Model Of Magnetorheological Damper Research Articles

Multi-condition adaptive detail characterization model of magnetorheological dampers and experimental verification

The theoretical model for predicting the damping characteristics of magnetorheological dampers (MRDs) is significant for enhancing the design efficiency of the control algorithm. However, some existing theoretical models face limitations in characterizing MRD damping characteristics simultaneously in terms of nonlinear detail characterization and adaptability to variable working conditions. Therefore, this paper proposed the Composite Double-Boltzmann (CDB) model combining the Double-Boltzmann (DB) function widely used in the field of biology and chemistry for its strong nonlinear characterization capability. Utilizing this model to fit the sinusoidal vibration testing data of the MRD prototype under variable combination working conditions, obtaining quantitative relationships between the undetermined parameters in the CDB model and the excitation current, vibration frequency, and amplitude to enable the model to address both the nonlinear details characterization of MRDs and adaptability to variable working conditions. Subsequently, the validity of the quantitative relationships were verified by comparing the calculated parameter values using the quantitative relationships with the original accurate parameter values. In order to verify the validity of the CDB model, extensive unknown working condition vibration tests were conducted on the MRD prototype under variable excitation currents, vibration frequencies, amplitudes and random excitation working conditions, employing the CDB and Tanh models to predict the damping characteristics, to compare to demonstrate the CDB model’s capability of adapting to variable working conditions while accurately characterizing the nonlinear details of MRD damping characteristics.

SIMULATION STUDY ON PARAMETRIC MODELLING OF MAGNETORHEOLOGICAL DAMPER SYSTEM

The Magnetorheological (MR) damper system serves as a semi-active suspension system designed to absorb road disturbances. This research aims to replicate the MR damper system through a parametric modeling approach, specifically employing the Simple Bouc-Wen Model, Spencer Model, and Hyperbolic-Tangent Model. The objective of this paper is to assess the effectiveness of these modeled MR damper systems with the utilization of a Fuzzy-PID controller. The simulation process is conducted within MATLAB Simulink, whereby a block diagram is devised based on equations related to the suspension system and the parametric models. The inputs for the system encompass sinusoidal and bump road profiles. The outcomes from the modeled MR damper systems reveal that the semi-active suspension system outperforms the passive suspension system. The primary simulation metrics under consideration include sprung displacement, sprung acceleration, and unsprung acceleration. Among the three MR damper models, the Hyperbolic-tangent model displays the most favorable performance, with a mean squared error of 51.44%, while the Bouc-Wen model exhibits the least favorable performance, registering a mean squared error of 25.96%. The integration of the Fuzzy-PID controller demonstrates an enhancement in the sprung suspension system, though the sprung acceleration remains relatively unchanged.

An invertible hysteresis model for magnetorheological damper with improved adaption capability in frequency and amplitude

It is found during the tests that the damping characteristics of the magnetorheological (MR) damper vary with the excitation amplitude and frequency. However, the existing MR damper models are not able to accommodate the change of excitation amplitude and frequency, which will lead to significant modeling errors. To deal with this problem, this paper analyzes the experimental data and obtains the regularity of the damping characteristics varying with the excitation. Subsequently, an excitation-adaptive MR damper model is constructed based on the hyperbolic tangent function. The proposed model is not only able to adapt to the change of excitation amplitude and frequency but also able to inverse, which is essential for MR damper controller construction. The fitting results show that compared with the existing models, the three normalized errors of the proposed model are improved from 22.61%, 13.96%, and 19.42%–6.30%, 3.81%, and 6.97%, respectively, indicating that the model excitation adaptivity is significantly improved. Furthermore, this study also proposed a damper controller based on the new model, and the simulation results verify the effectiveness of the controller. The proposed model brings the acceleration signal into the model to improve the model adaptivity, which introduces a novel approach to enhance the adaptivity of MR damper models.

Dual-stage theoretical model of magnetorheological dampers and experimental verification

The theoretical model for predicting the damping characteristics of magnetorheological dampers (MRDs) not only facilitates the optimization of MRD parameters, but also provides assistance for the theoretical design of MRDs. However, some existing models have limitations in fully characterizing the damping characteristics of MRDs. In this paper, the working stage of MRDs was categorized into yield and pre-yield stages based on whether the internal magnetorheological fluid attains the dynamic shear yield state or not, and the Herschel–Bulkley model with pre-yield viscosity (HBPV) and improved polynomial model (IPOL) were employed to respectively characterize the yield and pre-yield stages of MRDs. Subsequently, the HBPV-IPOL model was proposed to characterize the complete damping characteristics of MRDs in low-frequency vibration conditions, with considering the local loss effect of the fluid in the model. To accurately characterize the magnetic induction intensity in the MRD damping channel, employing the steady-state finite element method for magnetic field analysis; on this basis, dividing the damping channel to investigate the variation trends of the magnetic induction intensity in different regions. Simultaneously, the zero-field region hypothesis was proposed to quantitatively consider the influence of minute magnetic induction intensity in the traditional zero-field regions on the damping characteristics of MRDs. Finally, integrating the impact trends of currents in different regions, and employing the HBPV model to determine the impact magnitude of each region within the damping channel on the damping characteristics of the MRD in the yield stage. In the pre-yield stage, polynomial curves were fitted to experimental damping force–velocity curves, and the obtained polynomials were employed to predict the damping characteristics. Extensive experiments have been conducted on MRD samples to assess the predictive performance of the model on MRD damping characteristics under sinusoidal displacement excitation vibration conditions with different excitation currents, vibration frequencies and vibration amplitudes.

A Particle-Swarm-Optimization-Algorithm-Improved Jiles–Atherton Model for Magnetorheological Dampers Considering Magnetic Hysteresis Characteristics

As a typical intelligent device, magnetorheological (MR) dampers have been widely applied in vibration control and mitigation. However, the inherent hysteresis characteristics of magnetic materials can cause significant time delays and fluctuations, affecting the controllability and damping performance of MR dampers. Most existing mathematical models have not considered the adverse effects of magnetic hysteresis characteristics, and this study aims to consider such effects in MR damper models. Based on the magnetic circuit analysis of MR dampers, the Jiles–Atherton (J-A) model is adopted to characterize the magnetic hysteresis properties. Then, a weight adaptive particle swarm optimization algorithm (PSO) is introduced to the J-A model for efficient parameter identifications of this model, in which the differential evolution and the Cauchy variation are combined to improve the diversity of the population and the ability to jump out of the local optimal solution. The results obtained from the improved J-A model are compared with the experimental data under different working conditions, and it shows that the proposed J-A model can accurately predict the damping performance of MR dampers with magnetic hysteresis characteristics.

Response Characteristics and Suppression of Transverse Vibrations of Mine Hoisting Conveyances Excited by Multiple Faults

The failures of steel guides can excite complex and intense transverse oscillations of hoisting containers in the mine hoisting process. The present paper mainly contributes to reveal the response characteristics of the transverse oscillations of mine conveyances excited by various faults such as interface misalignment, local bulge, orbital gap, bending deformation, and orbital tilt. First, a rigid-flexible coupled virtual prototype model between the conveyance and the steel guide was established. Subsequently, the vibration response characteristics of the container under various single and coupling excitations were simulated and analyzed. Eventually, a new type of roller cage shoe with a magnetorheological damper was put forward to decrease the transverse impact responses. Based on the hyperbolic tangent model of magnetorheological dampers, a semiactive fuzzy PID method was studied to explore the vibration suppression of the container. The results showed the fuzzy PID method can play a good role in the vibration reduction. This paper can give a fine scheme for the virtual simulation and semiactive vibration control of the mine hoisting system.

Modeling of magnetorheological dampers based on a dual-flow neural network with efficient channel attention

Magnetorheological dampers (MRDs) are intelligent devices for semi-active control and are widely applied in vibration isolation. A high-fidelity modeling method is necessary to take full advantage of the controllable properties of MRDs. Therefore, a nested long short-term memory (NLSTM)-convolutional neural network-efficient channel attention (NLCE) modeling method based on a dual-flow neural network architecture is proposed herein. It uses the time, current, amplitude, frequency, displacement, and velocity as inputs and the damping force as the output. Extensive sinusoidal excitation experiments were conducted using a materials test system and two datasets (large and small sample numbers) were obtained. Five testing sets with different emphases were obtained from different experimental series. Four evaluation indexes were used for a quantitative comparison. First, after training with the large sample dataset, network ablation and comparison experiments were conducted based on a testing set-1. The mean absolute relative error (MARE) evaluation index decreased by 2.290% relative to that of the NLSTM (baseline), indicating that the NLCE method is optimal for predicting the motion characteristics of MRDs. Furthermore, after training with the small sample dataset, comparison experiments were conducted based on testing set-1 and testing set-2. The MAREs decreased by 3.984% and 0.871% relative to that of the NLSTM (baseline), respectively, indicating that the NLCE is also the best modeling method for small sample dataset. The visualization results from the above experiments verified the abilities of the NLCE modeling method for small sample-adaptation, fighting randomness, and identifying similarities. Finally, based on testing set-3, testing set-4 and testing set-5, the NLCE model trained with small sample datasets has high prediction accuracy in predicting the peak damping force (MAREs = 1.456%, 0.880%, and 1.482%, respectively), indicating a high prediction accuracy in the non-hysteretic region. Combining all of the experimental results shows that the NLCE is an effective method for predicting the motion characteristics of MRDs.

A Case Study of Magnetorheological Damper Models with Experimental Confirmation

This study aims to review and evaluate the performance of nonparametric and parametric models of magnetorheological (MR) dampers, which are commonly used as structural control devices. To do so, a comprehensive experimental investigation was conducted to examine the behavior of MR dampers to ascertain the performance of the control device while mimicking the alignment when it is used as a structural control device. A total of 156 performance tests were performed, and the results were compared with an optimal numerical Bouc-Wen model. The parameters obtained from performance testing were employed to define the coefficient of determination (R2), which reflects the accuracy of the damper model in predicting the performance of the control device subjected to different external forces. The findings suggest that the parameters of the MR damper obtained from testing the device in a horizontal orientation that simulates its position in practical structural control applications can be reliably predicted by the modified Bouc-Wen model. This study provides useful information on the efficiency and accuracy of MR damper models that can be utilized in the realm of structural vibration control.

A phenomenological model of magnetorheological damper considering fluid deficiency

The primary goal of this paper is to develop a new phenomenological model which is able to accurately describe the nonlinear behaviors of magnetorheological (MR) dampers with fluid deficiency. A multi-channel bypass MR damper with three working modes is tested on the dynamic testing system and the test results are presented for different excitation amplitudes, excitation frequencies, exciting currents, and MR damper working modes. Based on the experimental curves, the void-like phenomenon caused by fluid deficiency is observed and the essence of the phenomenon is deduced. A new phenomenological model is established accordingly, and the influence of model parameters on force-displacement curves and force-velocity curves are analyzed. The model is validated against experimental data, and the comparisons of this model with commonly used MR damper models, including the Bouc-Wen model and Bingham model, are carried out. It is concluded that the proposed phenomenological model has much higher accuracy than the Bouc-Wen model and Bingham model in describing the dynamic characteristics of fluid-deficient MR dampers.

Development of a new dynamic hysteresis model for magnetorheological dampers with annular-radial gaps considering fluid inertia and compressibility

Modeling the inherent non-linear dynamic hysteresis behavior of magnetorheological (MR) fluid dampers is a fundamental necessity for their practical implementation. Quasi-static models, have been developed under very low frequency and small amplitude excitation conditions, are only beneficial in the early stages of MR dampers design and are sufficient for manufacturing requirements. These models, however, have failed to predict the non-linear hysteresis behavior of MR dampers (i.e., force-displacement and force-velocity characteristics) under low to moderate ranges of frequency and displacement amplitudes. The main contribution of the present work is to formulate a novel physic-based dynamic model to predict the non-linear behavior of MR dampers featuring an annular-radial bypass valve under different applied currents, and low to moderate input excitations. The proposed model incorporates unsteady fluid behavior and the fluid compressibility effect on the hysteretic response without relying on experimental data to evaluate the model parameters. To derive the model, the velocity profile and the pressure drop have been derived by solving the fluid momentum equation via the Laplace transform technique and Cauchy residue theory. The continuity equation has been employed for considering the compressibility contribution to hysteretic response based on the variation of bulk moduli. The predicted results for the force-displacement and force-velocity behavior of the MR damper were subsequently compared with the experimental results. Results suggest the effectiveness of the proposed model for predicting the dynamic hysteresis characteristics of the annular-radial MR fluid dampers under the relatively sufficient variation of mechanical and magnetic loading conditions considered.

Accurate prediction of magnetorheological damper characteristics based on a new rheological constitutive model

Physical modeling of magnetorheological dampers (MRDs) plays a crucial role in understanding the dynamic characteristics, optimizing design, and developing control algorithms of MRDs. The systematic study of various factors indicates that an accurate magnetorheological fluid (MRF) rheological model can effectively improve the estimation accuracy of the MRD physical model. The difficulty in establishing an accurate MRF model lies in the rheological behavior of MRFs at low and medium shear rates (0.01 ∼ 103 s−1) measured by commonly used rheometers exhibits notable differences from that at extremely high shear rates (105 ∼ 107 s−1) in MRDs. Therefore, this paper proposes to estimate the rheological behavior of MRFs at extremely high shear rates using the exponential linear mixed analytical (ELMA) model with excellent description and prediction capabilities, combined with the infinite viscosity and nonlinear term decay rate constraints determined based on rheology and related limited rheological data. This paper constructs a series of predictive MRD physical models combined with other relevant information, from the simple analytical model to the complex numerical model. The simulation results of the monotube MRD physical model, constructed based on the ELMA model identified by the above method and considering all deformation and inertial effects, are consistent with the corresponding dynamic test results of the MRD, reflecting the effectiveness and prospect of the parameter identification method and physical model.

Fault detection combining adaptive degrees of freedom χ2-statistics and interval approach for nonlinear systems

An enlargement of the Adaptive degrees of freedom χ2-statistics (ADFC) method to fault detection for nonlinear systems with mixed uncertainties (stochastic and bounded uncertainties) is presented in this paper. The ADFC approach, primarily developped for fault detection in case of linear systems, is then combined with the Reinforced likelihood box particle filter (RLBPF). A residual generator is used, followed by the adaptive amplifier coefficient (a.a.c.) concept in the decision making stage. Then, the proposed approach is applied to a nonlinear Magneto-Rheological damper model to illustrate the efficiency of the method.

Selection of MR damper model suitable for SMC applied to semi-active suspension system by using similarity measures

Abstract This article discusses the research to determine the suitable magnetorheological (MR) damper model to produce the damping force generated by the sliding mode control (SMC) strategy. The MR damper models studied are parametric, i.e., the Bingham model, the Bouc-Wen model, and the Bouc-Wen model with a hyperbolic tangent function. The damping force of SMC usually includes sudden changes in the force and chattering. The research was carried out by calculating the value of the similarity measure of the damping force of the controller and the damping force of each model. The results show that the two Bouc Wen models had a high similarity measure. The Bouc Wen model with the hyperbolic tangent function was selected because it provides a sudden change of force and reasonable force tracking needed to develop the inverse MR damper model.

Bi-exponential model and inverse model of magnetorheological damper for the semi-active suspension of a capsule vehicle

The capsule vehicle is a new transportation system that travels in a sub-vacuum tunnel at a speed of about 1000 km/h, and adopts the electrodynamic suspension type levitation system. Accordingly, although it differs according to the driving speed, the vibration of capsule vehicle is expected to be greater than that of the wheel/rail type high-speed rail vehicles. Therefore, a method of applying a semi-active control technique using an MR damper as a secondary suspension of a capsule vehicle to improve passenger comfort is being studied. When performing semi-active control using an MR damper, the most important thing is to determine the current for the MR damper. However, it is difficult to determine the appropriate current for the MR damper because of the hysteretic characteristics of the MR damper. In this study, a practical model named the Bi-exponential model is presented for the application of semi-active control using MR dampers on a capsule vehicle. This Bi-exponential model well reflects the hysteretic characteristics of the MR damper, which makes it easy to obtain the inverse model for determining the current supplied to the MR damper. The semi-active control performance of the Bi-exponential model was evaluated by simulation and a HILS experiment, taking into account the vertical motion of a 1/4-car capsule vehicle. Also, the Bi-exponential model has been validated against the performance of the most commonly used Bouc-Wen model. As a result, the Bi-exponential model showed better hysteretic characteristics of MR dampers compared to the Bouc-Wen model. Furthermore, despite the simpler model compared to the Bouc-Wen model, the semi-active control performance of the Bi-exponential model was found to be better.

On an enhanced back propagation neural network control of vehicle semi-active suspension with a magnetorheological damper

To improve the ride quality of a vehicle, an enhanced vibration control method is presented for semi-active suspension (SAS) with magnetorheological (MR) damper by combining back propagation neural network (BPNN) and particle swarm optimization (PSO). Based on the test data of MR damper, a non-parametric model of MR damper using adaptive neuro-fuzzy inference system (ANFIS) is first established, and based on that, a dynamics model of the SAS system is derived. Next, a BPNN controller is designed to fulfill the effective control of the current in MR damper. Meanwhile, the improved PSO with adaptive weight and dynamic acceleration constant is introduced to optimize the weights and thresholds of the BPNN controller, which can avoid the designed BPNN falling into the local optimum and then improve the convergence rate of the designed controller. Besides, the stability of the developed controller is analyzed via Lyapunov stability theory. Different from the existing models and methods, the established model can well describe the dynamics behaviors of the actual MR damper, and the proposed control method has better adaptability, convergence speed and precision. Finally, a simulative investigation is performed to validate the effectiveness and feasibility of the proposed controller, compared to existing BP-PID control and the passive suspension, the vehicle acceleration of SAS with this proposed controller is respectively improved by 10% and 30%.

Parameter identification of Bouc-Wen model for MR damper by parameter sensitivity analysis and modified PSO algorithm

To solve the problems of the Bouc-Wen model with multi-identification parameters, low accuracy, complex methods, and difficulty in implement, this study proposes a new way for parameter identification of the Bouc-Wen model of the magnetorheological (MR) damper by parameter sensitivity analysis and modified PSO algorithm. The one-at-a-time method (OAT) of local sensitivity analysis is utilized to analyze the unknown parameters in the Bouc-Wen model to complete the model simplification. Then, the modified PSO algorithm is used to identify the parameters of the simplified Bouc-Wen model. Finally, with the relationship between the currents and identified parameters, a Bouc-Wen model for current control is constructed by the curve fitting method. The results confirm that the parameter identification efficiency achieved via the parameter sensitivity analysis is improved by 50% by reducing the parameters of the Bouc-Wen model from 8 to 4. Then, compared with the standard PSO (SPSO) algorithm, the modified one is accurate and stable, and the convergence speed is increased by 17.65% on average. At last, compared with the test data under three different sinusoidal excitations, the model’s accuracy is 89.11%, 92.56%, and 87.45%, respectively. The method proposed in this research can rapidly and accurately identify the Bouc-Wen model and lays a theoretical foundation for applying the MR damper model in vibration control.

Modeling and Second-Order Sliding Mode Control for Lateral Vibration of High-Speed Train With MR Dampers

The lateral vibration of high-speed train reduces the ride stability and passenger comfort. Semi-active suspension system is often adopted to suppress the lateral vibration of trains due to its low cost and low energy consumption in control, where magnetorheological (MR) damper is the main vibration absorber. In this paper, a full model of the controlled system that consists of the 3-degree of freedom train model and the hysteretic MR damper model is first built. Then, a second-order sliding mode (SOSM) controller is designed for the suppression of lateral vibration of train, where the hysteresis and non-hysteresis nonlinearities are addressed simultaneously and rigorously. Finally, comparative simulations are conducted under the excitation of the German low-interference track spectrum. The results show that the proposed controller can suppress the lateral vibration of high-speed train efficiently in the sense that, compared with the passive control, the internal model-based resonant control and repetitive learning control, the suspension ratio of root-mean-square of lateral acceleration is reduced by 96.98%, 35.70% and 10.54%, respectively.

Unsteady and hysteretic behavior of a magnetorheological fluid damper: Modeling, modification, and experimental verification

Although the quasi-static model is widely employed in various engineering fields to guide the design of magnetorheological (MR) dampers, it is not accurate enough to describe the dynamic behaviors of MR dampers. In this study, an unsteady Bingham plastic (US-BP) model that considers fluid inertia is established. The proposed model can realize flexible switching between flow mode and mixed mode by introducing a mode parameter. To employ the US-BP model for MR dampers under different excitations, a technique combining the Fourier series method and Laplace transform is developed to deduce the velocity profiles of MR fluids. Based on the US-BP model, the damping characteristics of an MR damper under different excitation frequencies, yield stresses, and mode parameters are theoretically investigated. Furthermore, an unsteady hysteretic Bingham plastic (USHY-BP) model that incorporates particle chain deflection theory is developed to characterize the hysteretic behavior and inertia effect of the damping force. Comparisons between the simulation results and the experimental data reveal that the US-BP model can predict the unsteady behaviors of damping forces caused by fluid inertia but fails to capture the hysteresis characteristic. The USHY-BP model achieves good performance and accuracy in characterizing the dynamic properties of MR dampers.

Nonparametric modeling of magnetorheological damper based on nonlinear black-box technique

Magnetorheological (MR) dampers are considered the most confident actuators for controlling vibratory systems due to their great advantages like high controllable dynamic range, low power consumption, and fail-safe devices. In this paper, a new nonparametric technique is utilised to model the MR-damper dynamics using Non-Linear Autoregressive Models with Exogenous Inputs (NLARX) approach. The proposed model is constructed based on the measured displacement, velocity, and damping forces of the commercial MR damper under various command voltages. The results of the nonparametric model show that such a model can expect the nonlinear dynamics of the MR damper under a wide range of different operating conditions. Furthermore, the proposed model output is compared with a well-known parametric model namely as Modified Bouc-Wen (MBW) model for additional validation. The comparison shows that the generated model can accurately track the measured damping force characteristics, work done by the damper, and the force-velocity hysteresis. It is also shown that the improvement of the damping force of the proposed model is better than the corresponding damping force of the parametric model which clearly shows the robustness of the generated model. The proposed model improves the root mean square (RMS) values of the experimental damping force by about 93.57% compared to an improvement of about 77.36% of the simulated damping force from the MBW model.

Optimal design and performance analysis of magnetorheological damper based on multiphysics coupling model

Magnetorheological (MR) fluid is a kind of intelligent magnetic material, and MR damper is widely used in various fields based on its rheological properties. Therefore, aiming at the problems of low optimization accuracy and efficiency in the optimization design process MR damper using single physical field analysis method, a multi-objective optimization design method for MR damper based on multiphysics coupling model was proposed. The magnetic circuit of the MR damper was calculated, and the mechanical model, electromagnetic field model, flow field model and stress field model of MR damper were established, respectively. A multiphysics coupling model of the MR damper was established in the COMSOL software. The multi-platform joint optimization model was setup, and a multi-objective optimization design method of DOE combined with the surrogate model was proposed. A test system was built up and the initial and optimal MR dampers were fabricated. The results show that the simulation and experimental error of the damping force and dynamic range of the optimal MR damper are only 4.9% and 8.8% at the applied current of 1.4 A, respectively. Also, the damping force and dynamic range of the optimal MR damper are increased by 21.9% and 11.9% compared with the initial MR damper, respectively, which verifies the accuracy of the multiphysics coupling model and effectiveness of optimal design.