absolute percentage error (MAPE), for the dynamic force curves and the relative error, RE DR , for MREA dynamic range. The results show that the RE PF , MAPE and RE DR of the NA-BPIM model are the smallest when the test condition is given, demonstrating that the dynamic model incorporating non-averaged acceleration is the best to predict MREA dynamic force under high-speed impacts.

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