Shape Memory Alloys Team:High Torque Rotary Actuator/Motor

Team Members:Uri Desai

Tim GuenthnerJ.C. ReevesBrad Taylor

Tyler Thurston

Gary Nickel NASA JSC MentorDr. 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?

5

1

2

3

4

Austenite

Deformed Martensite

Self-Accommodated

Martensite

1 2 3

45

Mf Ms AfAsTemperature

Stress

• Converting thermal energy to mechanical work.

Applications of SMAs Aerospace:

Airfoils, Boeing Chevrons, STARSYS

Medical 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

SMA WireDrive Shaft

Bias Spring Rack and Pinion

Where: Δθ = angle of rotation (rad)εtrans = transition strainL = length of SMA wireΔx = change in lengthR = respective radii

Modeling Wire Behavior: Angular Displacement

11

11

321 2

3 2

;

trans

trans

x

R

x L

L

R

R

R

2 23 2 1

3 3

23

1 3

trans

R R

R R

LR

R R

Modeling Wire Behavior: Moments and Torque

1

1 1 1 1

1 2

1 1 2 2

1

3 22

1 3

3 3 32

1 3

32

( )

SMA spring SMA

SMA

transSMA

transSMA

transSMA

F F F F F k x

T F R F k x R

T T

F R F R

F k L RF F

R

F k L R RT F R

R

nF k L R RT

R

Where:F = respective forcesR = respective radiik = spring constantFSMA = SMA recovery forceΔx = change in lengthη = efficiency of gear trainn = number of SMA wiresT = torque generated

Modeling Wire Behavior: SMA Analysis

0

2

02

trans elastic A M Ai

M A

SMAi

SMA

trans elastic ASMA M ASMA

M A

E ET T

E E

F

A

d E EF T T

E E

•Substituting above equation into previous moment equation

2

0 1 3

32

2trans elastic A transSMA M A

M A

d E En T T k L R R

E ET

R

Where: εtrans = actuation strainεelastic = elastic strainσi = recovery stress αA: coefficient of thermal expansion for austeniteT -T0: change in temperatureEM: Young’s Modulus for martensiteEA: Young’s Modulus for austenitedSMA = diameter of SMA wiren = number of SMA wires

• Typical actuation stress values: 21,755-29,000 psi

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° rotationMin: 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. PseudoelasticAf: -25°-125°C

Wire:: 0.012”-0.25”

~4-5%

Small Parts VaryingAf: 70° - 90°C

Wire: 0.006”-0.1”

~3-5%

Design Concept #2: Torque Tube Rotary Actuator

Drive Shaft

Bevel Gears

Torque Tubes Casing

Mechanism Operation

Drive Shaft

Torque Tubes

Bevel gear attached to drive shaft

Bevel gear attached to torque tube

Torque Tube Attachment Method

Casing

Torque Tubes

Torque Tube Analysis

max

Tc

JJG

TL

L

R

Where:T = applied torque J = polar moment of inertiac = radius of beamG = shear modulusL = length of beamφ = angle of twist

Analyzing a shape memory alloy torque tube:

RM

( )

M

M M

M M

elastic trans thermal

RM

elastic transR R

M

elastic MR R

L

R

L

R

TRG

J

Where:γ = shear strainγthermal= 0 (for isotropic material)RM = median radius of tube

M

transMR

M

RGJT

R L

Torque Analysis

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

This data based upon:G = 152,289.625 psiRM= 0.2 inL = 2 inJ = 0.0053 in4

ηtra

ns =2%

Heat Transfer: Overview

Drives SMA actuation Cp varies between 0.32 and 0.6 during actuation Material Properties (Nitinol)

Wire Properties

Torque Tube Properties

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

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

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 SMA Torque Tube Design Simple and feasible Flexibility in altering torque

versus output rotation: Gear Ratios

Less expensive to manufacture Light weight

Modular design Capable of extremely high torque

output Greater complexity Difficult to implement multi-

directional 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?