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Research Papers

Conglomerate Stabilization Curve Design Method for Shape Memory Alloy Wire Actuators With Cyclic Shakedown

[+] Author and Article Information
WonHee Kim

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown, Ann Arbor, MI 48109-2125wonhekim@umich.edu

Brian M. Barnes

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown, Ann Arbor, MI 48109-2125bmbarnes@umich.edu

Jonathan E. Luntz

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown, Ann Arbor, MI 48109-2125jluntz@umich.edu

Diann E. Brei

Department of Mechanical Engineering,  University of Michigan, 2250 G. G. Brown, Ann Arbor, MI 48109-2125dibrei@umich.edu

J. Mech. Des 133(11), 111010 (Nov 17, 2011) (10 pages) doi:10.1115/1.4004460 History: Received December 20, 2010; Revised June 20, 2011; Accepted June 22, 2011; Published November 17, 2011; Online November 17, 2011

The high energy density actuation potential of shape memory alloy (SMA) wire is tempered by conservative design guidelines set to mitigate complex factors such as functional fatigue (shakedown). In addition to stroke loss, shakedown causes practical problems of interface position drift between the system and the SMA wire under higher stress levels if the wire does not undergo a pre-installation shakedown procedure. Constraining actuation strain eliminates interface position drift and has been reported to reduce shakedown as well as increase fatigue life. One approach to limit actuation strain is using a mechanical strain limiter, which sets a fixed Martensite strain position—useful for the development of in-device shakedown procedures, which eliminates time-consuming pre-installation shakedown procedures. This paper presents a novel conglomerate stabilization curve design method for SMA wire actuators, which accounts for shakedown with and without the use of mechanical strain limiters to enable higher stress designs to maximize actuator performance. Shakedown experimental data including the effect of strain limiters along with stroke and work density contours form the basis for this new design method. For each independent mechanical strain limiter, the maximum of the individual postshakedown Austenite curves at a range of applied stress are combined into a conglomerate stabilization design curve. These curves over a set of mechanical strain limiters including the zero set provide steady-state performance prediction for SMA actuation, effectively decoupling the shakedown material performance from design variables that affect the shakedown. The use and benefits of the conglomerate stabilization curve design method are demonstrated with a common constant force actuator design example, which was validated in hardware on a heavy duty latch device. This new design method, which accounts for shakedown, supports design of SMA actuators at higher stresses with more economical use of material/power and enables the utilization of strain limiters for cost-saving in-device shakedown procedures.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Shakedown of shape memory alloy. During thermomechanical cycles, SMA wire changes its crystal structural phase between Austenite and Martensite. Both Martensite and Austenite strains generally increase, while the thermomechanical cycles repeat. However, because of the different rates of increase of Martensite and Austenite, the actuation stroke decreases. (70 °C Flexinol® 10 mil wire, 500 MPa)

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Figure 2

Negative of the lock actuator. At the cool Martensite phase, the actuator locks the system, and unlocks the system at the hot Austenite phase (a). Because of strain increase during shakedown, even with the same amount of stroke (Δi ≈ Δs), this actuator drifts thereby remaining locked (b).

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Figure 3

Traditional stress–strain curve SMA actuator design method and the effect of shakedown. The solid red and blue curves are stress–strain curves at the Austenite and Martensite phases before shakedown, and the green line is the system curve, which the SMA wire actuates against. The wire actuates between intersection points Ⓐ and Ⓜ at first cycle, however, after shakedown, the actuation strain increases to points ⓐ and ⓜ. A strain limiter such as a hard stop can limit the actuation strain protecting the compliant Martensite SMA wire; with a strain limiter, SMA wire actuates between the points Ⓐ and Ⓢ. The resolution of circled letters is poor.

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Figure 4

Schematic of shakedown experimental setup. Shakedown test apparatus is capable of controlling the heating and cooling of SMA wire, applying desired force, limiting the maximum strain, and measuring the tensile load and displacement.

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Figure 5

Shakedown processes with and without strain limiter. Without strain limiters, both Austenite and Martensite strains increase over cycles, which can cause a position drift interface problem in a device if the SMA wire does not undergo a separate shakedown process prior to installation. With a strain limiter, the Martensite strain is constrained, providing a stable interface position enabling a more cost effective in-device, or even in-operation shakedown process.

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Figure 6

Strain limiter position effects on strain shakedown. Shakedown processes with different strain limiters under 350 MPa stress show that shorter strain limiters reduce strain shakedown.

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Figure 7

Strain limiter position effects on stabilized stroke. Even though shorter strain limiters allow smaller strain shakedown, the resulting stabilized stroke is larger with longer strain limiters. (350 MPa)

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Figure 8

Effect of stress on strain loss, stabilized stroke, and work density (4% strain limiter). Austenite strain loss was increased with higher applied stress resulting smaller stabilized stroke. While stroke loss and stabilized stroke show monotonic relations with applied stress, work density, which is the multiplication of stabilized stroke and applied stress, shows a nonmonotonic relation with applied stroke allowing design tradeoffs.

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Figure 9

Reverse shakedown (80 Mpa). Shakedown processes with low applied stress (80 MPa and 126 MPa) show reverse shakedown. The Austenite strain decreases under zero strain and the Martensite strain decreases significantly, while both Austenite and Martensite strains increase during normal shakedown. The dotted line shows the 4% strain limiter test result.

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Figure 10

Optimal stroke contour. The maximum stroke can be obtained around 220 MPa stress, which is close to the manufacturer’s recommendation stress (180 MPa–190 MPa). Stroke is normalized as stroke in centimeter unit from 1 m SMA wire.

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Figure 11

Optimal work density contour. The maximum work density occurs at 400 MPa, which is higher than the recommended stress. This maximum work density is about two times larger than the guideline design work density.

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Figure 12

Conglomerate stabilization design curve (4% strain limiter curve). To create 4% strain limiter stabilization curve, Austenite stress–strain curves were created after test case A4–G4. The interpolation curve, which is thick red line, provides stabilized stroke prediction after shakedown.

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Figure 13

A set of conglomerate stabilization design curves. For different strain limiter positions, a family of conglomerate stabilization curves was created. These curves are used with corresponding strain limiter lines.

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Figure 14

SMA wire actuator design example with traditional design method. With the traditional stress–strain curve design method, a single-wire actuator would actuate between points Ⓐ and Ⓑ at 360 MPa stress with 5.95% stroke, and a double-wire actuator would actuate between points Ⓒ and Ⓓ with 5.33% stroke at 180 MPa stress in each. Before shakedown, single-wire design can provide longer stroke at first cycle, but double-wire design with manufacturer’s guideline stress (180–190 MPa) can provide longer stabilized stroke after shakedown. Moreover, higher stress design also increases the strain shakedown, which causes alignment problems between system and SMA wire.

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Figure 15

Conglomerate stabilization curve design method. A new conglomerate stabilization curve design method enables the use of SMA wire under higher stress leading economic use of material (shorter length of wire and corresponding savings in cost and actuation power).

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Figure 16

A latch release SMA actuator. For the physical validation of design example, a dead-weight latch release SMA actuator was built based on Sec. 3 design example. This structure designed to lock the aluminum plate in the cool Martensite phase, and unlock the plate in the hot Austenite phase.

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Figure 17

A latch release actuation test result. While single-wire design without strain limiter failed to unlock after 3cycles, both double wire with conservative guideline and single wire with a new design method using strain limiter unlocked the plate after 4000 cycles.

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