Magnetorheological Energy Absorber Research Articles

Impact behavior of a novel magnetorheological energy absorber based on wedge-shaped squeeze flow model

Magnetorheological (MR) energy absorbers (MREAs) have been extensively investigated as a means of dissipating impact energy and decreasing injury as well as used in a wide range of applications. When applied as an accidental collision buffer, however, problems can arise owing to the inertia of the sudden impact. In this study, a novel MREA with a gradient resistance gap structure working in a wedge-shaped squeeze flow model of a high-viscosity linear polysiloxane-based MR fluid was developed. The MREA has a continuously changing working gap and internal magnetic flux density gradient distribution representing a wedge-shaped structure. A Power-Law model inclusive of fluid minor losses (PLM)- of the damping force of an MREA with a wedge-shaped resistance gap was built to study the impact behavior. A second model also considered the effects of inertia (PLMI). The wedge angle was defined to quantitatively and comprehensively characterize the effects of the wedge-shaped resistance gap because of its significant influence on the dynamic characteristics. Two MREAs with wedge-shaped and equidistant working gaps were fabricated and tested using a drop tower facility with a mass of 600 kg. The experimental results show that the maximum damping force of the MREA with a wedge-shaped resistance working gap reached to as high as 235.8 kN and the dynamic range is increased by 6.5% compared to that with an equidistant working gap. The relative errors of the peak force for impact velocities between 2.8 and 4.2 m s−1 with no applied current were 1.84%–3.67% (PLM) and 0.63%–1.91% (PLMI), and with 3 A applied current were 2.35%–4.99% (PLM), and 1.24%–2.72% (PLMI), demonstrating that the PLMI-based model is capable of accurately predicting the dynamic behavior of the MREA.

Influence of biomechanical compliance on control performance of a magnetorheological sliding seat system

We investigate the feasibility of a sliding seat with a magnetorheological (MR) energy absorber (MREA) to minimize loads transmitted to a payload in a ground vehicle for frontal impact speeds ranging as high as 7 m/s (15.7 mph). The crash pulse for a given impact speed was assumed to be a rectangular deceleration pulse having a prescribed magnitude and duration. The control objective is to bring the seat system to rest using the available stroke, while accommodating changes in impact velocity and occupant mass ranging from a 5th percentile female to a 95th percentile male. The seat system was first treated as a single-degree-of-freedom (SDOF) rigid occupant (RO) model, and two control algorithms are developed: (1) constant Bingham number control and (2) constant force control. To explore the effects of occupant compliance on the adaptive seat system performance, a multi-degree-of-freedom (MDOF) compliant occupant (CO) model was integrated with the seat mass and the same control algorithms were used. Simulation results showed that the designed adaptive controllers successfully controlled load-stroke profiles to bring the seat system to rest in the available stroke and reduced occupant decelerations. Analysis showed extensive coupling between the seat structures and occupant biodynamic response.

Magnetorheological semi-active shock mitigation control. Part I: numerical analysis and preliminary tests

Minimizing shock loads transmitted to sensitive structures or equipment is the objective of shock mitigation control. The core of shock mitigation control using magnetorheological (MR) energy absorber (EA) to minimize impact load is to make full use of the piston stroke of MREA so as to achieve “soft-landing.” The key lies in the precise description of the hysteresis of MREA and the shock mitigation control method. In this part, a single-degree-of-freedom (SDOF) shock mitigation control system using MREA is established, and the corresponding dynamic model and drop-induced shock mitigation test system are established. Based on the optimal Bi number control method and constant force control theory, feedforward controllers featuring resistor-capacitor (RC) operator-based hysteresis model and Bingham model are established to realize “soft-landing” in sequence. Specific performance evaluation indexes for shock mitigation control systems, that is, average velocity change rate (AVCR) and velocity-acceleration conversion ratio (V-ACR), are proposed. The effectiveness of shock mitigation control methods with different models on the MREA-based shock mitigation control system in profiles of simulation and tests are compared and analyzed.

Magnetorheological semi-active shock mitigation control: Part II: System extension and application analysis

In Part I of this work, the dynamic model of drop-induced shock mitigation based on magnetorheological (MR) energy absorber (EA) was deduced. The shock mitigation control effectiveness of constant force control method and optimal Bi number control method were compared based on Bingham model and resistor-capacitor (RC) operator-based hysteresis model. In this part, to further explore the possibility of the application of MREA in the shock mitigation control system, a single-degree-of-freedom (SDOF) shock mitigation control system is built with MREA connected in parallel with a coil spring, which is then connected in series with a vehicle tire to build a one-fourth vehicle suspension shock mitigation control system. Next, the constant force control method and optimal Bi number control method are extended to the SDOF shock mitigation control system. Based on the concept of the optimal Bi number, a two-degree-of-freedom (2DOF) optimal Bi number control method applied to the one-fourth vehicle suspension system is proposed by decoupling and recoupling the damping and stiffness of the vehicle suspension system. Using the control methods conducted in Part I, the motion state of the drop-induced shock mitigation process is simulated and analyzed. The control performances of the control methods in the SDOF shock mitigation control system are compared. Besides, the average velocity change rate (AVCR) and velocity-acceleration conversion ratio (V-ACR) are used to evaluate the effectiveness and stability of the control methods. Finally, the conclusion that the 2DOF optimal Bi number control method can effectively realize the shock mitigation control of a one-fourth vehicle suspension system is verified.

Dynamic behavior of a magnetorheological fluid radial-flow-based energy absorber considering apparent slip boundary condition

Accurate theoretical models play a key role in the development of magnetorheological energy absorbers (MREAs). Traditionally, the apparent slip caused by non-uniformity interface (i.e., the separation of carrier fluid and magnetic particles at the wall) of the working medium is often ignored for simplifying theoretical models. However, the apparent slip influence the cross-sectional flow and decreased the theoretical accuracy of the damping force for MREA applied in the impact absorption area. In this study, a dynamic model with apparent slip boundary condition for radial-flow-based MREA was proposed. The effect of apparent slip layer thickness on the dynamic behavior of an MREA was qualitatively and quantitatively compared in terms of the following three aspects: (1) with the Power-Law constitutive model, theoretical models of the dynamic characteristics of the magnetorheological fluid (MRF) squeeze and MREA are presented based on the apparent slip boundary condition with the MRF behavior of the Navier–Stokes equation; (2) the accuracy of the theoretical model to predict MREA peak force and boundary velocity with different slip-layer thicknesses; and (3) global agreement of the dynamic force and range curves between the modeling and experimental results. The results show that the absolute values of the relative errors in the two models with a 2- and 0-µm thick slip layer were less than 3.73 and 7.41%, respectively, and that a 2-µm thickness can help predict the actual dynamic characteristic more efficiently under accidental collision loading conditions.

Hybrid modeling of the nonlinear behaviors for magnetorheological energy absorber

Precise forecast of strong nonlinear behaviors of magnetorheological energy absorber (MREA) plays a significant role in its semi-active control and engineering applications. This study proposes a hybrid model based on the support vector regression (SVR) and adaptive differential evolution (i.e., JADE) algorithm for MREA, called the JADE-SVR model. The JADE algorithm is employed to find the optimal hyperparameters of SVR to improve prediction accuracy and generalization ability. The JADE-SVR model is developed using the training data randomly partitioned from an impact test database, and then applied to predict the nonlinear behaviors of MREA in the test set, including force–time, force–displacement and force–velocity characteristics. It is demonstrated that the JADE-SVR model is capable of forecasting strong nonlinear behaviors of MREA under various impact conditions. Moreover, the JADE-SVR model is compared with other SVR-based models to validate its prediction accuracy and convergence rate further. In addition to four statistical indicators, a novel desirability function is used to assess the overall performance of these models. The results show that the JADE-SVR model has the optimal values for all the performance indices, and the largest overall desirability of 0.6274. Therefore, it can be concluded that the JADE-SVR model is the best one for forecasting the dynamic behaviors of MREA under high-impact loadings.

Unsteady extension of quasi-steady physical modeling and experimental verification of a magnetorheological energy absorber

Magnetorheological (MR) fluids are promising in controllable damping based on regulated apparent viscosity under magnetic field control, and they are employed in various damping devices such as automotive dampers and energy absorbers for artillery or landing gears by medium substitution with structural adaptations. In this study, we designed and fabricated a magnetorheological energy absorber (MREA) with disc springs as recoiling parts, modeled the MR fluid flow based on the Bingham constitutive model, and then carried out unsteady extension based on the quasi-steady model. The experimental tests of the MREA show that the unsteady extension of the quasi-steady model can designate the behaviors of the MREA in different impact speeds better than the original; thus, the controllability of the MREA is verified. An interesting phenomenon, where a rippled MREA peak force is observed at the saturated excitation when the impact speed is not so high and disappears when the impact speed is high enough, is accounted from the viewpoint of flow modeling and finally verified by more experimental results.

ANFIS with input space division for modeling magnetorheological energy absorber

A magnetorheological energy absorber (MREA) is a promising actuator for vibration and shock mitigation due to its continuous and controllable damping force. To take full advantage of this feature, a high-fidelity model that can accurately predict the MREA dynamic force is required. Therefore, this study focuses on proposing adaptive neural-fuzzy inference system (ANFIS) models for MREA that use the impact speed, displacement, velocity, acceleration and current as inputs and the MREA force as output. Three types of ANFIS models are developed based on different input space division methods, namely, the grid partition (GP) method, subtractive clustering (SC) algorithm and fuzzy c-means (FCM) algorithm. The best ANFIS model is chosen from each category by six criteria, i.e., mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), coefficient of variation (cov), coefficient of determination (R2) and training time. In addition, the desirability function is proposed to further decide the best model because these criteria do not have a uniform trend. Then, a comprehensive comparative analysis of the three best models is performed. The results show that the ANFIS model with 53 FIS rules generated by the FCM algorithm has the largest global desirability of 0.66782, demonstrating that it is the best one to predict the dynamic force of MREA under high-speed impacts. Accordingly, the values of MAE, MAPE, RMSE, cov and R2 of this model varied in ranges of 0.31679-0.57118, 4.34181-8.43942, 0.44808-1.03095, 6.14134-15.23283 and 0.98973-0.99834, respectively, for various data sets.

A minimum transmitted load control method for shock isolation mounts with magnetorheological energy absorbers

This paper proposed a minimum transmitted load (MTL) control method for drop-induced shock isolation mounts (SIM) with magnetorheological energy absorbers (MREAs). MTL control method consists of two parts of maximum damping force (MDF) control and one part of constant acceleration (CA) control, which can make the payload stop after fully utilize MREA stroke (soft landing) with minimum transmitted load. The control algorithm of MTL control method is derived in a single-degree-of-freedom (SDOF) system. The relationship between the controllable velocity range of MTL control method and parameters of shock isolation mounts is also derived. An optimal control method selection criterion between Bingham number (BN) control method and MTL control method is developed. The performance of MTL control method and selection criterion are shown by applying to the SIM system with variable drop velocities and system parameters. Results shows that MTL control method has the minimum transmitted load and the selection criterion is feasible.

A Dynamic Model and Parameter Identification of High Viscosity Magnetorheological Fluid-Based Energy Absorber with Radial Flow Mode.

The excellent suspension stability of the high-viscosity linear polysiloxane magnetorheological fluid (HVLP MRF) makes it a great controlled medium for magnetorheological energy absorbers (MREAs). In our previous work, the Herschel–Bulkley flow model (HB model) was used to describe the shear-thinning rheological behavior and establish the dynamic model of an HVLP MRF-based MREA with radial flow mode. However, as the established model was implicit, the MREA response time increased and the buffer effect was degraded. To improve the time response characteristics, an explicit dynamic model based on the HB model incorporating minor losses (called the E-HBM model) is proposed in this study. The model parameters were identified based on the HBM model. To verify the E-HBM model, five evaluation parameters for the energy absorption performance of the MREA, that is, peak force, mean force, crush force efficiency, specific energy absorption, and stroke efficiency, were introduced to compare the theoretical results with the experimental results obtained using a high-speed drop tower facility with a mass of 600 kg. Then, the relative error of the crush force efficiency, specific energy absorption, and stroke efficiency was quantitatively and comprehensively analyzed considering the E-HBM model and experimental results. The results indicate that the proposed E-HBM model agrees with the impact behavior of the radial flow mode MREA.

An improved constant deceleration control method with extended shock velocity range for magnetorheological energy absorber

This paper proposed an extended constant deceleration (ECD) control method that can be used in the shock mitigation system with magnetorheological energy absorbers (MREAs). The ECD control method has three sections: zero controllable force (ZCF) section, constant deceleration (CD) section, and maximum damping force (MDF) section. Under the control of ECD, the system can stop at the end of MREA stroke without exceeding the maximum allowable deceleration. The ECD control algorithm is derived in a single-degree-of-freedom (SDOF) system. The controllable velocity range and the required controllable damping force of ECD control method are also derived, which can provide feasible solutions for the design of shock isolation system with MREAs. The performance of ECD control method is shown by applying to the drop-induced shock mitigation system with different drop velocities, different maximum controllable damping force, and MREA stroke. The results shows that the ECD control method not only has a large controllable velocity range and small controllable damping force requirement, but also can minimize the load transmitted to the system.

An adaptive shock mitigation control method for helicopter seat system with magnetorheological energy absorbers

This research presents a minimal maximum deceleration (MMD) control method which can be used in the shock mitigation system with magnetorheological energy absorbers (MREAs). The proposed control method can make the payload stop at the end of the available MREA stroke with the lowest maximum deceleration, which does not exceed the deceleration threshold value and lead to the lowest occupant injury probability. The shock mitigation system controlled by MMD will experience constant deceleration control stage and maximum damping force control stage while making full use of the available MREA stroke. The comparative performance of the MMD control method with Bingham number (BN) control, constant deceleration (CD) control and minimum duration deceleration exposure (MDDE) control is shown. Then, the controllable drop velocity range and the required maximum MREA controllable damping force range of MMD control method is calculated. Subsequently, the optimal control method selection criterion among BN control method, CD control method and MMD control method is developed. Finally, the optimal selection criterion is applied to the drop induced shock mitigation system with varying payload velocity, payload mass (occupant type) and the maximum controllable damping force of MREA.

Optimal control of drop-induced shock mitigation using magnetorheological energy absorbers considering quadratic damping

The optimal control of a magnetorheological energy absorber (MREA) shock mitigation system is investigated considering quadratic damping in the MREA. To this end, the equation of motion of a single-degree-of-freedom (SDOF) shock suspension system using an MREA with quadratic damping is analyzed. To achieve a soft landing and to maintain stroking load below a maximum allowable value, it is required that the payload comes to rest after fully utilizing the available stroke. For low sink rates, a generalized Bingham number (quadratic) or GBN-Q control algorithm is developed that achieves a soft landing by selecting an initial magnetorheological (MR) force level or generalized Bingham number (GBN) for the quadratic damping at the initial sink rate. To cope with the cases above a critical sink rate, where the deceleration exceeds a maximum allowable threshold when using the GBN-Q control only, a minimum duration deceleration exposure-quadratic (MDDE-Q) controller is developed. This controller seeks to maintain the stroking load at its maximum allowable threshold until the payload slows such that the GBN-Q controller can be used to achieve the soft landing condition. The switching methodology between the GBN-Q controller and the MDDE-Q controller is discussed. Each control method relies on an optimal GBN that is computed to ensure a soft landing. Results show that the MDDE-Q controller can successfully minimize the exposure of the payload to the maximum allowable stroking load.

Experimental Test and Analysis of “Soft-landing” Control for Drop-induced Shock Systems using Magnetorheological Energy Absorber

Experimental Test and Analysis of “Soft-landing” Control for Drop-induced Shock Systems using Magnetorheological Energy Absorber

A novel passive adaptive magnetorheological energy absorber

For traditional magnetorheological (MR) shock absorbers, the damping force is proportional to the square of the impact velocity. The instantaneous peak value of the damping force can easily cause damage to the load structure or human body, which will reduce the buffering efficiency. The viscous damping force is significantly affected by the size of the gap. Therefore, by changing the flow gap under different buffer strokes by presetting, the damping force can be maintained at a constant output in the full piston stroke, thereby improving the buffer efficiency. That is, a large gap is used at high speed and a small gap is used at low speed. The increase of the magnetic damping force at a small gap is applied to compensate for the decrease of the viscous force at low speed. Only constant current needs to be applied during buffering, which can greatly reduce costs. Based on this idea, a novel MR damper based on axial variable damping gap (MRD-VDG) is proposed. The MRD-VDG design method for the constant value output of the damping force in the full piston stroke is discussed and applied. According to the different requirements of the damping force under different piston displacements, the damping gap of different axial position are preset to realize the constant value output of the damping force during the stroke. The damping force under different damping gaps is analytically derived according to the Bingham-plastic nonlinear flow model with minor losses. Combining with the finite element analysis to obtain magnetic fields at different damping gaps between piston and cylinder. To validate the performance of the proposed design method, the prototype of MRD-VDG is fabricated. Damping characteristic test and impact test are performed to measure the damping characteristics of the MRD-VDG under different excited conditions. The results show that the piston displacement history of the damping force in the experiment is agreed well with the displacement history of the desired F-S curve under the assumed speed. The buffer efficiency of the prototype under designed conditions (the ratio of the corrected theoretical constant damping force to the actual peak damping force) exceeds 90%. This demonstrates the effectiveness of the MRD-VDG design. This design method has significant application prospects under impact condition without complex control (such as gun buffer, landing buffer, etc.)

Adaptive magnetorheological energy absorber control method for drop-induced shock mitigation

This paper presents a minimum duration deceleration exposure (MDDE) control method for drop-induced shock mitigation system using a magnetorheological energy absorber (MREA) at high sink rates. The key MDDE control goal is that the payload should come to rest after fully using the available MREA stroke, that is, to accomplish a soft landing, without exceeding the maximum allowable deceleration and simultaneously minimizing the duration of exposure to the maximum allowable deceleration. The MDDE control algorithm is developed as follows for a given available stroke. The payload deceleration is initially set to the maximum allowable value and held constant until the remaining damper stroke and payload velocity are such that the Bingham number control can be used for the terminal trajectory to ensure a soft landing. The sink rate range of the MDDE control is calculated and the results show that the MDDE control can be utilized at high sink rates, whereas prior Bingham number control can be used only at sufficiently low sink rates without violating the maximum allowable deceleration constraint. An optimal criterion to switch from the BN control method to MDDE control method is developed. Finally, the optimal control method is applied for a helicopter seat suspension system by optimal selection criterion to automatically accommodate varying sink rate (drop velocity) and occupant weight.

A design methodology based on full dynamic model for magnetorheological energy absorber equipped with disc springs

The spring of magnetorheological energy absorber (MREA) is an indispensable component that provides a restoring force for the piston back to the initial position. To reduce impact force, the stroke of a typical MREA is usually sacrificed (i.e., extended stroke and prolonged buffer time). In some situations, however, a fast return of piston is required and the impact load is huge. It is difficult for conventional coil/gas springs to qualify due to the limitations in obtaining high stiffness. In this study, we employ the disc spring as a rebound element for MREA because of its feature in providing large force within narrow deformation. Optimal designs are significant for improving the MREA performance, but most of them have been developed based on the quasi-static model that ignores inertia effect. However, the inertia effect becomes an important role in dynamic behavior under high-speed impacts. Most recently, we proposed a full dynamic model considering inertia effect by using the non-averaged acceleration. As a further step, this study presents a design methodology based on this full dynamic model for an MREA with disc spring. The design objective is to identify the geometric dimensions of disc spring and MR valve to return the piston back to its initial position as fast as possible after a fast impact loading. The design flowcharts for disc spring and MR valve are presented. The load-deflection relationship of disc spring is obtained based on Almen–Laszlo theory. The magnetic field intensity in the MR gap is analyzed by using Kirchhoff’s law and the magnetic flux conversation rule. Two identical MREAs are fabricated and tested via a high-speed drop tower system. The effectiveness of the design methodology is validated by a comparison of MREA behaviors between the tests and full dynamic modeling.

A comparative analysis of magnetorheological energy absorber models under impact conditions

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, REPF, for MREA peak force, the mean absolute percentage error (MAPE), for the dynamic force curves and the relative error, REDR, for MREA dynamic range. The results show that the REPF, MAPE and REDR 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.

Design optimization of a bi-fold MR energy absorber subjected to impact loading for skid landing gear applications

Dynamic range is an important characteristic index to evaluate the performance of magnetorheological energy absorbers (MREAs). In high-speed impact, the dynamic range may fall into the uncontrollable zone due to the increase in the off-state damping force. This is attributed to the transition of the flow from laminar to turbulent state. Thus, it is important to design optimize the MREA to maintain high controllability. To accurately evaluate the damping force, Bingham plastic model with minor loss factors (BPM) has been utilized to formulate the problem. The magneto-static analysis of the MREA valve has been conducted analytically and using magnetic finite element analysis in order to obtain the induced magnetic flux in the MR fluid active gap region against the applied current. Then, using BPM, a design optimization problem has been formulated to optimally design a bi-fold MREA to maximize its dynamic range at an impact velocity of 5 m s−1 while satisfying the constraints. Both genetic algorithm and sequential quadratic programming methods are utilized to capture the accurate global optimal solution. Finally, the performance of the optimized bi-fold MREA is evaluated first under different impact velocities, input currents, and then compared with that of equivalent single-flow path MREA.

Monitoring sedimentation of magnetorheological fluids using a vertical axis monitoring system with a low aspect ratio sensor coil**This research was conducted at the University of Maryland while the first author was a visiting student.

Adaptive energy absorbers (EAs) utilizing magnetorheological fluids (MRFs) are currently being investigated for severe impact or shock mitigation problems because magnetorheological energy absorbers can adjust stroking load to account for severity of impact and payload mass. Utilizing MRFs in such EAs requires a highly stable suspension that maintains a uniform concentration. Suspension stability of MRFs can be studied using a MRF column and an automated vertical axis inductance monitoring system (AVAIMS), where an inductance sensor is translated up and down the vertical MRF column to track the mud-line, defined as the boundary between the clarified fluid at the top of the column and the MRF below. The rate of descent of the mud-line is typically referred to as the sedimentation rate of the MRF. In this paper, a refined inductance sensor is developed that features a low aspect ratio coil to better localize rapid changes in concentration or sedimentation zone boundaries, as well as to improve symmetry of the applied magnetic field in the MRF sample enclosed by the sensor. This low aspect ratio solenoid (LARS) sensor was developed to measure the vertical distribution of the concentration of carbonyl iron particles in the MRF column. Compared with the high aspect ratio solenoid sensor used in our prior work, the results of FEM simulation and sedimentation experiments demonstrate that the LARS sensor was better able to localize rapid changes in concentration or density. Using the AVAIMS with the refined LARS sensor, a method was developed, based on the measured concentration gradient profile, to identify sedimentation zone boundaries in an MRF column, and these results were compared to our prior work using the measured concentration profile only. Sedimentation zone boundaries that are consistent with Kynch’s sedimentation theory were obtained using the concentration gradient profile method, such as monotonically descending mud-line, linearly ascending gel-line, and linearly ascending cake-line. Key metrics to characterize the time histories of the sedimentation zone boundaries are measured including mud-line descent rate, gel-line ascent rate, and cake-line ascent rate. Identification of sedimentation zone boundaries using the LARS sensor in conjunction with the concentration gradient profile method exhibited two main advantages including the direct measurement and improved localization of the large concentration change that occurs at a sedimentation zone boundary, and the elimination of sensor bias.