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Using a smart fluid, for example, magnetorheological or electrorheological, in a hydrostatic bearing gives the possibility to actively change the bearing properties during operation. This work presents an analytical model to predict the load and stiffness of a planar hydrostatic bearing lubricated with a Bingham plastic fluid. The model is validated with the use of a numerical model that uses the Bingham–Papanastasiou regularization to achieve convergence. The model gives insight into the size of the operational range of the bearing and the load characteristic.

Electrorheological finishing method is a promising method for small parts fabrication. The small footprint of the tool can provide material removal by virtue of numerical control machine. The characteristics of electrorheological polishing fluid is tested by Haake CV20 rheometer. The dependence of shear stress and viscosity of the electrorheological polishing fluid under different supply voltage, as well as the field dependence of shear stress of ER polishing fluid at different shear rate, was obtained. Hydrodynamic pressure model in working area was studied based on the phenomenon of hydrodynamic lubrication theory of Bingham fluid, and it is proved that the pressure distribution is the dominant factor on the footprint shape. The experiments further showed that the efficiency of material removal is a combined action of hydrodynamic pressure and wheel speed.

A key challenge when designing linear stroke magnetorheological energy absorbers for high-speed impact is that high piston speeds in linear stroke magnetorheological energy absorbers induce high Reynolds number flows in the magnetic valve of the magnetorheological energy absorber, so that achieving high controllable dynamic range can be a design challenge. So far, the research on magnetorheological energy absorbers has typically assumed that the off-state force increases linearly with piston velocity. But at the higher piston velocities occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. This problem was recognized in our prior work, where it was shown that minor losses are important contributing factors to off-state damping. In this study, a nonlinear analytical magnetorheological energy absorber model is developed based on a Bingham-plastic nonlinear flow model combined with velocity squared dependent minor loss factors. This refined model is denoted as the Bingham-plastic nonlinear flow model with minor losses. From this Bingham-plastic nonlinear flow model with minor losses, an effective design strategy is presented for conventional magnetorheological energy absorbers. The Bingham-plastic nonlinear flow model with minor losses is validated via computational fluid dynamics simulation, so that magnetorheological energy absorber performance can be analytically verified before being manufactured. The magnetorheological energy absorber is fabricated and tested up to an effective piston velocity of 5 m/s by using the high-speed drop tower facility at the GM R&D Center. Comparison of our analysis with measured data is conducted, and the effective design of the magnetorheological energy absorber using the Bingham-plastic nonlinear flow model with minor losses is validated.

It is known that a quasi-static analysis without considering fluid inertia is usually used for magnetorheological damper design. However, fluid inertia terms need to be incorporated into the governing Navier–Stokes equation in practical application for oscillatory or unsteady fluid flow. In this article, an unsteady flow of magnetorheological fluids within flow mode magnetorheological dampers was theoretically investigated under sinusoidal displacement excitation. Based on the governing Navier–Stokes equation, incorporating the boundary and initial conditions, central numerical velocity solutions of magnetorheological fluids within magnetorheological damping channel were developed and used to confirm the damping force using both Bingham plastic and Herschel–Bulkley models of magnetorheological fluids. To simplify the governing equation of Herschel–Bulkley flow, an approximation method replacing Herschel–Bulkley model velocity with Bingham plastic model velocity during calculating effective viscosity shear rate of Herschel–Bulkley model is proposed and used. For given magnetorheological fluid properties and flow mode magnetorheological damper geometry, under different yield stresses, sinusoidal excitation frequencies, and power-law exponent of Herschel–Bulkley model, the effects of magnetorheological fluid inertia terms on work and characteristic diagrams of magnetorheological dampers are discussed.

This article presents a transient model of a magnetorheological damper, which takes into account the effect of Duhamel’s superposition of the variation of magnetorheological damper piston velocity with time. The magnetorheological fluid flow channel studied in this work is in the shape of an annular gap between the piston and the bore of the cylinder of the magnetorheological damper. The model was derived using a Bingham plastic model for shear stress versus shear rate behaviour of the magnetorheological fluid by applying the combination of Laplace and Weber transforms to the Navier–Stokes equations for obtaining the analytical solutions of the velocity in the sheared regions in a given cross section of an annular magnetorheological fluid flow channel. The solution is further modified to include the effect of time variation of piston velocity by using Duhamel’s superposition integral. The equations of the velocity profiles have been used to obtain the equations of mass flow rate balance, velocity compatib...

Utilizing the integration by parts rule, a simple and general computational method is proposed for solving quasi-steady parallel plate flow problems and most types of fluids can be handled by this method, such as the Newtonian fluid, the Power-law fluid, the Bingham fluid, and the Herschel-Bulkley fluid. The flow rate-pressure gradient relation for quasi-steady parallel plate flows is derived based on an abstract piecewise constitutive equation. Moreover, the flow rate is directly expressed in terms of the constitutive equation in this method, so high efficiency is achieved. As an application example of the proposed method, a new quasi-steady magnetorheological damper model more general than the existing ones is developed with the material non-linearities considered in both the pre-yield and post-yield regimes. Finally, conversions of this model to the Bingham model, the Herschel-Bulkley model, the Biviscous model, etc., are demonstrated.

The electrorheological (ER) fluid is a fluid that shows non-Newtonian fluid characteristics when the electrical field is applied. In this study, an experiment of an ER fluid viscous damper, in which an ER fluid is enclosed in the gap of a piston—cylinder system, is carried out to investigate the performances of the ER fluids and the effects of the electric field on the impulse response of the damper when an impulsive force is applied to it. To validate the experimental observations, a theoretical cylinder displacement formula of the damper is derived based on the Bingham approximation and the Stokes flow assumption of the test ER fluids in the damper. The present study shows that, when strength of the applied electric field and concentration of the ER fluids increase, the oscillation amplitudes of the cylinder displacement reduce. In other words, the ER damping effect is improved when the strength of the electric field increases.

This article summarizes the work carried out in the development of hydrodynamic lubricated journal bearings with magnetic fluids. Two different fluids have been analyzed: one is the ferrofluid from FERROTEC APG s10n and the other is the magnetorheological (MR) fluid from LORD Corp., MRF122-2ED. Theoretical analysis has been carried out with numerical solutions of Reynolds equation, based on apparent viscosity modulation for ferrofluid and Bingham model for MR fluid. To validate this model, one test bench has been designed, manufactured, and set up, where preliminary results showed in this article demonstrate that magnetic fluids can be used to develop active journal bearings.

The resistance to flow of magnetorheological (MR) fluids is greatly increased by the application of a magnetic field. At present, most devices exploiting this MR fluid behavior are pistons executing straight-line motion. The MR fluids in these devices are subjected to shear flow, and are modeled by either the Bingham plastic or Herschel-Buckley models, both 1D, phenomenological continuum-level forms relating strain rate, magnetic field magnitude, and stress magnitude, and fit to continuum-level empirical measurements. We employ a multiscale model of the MR fluid introduced in an earlier paper, which integrates nanoscale behavior over a mesoscale volume to deduce continuum properties. This approach replaces many of the phenomenological features of the Bingham plastic and Herschel-Buckley models with first principles, and isolates those few phenomenological features that remain into a single scalar term. The model is compared to the Bingham plastic and Herschel-Buckley models, assessing each model’s ability to capture the experimentally measured mechanical response of a particular MR fluid-based damper to specified magnetic fields. The result of this comparison is that, our model possesses the flexibility to best match the measured behavior of the MR fluid device observed in our experiments, with fewer required experimental measurements.

Storage and loss moduli of an MRF submitted to a magnetic field, as measured by a plate—plate magnetorheometer versus shear amplitude in oscillatory shear, exhibit a complex non-linear response. Above a critical amplitude, the storage modulus decreases strongly, while the loss modulus passes through a distinct maximum. The periodic shear stress signal changes from sinusoidal to saw-tooth like. A mechanical analogue, consisting of a Bingham element (friction element and damper arranged in parallel) and elastic spring in series, is capable to capture the measured behaviour. Model predictions for the time-dependent shear stress and resulting moduli at agitation frequency (fundamental mode) for various amplitudes are discussed and the determination of model parameters from the experimental data is addressed. The linear radial shear strain profile in plate—plate geometry causes a smearing of the moduli and shift to higher amplitudes by about a factor of 4/3. The conversion from physical to engineering parameters for an MR device is demonstrated for disk clutches using cone—plate and plate—plate geometry. Complications due to a nonhomogeneous shear in the device are addressed. The elastic modulus of the MRF may be relevant for vibration damping and may cause some shift in the resonance frequency of the device.

Microprocessor-controlled prosthetic knees, which rely on magnetorheological (MR) technology, have the potential to increase the comfort and quality of life of amputees. The focus of this study is on a prosthetic knee which is currently on the market and manufactured by the company Ossur Inc. The knee uses magnetic fields to vary the viscosity of the MR fluid, and thereby its flexion resistance. The torque transmissibility of the knee greatly depends on the magnetic field intensity in the MR fluid. The objective of this study is to investigate the strength of the magnetic field and the braking torque in the knee, for a few selected design parameters, and to determine which changes can be made to the existing design in order to maximize the torque output. The magnetic field in the fluid is evaluated by finite element analysis and the torque is calculated by using a Bingham visco-plastic model. A parametric study is carried out for several design parameters where the effect of variation in each parameter on the braking torque is observed. The results of this study give a valuable insight into which parameters should be prioritized for future changes of the knee, with regard to strength and comfortability.

The present work investigates the transient response of a three-layer sandwich beam with an electrorheological (ER) core. Electrorheological fluids are a class of smart materials, which exhibit reversible changes in mechanical properties when subjected to an electric field. As applying an electric field to the core layer changes the dynamic characteristics of the structure, the ER layer can be used for suppressing the vibrations and reducing the settling time of the beam. A finite element model of the structure is developed and a direct integration algorithm is used to simulate the impulse response of the proposed sandwich beam. The core is modeled as a Bingham plastic material and effects of changes in the applied electric field on the structure settling time and its natural frequencies are represented for several thickness ratios. The variations of damping force vector, due to the dependence of the ER fluid shear stress, to the sign of shear rate, are considered in each iteration. The ER layer thickness and the applied electric field level have a significant influence on the damping behavior of the model.

This study presents robust control performance of a direct current (DC) motor with brake system adopting the giant electrorheological (GER) fluid, whose distinguished feature is an extremely high value of yield stress. As a first step, Bingham characteristics of the GER fluid is experimentally investigated using the Couette type electroviscometer. A cylindrical type of electrorheological (ER) brake is then devised based on the Bingham model, and its braking torque is experimentally evaluated. The ER break is then incorporated with a DC motor. After formulating the governing equation of motion for the DC motor with ER brake system, a sliding mode control algorithm, which is very robust to external disturbances and parameter uncertainties, is synthesized and experimentally realized in order to achieve desired rotational speed trajectories. The tracking responses of the control strategy are then evaluated for various sinusoidal trajectories. In addition, their tracking errors are evaluated and compared with those obtained from traditional PID controller.

Quasisteady modeling of linear stroke flow mode magnetorheological (MR) (or electrorheological (ER)) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the variable yield stress of the fluid, τy, is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a pre-yield condition where the local shear stress is less than the yield stress, τy, or (2) a post-yield condition, where the local shear stress is greater than the yield stress, τ > τ y, so that the material flows with a constant post-yield viscosity. The objective of this study is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits post-yield shear thinning or thickening behavior, that is, the post-yield viscosity is a function of shear rate. A Herschel—Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results — velocity profile, pre-yield thickness, and damping coefficient — are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.

A magnetorheological (MR) fluid, modeled as a Bingham plastic (BP) material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a BP model is an idealization to physical MR behavior, albeit a useful one. A better approximation involves modifying both the preyield and postyield constitutive behavior as follows: (1) assume a high viscosity preyield behavior when the shear stress is less than the transition stress, and (2) assume a power law fluid (i.e., strain rate dependent viscosity) when the shear stress is greater than the transition stress. Assuming a power law fluid in postyield allows the model to account for shear thinning behavior exhibited by MR fluids at higher strain rates. Such an idealization for MR fluid constitutive behavior is called an viscous-power law model, or a Herschel—Bulkley (HB) model with preyield viscosity. This study develops a quasi-steady analysis for such a constitutive MR fluid behavior applied to an MR flow mode damper. Closed form solutions are developed for the fluid velocity, as well as key performance metrics, such as damping capacity and dynamic range (ratio of field-on to field-off force). For the given fluid properties and flow mode damper geometry, the fluid velocity profile and gradient, and the relationship of the damper force and piston velocity are analyzed. In addition, specializations to existing models, such as the HB, biviscous, and BP models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.

This study focuses on the design, development, and testing of a new magnetorheological fluid (MRF) damper for high-mobility multi-purpose wheeled vehicle (HMMWV). The new damper is designed to provide controllability while keeping the same geometrical dimensions as the original equipment manufacturer (OEM) damper. To design a fail-safe MRF damper, MRF behavior is simulated using the Bingham Plastic model, and the magnetic field distribution is obtained by a three-dimensional electromagnetic finite element analysis. A fail-safe MRF damper is referred to one which retains a minimum damping capacity comparable to that of OEM damper in the event of a power supply or electronic system failure. The proposed MRF damper is designed to achieve non-symmetrical force characteristics with different force responses at rebound and compression phases. Theoretical predictions and experimental results are presented for the force—displacement and force— velocity behaviors of the damper under different input motions, various magnetic fields, and different MR fluids.

Most of the commercially available magnetorheological (MR) fluids are only tested up to 1200 1/s shear rates but with no magnetic field. Data are rarely available at high shear rates with magnetic field applied. In most of the applications where MR fluids are used, such as MR rotary brakes or MR translational dampers, the shear rates can be in the order of thousands and in some applications, the shear rates could be in the order of ten thousands (1/s) and higher. At these high shear rates, most MR fluids will be shear thinning and Bingham model will be inappropriate to use. The focus of this study is on the mathematical modeling of a drum-type MR rotary brake using the Herschel-Bulkey model.

This article presents the performance evaluation of two different bypass-type magneto-rheological (MR) shock dampers for high impulsive force systems, one of which is a single-ended damper and the other a double-ended one. First of all, MR shock dampers are designed and manufactured on the basis of the Bingham properties of MR fluid and the result of the magnetic field analysis for the magnetic circuit. After experimental investigations on both the magnetic field-dependent damping force and the response characteristics, the quasi-steady state models describing the dynamic behavior of the proposed dampers are formulated. Then, a simple one degree-of-freedom mass-drop system as a test bench for the MR shock dampers is constructed, and the simple and practical control algorithm is proposed in consideration of dynamic characteristics of the shock control system. Finally, in order to investigate their dynamic characteristics and control performances under shock condition, a comparison study is conducted through a series of experiments and simulations. The results show the controllability and adaptability of the proposed MR shock dampers for shock or impulsive force as well as the effectiveness of the proposed control algorithm.

This study examines the field-dependent hysteretic behavior of a magnetorheological (MR) fluid and its identification using a Preisach model. The field-dependent shear stress of a commercially available MR fluid is measured using a parallel disk rheometer, and its shear stress versus shear rate hysteretic behavior is measured. To demonstrate the applicability of the Preisach model to MR fluid hysteresis modeling, two significant properties are empirically studied; the minor loop property and the wiping-out property. Using these data, the Preisach model for the MR fluid is identified using experimental first order descending curves. The effectiveness of the identified hysteresis model is verified in the time domain by comparing the reconstructed to the measured field-dependent shear stress. In addition, the identified hysteresis is compared to the conventional Bingham model.

The analytical solution obtained in this study permits the hydrodynamic calculation of Bingham fluid flow in the annular gap of an electrorheological (ER) damper when the yield stress and plastic viscosity depend on the inhomogeneity of the electrical field strength. The main parameters that influence the dissipation processes have been determined. The analytical dependence of the dissipation capacity of the ER damper versus the electric field strength has been obtained.

The magnetorheological (MR) shock absorber is one of the most promising new devices for vibration reduction. Many investigations have been carried out on low velocity and frequency applications of MR devices. The use of the MR shock absorber under impact load is of great interest. The now widely used MR damper models, such as the Bingham model, cannot explain sufficiently the shear thinning behavior under impact loads. However, the Herschel–Bulkley model can be used to explain the same. The main purpose of this study is to analyze the behavior of the MR shock absorber under impact load and to verify the analytical conclusions and experiments. First, some dynamic simulations on the MR shock absorber under impact loads in Matlab and Simulink are carried out. The model describes the dynamic characteristics especially the shear thinning behavior of the shock absorber, based on this model, then analyzes the variations of piston acceleration and back cavity pressure of MR shock absorber at both same and different flow indices. A test rig is developed to test the characteristics of the long-stroke MR shock absorber under impact loads. Comparisons between the simulation and the test results are made to validate our conclusions. The results indicate that the peak acceleration value of the piston rod and the pressure of the back cavity are decided by the peak value and the duration of the impact force. The peak value of the acceleration and the cavity pressure cannot be changed, but the transitional time of the acceleration of the piston and the pressure of the back cavity of MR shock absorber can be controlled by changing the applied current in the electromagnetic coil. MR shock absorbers will be the most promising shock reduction device under an impact environment.

This study examines identification of rheological parameters for a constitutive model characterizing the rheological behavior of a ferrous nanoparticle-based magnetorheological (MR) fluid. Particle size is nominally 28 nm and the MR fluid has a weight fraction of 27.5% Fe. A constant shear rate rheometer is used to measure flow curves (shear stress vs. shear rate), as a function of applied magnetic field, of an MR suspension of nanometer-sized iron particles in hydraulic oil. The MR fluid is characterized using both Bingham-plastic (BP) and Herschel-Bulkley (HB) constitutive models. These models have two regimes that can be characterized by a field-dependent yield stress: pre-yield implies that the local shear stress is less than the yield stress, and post-yield implies that the local shear stress is greater than the yield stress. Both models of MR fluid behavior assume that the MR fluid is rigid in the pre-yield regime. However, the post-yield behavior is different. The BP model assumes that the post-yield increase in shear stress is proportional to shear rate. However, the HB model assumes that the post-yield increase in shear stress is proportional to a power law of shear rate. Identification of the model parameters is complicated by model non-linearities, as well as variance in experimental data. The rheological parameters of the BP and HB models are identified using both a gradient-based least mean square minimization procedure, as well as a genetic algorithm (GA). The HB model is shown to represent better, the rheological behavior of the ferrous nanoparticle-based MR fluid. Also, the GA performs better than the gradient-based procedure in minimizing modeling error.

In this work, a mixed mode-type magneto-rheological fluid mount (MR mount in short) is devised by considering the nondimensional formulation of Bingham plastic flow, and applied to vibration control of a structural system subjected to external excitations. The structural system consists of a vibrating mass, semi-active MR fluid mount, and passive rubber mounts. The MR mount is installed on the beam structure as a semi-active actuator and supports the vibrating mass, while the flexible beam structure is supported by two passive rubber mounts. After verifying the field-dependent damping force characteristics of the MR mount, the governing equation of the structural system is derived in the modal coordinate and rewritten as a state space control model. The linear quadratic Gaussian (LQG) controller is then formulated in order to attenuate vibration of the structural system. The LQG controller is experimentally realized and control responses such as accelerations and transmitted forces of the structural system are presented in the frequency domain.

The hydrodynamic characteristics of journal bearings with electrorheological (ER) fluid lubrication are studied in this article. The external applied electric field is partially imposed on the contractive part (arcwise) of the journal bearings. The bearing has a finite length and operates under incompressible laminar flow with steady conditions. The full three-dimensional Navier-Stokes (N-S) equations are solved numerically. The modified Bingham plastic model is used to describe the behavior of the ER fluid. In this study, the cavitation effects are also considered using viscosity modeling. The effects of electric field and eccentricity on the performance of journal bearings are investigated comprehensively.

We validate and assess the applicability of an Eyring constitutive model. The Bingham plastic model has a zero shear rate discontinuity, which leads to inaccuracies in modeling and simulation, and is characterized by two rheological constants for a constant field: yield stress and postyield viscosity. The Eyring model has a smooth transition through the zero shear rate condition, and also has two rheological constants for a constant field. An electrorheological (ER) damper having a damping level comparable to a shock absorber for a small-sized passenger car damper is manufactured, and its performance is predicted using the Eyring model. To accurately identify the rheological parameters of the Eyring model, a parameter identification method was used. The damping force versus piston displacement and velocity behaviors of the ER damper are experimentally measured with respect to applied electric field and excitation frequency. To validate the Eyring model, the experimental results are compared with predictions in the damping force versus piston displacement and velocity behaviors.

A numerical simulation is conducted to clarify the unsteady flow behavior and drag force around the oscillating flat plate immersed in MR fluids under the applied magnetic field. A modified Bingham model is adopted to take continuous viscous flow behavior at the very small shear rate and also magnetically variable yield stress into account. The measured yield stress is given to the model as a function of magnetic field intensity. The governing equations for the oscillating flat plate and unsteady MR fluids flow are derived by a modified Bingham model taking magnetic body force, yield stress and viscous force into account. The effects of magnetic field intensity, oscillation frequency and amplitude and further plate thickness on the fluid flow and damping characteristics around the oscillating flat plate are clarified by the numerical simulation.

Electrorheological (ER)and magnetorheological (MR)fluids are characterized by an increase in dynamic yield stress upon application of a magnetic field. The Bingham plastic model has proven useful in modeling flow mode dampers utilizing ER and MR fluids. However, certain MR fluids can exhibit shear thinning behavior, wherein the fluid’s apparent plastic viscosity decreases at high shear rates. The Bingham plastic model does not account for such behavior, resulting in overprediction of equivalent viscous damping. We present a Bingham biplastic model that can account for both shear thinning and shear thickening behaviors. This approach assumes a bilinear post yield viscosity, with a critical shear rate specifying the region of high shear rate flow. Furthermore, the model introduces non-dimensional terms to account for the additional parameters associated with shear thinning and thickening. A comparison is made between Bingham plastic and Bingham biplastic force responses to constant velocity input, and equivalent viscous damping is examined with respect to nondimensional parameters.

Adaptive structures contain parts whose properties may be tuned so as to suit some purpose. Certain fluids change viscosity when subjected to an electrical field. This paper concerns the behaviour of such an electrorheological fluid, ERF, which may be characterized as visco-plastic with some elasticity present. The stress response to a prescribed strain is studied in tests. Various models for describing the observed behaviour are analyzed. Results show that modelling the ERF as a Bingham fluid gives a rather close fit for low field strength. A solid mechanics model which displays yielding with kinematic strain hardening is preferred for high field strength as it then describes the observed amplitude and frequency dependence quite well. Relevant constants for investigated models are listed as functions of the field strength. The electrical behaviour is essential in designing parts for on-line response of structures, in order to control vibrations. Results show that a damper containing ERF responds to applied voltage as a capacitor whose leak resistance depends on voltage whereas its capacity does not. AC as well as DC fields are treated. When subjected to harmonic displacement the force response of the damper contains superharmonics owing to the non-linearity of the ERF. In AC powered dampers, intermodulation frequencies between field and displacement are identified.

This paper presents torque control characteristics of ER (electro-rheological) and MR (magneto-rheological) clutches. As a first step, Bingham properties of ER and MR fluids are experimentally distilled under the shear mode. A nondimensional model of the clutches is established for reasonable comparison. Two clutches have the same principal design parameters such as outer radius of the disc and electrode gap size. Following the manufacturing of two clutches on the basis of the nondimensional model, field-dependent torque levels are experimentally evaluated. A PID (proportional-integral-derivative) controller is then designed and experimentally realized to achieve desired torque. Both regulating and tracking torque control responses of the two clutches are evaluated and compared. In addition, control durability for torque tracking is undertaken to provide a practical feasibility of the proposed clutches.

The Bingham plastic constitutive model has been widely used to predict the post-yield behavior of electro- and magneto-rheological fluids (ER and MR fluids). However, if these fluids experience shear thinning or shear thickening, the Bingham plastic model may not be an accurate predictor of behavior, since the post-yield plastic viscosity is assumed to be constant. In a recent study, it was theoretically and experimentally demonstrated that the Herschel-Bulkley fluid model can be successfully employed when evaluating non-Newtonian post-yield behavior of ER and MR fluids. In this paper, we extend our previous work and adopt the Herschel-Bulkley model to include a detailed analysis of ER and MR fluid dynamics through pipes and parallel plates. Simplified explicit expressions for the exact formulation are also developed. It is shown that the proposed simplified model of the Herschel-Bulkley steady flow equations for pipes and parallel plates can be used as an accurate design tool while providing a convenient and generalized mathematical form for modeling ER and MR fluids. Theoretical and experimental analyses are presented for a MR fluid damper, which is designed, developed, and tested at the University of Nevada, Reno (UNR).

We experimentally validate nonlinear quasi-steady electrorheological (ER) and magnetorheological (MR) damper models, using an idealized Bingham plastic shear flow mechanism, for the flow mode of damper operation. An electrorheological valve or bypass damper was designed, and fabricated using predominantly commercial off-the-shelf hydraulic components. Both the hydraulic cylinder and the bypass duct have cylindrical geometry, and damping forces are developed in the annular bypass via Poiseuille (flow mode) flow. Damper models assume parallel plate geometry. Three nondimensional groups are used for damper analysis, namely, the Bingham number, Bi, the nondimensional plug thickness, 6, and the area coefficient defined as the ratio of the piston head area, AP, to the cross-sectional area of the annular bypass, Ad. In the flow mode case, the damping coefficient, which is defined as the ratio of equivalent viscous damping of the Bingham plastic material, Ceq, to the Newtonian viscous damping, C, is a function only of the nondimensional plug thickness. The damper was tested using a mechanical damper dynamometer for sinusoidal stroke of 2 in., over a range of frequencies below 0.63 Hz. The damping coefficient vs. nondimensional plug thickness diagram was experimentally validated using these data over a range of damper shaft velocities or frequencies and applied electric fields. Because the behavior of ER and MR fluids are qualitatively similar, these ER damper modeling results can be extended to analysis of flow mode MR dampers.

A method for the rapid solution of flows of electrically structured fluids of the particle/liquid type is described. The technique is indicated for heavily loaded fluids and for flows in complex controller geometries. Its basis lies in the modification of a commercial computer routine which can deal with Bingham plastics, by the inclusion of a sub-routine which represents the ERF/MRS constitutive equations for a wide range of excitation. The entire system of working is validated against known and well proven analytical and experimental results.

The hysteresis behavior of a linear stroke magnetorheological damper is characterized for sinusoidal displacement excitation at 2.0 Hz (nominal). Four different modeling perspectives are discussed for purposes of system identification procedures, including: (1) equivalent viscous damping, (2) nonlinear Bingham plastic model, (3) nonlinear biviscous model, and (4) nonlinear hysteretic biviscous model. By progressively adding model parameters with which to better represent pre-yield damper behavior, the force vs. velocity hysteresis model is substantially improved. The three nonlinear models represent the force vs. displacement hysteresis behavior nearly equally well. Thus, any of the three nonlinear damper models could be used equally successfully if only a prediction of energy dissipation or damping were of interest. The nonlinear hysteretic biviscous model provides the best representation of force vs. velocity hysteresis of the four models examined here.

The controllable rheological behaviour of Electro-Rheological Fluids (ERF) is useful in engineering systems where variable performance is required. In particular the ERF have properties which are changed by an imposed electric field. In this paper a generalised Reynolds equation is solved using finite element techniques in order to simulate the behaviour of misaligned journal bearings lubricated with ERF. The Bingham plastic model is used to described the behaviour of the ERF, when the fluid is in flow mode. It is found that the applied electric field has a substantial influence on the load carrying capacity and the misaligned attitude of the journal bearings. It is concluded that the electric field imposed on the electro-rheological lubricant tends to align the journal in the bearing, making thus the misalignment angle smaller. Thus by changing the electric field it is possible to control the dynamic behaviour of rotor-bearing systems.

A numerical analysis is performed on the flow characteristics of an electrorheological (ER) fluid when fully developed ER fluid flow in a channel is instantly subjected to electric fields. The Bingham plastic model is used to describe the ER fluid behavior. The flow field is assumed to be incompressible and isotropic. The SIMPLER algorithm with staggered grid system is employed to solve the momentum and continuity equations governing the steady state, laminar flow. The effects of electric field intensity and upper wall velocity changes on velocity profiles are investigated.

Electrorheological Fluids were prepared by using small (approximately 63 μ) silica particles and fluids with very different dielectric constants (∈). The results of the rheological characterization of the above Electrorheological Fluids show dramatic changes depending on the relative polarity of the particle and liquid phases of the particular ERF. These results are discussed under the light of the various theoretical mechanisms proposed in the literature for Electrorheological Fluids.