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Magnetorheological (MR) disk-type isolating dampers are the semi-active control devices that use MR fluids to produce controllable squeezing force. In this paper, the analytical endeavor into the fluid dynamic modeling of an MR isolating damper is reported. The velocity and pressure distribution of an MR fluid operating in an axisymmetric squeeze model are analytically solved using a biviscosity constitutive model. Analytical solutions for the flow behavior of MR fluid flowing through the parallel channel are obtained. The equation for the squeezing force is derived to provide the theoretical foundation for the design of the isolating damper. The result shows that with the increase of the applied magnetic field strength, the squeezing force is increased.

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MR fluids are materials of micron-sized and magnetized particles in a carrier fluid. In the absence of an applied magnetic field, MR fluids flow freely. The fluids exhibit Newtonian-like behavior. Upon application of a magnetic field, these fluids exhibit viscoplastic behavior with yield strength [

The MR isolating damper is one such device that provides controllable squeezing force. Altering the strength of an applied magnetic field will change the squeezing force of the MR isolating damper [

In this paper, biviscosity model is used to describe the constitutive characteristics of MR fluids subject to an applied magnetic field. The operational principle of the MR isolating damper is introduced. Analytical solutions for the axisymmetric squeeze flow behavior of a biviscosity fluid are obtained. The velocity equation and the location of the unyield flow region are obtained. The expression for the squeezing force is derived to provide the theoretical foundation for the design of the isolating damper. The result shows that with the increase of the applied magnetic field strength, the dynamic yield stress of the MR fluid goes up rapidly, and the squeezing force is increased.

The schematic configuration of the proposed circular plate MR isolating damper is shown in Figure

Operational principle of a circular plate MR isolating damper.

Figure

Squeeze model of MR fluid between two parallel disks.

To circumvent the “squeeze-flow paradox” of the Bingham model [

Biviscosity model of MR fluid.

The constitutive equation of the biviscosity model can be represented by the following two expressions [

It is evident from the constitutive equation that the biviscosity constitutive model can be divided into two regions based on the dynamic yield stress. The MR fluid to be yielded when the magnitude of the fluid’s internal stress is greater than the yield stress

For the disc-type squeeze flow model in Figure

By integrating (

The MR fluid exhibits Newtonian behavior in the absence of an applied magnetic field, applying boundary conditions of

According to the assumptions, the momentum equation in the

By integrating (

Assume that

As seen in Figure

In yield region

Using the boundary conditions (

In unyield region

The velocity profile in unyield region

Similar to the previous analysis, by using the boundary conditions of

The pressure gradient

When

When

So

The force acting on the bottom disc can be obtained by integrating the pressure along the radial direction:

The subsection integral is used to get the force as

The boundary conditions of pressure are

A typical MR fluid is used in this paper. Figure

Yield strength versus magnetic field strength.

The relationship between the pressure gradient and the radius with apparent yield stress value of 30 kPa is shown in Figure

The pressure gradient versus radius.

When the strength of magnetic field is 100 kAmp/m, the yield surface determined by (

The yield surface along the radial direction.

The velocity profiles can be obtained by (

Velocity profiles for different location of radius.

The squeezing force versus magnetic field strength is shown in Figure

Squeezing force versus magnetic field strength.

The flow behaviors of MR fluid in circular plate MR isolating damper are investigated theoretically in this paper. The equations for the velocity and the squeezing force are derived to provide the theoretical foundation for the design of the MR isolating damper. The unyield region of MR fluid tends to move toward the symmetry plane of working gap as the radius increases. With the increase of the applied magnetic field strength, the squeezing force increased.

This work is supported by Project 51175532 by the National Natural Science Foundation of China and key Project 2011BA4028 by Natural Science Foundation Project of CQ CSTC.