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A transmission method of magnetorheological (MR) fluid in cylindrical-type driven by shape memory alloy (SMA) spring with the thermal effect was proposed. The torque can change rapidly with temperature. Based on the thermal effect of SMA, the expression for displacement of SMA spring was established. The rheological property of MR fluid under the magnetic fields was described by Bingham model. Based on momentum equation, the shear flow of MR fluid between two cylinders was analyzed and the expressions of flow velocity and torque have been obtained. The experimental results show the output displacement of SMA spring and the transmit torque of MR fluid is directly proportional to the temperature and the applied magnetic field, respectively.

MR fluids and SMAs are known as smart materials for their properties can change rapidly on different external conditions. By applying a magnetic field, the fluids show the viscoplastic behavior with yield strength [

MR transmission is a device that transmits torque by the shear stress of the MR fluids. It has the property that their transmitting torque changes quickly in response to an external magnetic field. A literature review indicates that the transmission using MR fluids can be classified as having either disc-type or cylindrical-type [

In order to rationally design the MR transmission devices driven by SMA spring under thermal effect a designer should analyzes the output displacement of SMA springunder thermal effect, and the torque transmission ability of MR fluid. In this paper, Bingham model is used to describe the constitutive characteristics of MR fluids subject to an applied magnetic field. The expressions for the output displacement of SMA spring and the torque of the cylindrical type MR transmission are established to provide the theoretical foundation for the design of MR device.

The schematic of the cylindrical MR transmission driven by SMA spring under thermal effect is shown in Figure

MR fluid shear transmission driven by SMA between two cylinders.

The displacement of bias type SMA actuating device based on SMA spring can be expressed as follows [

Consider

The theoretical and the experimental results of the relationship between output displacements and temperatures of SMA spring are shown in Figure

The displacements of SMA spring versus temperatures.

Figure

Circular flow of MR fluid between two cylinders.

In the cylindrical coordinate system, the momentum equation of the shear flow in

In order to analyze the behavior of MR fluids flow in the gap between two cylinders, the following assumptions are given: the fluid is incompressible. There is no flow in radial direction and axial direction, but only tangential flow. The flow velocity of MR fluid is a function of radius. The pressure in the thickness direction of MR fluid is a constant one. The strength of magnetic field in the working gap of the activation region is well distributed. In the cylindrical coordinate system (

In the mode of flow, assume that the MR fluid within the gap is regarded as a cylindrical fluid. The momentum equation of the shear flow at the narrow gap may be approximated by

Ignore the wall slip effect, and the boundary conditions of MR fluid flow can be expressed as

The behavior of MR fluids is similar to Newtonian fluid without applied magnetic field. When a magnetic field is applied, the characteristics of MR fluids can be described by Bingham model [

Integrating the momentum equation (

The flow velocity

Applying the boundary conditions in ((

Submit ((

As shown in Figure

The torque

Figure

The overall sketch of performance experimental system for cylindrical-type MR fluid transmission driven by shape memory alloy.

The performance experimental system for cylindrical-type MR fluid transmission driven by shape memory alloy.

For this example, we use a typical MR fluid. Figure

Yield stress versus magnetic flux density.

When temperature is 60°C and the speed of driving shaft is 60 r/min, the relationship between the transmission torque of MR fluid between two parallel cylinders and the field current in coil assembly was obtained according to the test system in Figure

Torque versus field current.

Torque versus speed.

The results show that the torque measured by experiment has the same trend with the calculated value basically. The deviation between experimental and theoretical values is brought by the error of yield stress, the structural error, the magnetic flux leakage, the simplification of theoretical analysis model, and so on.

Based on the heating and driving characteristics of SMA, the relationship between displacement and temperature of SMA spring was analyzed. The experimental results were well satisfied with the theoretical results. In the range of phase transition temperature, the output displacement of SMA spring increases with the rising of temperature.

The MR fluid can be driven into working chamber by SMA Spring. The volume of MR fluid in working chamber increases with the increasing of output displacement of SMA spring.

Based on rheological characteristics of MR fluid, the flow and transmission of MR fluid between two cylinders were analyzed, and the equations of flow velocity and transmit torque of MR fluid between two cylinders were obtained. The transmit torque of MR fluid between two cylinders increases with the increasing of applied magnetic field.

This work was supported by the National Natural Science Foundation of China (51175532 and 11272368) and by the Natural Science Foundation Project of CQ CSTC (key project CSTC, 2011BA4028).