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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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 ]. This model captures the damper behavior in the preyield zone, in terms of the hysteresis.

The performance indexes for all the experiments customized and full models are shown electrorheologicaal Table 3. Section 6 shows the results and evaluates the performance of the customized model. Finally, the customized model, Figure 12 dgenerates a similar density of experimental data for extension forces and slightly larger compression forces.

### An electrorheological fluid vibration damper – IOPscience

The main contribution of this method is the dqmper that by analyzing the experimental data i. The first one is the most common, the cylindrical type, in which the ER fluid flows through an annular channel where the electric field is applied. These results were also validated with two-dimensional density plots. There are several contributions in this topic [ 23 ].

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Increased clock period signal ICPSFigure 3 band dampsr binary signal PRBSFigure 3 csequences are used to analyze the damper transient response under actuation signal variations. Based on those observations, 3a3b were customized for this ER damper; the following asymmetric model for the ER damper is proposed: Also, at the postyield zone, an average force gain FM is obtained, based on the average value in which the yield of the force occurs eleectrorheological each manipulation value.

The density plots are scatter plots that use different colors to indicate the density of incidences in different zones of the diagram; blue color indicates a lower number of occurrences i. 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. In the FV diagram the yield point is a Cartesian point where the damping force becomes independent of the velocity.

However, most of them are highly dependent on internal physical properties of the damper usually confidential informationdemand too much computational effort, or fail to capture the nonlinear behavior of the ER damper. This is result of the actuation and manipulation signals used in that experiment, because the DSFS signal captures best the dynamical behavior of the damper in its whole range of operation while the RP only explores a limited zone.

The customized model, Figures 11 e and 11 fshows the best modeling performance since the nonlinearities added by the manipulation signal are well described and the low and high damping forces are correctly identified. These tools will lead to realistic macroscopic force displacement models for the damper unit, and possibly to the design of optimal damper geometries.

Based on design of experiments DoEthe representative behavior of the damper into the automotive domain can be obtained. Semiactive SA suspension systems use a particular type of shock absorber which is capable of online modifying the amount of energy that can dissipate. In the Eyring-plastic model the force is considered a nonlinear function of the velocity: 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.

This means that ideally it behaves as a solid at low stress efforts, but it flows as a viscous fluid when this force reaches its yield stress. This method requires experimental data of the ER damper. In these equations, the use of the tanh function is replaced with the so-called squash function: This explains why in the experiment the ESR is almost the double of the one achieved with the full model.

Mathematical Problems in Engineering. The authors declare that there is no conflict of interests regarding the publication of this paper.

## An electrorheological fluid vibration damper

This combination, at high frequencies, introduces high variability in the force; variability induces more hysteresis in the measured force. 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. Equation 3b represents the SA forcewhere is the manipulation applied to the damper, is the force gain due to manipulation, anddescribe the behavior of the damper in the preyield zone.

Since in the model customization step those terms were excluded, the model was less effective in capturing those highly hysteric behaviors. If the SA damper has an asymmetric behavior the model needs to have different coefficients for positive and negative velocities.

The customized model ends with a short equation with high performance. In the FD diagram the experimental data presents higher density with small forces, especially in compression, Figure 12 e. Analyzing the ESR index, the customized model had the best modeling performance for all experiments, followed by the Eyring-plastic model. Subscribe to Table of Contents Alerts. Comparison of estimated green and experimental black data based on. The ER fluid, when exposed to the electric field, behaves as a viscoelastic material, known as a Bingham plastic.

State of the Art There are many mathematical models to reproduce the characteristic behavior of the ER damper.

This force peaks appear also in Figures 8 c and 8 d and Figures 9 c and 9 dwhere the real data differ from the estimated data in the top and bottom zones of the diagrams. In addition, DSFS sequence has a similar frequency spectrum experienced by automotive suspension systems.

The proposal does not need prior knowledge of the damper such as physical properties, dimensions, and so forth, just experimental data. The FM diagram is important for control systems purposes. 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.

On the other hand, the DSFS signal is used to analyze the transient response and the hysteresis loops when changes in magnitude and frequency are present.

The results show, as expected, that the Choimodel spends less than half the time 0. 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.

This model represents the hysteretic behavior of the ER damper in postyield zone and its increment due to the frequency, but the assessment of the model is done with constant conditions of frequency displacement and electric field.

The passive FV and FD experimental diagrams, Figures 5 a and 5 bare analyzed and the following characteristics can be identified: