Design and Testing of Linear Shape Memory Alloy Actuator

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1 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 Design and Testing of Linear Shape Memory Alloy Actuator Quentin A. Donnellan Advisor: Dr. Dimitris C. Lagoudas Starsys Research and Applied Physics Laboratories (APL) at John Hopkins have developed five miniature SMA-based mechanisms to address the need on satellite platforms for non-explosive actuation (NEA), as reported by NASA Langley. One of the five mechanisms proposed by APL is a linear actuator which incorporates the use of a bias spring and a SMA wire deformed in tension to produce a stroke. The purpose of this summer's research is to design and validate a similar actuator, which incorporates a SMA spring deformed in compression to produce a more significant stroke than APL's SMA wire actuator. I I. BACKGROUND N response to the need for miniature mechanisms for small satellites, Starsys Research and Applied Physics Laboratory (APL) at John Hopkins University have developed the following miniature devices : Micro Sep-Nut Mini Sep-Nut Rotary latch Burn Wire Release Mini Linear Actuator Mini Redundant Release In 00, Texas A&M University s Active Materials Lab conducted analysis and testing on the rotary latch mechanism which incorporates the use of a torsional Shape Memory Alloy (SMA) spring. This report presents research conducted on the design and testing of a mini linear actuator in an effort to improve that technology. II. INTRODUCTION In an effort to support APL in the advancement of miniaturized mechanism development, the Aerospace Engineering Department s Active Materials Lab at Texas A&M University has conducted research on a SMA based mini linear actuator. The focus of this research was to design a linear actuator as an improvement to the one proposed by APL. Specifically, the actuator designed by APL incorporates the use of a SMA wire and a steel bias spring. The SMA wire, originally in martensite phase, regains strain when heated above the austenite transition temperature and compresses the bias spring. The bias spring returns the mechanism to its original state when the SMA wire is cooled through the martensite transition temperature. This action of heating the SMA wire and allowing it to cool is a valid means of producing a linear motion, or stroke. However, since a typical SMA wire can only recover approximately % strain, significant, or even noticeable, stroke lengths can not be achieved. The research conducted this summer suggests that by replacing the SMA wire in the APL concept with a SMA spring, a more significant stroke length can be achieved. A. Preliminary Analysis III. DESIGN In its report, APL outlined certain goals that would be desired of any linear actuator. These goals became the initial design factors. Stroke length: 0. in. Force: - lb.

in.) to exert the desired forces. This led to the early conclusion that actuators employing the use of SMA springs are unable to exert forces comparable to similar actuators which use SMA wires.

2 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 Holding Force: -0 lb. Actuation time: 0-00 ms Total Actuations: cycles However, initial calculations using standard spring theory led to the observation that it is not possible for springs of the desired size (Ø<. in.) to exert the desired forces. This led to the early conclusion that actuators employing the use of SMA springs are unable to exert forces comparable to similar actuators which use SMA wires. Thus, the design factors were modified for an actuator designed for maximum stroke length at minimum size without high force requirements. Stroke Length: 0. in. Actuation Time: 0-00 ms Total Actuations: cycles Force: TBD Minimum size, power, and mass B. Concept The following image shows the concept that was designed to meet the above criteria: Because the above system is unique in its design, a model had to be developed to accurately predict the dimensions of the SMA spring (produced from SMA wire in the Active Materials Lab). The following terms are useful when developing this model: cool SMA (low modulus) SMA compression spring (outside) Washer L s L s L a Section view δ Cooled actuator (resting state) D Steel bias spring (inside) D Below are calculations for the two heated spring SMA linear actuator concept assuming linear elastic response (high modulus) from the SMA spring (this assumption will be tested later). These two springs are concentric and thus share the same deflection axis (hence a linear system). The following equations set up this system as a conservation of deflection () in D in terms of shear modulus (G), wire diameter (d), spring diameter (D), force (F), and number of coils (n a ). F = kδ (general spring theory) 4 Gd k = D n 8 a 8D na 4 δ = F (.) Gd This equation is hard to work with because the number of coils term (n a ) is abstract before the spring is actually built. The following relationship can be used to simplify Equation.: L s = n d (.) a 8D Ls δ = F (.) Gd In the above equation, L s is the solid length of the spring. Now that an equation for deflection has been established the steel extension spring can be analyzed. The only modification that has to be made to Equation. is an account for the initial tension, F i, in the steel spring (this value will be experimentally determined). 8D Ls ( F Fi ) Gd δ = (.4) Above, the deflection (stroke length) resulting from a force F applied to the steel bias spring is solved for. This force (minus the initial tension) is exactly the compression force exerted by the SMA spring when heated. The free length of the SMA spring L f (the length the spring will be trained to remember) will be greater than that of the actuator L a so that when attached to the steel spring, an equilibrium length equal to L a is achieved (i.e. in the absence of the steel spring the SMA spring is greater in length). Furthermore, when the SMA is cooled, it is compressed to its solid length L s by the steel bias spring. Thus the actuator length is equal to the SMA spring solid length plus the stroke length:

3 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 La = Ls + δ (.) It is also known that the free length of the SMA spring minus the deflection resulting from the force exerted by the bias spring F is equal to the actuator length L a (.8). F minus the force exerted by the bias spring should be equal to zero if this system is at equilibrium (bias spring cancels out SMA spring). 0 = ( ) (.6) F F F i 8D Ls F G d δ = (.7) L = L δ (.8) a f Using these concepts and combining with (.), an equation for the free length of the SMA spring can be created (.9). Lf = Ls + δ + δ (.9) 8D Ls f s δ ( i ) L = L + + F F (.0) G d 8D Lf L = s + ( F Fi ) δ + G d d = steel spring wire diameter d = SMA spring wire diameter D = steel spring diameter D = SMA spring diameter G = steel spring shear modulus G = SMA spring shear modulus (.) However, F is abstract. This is the force required to extend the steel spring by the stroke length accounting for the initial tension, so replacing F with its components (.4) makes this equation easier to solve. G d F = + F (.) δ 8D Ls G d 8D Lf = L + + i s δ δ 8D Ls Gd (.) This equation is simple to evaluate recognizing that the only variables are the springs mean diameters (D & D ) and the wire diameters (d & d ). The stroke length is a design specification as are the solid lengths of each spring. The shear modulus G varies from material to material, but it is known for any material chosen. In terms of the mean diameter the outer diameter is as follows: Do = D + d (.4) Do = D + d (.) The steel spring s outer diameter must be less than the inner diameter of the SMA spring in order for it to fit inside. Here c is introduced as the distance between the inside of the SMA spring and the outside of the steel spring. A relationship between the outer diameter of the SMA spring and the diameter of the steel spring can now be established. D = D c (.6) o i ( ) D + d = D d c (.7) o Combining the spring index C with Equations.4 &.6 yields equations (.9 &.0) with 4 unknowns (C, C, d, d ) C d d D o D d D o = (.8) D o + = C Do d c = C + (.9) (.0) C has a finite range (4-) with an ideal literature value of 9, and thus numerical iterations can solve for the appropriate combination of C & C which satisfy Equation.. In this manner can exact measurements of both the steel spring and SMA spring be determined. C. Construction With the knowledge gained from the above calculations, a custom actuator can be constructed to meet the design requirements exactly. However, availability of certain materials limits the ability to produce an actuator that is perfectly accurate. So, materials were chosen which most closely match the calculated values. The following are the final dimensions for the two springs: (Steel Spring) F =.94 N i L =.08 mm s d = 0.4 mm D = 4.8 mm (SMA Spring) L = 0.97 mm f L = 0. mm s d = 0.8 mm D = 6.0 mm c SMA spring bias spring

Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 4 The steel spring dimensions are based on a pre-existing spring found in the lab.

This heat treatment will ensure that the SMA will memorize the shape of a compression spring at length L f. After the heat treatment the SMA is quenched in a water bath.

4 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 4 The steel spring dimensions are based on a pre-existing spring found in the lab. The SMA spring was constructed out of existing SMA wire (also found in the lab). This was accomplished by winding the wire with the use of a mandrel and then heating in an oven at 00ºC for 0 minutes. This heat treatment will ensure that the SMA will memorize the shape of a compression spring at length L f. After the heat treatment the SMA is quenched in a water bath. Once the SMA spring is produced the actuator is ready for assembly. The steel spring is placed inside the SMA spring and then the end loops of the steel spring are forced through washers to secure the SMA spring. IV. EXPERIMENTAL SET-UP To determine the stroke length of the actuator, the SMA spring is attached to a power source. This source is regulated by a LabView program which regulates the power in the following manner: 6V for 0.0 seconds ( on time ) 0V for 0.0 seconds ( off time ) The above procedure was developed through trial and error to produce even heating from ºC to 9ºC. This successfully heats the SMA wire through the austenite transition temperature. SMA spring Steel Spring Actuator cool heated D. Actuator Characterization washer Now that the actual actuator is built, its behavior can be characterized. Starting with the steel extension spring, a simple hanging weight test can produce a force vs. displacement function. Knowing the dimensions of the SMA spring a prediction of its force vs. displacement function can be obtained (because the SMA spring is a compression spring, a weight test is difficult to conduct). These two functions are plotted on the same axis: The measured stroke length was 7. mm. Plotted on the same force vs. deflection graph reveals good correspondence between the predicted value of the stroke length and the actual value. Force (N)... y = 0.77x actual stroke length 7. mm Force (N).. y = 0.77x Deflection (mm) Steel Spring Response Predicted SMA Linear Fit, Steel Spring Response Deflection (mm) Steel Spring Response Predicted SMA Linear Fit, Steel Spring Response However, all of these results are based on the assumption that the SMA spring responds in a linear elastic manner. To make the calculations easy, the assumption was made that the SMA (when heated) is entirely in the austenite form. In order for the above results to be valid, this assumption must be proved. To do this, the loading path of the SMA must be determined to ensure that the spring is, indeed, entirely composed of austenite phase. Theoretically, where these two functions intersect represents the stroke length of the actuator (the equilibrium position where the negative displacement of the compression spring equals the positive displacement of the extension spring).

5 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 Stress (MPa) A B Temperature (C) Loading Path As Af The start of the loading path (A) is simple enough to determine (on a stress vs. temperature graph): zero stress, room temperature (ºC). Because the steel spring exerts no force until it is stretched, no change in stress is observed until the SMA starts regaining strain (thus stretching the steel spring). This can be observed experimentally as the moment the actuator begins moving and is plotted as the point where the zero stress line intersects the austenite start temperature slope (B). From there, the stress is constantly increasing due to the fact that the steel spring is being stretch more and more as the SMA is heated and expands. The stress will increase all the way until the SMA stops moving. Taking the stroke length at this point the force exerted by the steel spring can be determined (plug the stroke length into F=kx for the steel spring). Since the system is at equilibrium, this force is also equal to the force exerted by the SMA spring. The shear stress can be determined from this: 8WDF τ = π d 4C 0.6 W = + 4C 4 C W is the Wahl Correction factor (accounting for the curvature of the spring. Using a simple Mohr s circle (zero minimum stress) the shear stress can be translated to normal stress and can be plotted on the above graph. This point (C) corresponds to the point where the max stress line (determined with Mohr s circle as mentioned) intersects the austenite finish temperature slope. Next, the SMA is heated all the way to 9ºC (D). By connecting the points A,B,C,D a loading path can be plotted on the same graph as the SMA s phase diagram (determined experimentally). Point D on this graph represents the fully heated actuator. This point is comfortably within the 00% austenite phase C D (any point to the right of the Af line). Thus, the assumption that the SMA spring responds in a purely linear elastic (austenitic) manner is valid. V. FINDINGS AND RESULTS The following recaps the major results of the experimental testing: Stroke length Goal:. in. Actual:.8 in. Activation time Goal: 0-00 ms. Actual: > s The stroke length of the actuator fell very close to the targeted value and actually exceeded it. The activation time did not quite meet the goal set. The following are several, experimentally validated, means of increasing the activation time: Increase voltage Reduce off time, increase on time Achieving better electrical connection between leads and SMA wire Because the actuator is so small, it is difficult to establish a secure connection between the power source and the SMA wire. In addition, the space between the SMA spring and the steel spring is so small that often the two springs will touch. When this happens, the current that should pass only though the SMA may actually pass though the steel spring. This will result in uneven heating of the SMA wire. VI. CONCLUSIONS very small gap between the SMA spring and the steel spring This research has proved that a SMA spring based linear actuator is effective at producing large stroke lengths at the cost of high force exertion. Also, several improvements on this design need to be made before it should be considered reliable technology. The electrical connection between the SMA wire and the power source should be examined in detail. The steel spring should also be electrically isolated from the SMA spring so that no current accidentally passes through the steel spring, which would result in uneven heating of the SMA. This

Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 6 isolation can be achieved by some sort of barrier placed in the gap between the two springs.

6 Final Report, National Science Foundation Research Experience for Undergraduates, Summer 00 6 isolation can be achieved by some sort of barrier placed in the gap between the two springs. non-conducting barrier Another significant issue with the design is the time between actuations, currently at ~0 seconds. In order to decrease this time, some sort of cooling element should be introduced to effectively conduct heat away from the SMA. This would allow for the SMA to be cooled more rapidly, bringing the actuator back to its original state faster and thus increasing actuation rate. One way to achieve this might be to encase the actuator in some sort of tube and run a cooling liquid through the tube when necessary. ACKNOWLEDGMENTS Dr. Dimitris C. Lagoudas, PI Director, Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles (TiiMS) Magdalini Lagoudas Assistant Director, Spacecraft Technology Center Darren Hartl Graduate Student, Texas A&M University Aerospace Engineering REFERENCES [] Brett Huettl, Cliff Willey, Design and Development of Miniature Mechanisms for Small Spacecraft, 4 th AIAA/USU Conference on Small Satellites [] Darren Hartl, Olivier Godard, Analysis of Rotary SMA Actuators.00

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