A method for modeling Electro-Rheological (ER) dampers is proposed. It consists in two sequential steps: Characterization and Customization. Both steps are. This study presents nondimensional analysis of an Eyring constitutive model to describe the field-dependent behavior of an electrorheological. This paper presents the design, analysis, testing and modeling of an electrorheological (ER) fluid damper developed for vibration and seismic.

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This method requires experimental data of the ER damper. In this study it is proposed: Indexed in Science Citation Index Expanded.

If the value of the ESR is 0, it indicates that the model estimates exactly the damper force; however, a value of 1 indicates that the model only predicts the mean value of the damper force. Herein it is proposed to combine the concepts of passive control with the benefits of active control, to produce an optimal, yet stable and reliable damping system. In Figure 7 b the stiffness of the damper is affected when the frequency is incremented; also it is notorious how the stick-slip phenomenon became greater as the manipulation increases.

Introduction In an automotive suspension system the shock absorber has the purpose of dissipating the energy of the motion of the vehicle caused by the road disturbances.

The error-to-signal Ratio ESR performance index was used to evaluate the model accuracy. This test consists in measuring the time that the model takes to compute a vector of data points; in this case the selected vector contains 58, data points. The advantage of this model is the few number of constants but it does not seem to be very accurate; also it needs a set of constants for every field manipulation interval.

Later [ 7 ] shows two different types of ER damper configurations. Passive suspension systems are tailored to achieve a tradeoff of these objectives [ 1 ]. It can be observed that in almost all experiments the customized model shows same results as the full model, with the exception of.

Therefore, the discarded terms in the customized model has little effect in the response of this damper; this is consistent with the results obtained in the characterization step.

After long inactive periods settling of the suspension occurs which results to loss of the fluid ER activity. These results were also validated with two-dimensional density plots. In the experimental FV diagram, Figure 12 athe higher density of data appears with small compression forces while in the Choi model, Figure 12 bthe higher density appears with larger forces; hence, this model represents a stiffer damping force than the real damper at low velocities.

In the DoE step, the experiments are defined on the automotive range of operation. Since the model should be well suited for real time implementations, there was another comparative test done to all the models. The modeling method comprehends two simple steps: The DoE consists of a combination of displacement and actuation sequences i.

## An electrorheological fluid vibration damper

This ER damper is subjected to the stick-slip phenomenon, especially in positive velocity; according to [ 5 electrodheological this phenomenon appears in the ER damper as a force overshot when the flow changes its direction in the annular duct.

At the yield point the damper fluid behavior changes from a pseudoplastic to a quasisolid [ 17 ]. This model can represent the behavior in both the preyield and the postyield zone but needs the identification of every parameter in each combination of frequency and field intensity; the accuracy of the model depends on how small are the considered intervals of the variables, but when changing the between this levels the model does not consider a transient response of the force.

Several of the existing ER fluids consist of particle suspensions within a dispersant phase. Section 6 shows the results and evaluates the performance of the customized model. The proposed method does not need a priori knowledge i. The results show, as expected, that the Choimodel spends less than half the time dmper. A series of displacement sequences and actuation signals were used to capture the static and dynamic relations between velocity, displacement, actuation signal, and the damper force [ 14 ].

The ICPS is a signal with random amplitude variations, whereas the PRBS is a signal whose amplitude switches between two constant values with a random frequency. The relation between the SA force and the PWM duty cycle becomes evident; electrorhfological relationship is asymmetrical, Figures 7 a and 7 b.

The Choi model is not able to generate small forces due to the use of a discontinuous function; this explains why this model could not predict the small forces present on the experimental data.

## ERF damper

Also, when compared with well-known models, the results have better performance, an average of The ER damper models are also qualitatively compared using density plots in order to identify if these models predict correctly the distribution of the experimental data. According to [ 22 ], since the experiment is a RP the zones with higher density of occurrences should be at low velocities for the FV diagram; in the case of the FD diagrams these zones should be in the small displacement range; on the other hand this experiment has a PRBS actuation signal; therefore the higher density zones must be in the ends of the control signal 0.

Most of the models are dependent on internal dampet properties of the damper, ER fluid, and its design; this makes the implementation of these models very restricted i. Figure 12 presents a comparison of the density plots of experiment.

If the SA damper has an dlectrorheological behavior the model needs to have different coefficients for positive and negative velocities. Abstract Funding Institution Comments. The preyield and postyield zones depend on the actuation signal but only the preyield zone depends on the damper velocity.

### Method for Modeling Electrorheological Dampers Using Its Dynamic Characteristics

The Choi and Eyring-plastic models present smaller forces than the customized model. Nonetheless, the FM diagram obtained with the customized model resembles the experimental data the most. The electrorheological ER damper is a hydraulic device, which is filled with a mixture of low viscosity oil and particles that are sensitive to electrorheplogical electric field.

The experimental system and Design of Experiments are shown in the next section. The authors do not evaluate the effects of the frequency in the model and the transient behavior of the force during changes in intensity of the electric field, which is important for control purposes.

The passive FV and FD experimental diagrams, Figures 5 a and 5 electrorheoogicalare analyzed and the electrrheological characteristics can be identified: This combination, at high frequencies, introduces high variability in the force; variability induces more hysteresis in the measured force.

The behavior of the SA component of the force is presented in Figure 7. In order to analyze the effectiveness of the customized model, a comparative analysis with other two well-known models was carried out: Elecrtorheological sequences ensure the ER damper will be tested in the automotive domain. The authors declare that there is no conflict of interests regarding the publication of this paper. Density plots of experimental and estimated data for different models experiment.

It represents the ratio between the variance of the estimation error and the variance of the experimental damper force [ 21 ]. Following the electtorheological line in terms of parametric models, [ 8 ] describes a hydromechanical based model.