Differential hysteresis modeling of a shape memory alloy wire actuator

In this paper, we develop a complete mathematical model of a shape memory alloy (SMA) wire actuated by an electric current and a bias spring. The operation of the SMA actuator involves different physical phenomena, such as heat transfer, phase transformation with temperature hysteresis, stress-strain variations and electrical resistance variation accompanying the phase transformation. We model each of these phenomena in a modular fashion. A key feature of the proposed model is that one or more of its modules can be extended to fit other SMA applications. At the heart of the proposed model is a differential hysteresis model capable of representing minor hysteresis loops. We generate the temperature profile for the hysteresis model using lumped parameter analysis. We extend the variable sublayer model to represent actuator strain and electrical resistance. This model can be used to develop a position control system for the actuator. Simulation results from the model are found to be in good agreement with experimental data.

[1]  G. Carman,et al.  Thermo-mechanical characterization of shape memory alloy torque tube actuators , 2000 .

[2]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations , 1999 .

[3]  J. D. Harrison,et al.  Use of TiNi in Mechanical and Electrical Connectors , 1975 .

[4]  Jayanth N. Kudva,et al.  Overview of the DARPA/AFRL/NASA Smart Wing Phase II program , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[5]  Yong Liu,et al.  Detwinning process and its anisotropy in shape memory alloys , 2001, SPIE Micro + Nano Materials, Devices, and Applications.

[6]  A. A. Likhachev,et al.  Differential Equation of Hysteresis : Application to Partial Martensitic Transformation in Shape-Memory Alloys , 1995 .

[7]  Thomas J. Pence,et al.  A constitutive model for hysteretic phase transition behavior , 1994 .

[8]  J. L. Mcnichols,et al.  Thermodynamics of Nitinol , 1987 .

[9]  Paolo Dario,et al.  Shape memory alloy micromotors for direct-drive actuation of dexterous artificial hands , 1989 .

[10]  Minoru Hashimoto,et al.  Application of shape memory alloy to robotic actuators , 1985 .

[11]  Chi-Hsu Wang,et al.  Design of fuzzy walking pattern (FWP) for a shape memory alloy (SMA) biped robot , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[12]  Gangbing Song,et al.  Position control of shape memory alloy actuators with internal electrical resistance feedback using neural networks , 2004 .

[13]  C. M. Wayman,et al.  Shape-Memory Materials , 2018 .

[14]  Vladimir Brailovski,et al.  Temporal characteristics of shape memory linear actuators and their application to circuit breakers , 1996 .

[15]  L. C. Brinson,et al.  Phase diagram based description of the hysteresis behavior of shape memory alloys , 1998 .

[16]  Optimization Toolbox , 2001, Optimizations and Programming.

[17]  X. Wu,et al.  The variation of electrical resistance of near stoichiometric NiTi during thermo-mechanic procedures , 1999 .

[18]  David W. L. Wang,et al.  Modeling and L2-stability of a shape memory alloy position control system , 1998, IEEE Trans. Control. Syst. Technol..

[19]  Véronique Michaud,et al.  Can shape memory alloy composites be smart , 2004 .

[20]  S. Hirose,et al.  Mathematical model and experimental verification of shape memory alloy for designing micro actuator , 1991, [1991] Proceedings. IEEE Micro Electro Mechanical Systems.

[21]  D. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part IV: modeling of minor hysteresis loops , 1999 .

[22]  Gangbing Song,et al.  Position control of SMA actuators with internal electrical resistance feedback , 2003, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[23]  Koji Ikuta,et al.  Shape memory alloy servo actuator system with electric resistance feedback and application for active endoscope , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[24]  William S. N. Trimmer,et al.  Microactuators for aligning optical fibers , 1989 .

[25]  K. J. Gabriel,et al.  A micro rotary actuator using shape memory alloys , 1988 .