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This paper aims to study a mathematical model explaining the impacts influence of heat transfer on magnetohydrodynamics oscillatory flow for Bingham Fluid with variable viscosity through a porous channel. The governing equations are solved numerically by developing a suitable finite difference scheme. As an application of the theory in the field of magneto. We used the perturbation method to obtain a clear formula for fluid motion. The results obtained are illustrated by graphs after we reached the momentum equation solution, and used the MATHEMATICA program for plot the velocity and temperature of the fluid for two types of flow (Poiseuille and Couette).

Smoothed Particle Hydrodynamics (SPH) is a mesh-free numerical method that models the movement of particles in the Langrangian method. SPH method treats the domain as discrete particles instead of continuous entities, making it more accurate to model phenomenons that have a big deformation. The purpose of this research is to analyze the interaction between soil and water particles, based on the particle movements, density, pressure, internal forces, and external forces. This research continues the previous research of interaction between fluid-fluid particles in SPH by applying the Bingham fluid model to one type of fluid to represent coarse-grained soil particles. In the future, we hope this research can be further developed into a liquefaction prediction model by quantifying the main factors of liquefaction, such as the amplitude of shear strain, effective stress reduction, and excess pore water pressure.

Currently, such types of engineering work as construction of classic buildings and structures, as well as erection of new ones that have an irregular shape, i.e. curved, arched, elliptical, round and similar surfaces, can be performed using complex technological equipment, such as combined external or internal formwork, the use of shotcrete technology together with the off-formwork construction technologies (3D printers). One of the prerequisites for uniform transportation of media by a concrete pump through pipelines, concrete conveying pipes, and most importantly, their homogeneous distribution by an extruder during layering, is a study based on mathematical modeling and comparative analysis of mathematical models of the flow of Shvedov-Bingham fluids in pipelines of various cross-sections, determining the performance, optimal rheological properties of mortars and concrete liquids. This will allow further control of their fluidity and plastic viscosity during the extrusion process.

This paper aims at optimum design formulation of a rotary disk-type magneto-rheological (MR) fluid damper to increase its torsional vibration control performance. The objective is to maximize the torsional damping torque for a given volume, geometric and inertia constraints. The damping torque has been derived based on Bingham plastic model for a commercial MR fluid provided by Lord corporation. As MR fluid's yield strength directly depends on the applied magnetic field intensity, an analytical magnetic circuit analysis has been conducted to approximately evaluate the magnetic field intensity in the MR fluid gap. A finite element model of the rotary MR damper has also been developed to evaluate the magnetic field distribution. A formal design optimization problem has then been formulated to maximize the dynamic range for a given volume under geometric, inertia and torque ratio constraints. Genetic Algorithm (GA) combined with Sequential Quadratic Programming (SQP) method has been utilized to accurately capture the global optimum solution. Finally, a proof-of-concept of the optimal design has been manufactured and then tested experimentally to investigate the generated damping torque under different current excitation and also to validate the model and optimization strategy.

The MHD peristaltic motion of Bingham fluid through a uniform channel is examined under the influence of long wavelength and small Reynolds number. The impact of variable thermal conductivity, convective heat transfer, porous boundaries, and wall properties are considered. The semi-analytical technique is utilized to solve the governing nonlinear temperature equation. The effects of different parameters on the physiological quantities of interest are captured with the assistance of MATLAB programming. The assessment reveals that an ascent in a magnetic parameter reduces the velocity field. Further, an increment in the estimation of variable thermal conductivity upgrades the temperature profiles. Besides, the trapped bolus is a function of a porous parameter, and an increase in porous parameter will have the proportional increment in the other parameter.

The paper presents the calculation results of local pressure loss coefficient in three different models of a gate valve in their two opening positions. The study was carried out on ice slurry with the mass fraction of ice particles of 30%, 25%, 20%, 15%, 10% and 5%. The slurry is considered to be the Bingham Plastic liquid within this study and the local loss coefficient data were provided thanks to the obtained results of the local resistance calculations in the fittings tested in the experimental investigation. The transitional behavior of ice slurry has been detected. The value of the local pressure loss coefficient decreases firstly up until transition point then it remains constant in the turbulent flow regime. The ice crystals content directly determines its value, as the larger ice mass fraction in the mixture, the greater value of the loss coefficient. Declining opening position of the gate valves results in decreasing the value of the loss coefficient data in relation to the Reynolds number for Bingham liquid.

The effects of nanoparticles such as Fe 3O4,TiO2, and Cu on blood flow inside a stenosed artery are studied. In this study, blood was modelled as non-Newtonian Bingham plastic fluid subjected to periodic body acceleration and slip velocity. The flow governing equations were solved analytically by using the perturbation method. By using the numerical approaches, the physiological parameters were analyzed, and the blood flow velocity distributions were generated graphically and discussed. From the flow results, the flow speed increases as slip velocity increases and decreases as the values of yield stress increases.

A micro?macro model is formulated for the magnetomechanical behavior of magnetorheological fluids (MRFs) based on micromechanics and a statistical approach. It includes two stages: (1)?the analysis of the aggregation of the particles in an MRF into chains of dipoles aligning in the direction of the applied magnetic field and its contribution to resistance against shear deformation, and (2)?the attainment of solid-like mechanical properties of the MRF by assuming numerous chains inclining with the angles arranged in a normal distribution. This model takes into account the effect of each of the main influencing factors, such as the intensity of magnetic induction, the size and the volume fraction of particles, shear strain rate and saturation magnetization, etc, on the critical shear stress of MRFs. The effect of typical governing parameters on the behavior of MRFs is investigated individually, which shows the capability of the proposed model in the description of the magnetorheological behavior of MRFs. The common Bingham's model of viscoplasticity and the dual-viscosity model can be obtained from the proposed model as special cases. The model is comprehensive, simple, and can easily be used for the initial design and optimization of high-performance MRFs.

This paper presents the geometric optimal design of magnetorheological (MR) valves in order to improve valve performance, such as pressure drop. The optimization problem is to find the optimal geometric dimensions of MR valves constrained in a specific volume. After describing the configuration of MR valves, their pressure drops are investigated on the basis of the Bingham model of an MR fluid. Then, the valve ratio, which is an objective function, is derived by considering the field-dependent (controllable) and viscous (uncontrollable) pressure drops of the MR valves. Subsequently, the optimization procedure using a golden-section algorithm and a local quadratic fitting technique is constructed via a commercial finite element method (FEM) parametric design language. From the constructed optimization tool, optimal solutions of the MR valves, which are constrained in a specific cylindrical volume defined by its radius and height, are calculated and compared with analytical ones. In addition, several different types of MR valves are optimized in the same specific volume and results are presented.

This paper presents the braking performances of a vehicle anti-lock brake system (ABS) featuring an electro-rheological (ER) valve pressure modulator. As a first step, the principal design parameters of the ER valve and hydraulic booster are appropriately determined by considering the Bingham property of the ER fluid and the braking pressure variation during the ABS operation. An ER fluid composed of chemically treated starch particles and silicone oil is used. An electrically controllable pressure modulator is then constructed and its pressure controllability is empirically evaluated. Subsequently, a quarter-car wheel slip model is established and integrated with the governing equation of the pressure modulator. A sliding mode controller for slip rate control is designed and implemented via the hardware-in-the-loop simulation (HILS). In order to demonstrate the superior braking performance of the proposed ABS, a full car model is derived and a sliding mode controller is formulated to achieve the desired yaw rate. The braking performances in terms of braking distance and step input steering are evaluated and presented in time domain through full car simulations.

A key aspect of application of electrorheological (ER) and magnetorheological (MR) fluids is the characterization of rheological properties. In this study, two rotational viscometers to measure the field-dependent flow behavior (shear stress versus shear rate) of ER/MR fluids are theoretically analyzed. One is a rotational coaxial cylinder viscometer, and the other is a rotational parallel disk viscometer. The equations between shear stress and torque as well as shear rate and angular velocity are derived on the basis of the Bingham-plastic, biviscous, and Herschel–Bulkley constitutive models. The shear stress for the rotational coaxial cylinder viscometer can be straightforwardly calculated from the measured torque. However, in order to determine the shear rate, three approximation methods are applied. Meanwhile, the shear stress and shear rate in the rotational parallel disk viscometer can be obtained directly from the torque and angular velocity data. In order to comprehensively understand the flow behavior of ER/MR fluids with respect to the constitutive models, nondimensional analyses are undertaken in this study.

By using magnetorheological (MR) fluid in place of lubricating oil in a traditional squeeze film damper (SFD), one can build a variable-damping SFD, thereby controlling the vibration of a rotor by controlling the magnetic field. Assuming a Bingham model, the Reynolds equation for an MR fluid squeeze film is developed and solved to provide expressions for the velocity, the pressure distribution and the damping force. Electromagnetic theory is used to calculate the magnetic pull force between the magnetic poles in the damper. The mechanical properties of the squeeze film and the unbalance response characteristics of an MR fluid SFD–rigid rotor system are analyzed theoretically. An MR fluid SFD is designed and manufactured, and the unbalance response properties and control method of a flexible rotor supported on the damper are studied experimentally. The study shows that the magnetic pull force can decrease both the first critical speed and the critical amplitude; the film damping force can decrease the amplitude at the undamped critical speeds, but increase the amplitude in a speed range between two undamped critical speeds. The damper may have the best control effect to minimize the vibration within the range of all working speed by using the on–off control method.

This paper is a study on the development of an active buffer for railway vehicles using electrorheological (ER) fluid as a functional material. The coupler force is controlled by adjusting the electric field applied to the ER fluid. A prototype buffer, which consists of a hydraulic cylinder, an ER bypass slit valve and a PID feedback controller, is fabricated. The damping force is developed in the ER valve both through the bypass slit and at the piston–cylinder gap. In the theoretical analysis, it is assumed that the flow of the ER fluid through the bypass slit is the Bingham plastic flow-mode flow while it is in the Newtonian mixed-mode flow in the piston–cylinder gap. The force opposed by the buffer is obtained as a function of the shaft velocity and the electric field applied to the ER fluid. The theoretical results are compared with the experimental results. Further, an active control test using the PID feedback controller is carried out for the problem where the shaft reaction force is retained at a constant prescribed strength while the shaft is translating at a constant velocity. Both results show that the coupler force of the railway vehicle can be controlled effectively by using the proposed electrorheological bypass damper.

Electrorheological (ER) and magnetorheological flow mode dampers can exhibit biviscous damping behavior. Such behavior is characterized by a high damping pre-yield region for low velocities, with a transition to a relatively lower post-yield damping, once the damper force exceeds the static yield force of the damper. The biviscous damping behavior is typically the result of leakage, that is, a second path of Newtonian flow in addition to the Bingham plastic flow through the ER or MR valve. We experimentally demonstrate such bilinear damping behavior in a monotube ER shock absorber. Leakage is typically introduced to smooth the force response of the damper as the damper undergoes transitions through the low velocity. The ER fluid is typically assumed to behave as a Bingham plastic fluid. Thus, two perspectives are examined for modeling damping performance of the ER monotube shock absorber. First, the quasisteady Bingham plastic analysis is coupled with a mechanical analysis of the leakage effects. Second, a biviscous constitutive perspective is described that allows the leakage effects to be described as an apparent pre-yield viscosity of the ER fluid. Both perspectives prove to be useful in describing damping performance of the ER monotube shock absorber.

We present an improved experimental validation of our nonlinear quasi-steady electrorheological (ER) and magnetorheological damper analysis, using an idealized Bingham plastic shear flow mechanism, for the flow mode of damper operation with leakage effect. To validate the model, a double-acting ER valve or bypass damper was designed and fabricated. Both the hydraulic cylinder and the bypass duct have cylindrical geometry, and damping forces are developed in the annular bypass via Poiseuille flow. The ER fluid damper contains a controlled amount of leakage around the piston head. The leakage allows ER fluid to flow from one side of the piston head to the opposite side without passing through the ER bypass. For this flow mode damper, the damping coefficient, defined as the ratio of equivalent viscous damping of the Bingham plastic material, Ceq, to the Newtonian viscous damping, C, is a function of the non-dimensional plug thickness only. The damper was tested for varying conditions of applied electric field and frequency using a mechanical damper dynamometer. In this analysis, the leakage damping coefficient with incorporated leakage effects, predict the amount of energy dissipated for a complete cycle of the piston rod. Measured force verses displacement cycles for multiple frequencies and electric fields validate the ability of the non-dimensional groups and the leakage damping coefficient to predict the damping levels for an ER bypass damper with leakage. Based on the experimental validation of the model using these data, the Bingham plastic analysis is shown to be an effective tool for the analysis-based design of double-acting ER bypass dampers.

Semi-active control of buildings and structures with magnetorheological (MR) dampers for earthquake hazard mitigation represents a relatively new research area. In this paper, the Bingham model of MR damper is introduced, and the formula relating the yielding shear stress and the control current of MR dampers is put forward that matches the experimental data. Then an on-line real-time control method for semi-active control of structures with MR dampers is proposed. This method considers the time-delay problem of semi-active control, which can solve distortion of the responses of structures. Finally, through a numerical example of a three-storey reinforced concrete structure, a comparison is made between controlled structure and uncontrolled structure. The calculated results show that MR dampers can reduce the seismic responses of structures effectively. Moreover, the on-line real-time control method is compared with the traditional elastoplastic time-history analysis method, and the efficacy of the on-line real-time control method is demonstrated. In addition, the Levenberg–Marquardt algorithm is used to train the on-line control neural network, and studies show that the algorithm has a very fast convergence rate.

The electrorheological (ER) fluid between two circular electrodes subjected to oscillatory squeeze flow is studied theoretically in this paper. The ER fluid is modeled as a bi-viscous fluid with Bingham-like behavior. The inertia due to the oscillatory flow of the fluid is taken into account. The solution is derived in the complex domain. The magnitude of the total reactive force on the upper electrode and its phase lag with respect to the electrode displacement are calculated numerically. The results show that the phase lag is more sensitive to the inertia effect than the magnitude of the reactive force. It is also shown that, within 10% discrepancy in the magnitude of reactive force, the quasi-static model can be used with actuating frequency lower than 400 Hz for the examples studied.

The steady shear electrorheological (ER) response of poly(3, 4-ethylenedioxythiophene): poly(styrene sulfonate)/polystyrene (PEDOT:PSS/PS) composite particles, which were initially fabricated from Pickering emulsion polymerization, was tested with a 10 vol% ER fluid dispersed in a silicone oil. The model independent shear rate and yield stress obtained from the raw torque-rotational speed data using a Couette type rotational rheometer under an applied electric field strength were then analyzed by Tikhonov regularization, which is the most suitable technique for solving an ill-posed inverse problem. The shear stress-shear rate data also fitted well with the data extracted from the Bingham fluid model.

Hard-magnetic chromium dioxide nanoparticles with a rod-like shape were introduced as an additive to a soft-magnetic carbonyl iron (CI)-based magnetorheological (MR) fluid. The magnetic stimuli-response of the MR fluid in terms of the steady shear and dynamic oscillation tests was examined using a rotational rheometer. While the Bingham fluid model fitted the flow curves, the dynamic yield stress followed the universal yield stress scale function quite well. Compared to the CI-based MR fluid without chromium dioxide nanoparticles, the MR fluid with the chromium dioxide additive exhibited remarkably higher yield behavior with increasing magnetic field strength, enhancing its MR performance and dispersion stability.

It is now well known that smart fluids (electrorheological (ER) and magnetorheological) can form the basis of controllable vibration damping devices. With both types of fluid, however, the force/velocity characteristic of the resulting damper is significantly nonlinear, possessing the general form associated with a Bingham plastic. In a previous paper the authors suggested that by using a linear feedback control strategy it should be possible to produce the equivalent of a viscous damper with a continuously variable damping coefficient. In the present paper the authors describe a comprehensive investigation into the implementation of this linearization strategy on an industrial scale ER long-stroke vibration damper. Using mechanical excitation frequencies up to 5 Hz it is shown that linear behaviour can be obtained between well defined limits and that the slope of the linearized force/velocity characteristic can be specified through the choice of a controller gain term.

A mixture of fluid and solid particles with high sediment concentration (hyperconcentration) is described by a non-Newtonian rheological model incorporating the yield stress, a linear (viscous) stress, and a quadratic (turbulent-dispersive) term. Unsteady flow of hyperconcentration down an inclined plane is studied: first the set of equations governing the flow are derived, then velocity profiles for steady uniform motion are illustrated. The solution for unsteady state flow is obtained in term of permanent waves; their speed is derived and the possible surface profiles are illustrated as functions of a dimensionless parameter describing the relative importance of the linear and quadratic term. When the viscous stress overwhelms the turbulent-dispersive one, earlier relations for a Bingham fluid are recovered. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of permanent waves propagating up a slope.

We develop nonlinear quasi-steady electrorheological (ER) and magnetorheological (MR) damper models using an idealized Bingham plastic shear flow mechanism. Dampers with cylindrical geometry are investigated, where damping forces are developed in an annular bypass via Couette (shear mode), Poiseuille (flow mode) flow, or combined Couette and Poiseiulle flow (mixed mode). Models are based on parallel plate or rectangular duct geometry, and are compared to our prior 1D axisymmetric models. Three nondimensional groups are introduced for damper analysis, namely, the Bingham number, , the nondimensional plug thickness, , and the area coefficient defined as the ratio of the piston head area, , to the cross-sectional area of the annular bypass, . The approximate parallel plate analysis compares well with the 1D axisymmetric analysis when the Bingham number is small, or , or the nondimensional plug thickness is small, . Damper performance is characterized in terms of the damping coefficient, which is the ratio of the equivalent viscous damping constant, , to the Newtonian viscous damping constant, C. In shear mode, the damping coefficient is a linear function of the Bingham number. In flow mode, the damping coefficient is a function of the nondimensional plug thickness only. For the mixed mode damper, the damping coefficient reduces to that for the flow mode case when the area coefficient is large. The quasi-steady damping coefficient versus nondimensional plug thickness diagram is experimentally validated using measured 10 Hz hysteresis cycles for a electrorheological mixed mode damper.

We investigate the hydrodynamic properties of Fe3O4 kerosene-based ferrofluids with narrow particle size distribution. The ferrofluids are synthesized by improving chemical coprecipitation technique. A narrow distribution of 8.6–10.8 nm particle sizes is obtained from the magnetization curve with the free-form model based on the Bayesian inference theory. The fitting result is consistent with average particle size obtained from x-ray diffraction. With the increase of applied magnetic field and magnetic particle concentration, apparent viscosity of ferrofluids increases. At concentration 4.04%, the type of flow for the ferrofluid transforms from Newtonian to Bingham plastic fluid as the applied magnetic field increases.

Electrorheological- (ER-) fluid-based dashpot dampers have smart capabilities because ER fluids undergo large changes in yield stress as electric field is applied. Our objective is the development and experimental validation of quasi-steady dashpot damper models, based on an idealized nonlinear Bingham plastic shear flow mechanism, for purposes of preliminary design and performance predictions. The data required for the Bingham plastic model is normally supplied by ER fluid suppliers, that is, plastic viscosity and dynamic yield stress as a function of applied field, as determined from a shear stress versus shear strain rate diagram. As force is applied to the dashpot damper, the ER fluid flows through an annulus between the concentric inner and outer electrodes. The idealized Bingham plastic shear flow mechanism predicts that three annular flow regions develop as a function of the local shear stress. In the central pre-yield or plug region, the local shear stress is less than the dynamic yield stress, so that the plug behaves like a rigid solid. The remaining two annular regions, adjacent to the electrodes, are in the post-yield condition and correspond to the shear stress exceeding the dynamic yield stress, so that the material flows. Equivalent viscous damping performance of an ER fluid dashpot damper is strongly coupled with the plug behavior. For a constant force, as the applied field increases, so does the plug thickness and equivalent viscous damping. For a constant applied field, as the force increases, the plug thickness and equivalent viscous damping both decrease. The passive and active or field-dependent damping behavior of an ER-fluid-based dashpot damper can be designed for a specific application using these quasi-steady Bingham plastic models.

An interesting extension in the use of magnetic fluids has resulted from the development of magnetic fluid composites obtained by dispersing micrometre-sized non-magnetic particles in a magnetic fluid. The composites possess a yield stress in a magnetic field which can be described at sufficiently high strain rates by the Bingham relation , where is the shear stress perpendicular to the applied field, the extrapolated yield stress, the strain rate and the plastic viscosity. Thus, a composite, particle concentration , in a field 0.036 T with has a yield stress of 26 Pa. The yield stresses obtained experimentally for different and correspond well to values predicted theoretically by Rosensweig using a determination of based on a continuum concept of unsymmetric stress that develops in the deformed but unyielded anisotropic medium.

Adaptive landing gear dampers that can continuously adjust their stroking load in response to various operating conditions have been investigated for improving the landing performance of a lightweight helicopter. In prior work, adaptive magnetorheological (MR) landing gear dampers that maintained a constant peak stroking force of 4000 lbf across sink rates ranging from 6 to 12 ft s−1 were designed, fabricated and successfully tested. In this follow-on effort, it is desired to expand the high end of the sink rate range to hold the peak stroking load constant for sink rates ranging from 6 to 26 ft s−1, thus extending the high end of the speed range from 12 (in the first study) to 26 ft s−1. To achieve this increase, a spring-based relief valve MR landing gear damper was developed. In order to better understand the MR landing gear damper behavior, a modified nonlinear Bingham Plastic model was formulated, and it incorporates Darcy friction, viscous forces across the MR and relief valves to better account for the damper force behavior at higher speeds. In addition, gas pressure inside the MR damper piston is considered so the total damper force includes a gas force. The MR landing gear damper performance is characterized using drop tests, and the experiments are used to validate model predictions data at low and high nominal impact speeds up to 26 ft s−1 (shaft velocity of 9.6 ft s−1).

This paper presents dynamic viscoelastic properties of magnetorheological (MR) grease under variation of magnetic fields and magnetic particle fractions. The tests to discern the field-dependent properties are undertaken using both rotational and oscillatory shear rheometers. As a first step, the MR grease is developed by dispersing the carbonyl iron (CI) particles into grease medium with a mechanical stirrer. Experimental data are obtained by changing the magnetic field from 0 to 0.7 T at room temperature of 25 °C. It is found that a strong Payne effect limits the linear viscoelastic region of MR grease at strains above 0.1%. The results exhibit a high dynamic yield stress which is equivalent to Bingham plastic rheological model, and show relatively good MR effect at high shear rate of 2000 s-1. In addition, high dispersion of the magnetic particles and good thermal properties are proven. The results presented in this work directly indicate that MR grease is a smart material candidate that could be widely applicable to various fields including vibration control.

Two types of electrorheological (ER) fluid vibration damper are compared. It was found that a damper using the shear mode of the fluid has a much greater range of damping than a damper operating in the valve mode. A rotary damper using ER fluid in the shear mode was modelled analytically assuming the fluid responded as a Bingham plastic. The resulting nonlinear damping model consisted of an off-field viscous damping component and an on-field Coulomb damping component. To analyse the transient response of the damper an electrically equivalent model was developed. A damper was built and tested and the experimental results are presented.

We find a nonlinear relationship between the shear stress and shear rate of electrorheological (ER) fluids with aluminosilicate suspension in the original zone corresponding to low shear rates. Beyond the original zone, the ER fluids behave like a Bingham plastic fluid, and their viscosity is nearly constant.

The transport properties of unexcited and excited electro-rheological (ER) fluid in combined Couette and Poiseuille flow are investigated. In particular the question of whether the fluid can be considered as a continuum with Bingham plastic constitutive properties, even though it is a two-phase solid-liquid mixture, is addressed. The hydrodynamic pressures generated using ER fluid in a Rayleigh step bearing at the limiting condition of zero net flow rate were measured. The properties exhibited by the fluid are compared with independently obtained data showing the continuum principle to be applicable to the flows examined.

This paper focuses on the optimal design of a compact and high damping force engine mount featuring magnetorheological fluid (MRF). In the mount, a MR valve structure with both annular and radial flows is employed to generate a high damping force. First, the configuration and working principle of the proposed MR mount is introduced. The MRF flows in the mount are then analyzed and the governing equations of the MR mount are derived based on the Bingham plastic behavior of the MRF. An optimal design of the MR mount is then performed to find the optimal structure of the MR valve to generate a maximum damping force with certain design constraints. In addition, the gap size of MRF ducts is empirically chosen considering the 'lockup' problem of the mount at high frequency. Performance of the optimized MR mount is then evaluated based on finite element analysis and discussions on performance results of the optimized MR mount are given. The effectiveness of the proposed MR engine mount is demonstrated via computer simulation by presenting damping force and power consumption.

So far quasi-steady models are usually used to design magnetorheological (MR) dampers, but these models are not sufficient to describe the MR damper behavior under unsteady dynamic loading, for fluid inertia is neglected in quasi-steady models, which will bring more error between computer simulation and experimental results. Under unsteady flow model, the fluid inertia terms will bring error calculated upto 10%, so it is necessary to be considered in the governing equation. In this paper, force-stroke behavior of MR damper with flow mode due to sinusoidal loading excitation is mainly investigated, to simplify the analysis, the one-dimensional axisymmetric annular duct geometry of MR dampers is approximated as a rectangular duct. The rectangular duct can be divided into 3 regions for the velocity profile of the incompressible MR fluid flow, in each region, a partial differential equation is composed of by Navier-Stokes equations, boundary conditions and initial conditions to determine the velocity solution. In addition, in this work, not only Bingham plastic model but the Herschel—Bulkley model is adopted to analyze the MR damper performance. The damping force resulting from the pressure drop of unsteady MR dampers can be obtained and used to design or size MR dampers. Compared with the quasi-steady flow damping force, the damping force of unsteady MR dampers is more close to practice, particularly for the high-speed unsteady movement of MR dampers.

The current practice of designing magneto-rheological (MR) fluid-based devices is, to a large extent, based on simple phenomenological models like the Bingham model. Though useful for initial force or torque estimation and sizing, these models lack the capability to predict performance degradation due to changes in the particle volume fraction distribution. The present work demonstrates the use of the two-fluid model for predicting the particle volume fraction distribution inside a device in the absence of a field and proposes a novel modeling scheme which can simulate the fluid flow in the presence of a field. This modeling scheme can be used to (a) visualize flow patterns inside a device under various operating conditions, (b) predict the spatial distribution of particles inside a device after multiple operating cycles, (c) assist in estimating the extent of performance degradation due to non-uniform particle distribution and (d) enable testing of various design strategies to mitigate such performance issues using simulations. This is illustrated through numerical examples of a few case studies of typical MR device configurations.

This paper examines the chain structure factor evolution of electrorheological (ER) fluids in compressive flow. The yield strength of ER fluids was modeled based on a single pair electrostatic interaction between particles and the structure factor, which includes all the effects except the single pair electrostatic interaction between particles presented by the local electric field strength between particles. Both the mechanical and electrical properties of ER fluids in compressive flow have been experimentally determined. The nominal shear yield stress of the ER fluid in compressive flow was derived by assuming that it was a transformed shear flow of a Bingham fluid. The single pair particle interaction strength is related to the measured electric current, which reflects the local electric field strength between particles. The structure factor evolution in compressive flow was derived by comparing the nominal shear yield stress and the single pair particle interaction strength. As expected, the calculated structure factor increased significantly using this method, much higher than that described by the many-body effect and the difference of dipole–dipole interaction and multi-dipole interaction between particles. Direct mechanical contacts and frictional forces between particles are thought to contribute significantly to the high structure factor and nominal shear yield stress of the ER fluid in compressive flow. This behavior might be similar in magnetorheological (MR) fluids.

A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.

This paper presents damping force control performances of a magnetorheological (MR) damper via a new control strategy considering hysteretic behavior of the field-dependent damping force. In order to achieve this goal, a commercial MR damper, Delphi Magneride™ which is applicable to a high-class passenger vehicle is adopted and its field-dependent damping force is experimentally evaluated. The MR damper has two types of damping force hysteretic behavior. The first is velocity-dependent hysteresis and the other is field-dependent hysteresis. Since the magnetic field is directly connected with control input, the field-dependent hysteresis largely affects the control performances of the MR damper system. To consider the field-dependent hysteretic behavior of the MR damper, a Preisach hysteresis model is established and its first-order descending (FOD) curves are experimentally identified. Subsequently, a feedforward hysteretic compensator associated with the biviscous model and inverse Bingham model is formulated to achieve the desired damping force. The control algorithm is experimentally implemented and damping force controllability for sinusoidal and arbitrary trajectories is evaluated in terms of accuracy and input magnitude. In addition, vibration control performances of the MR suspension system are experimentally evaluated with a quarter-vehicle test facility.

This paper presents an optimal design of a passenger vehicle magnetorheological (MR) damper based on finite element analysis. The MR damper is constrained in a specific volume and the optimization problem identifies the geometric dimensions of the damper that minimize an objective function. The objective function consists of the damping force, the dynamic range, and the inductive time constant of the damper. After describing the configuration of the MR damper, the damping force and dynamic range are obtained on the basis of the Bingham model of an MR fluid. Then, the control energy (power consumption of the damper coil) and the inductive time constant are derived. The objective function for the optimization problem is determined based on the solution of the magnetic circuit of the initial damper. Subsequently, the optimization procedure, using a golden-section algorithm and a local quadratic fitting technique, is constructed via commercial finite element method parametric design language. Using the developed optimization tool, optimal solutions of the MR damper, which are constrained in a specific cylindrical volume defined by its radius and height, are determined and a comparative work on damping force and inductive time constant between the initial and optimal design is undertaken.

Magnetorheological (MR) fluids typically are suspensions of spherical micron-sized ferromagnetic particles suspended in a fluid medium. They are usually thought of as Bingham-plastic fluids characterized by an apparent yield stress and viscosity. Partial substitution of the micron-sized iron particles with rod-shaped nanowires constitutes a dimorphic MR fluid. In this study, we investigate the influence that nanowires have on the magnetorheological and sedimentation properties of MR fluids. A variety of conventional and dimorphic MR fluid samples were considered for this study with iron loading ranging from 50 to 80 wt%. The nanowires used in this study have mean diameters of 230 nm and a length distribution of 7.6 ± 5.1 µm, while the spherical particles have a mean diameter of 8 ± 2 µm. Flow curves were measured using a parallel disk rheometer and a sedimentation measuring instrument was constructed for quantifying sedimentation velocity. The Bingham yield strength and sedimentation velocity of the dimorphic MR fluids are then compared to those of conventional MR fluids incorporating spherical particles.

Self-contained actuation systems, based on frequency rectification of the high frequency motion of an active material, can produce high force and stroke output. Magnetorheological (MR) fluids are active fluids whose rheological properties can be altered by the application of a magnetic field. By using MR fluids as the energy transmission medium in such hybrid devices, a valving system with no moving parts can be implemented and used to control the motion of an output cylinder shaft. The MR fluid based valves are configured in the form of an H-bridge to produce bi-directional motion in an output cylinder by alternately applying magnetic fields in the two opposite arms of the bridge. The rheological properties of the MR fluid are modeled using both Bingham plastic and bi-viscous models. In this study, the primary actuation is performed using a compact terfenol-D rod driven pump and frequency rectification of the rod motion is done using passive reed valves. The pump and reed valve configuration along with MR fluidic valves form a compact hydraulic actuation system. Actuator design, analysis and experimental results are presented in this paper. A time domain model of the actuator is developed and validated using experimental data.

This study presents an optimal design for magnetorheological (MR) valves for minimizing the control energy to be applied to coils to control the pressure drop of the valves. The optimization problem identifies parameters such as applied current, coil wire size and geometric dimensions of the valves which satisfy the specified pressure drop and inductive time constant requirements. After describing the configuration of MR valves, their pressure drops are obtained on the basis of the Bingham model of MR fluid. Then, the control energy which is an objective function and the inductive time constant are derived. Subsequently, an optimization procedure using a golden-section algorithm and a local quadratic fitting technique is constructed via a commercial finite element method parametric design language. Using the optimization tool developed in this study, optimal MR valve configurations are identified, which are constrained to a specific cylindrical volume defined by its radius and height. In addition, optimization results for MR valves with different required pressure drops and different constrained volumes are obtained and presented.

In this study, three types of shear mode damper using magnetorheological (MR) fluids are theoretically analyzed: linear, rotary drum, and rotary disk dampers. The damping performance of these shear mode MR dampers is characterized in terms of the damping coefficient, which is the ratio of the equivalent viscous damping at field-on status to the damping at field-off status. For these three types of shear mode MR damper, the damping coefficient or dynamic range is derived using three different constitutive models: the Bingham–plastic, biviscous, and Herschel–Bulkley models. The impact of constitutive behavior on shear mode MR dampers is theoretically presented and compared.

A theoretical explanation of the shear-stress characteristics of a Bingham fluid as given by a cone-and-plate viscometer is developed for the case when the fluid is separated from the surfaces of the instrument by a thin layer of Newtonian liquid. It is shown to apply qualitatively to china clay suspensions and a method of deriving the true parameters of the fluid from the flow curve is given.

This class of fluids is characterized by the fact that, provided the temperature of the fluid remains constant, the shear rate depends only on the shear stress and is a single valued function of it. Newtonian fluids which have a viscosity that is independent of the shear rate are described. This behaviour is exhibited by all gases and, in general, liquids, and solutions of materials of low molecular weight. Fluids whose viscosity is a single valued function of shear rate are termed non-Newtonian fluids. Solutions or melts of high molecular weight, particular high polymers and suspensions of solids in liquids fall into this sub-group. This third subgroup described consists of fluids with Bingham plastic and plastic behaviour, shear-thinning behaviour and shear-thickening behaviour.

It is shown how to determine the yield value f and the plastic viscosity η of a Bingham body by means of a parallel-plate plastometer. Calculation have been made starting from the general equations of motion for Bingham body, and the relationship between the thickness h of the specimen and the time t has been obtained when a constant force is applied perpendicularly to the plates. Calculations have been made for the two cases: a) The plates are larger than the specimen; thus the volume of the specimen between the plates is constant. b) The specimen is larger than the plates; thus the area under compression is constant. The formulae are reduced to the well-known equations derived by Stefan and Healey for Newtonian liquid in the limit f→0.