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Shape Memory Alloys Team: High Torque Rotary Actuator/Motor Team Members: Uri Desai Tim Guenthner J.C. Reeves Brad Taylor Tyler Thurston Gary Nickel NASA JSC Mentor Dr. Jim Boyd Faculty Mentor Reid Zevenbergen Graduate Mentor Outline Project Goal: Fall 2008 Fundamentals of Shape Memory Alloys Design Concepts Heat Transfer Analysis Comparison and Recommendations Future Tasks: Spring 2009 Questions Project Goal: Fall 2008 Research and understand SMAs and their applications Research current conventions: Electric motors Develop concepts for a Rotary Actuator/Motor driven by SMAs Evaluate concepts Conduct initial analysis of chosen concepts Select a baseline design Motivation: Design a motor that will have a higher torque per unit volume and less weight than current motors. What are Shape Memory Alloys? 1 2 3 Stress 5 Deformed Martensite 4 2 • Converting thermal energy to mechanical work. 3 Self- 1 Accommodated Martensite 4 Austenite 5 Mf Ms As Af Temperature Applications of SMAs Aerospace: Medical Airfoils, Boeing Chevrons, STARSYS Stints, Instrumentation Other Eyeglasses frames, Locking mechanisms, Underwires, etc. Electric Motors Most applications for space utilize electric motors. Electric motors are very dense and therefore there is a weight penalty Electric motors operate better at higher speeds and lower torque: For low torque applications, a gear box must be added to the motor, which increases the weight. Pittman motors have been used, in this case, as an example of electric motors with higher than average torque densities. Highest torque density from Pittman motor studied: 6.83 oz in Design Concept #1: Wire Rotary Actuator Bias Spring Rack and Pinion Drive Shaft SMA Wire Modeling Wire Behavior: Angular Displacement 1 x R1 x trans L 1 trans L R1 2 R3 1 2 ; 3 R2 R2 R2 3 2 1 R3 R3 3 trans LR2 R1 R3 Where: Δθ = angle of rotation (rad) εtrans = transition strain L = length of SMA wire Δx = change in length R = respective radii Modeling Wire Behavior: Moments and Torque F F1 FSMA Fspring FSMA k x T1 F1 R1 ( FSMA k x) R1 T1 T2 F1 R1 F2 R2 F3 F2 F T3 F3 R3 trans k L R1 SMA F R2 trans k L R1 R3 SMA R2 nFSMA k trans L R1 R3 T3 R2 Where: F = respective forces R = respective radii k = spring constant FSMA = SMA recovery force Δx = change in length η = efficiency of gear train n = number of SMA wires T = torque generated Modeling Wire Behavior: SMA Analysis E E A i trans elastic A T T0 M E E M A i FSMA ASMA FSMA E EA d SMA trans elastic A T T0 M E E 2 M A 2 Where: εtrans = actuation strain εelastic = elastic strain σi = recovery stress αA: coefficient of thermal expansion for austenite T -T0: change in temperature EM: Young’s Modulus for martensite EA: Young’s Modulus for austenite dSMA = diameter of SMA wire n = number of SMA wires • Typical actuation stress values: 21,755-29,000 psi •Substituting above equation into previous moment equation d 2 EM E A trans elastic A trans SMA n T T0 k L R1 R3 E E 2 M A T3 R2 Results Pittman Motor: Model GM14X02 Torque: 107 oz in Torque Density: 6.83 oz/in2 SMA Wire Application 1 wire with diameter of 5mm or 10 wires with diameter of .02in (equivalent of 5mm) Torque Density: Max: 1250 oz/in2 @ 5.5° rotation Min: 33.5 oz/in2 @ 115.5 ° rotation SMA Wires Company Transformation Temperature Sizing Strain Dynalloy Flexinol:: Af: 70° - 100°C Nitinol:: Af: 80° - 90°C Flexinol:: 0.001”-0.02” Nitinol:: 0.004”-0.01” ~4-5% SMA, Inc. Pseudoelastic Af: -25°-125°C Wire:: 0.012”0.25” ~4-5% Small Parts Varying Af: 70° - 90°C Wire: 0.006”0.1” ~3-5% Design Concept #2: Torque Tube Rotary Actuator Torque Tubes Casing Drive Shaft Bevel Gears Mechanism Operation Torque Tubes Bevel gear attached to drive shaft Drive Shaft Bevel gear attached to torque tube Torque Tube Attachment Method Casing Torque Tubes Torque Tube Analysis Tc J JG T L L max R Where: T = applied torque J = polar moment of inertia c = radius of beam G = shear modulus L = length of beam φ = angle of twist Analyzing a shape memory alloy torque tube: elastic trans thermal RM R M L RM ( Relastic Rtrans ) M M R G Relastic M M L RM TRM J Where: γ = shear strain γthermal= 0 (for isotropic material) RM = median radius of tube GJ RM trans T RM RM L Torque Analysis Angle of Twist (deg) 0 0 10 20 30 40 γtrans Max Torque (oz-in) Torque (φ = 8°) (oz-in) 2% 10558.6 3069.4 3% 15837.9 8348.7 4% 21117.2 13627.9 5% 26396.5 18907.3 6% 31675.8 24186.6 -5000 Torque (oz-in) -10000 -15000 -20000 -25000 -30000 -35000 This data based upon: G = 152,289.625 psi RM= 0.2 in L = 2 in J = 0.0053 in4 Heat Transfer: Overview Drives SMA actuation Cp varies between 0.32 and 0.6 during actuation Material Properties (Nitinol) Density Resistivity Cp Activation Relaxation Austenite 6.45 g/cc 76 μΩcm 0.322 J/g°C 78 °C - Martensite - 82 μΩcm 0.322 J/g°C - 42 °C Trans. - - 0.6 J/g°C 68 °C 52 °C Wire Properties Radius 1 Radius 2 Length Voltage Power Conv. Coeff. Tempa 0 cm 0.05 cm 10 cm 0.2 V 0.44 W 0.01 W/cc K 20 °C Torque Tube Properties Radius 1 Radius 2 Length Exterior Heat Conv. Coeff. Tempa 0.3 cm 0.5 cm 5 cm 110 W – 70 W 0.1 W/cc K 20 °C Heat Transfer: Wire Resistive Heating 4 seconds to heat Forced Air Cooling 4 seconds to cool Cycle Time: 8 Seconds Heat Transfer: Torque Tube Contact Conductive Heating 8 seconds to heat Forced Air Cooling 10.5 seconds to cool Cycle Time: 18.5 Seconds Compare/Contrast and Future Recommendation SMA Wire Design Simple and feasible Flexibility in altering torque versus output rotation: Gear Ratios Less expensive to manufacture Light weight SMA Torque Tube Design Modular design Capable of extremely high torque output Greater complexity Difficult to implement multidirectional rotation More expensive to manufacture Recommendation: The SMA Team recommends pursuing the SMA wire application due to its simplicity, feasibility and low cost. This design meets our objective of designing a rotary motor that has high torque per unit volume while maintaining a small weight. Future Tasks: Spring 2009 Detailed analysis of SMA wire application Detailed design of SMA wire application Build working prototype Test and compare results to theoretical Questions?