Numerical modeling of shape memory alloy linear actuator
Tóm tắt
The demand for shape memory alloy (SMA) actuators in high-technology applications is increasing; however, there exist technical challenges to the commercial application of SMA actuator technologies, especially associated with actuation duration. Excessive activation duration results in actuator damage due to overheating while excessive deactivation duration is not practical for high-frequency applications. Analytical and finite difference equation models were developed in this work to predict the activation and deactivation durations and associated SMA thermomechanical behavior under variable environmental and design conditions. Relevant factors, including latent heat effect, induced stress and material property variability are accommodated. An existing constitutive model was integrated into the proposed models to generate custom SMA stress–strain curves. Strong agreement was achieved between the proposed numerical models and experimental results; confirming their applicability for predicting the behavior of SMA actuators with variable thermomechanical conditions.
Tài liệu tham khảo
Mohd Jani J, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mater Des 56:1078–1113. doi:10.1016/j.matdes.2013.11.084
Otsuka K, Wayman C (1998) Shape memory materials. Cambridge University Press, Cambridge
Lagoudas DC (2010) Shape memory alloys: modeling and engineering applications, 1st edn. Springer, New York
Hartl DJ, Lagoudas DC (2007) Aerospace applications of shape memory alloys. Proc Inst Mech Eng G 221:535–552
Tadesse Y, Thayer N, Priya S (2010) Tailoring the response time of shape memory alloy wires through active cooling and pre-stress. J Intell Mater Syst Struct 21:19–40
Bhattacharyya A, Lagoudas DC, Wang Y, Kinra VK (1995) On the role of thermoelectric heat transfer in the design of SMA actuators: theoretical modeling and experiment. Smart Mater Struct 4:252
Huang S, Leary M, Ataalla T, Probst K, Subic A (2012) Optimisation of Ni–Ti shape memory alloy response time by transient heat transfer analysis. Mater Des 35:655–663. doi:10.1016/j.matdes.2011.09.043
Leary M, Schiavone F, Subic A (2010) Lagging for control of shape memory alloy actuator response time. Mater Des 31:2124–2128. doi:10.1016/j.matdes.2009.10.010
Hunter IW, Hollerbach JM, Ballantyne J (1991) A comparative analysis of actuator technologies for robotics. Robot Rev 2:299–342
Liang C, Rogers C (1997) One-dimensional thermomechanical constitutive relations for shape memory materials. J Intell Mater Syst Struct 8:285–302
Ma J, Karaman I, Noebe RD (2010) High temperature shape memory alloys. Int Mater Rev 55:257–315
Mohd Jani J, Huang S, Leary M, Subic A (2015) Analysis of convective heat transfer coefficient on shape memory alloy actuator under various ambient temperatures with finite difference method. Appl Mech Mater 736:127–133. doi:10.4028/www.scientific.net/AMM.736.127
Leary M, Huang S, Ataalla T, Baxter A, Subic A (2013) Design of shape memory alloy actuators for direct power by an automotive battery. Mater Des 43:460–466. doi:10.1016/j.matdes.2012.07.002
Boyd JG, Lagoudas DC (1996) A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. Int J Plast 12:805–842. doi:10.1016/S0749-6419(96)00030-7
Achenbach M (1989) A model for an alloy with shape memory. Int J Plast 5:371–395. doi:10.1016/0749-6419(89)90023-5
Çengel YA, Ghajar AJ (2011) Heat and mass transfer: fundamentals & applications. McGraw-Hill, New York
Majumdar P (2005) Computational methods for heat and mass transfer, 1st edn. Taylor and Francis, New York
Huang S, Jani JM, Leary M, Subic A (2013) The critical and crossover radii on transient heating. Appl Therm Eng 60:325–334. doi:10.1016/j.applthermaleng.2013.06.052
Bonacina C, Comini G, Fasano A, Primicerio M (1973) Numerical solution of phase-change problems. Int J Heat Mass Transf 16:1825–1832. doi:10.1016/0017-9310(73)90202-0
Neugebauer R, Bucht A, Pagel K, Jung J (2010) Numerical simulation of the activation behavior of thermal shape memory alloys. 76450J–76450J-12
Brinson LC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct 4:229–242. doi:10.1177/1045389x9300400213
Ahn KK, Kha NB (2008) Modeling and control of shape memory alloy actuators using Preisach model, genetic algorithm and fuzzy logic. Mechatronics 18:141–152. doi:10.1016/j.mechatronics.2007.10.008
Kohl M (2010) Shape memory microactuators (microtechnology and MEMS), 1st edn. Springer, Berlin
Otsuka K, Wayman C (1999) Shape memory materials. Cambridge University Press, Cambridge
Walker J (2008) Fundamental of physics, 8th edn. Wiley, New York
Novák V, Šittner P, Dayananda GN, Braz-Fernandes FM, Mahesh KK (2008) Electric resistance variation of NiTi shape memory alloy wires in thermomechanical tests: experiments and simulation. Mater Sci Eng A 481–482:127–133. doi:10.1016/j.msea.2007.02.162
Lagoudas DC, Bo Z (1999) Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II: material characterization and experimental results for a stable transformation cycle. Int J Eng Sci 37:1141–1173. doi:10.1016/S0020-7225(98)00114-1
Bekker A, Brinson LC (1998) Phase diagram based description of the hysteresis behavior of shape memory alloys. Acta Mater 46:3649–3665. doi:10.1016/S1359-6454(97)00490-4
Brailovski V, Trochu F, Daigneault G (1996) Temporal characteristics of shape memory linear actuators and their application to circuit breakers. Mater Des 17:151–158. doi:10.1016/S0261-3069(96)00049-0
Tanaka K (1986) A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior. Res Mech 18:251–263
Auricchio F, Lubliner J (1997) A uniaxial model for shape-memory alloys. Int J Solids Struct 34:3601–3618. doi:10.1016/S0020-7683(96)00232-6
De la Flor S, Urbina C, Ferrando F (2006) Constitutive model of shape memory alloys: theoretical formulation and experimental validation. Mater Sci Eng A 427:112–122. doi:10.1016/j.msea.2006.04.008
Bergman TL, Lavine AS, Incropera FP, DeWitt DP (2011) Fundamentals of heat and mass transfer, 7th edn. Wiley
Carslaw H, Jaeger JJC (1959) Conduction of heat in solids. Oxford University Press, London
Eisakhani A, Ma W, Gao J, Culham JR, Gorbet R (2011) Natural convection heat transfer modelling of shape memory alloy wire. In: Smart materials, structures and NDT in aerospace. CANSMART CINDE IZFP, Montreal
Churchill SW, Chu HHS (1975) Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int J Heat Mass Transf 18:1049–1053. doi:10.1016/0017-9310(75)90222-7
Churchill SW, Bernstein M (1977) A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. J Heat Transf 99:300–306. doi:10.1115/1.3450685
Van Der Hegge Zijnen BG (1956) Modified correlation formulae for the heat transfers by natural and by forced convection from horizontal cylinders. Appl Sci Res 6:129–140. doi:10.1007/BF03185032
Ozisik MN (1987) Basic heat transfer. R.E. Krieger Publishing Company, Malabar
Elahinia MH, Ahmadian M (2005) An enhanced SMA phenomenological model: II. The experimental study. Smart Mater Struct 14:1309
Hoffman JD, Frankel S (2001) Numerical methods for engineers and scientists. CRC Press, Boca Raton
Iserles A (1996) A first course in the numerical analysis of differential equations. Cambridge University Press, Cambridge
Ozisik N (1994) Finite difference methods in heat transfer, 1st edn. CRC Press, Boca Raton
Smith GD (1985) Numerical solution of partial differential equations: finite difference methods. Oxford University Press, Oxford
Potapov PL, Da Silva EP (2000) Time response of shape memory alloy actuators. J Intell Mater Syst Struct 11:125–134. doi:10.1106/xh1h-fh3q-1yex-4h3f
Velázquez R, Pissaloux E (2012) Modelling and temperature control of shape memory alloys with fast electrical heating. Int J Mech Control 13:1–8
Incropera F, DeWitt D (1985) Introduction to heat transfer. Wiley, New York
Shahin AR, Meckl PH, Jones JD, Thrasher MA (1994) Enhanced cooling of shape memory alloy wires using semiconductor ‘heat pump’ modules. J Intell Mater Syst Struct 5:95–104
Crank J, Nicolson P (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Math Proc Camb Philos Soc 43:50–67. doi:10.1017/S0305004100023197
Wang B, Han J, Sun Y (2012) A finite element/finite difference scheme for the non-classical heat conduction and associated thermal stresses. Finite Elem Anal Des 50:201–206
Chun CK, Park SO (2000) A fixed-grid finite difference method for phase change problems. Numer Heat Transf B 38:59–73. doi:10.1080/10407790050131561
Jaluria Y, Atluri S (1994) Computational heat transfer. Comput Mech 14:385–386. doi:10.1007/BF00377593
Leary M, Mac J, Mazur M, Schiavone F, Subic A (2010) Enhanced shape memory alloy actuators. In: Sustainable automotive technologies 2010. Springer, Berlin, pp 183–190
Charney JG, Fjörtoft R, Von Neumann J (1950) Numerical integration of the barotropic vorticity equation. Tellus A 2:237–254
Voller VR, Cross M, Markatos NC (1987) An enthalpy method for convection/diffusion phase change. Int J Numer Methods Eng 24:271–284. doi:10.1002/nme.1620240119
Dynalloy, Inc. (2007) In: Dynalloy, Inc. (ed) Technical characteristics of Flexinol actuator wires. Dynalloy, Inc., Costa Mesa