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Research Papers

Dynamic Thermomechanical Modeling of a Wet Shape Memory Alloy Actuator

[+] Author and Article Information
Joel D. Ertel

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112

Stephen A. Mascaro

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112smascaro@mech.utah.edu

J. Dyn. Sys., Meas., Control 132(5), 051006 (Aug 19, 2010) (9 pages) doi:10.1115/1.4002067 History: Received September 11, 2007; Revised May 20, 2010; Published August 19, 2010; Online August 19, 2010

This paper presents combined thermal and mechanical models of a wet shape memory alloy (SMA) wire actuator. The actuator consists of a SMA wire suspended concentrically in a compliant tube. Actuation occurs as hot and cold water that are alternately pumped through the tube to contract and extend the wire, respectively. The thermomechanical model presented in this paper accounts for the nonuniform temperature change of the SMA wire due to alternating the temperature of the flow along the wire. The thermal portion of the model consists of analysis of the heat transfer between the fluid and the SMA wire. Heat loss to the environment and the temperature change of the fluid through the actuator are taken into account. Based on this analysis, the temperature of the wire at segments along its length can be determined as a function of time. The mechanical portion of the model approximates the strain-martensite fraction and martensite fraction-temperature relationships. By combining the thermal and mechanical models, the displacement of the wire can be determined as a function of time. The combined thermomechanical model will be useful for predicting the performance of wet SMA actuators in a variety of applications.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 12

The above plots show a comparison of the model derived in this paper with experimental data. The experimental data were taken while alternating hot and cold water every second at a flow rate of approximately 3 ml/s; (a) shows the results for 0.254 mm diameter wire, (b) for 0.305 mm, (c) for 0.381 mm, and (d) for 0.508 mm.

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Figure 11

The above plots show a comparison of the model derived in this paper with experimental data. The experimental data were taken while alternating hot and cold water every second at a flow rate of approximately 2 ml/s; (a) shows the results for 0.254 mm diameter wire, (b) for 0.305 mm, (c) for 0.381 mm, and (d) for 0.508 mm.

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Figure 10

The above diagram shows the experimental setup that was used to measure the displacement-time curve of a wet SMA actuator. A weighted platform was used to provide a constant load. Thermocouples were placed at each end of the actuator to measure the inlet and outlet temperatures. In some cases, a flow meter was used to measure the flow rate. In other cases, it was calculated based on thermocouple readings.

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Figure 9

The stress-strain curve of a Flexinol® wire was determined by incrementally adding weight to a hanging wire and measuring the displacement. The wire was of diameter 0.305 mm and length 310 mm.

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Figure 8

The data shown above are the temperature responses of the thermocouple at various positions in the tube. Based on a best-fit first-order model the time constant of the temperature response increased along the length of the tube.

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Figure 7

A type E thermocouple was constructed to test the heat transfer model. The thermocouple wire diameter was the same as that of the SMA wire making the heat transfer conditions as similar as possible to a wet SMA actuator.

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Figure 6

The modeled response of a wet SMA actuator is shown above. The model predicts about 8 mm is travel. It should be noted that the reverse transformation (cooling) occurs more quickly than the forward transformation (heating).

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Figure 5

Each branch of the bond graph represents a segment of the actuator. Although this bond graph shows three segments, an actuator that was divided into n segments would have n branches in its bond graph. The branches stem from a zero-junction, implying the actuator segments share a common force and that their velocities add. The effort source and inertance at the bottom represent the weight and inertia of the mass hanging from the actuator. The effort sources at the top represent the wire temperature.

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Figure 4

The stress-strain relationship of nitinol is nonlinear because of martensite detwinning. Twinned martensite exhibits a modulus of elasticity Em, while detwinned martensite exhibits a modulus Ed. During detwinning the modulus Et is much lower that either of the other two moduli. Detwinning begins at a strain value of εmy and ends at εmy.

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Figure 3

A numerical method is used to determine the temperature profiles of the actuator wire, fluid, and tube. The temperature response of each segment of the actuator is calculated based on the temperatures at each position. The fluid is then advanced by one position and the temperature response calculated again at each point.

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Figure 2

Diagram of a differential control volume of the actuator. The arrows indicate the heat transfer that occurs in the radial direction as well as the heat transfer due to fluid flow into and out of the control volume.

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Figure 1

A wet SMA actuator consists of a shape memory alloy wire in a compliant tube. The wire is anchored at both ends of the tube causing the entire system to contract with the SMA wire. The fluid used in this system is water.

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