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Research Papers

Forward and Inverse Analyses of an SMA Actuated Compliant Link

[+] Author and Article Information
A. Banerjee, B. Bhattacharya, A. K. Mallik

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

J. Mechanisms Robotics 3(2), 021003 (Mar 10, 2011) (10 pages) doi:10.1115/1.4003528 History: Received April 26, 2009; Revised March 07, 2010; Published March 10, 2011; Online March 10, 2011

This paper presents forward and inverse analyses of the response of a compliant link actuated by a discretely attached shape memory alloy (SMA) wire subjected to a time-varying input voltage. The framework for a constrained recovery of the shape memory alloy wire is developed from a robust numerical model. The model for the large deflection of a beam element due to follower forces resulting from discrete actuation using a SMA wire is coupled with the proposed framework. Thus, the response of the link is correlated with the input voltage. The algorithm for implementing this framework has been demonstrated along with some numerical examples. Experiments have also been conducted on a SMA actuated cantilever beam, and the results are compared with those of the simulations. A qualitative agreement between the two is observed. It is concluded that the theoretical results can provide a reference signal for active control of the link to achieve higher accuracy.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A deformed cantilever beam due to discrete actuation using SMA wire

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Figure 2

End forces and moments applied on the beam by the attached SMA wire

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Figure 3

A typical phase diagram of SMA

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Figure 4

A general thermomechanical path in the forward transformation strip

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Figure 5

A general thermomechanical path in the reverse transformation strip

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Figure 6

Simplified phase transformation zones

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Figure 7

Experimental setup

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Figure 8

Block diagram of the experimental procedure

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Figure 9

(a) (A) Voltage applied to the SMA wire, (B) temperature of the SMA wire, and (C) resulting link response. (b) Variation in the (A) volume fraction of total martensite and (B) volume fraction of stress induced martensite. (c) Variation in stress within the SMA wire with temperature.

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Figure 10

(A) Step voltage of (a) 1.3 V, (b), 1.4 V (c), 1.5 V and (d) 1.7 V applied to the SMA wire attached to a compliant link, (B) theoretical, and (C) experimental link responses.

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Figure 11

(A) Ramp input voltage having equal rise, dwell, and fall times of 10 s and maximum voltage of (a) 1.3 V, (b) 1.4 V, (c) 1.5 V, and (d) 1.7 V as applied to the SMA wire, (B) theoretical, and (C) experimental link responses.

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Figure 12

(a) (A) Desired continuous response and (B) required voltage to be applied to the SMA wire to get the desired response as obtained from inverse analysis. (b) (A) Desired continuous response, (B) theoretical response due to the voltage profile presented by curve B of Fig. 1, (C) experimental response in first cycle due to the same voltage, (D) experimental response due to the same voltage in tenth cycle, (E) experimental response due to the same voltage in 20th cycle, and (F) experimental response due to the same voltage in 30th cycle.

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Figure 13

(a) (A) Desired step response and (B) required voltage to be applied to the SMA wire to get the desired response as obtained from inverse analysis. (b) (A) Desired step response, (B) theoretical response, experimental responses in (C) first cycle, (D) 10th cycle, (E) 20th cycle, and (F) 30th cycle, due to the application of the voltage profile presented by curve B in (a).

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