Diese Präsentation wurde erfolgreich gemeldet.
Die SlideShare-Präsentation wird heruntergeladen. ×

ECTC Presentation

Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Nächste SlideShare
Lecture 6
Lecture 6
Wird geladen in …3
×

Hier ansehen

1 von 34 Anzeige

Weitere Verwandte Inhalte

Diashows für Sie (20)

Ähnlich wie ECTC Presentation (20)

Anzeige

ECTC Presentation

  1. 1. Early Career Technical Conference 2016 Heat Transfer Modelling and Bandwidth Determination of SMA Actuators in Robotics Applications Tyler Ross Lambert Auburn University Department of Mechanical Engineering Austin Gurley and David Beale 1
  2. 2. Introduction 2 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions 150 g mass lifted by SMA actuator (21 ksi of pressure)
  3. 3. Shape Memory Alloy (SMA) Background • Shape Memory Alloys (SMA) are specially alloyed materials that change crystalline structure when heated and cooled, or when stressed and relaxed, which results in the alloy contracting with large force. • Why use an SMA actuator? • SMA wire actuators can be driven via heating through the use of an electric current, eliminating noise during operation. • SMA wire actuators can act as their own built-in position sensor, drastically reducing costs in robotic designs. • Nickel Titanium alloy (Nitinol), a common SMA, is relatively cheap and robust. 3 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  4. 4. Objectives of Analysis  Objectives  Model SMA bandwidth in terms of wire size  Can an SMA actuator move fast enough to work in your robotic application?  Model SMA efficiency in terms of size  What are the power demands of using an SMA actuator in your robotic application?  Bandwidth and efficiency are the two main drawbacks with SMA actuators. 4 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  5. 5. Crystalline Phase Changes  Crystalline Phases  Martensite Phase  Characterized by colder temperatures and higher stresses  Required some deformation from preload to avoid “twinned Martensite”  Austenite Phase  Characterized by higher temperatures and lower stresses 5 [1] Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  6. 6. SMA Phase Transformation Diagram 6 [2] Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  7. 7. Super-Elastic and Shape Memory Effects 7 [2] Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  8. 8. Heat Transfer Analysis 8 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions  Heat Transfer Modelling  Why is it important?  Accurate heat transfer model can allow for powerful predictions to be made for several system properties.  Thermal time constant/eigenvalue → bandwidth  Input power → efficiency  Temperature Response → rise time  How it was done  Energy balance from First Law of Thermodynamics and use empirical models.
  9. 9. Heat Transfer Energy Balance m - mass of the wire cp - specific heat of the SMA ΔH - change in energy associated with a phase transformation (“latent heat of transformation”) ξ – phase fraction (percent martensite) T - uniform temperature of the wire t - time I - current through the wire R(ξ) - resistance in the wire as a function of its phase fraction h - convection coefficient between the wire surface and the surrounding fluid As - surface area of the wire in contact with the surrounding fluid T∞ - temperature of the ambient fluid surrounding the wire 𝑚𝑚 𝑐𝑐𝑝𝑝 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 + 𝛥𝛥𝛥𝛥 ̇𝜉𝜉 = 𝐼𝐼2 𝑅𝑅 𝜉𝜉 − ℎ𝐴𝐴𝑠𝑠 𝑇𝑇 − 𝑇𝑇∞ The behavior of an SMA actuator driven by an electrical input and cooled via convection is given by: 9 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  10. 10. Heat Transfer Analysis Assumptions Closed form solutions for this equation exist when the following assumptions are made:  The wire has a uniform temperature.  The wire is long enough so that boundary effects can be ignored at anchor points [wire must be greater than 148.8 mm for this assumption to be true (Furst 2012)].  The wire operates safely outside of the transformation bound (so the latent heat of transformation can be neglected).  The crystalline phase fraction is constant throughout the wire ( ̇𝜉𝜉 = 0). 10 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  11. 11. Heat Transfer Simplified Model 𝑚𝑚𝑐𝑐𝑝𝑝 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 = 𝐼𝐼2 𝑅𝑅 − ℎ𝐴𝐴𝑠𝑠 𝑇𝑇 − 𝑇𝑇∞ The thermal behavior of an SMA actuator given these assumptions is given by the simplified equation: The closed form solution is then given by: 𝑇𝑇 𝑡𝑡 = 𝑇𝑇∞ + 𝐼𝐼2 𝑅𝑅 ℎ𝐴𝐴𝑠𝑠 + 𝑇𝑇0 − 𝑇𝑇∞ − 𝐼𝐼2 𝑅𝑅 ℎ𝐴𝐴𝑠𝑠 𝑒𝑒 − ℎ𝐴𝐴𝑠𝑠 𝑚𝑚𝑐𝑐𝑝𝑝 11 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  12. 12. Heat Transfer Simplified Model The equation can be further simplified by noting: 𝐴𝐴𝑠𝑠 = 𝜋𝜋𝜋𝜋𝜋𝜋 and 𝑚𝑚 = 𝜌𝜌𝜌𝜌 𝑑𝑑 2 2 𝐿𝐿 The closed form solution now takes the form: And for the homogenous case where the wire is not being electrically heated: This model is only as valuable as the approximation for h. 𝑻𝑻 𝒕𝒕 = 𝑻𝑻∞ + 𝑰𝑰𝟐𝟐 𝑹𝑹 𝐡𝐡𝝅𝝅𝝅𝝅𝝅𝝅 + 𝑻𝑻𝟎𝟎 − 𝑻𝑻∞ − 𝑰𝑰𝟐𝟐 𝑹𝑹 𝐡𝐡𝝅𝝅𝝅𝝅𝝅𝝅 𝒆𝒆 − 𝟒𝟒𝟒𝟒 𝝆𝝆𝝆𝝆𝒄𝒄𝒑𝒑 d – wire diameter L – wire length 𝜌𝜌 – wire density 𝑻𝑻 𝒕𝒕 = 𝑻𝑻∞ + 𝑻𝑻𝟎𝟎 − 𝑻𝑻∞ 𝒆𝒆 − 𝟒𝟒𝟒𝟒 𝝆𝝆𝝆𝝆𝒄𝒄𝒑𝒑 12 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  13. 13. Heat Transfer Coefficient  The heat transfer coefficient, h, is defined as: ℎ = 𝑘𝑘𝑓𝑓𝑓𝑓 𝑓𝑓𝑓𝑓 𝑓𝑓 Nu𝐷𝐷 𝑑𝑑  The thermal conductivity of a fluid is usually tabulated for a given temperature, but the Nusselt number must be found using empirical formulas. 𝑘𝑘fluid – thermal conductivity of the ambient fluid Nu𝐷𝐷– surface averaged Nusselt number d – wire diameter 13 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  14. 14. Empirical Models for Nusselt Number  Empirical Models for Heat Transfer Coefficient  Forced Convection  Churchill-Bernstein Relationship  Valid for a cylinder in a crossflow where Re𝐷𝐷Pr ≥ 0.2  Nu𝐷𝐷 = 0.3 + 0.62Re𝐷𝐷 1/2 Pr1/3 1+ 0.4 Pr 2/3 1/4 1 + Re 𝐷𝐷 282000 5/8 4/5  Natural Convection  Horizontal Cylinder  Nu𝐷𝐷 = 0.6 + 0.387Ra1/6 1+ 0.559 Pr 9/16 8/27 2  Vertical Cylinder 𝑑𝑑 > 35𝐿𝐿 ( Ra Pr )1/4  Nu𝐷𝐷 = 0.825 + 0.387Ra1/6 1+ 0.492 Pr 9/16 8/27 2 𝐏𝐏𝐏𝐏 - Prandtl Number 𝐑𝐑𝐑𝐑 – Rayleigh Number 𝑹𝑹𝑹𝑹𝑫𝑫 - Reynolds Number 14 [3] Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  15. 15. Cooling Response Comparison 15 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Forced Convection Natural (Free) Convection Intuitively, forced convection results a much faster cooling rate.
  16. 16. Heat Transfer Coefficient The heat transfer coefficient can then be approximated for the wire by substituting in for the wire properties and assuming the wire is cooling via natural convection in still air. We reduce the model to the following form: ℎ 𝑇𝑇, 𝑇𝑇∞ , 𝑑𝑑 = 65.5𝑒𝑒− 𝑑𝑑 4(𝑇𝑇− 𝑇𝑇∞) 1 6 W m2K d – wire diameter in mm 16 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  17. 17. Heat Transfer Coefficient 17 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  18. 18. Cooling/Heating Bandwidth  The cooling/heating bandwidth of the system reflects how fast the system input (either the ambient temperature or electrical power) can be cycled before the ability of the wire to cool itself is impeded.  This quantity can be found from the time constant from the original differential equation: 𝑓𝑓−3 𝑑𝑑𝑑𝑑 = 1 2𝜋𝜋 𝜏𝜏 = λ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐 𝑐𝑐 = 4ℎ 2𝜋𝜋𝜋𝜋𝜋𝜋𝑐𝑐𝑝𝑝  This metric allows for an estimate of the transformation bandwidth by comparing how much the thermal response can be attenuated to the frequency at which the SMA actuator will not undergo a phase transformation. 18 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  19. 19. Cooling/Heating Bandwidth  For natural convection: λ𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ≈ 0.0086 𝑑𝑑2 19 λ = 0.0086d-2 λ = 0.0926d-1.562 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 ThermalTransformationBandwidth(Hz) Wire Diameter (mm) Thermal Transformation Bandwidths (Hz) 25°C, still air 35°C, still air 20°C, v = 2 m/s Ambient Air Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  20. 20. Transformation Bandwidth  The cooling bandwidth underestimates the transformation bandwidth  Neglects heat of transformation  Does not account for the additional thermal signal attenuation the system can handle 20 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions 𝑇𝑇𝑀𝑀𝑓𝑓 𝜏𝜏𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐 𝑐𝑐 𝑇𝑇𝐴𝐴𝑓𝑓 𝑡𝑡 𝑀𝑀𝑓𝑓 𝑡𝑡𝐴𝐴𝑓𝑓 32
  21. 21. Transformation Bandwidth  More accurate bandwidth determination can be obtained by analyzing the cooling response when the wire is hot and finding the time taken for the wire to reach the Martensitic transformation bound: λ𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1 2𝑡𝑡𝑀𝑀  This makes several assumptions  The wire undergoes constant external stress  Film temperature of surrounding air remains constant at all points in time  Heating time is the same as cooling time 21 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  22. 22. Transformation Bandwidth  The transformation bandwidth was then found for three common cases for several wire diameters.  For most wires, the empirical scheme derived for the horizontal wire suffices for modelling bandwidth: 𝜆𝜆𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 0.0099 𝑑𝑑2 , 𝑑𝑑 < 35𝐿𝐿 ( Ra Pr )1/4 22 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  23. 23. General Rules for SMA Bandwidth 23 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Increase in: Bandwidth Air Speed ↗ Air Temperature ↘ Wire Diameter ↘  Bandwidth increases as convective heat transfer increases.  Bandwidth decreases as heating/cooling times increase with larger diameter wires.
  24. 24. SMA Actuator Efficiency Equation  Nitinol wire characteristics  Transformation strain with no external stress (𝜀𝜀𝐿𝐿): 4%  Transformation Contraction Stress (Ω): 150 MPa  Latent Heat of Transformation (∆𝐻𝐻): 24.2 J/g The work done upon transformation of the actuator is then: 𝑊𝑊 = 𝐿𝐿𝜀𝜀𝐿𝐿Ω𝐴𝐴 The electrical power required to actuate the Nitinol can be approximated by the power lost to convection plus the latent transformation energy plus the energy required to raise the wire temperature. The wire efficiency can then be calculated as: 𝜂𝜂 = 𝜀𝜀𝐿𝐿Ω 𝑑𝑑 4ℎ(𝑇𝑇 − 𝑇𝑇∞)𝑡𝑡 + 𝜌𝜌𝑑𝑑(𝑐𝑐𝑝𝑝∆𝑇𝑇 + ∆𝐻𝐻) 24 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  25. 25. SMA Actuator Efficiency Simplified Model  Assume 𝑡𝑡 ≈ 𝑚𝑚 𝑐𝑐𝑝𝑝∆𝑇𝑇+ ∆𝐻𝐻 𝑉𝑉𝑉𝑉 = 𝜌𝜌𝜌𝜌𝑑𝑑2 𝐿𝐿 𝑐𝑐𝑝𝑝∆𝑇𝑇+ ∆𝐻𝐻 4𝑉𝑉𝑉𝑉 , then the efficiency and transformation time can be found from only known quantities: 25 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  26. 26. General Rules for SMA Efficiency  Efficiency typically ranges from 1% - 3% for NiTi alloys. 26 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Increase in: Efficiency Air Speed ↗ Wire Diameter ↗ Input Power ↗ Wire Length ↘ Air Temperature ↘
  27. 27. Experimental Results  Experimental Setup  Testing Apparatus: Single leg of 18 DOF Hexapod Robot  Wire Diameter: 0.125 mm  Wire Length: 60 mm  Heating method: PWM output from microcontroller with sinusoidal sweep of duty cycle  Sensors: Self-Sensing Probe 27 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Powered Terminal Blocks Moving Hinge Self-Sensing Probe Antagonist Springs
  28. 28. Experimental Results 𝝀𝝀 𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 = 𝟎𝟎. 𝟔𝟔𝟔𝟔 𝐇𝐇𝐇𝐇 28 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Predictions 𝝀𝝀𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 = 𝟎𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎 (𝟎𝟎. 𝟏𝟏𝟏𝟏𝟏𝟏)𝟐𝟐 = 𝟎𝟎. 𝟓𝟓𝟓𝟓𝟓𝟓𝟓𝟓 𝐇𝐇𝐇𝐇 𝝀𝝀𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 ≈ 𝟎𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎 (𝟎𝟎. 𝟏𝟏𝟏𝟏𝟏𝟏)𝟐𝟐 = 𝟎𝟎. 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐇𝐇𝐇𝐇 Percent Error: 3%
  29. 29. Conclusions  Bandwidth can be computed to within three percent error for SMA actuators.  This information can be used to size up SMA actuators depending on the needs of the project and can help when designing a controller to control these systems.  The efficiency of an SMA actuator can be modelled and approximated  This information helps gauge the power needs to maintain a system of SMA actuators. 29 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  30. 30. Demonstrations using SMA Actuators 30 18 DOF Hexapod Robot Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  31. 31. Demonstrations using SMA Actuators 31 Ball-Beam Balancer Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  32. 32. Demonstrations using SMA Actuators 32 Actuated Gimbal for Solar Panel Alignment Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions Human Hand Replica Small Bug
  33. 33. References 33 [3] The McGraw-Hill Companies, Inc. Heat and Mass Transfer: Fundamentals & Applications Fourth Edition in SI Units Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011 [1] Alchetron. Alchetron Technologies Pvt. Ltd. “Nickel Titanium”. 2016. http://alchetron.com/Nickel- titanium-156127-W [2] Gurley, Austin. Auburn University. “Robust Self Sensing in NiTi Actuators Using a Dual Measurement Technique”. SMASIS Conference on Smart Materials, Adaptive Structures and Intelligent Systems. 2016. Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions
  34. 34. Questions and Discussion 34 Introduction Background Heat Transfer Bandwidth Efficiency Experiments Conclusions

×