DOI: 10.5061/dryad.2bvq83bx3
title: Hybrid dynamic model for shape memory alloy linear and unimorph actuators

description: Shape memory alloy morphing actuators are a type of soft actuator with
 many attractive properties. These actuators exhibit large deformation,
 small form factor, self-sense ability, and physical reservoir computing
 potential, while also being inexpensive. These morphing actuators are
 composed of active shape memory alloy wires and a passive base layer that
 is used to magnify the overall deflection. Although morphing actuators
 have great potential, the modeling of shape memory alloy actuators is
 difficult due to both shape memory alloy characteristics and the
 nonlinearity of the passive layer. Here, a hybrid dynamical model is
 proposed that couples the phase kinetics & thermal modeling for
 the shape memory alloy with a dynamic Cosserat nonlinear beam model. This
 hybrid model is benchmarked against linear and morphing experimental
 actuators. The model resulted in a root mean squared error of 1.48 mm and
 1.63 mm for the morphing actuator configuration for two different
 actuators. This model can expand the capability and design of novel
 morphing actuators for a designed deformation profile for use in soft
 robotics.
description: An Edgertronic SC2+ camera (Sanstreak Corp., San Jose, CA) is
 used to record the movement of the actuator for both the linear and
 bending actuation at a frame rate of 100 Hz. Reflective markers are
 adhered to the actuators in order to track their motion. For the linear
 SMA actuator, the reflective makers are placed on the ends of the wire in
 order to measure the length of the SMA wire during testing. For the
 bending actuators, reflective markers are adhered on the side of the
 actuator at the locations of the offset holders. These markers are used to
 track the configuration of the actuator at locations of approximately 10
 mm. An N6705C DC power analyzer (Keysight, Santa Rosa, CA) was used to
 supply the input power to heat the SMA wire. This power supply also has a
 built in waveform generator and data logger. The waveform generator was
 used to test the results for a variety of input current waves for the
 linear actuator. The data logger recorded the current output of the
 device, which is then used as an input for the dynamic model. Visual
 markers were used to sync the power data with the visual data from the
 camera. The camera begins to record and then the input waveform is
 started. When the waveform begins recording, an LED light is triggered
 "ON''. The LED is in view of the camera and used to sync
 the start of the input power data with the frame from the high speed
 camera at which the input waveform began. MATLAB's Image Processing
 Toolbox was used to process the visual data from the camera and calculate
 the x and y positions of the reflective markers attached to the actuators
 at every frame.
description: # Hybrid Dynamic Model for Shape Memory Alloy Linear and Unimorph
 Actuators
 [https://doi.org/10.5061/dryad.2bvq83bx3](https://doi.org/10.5061/dryad.2bvq83bx3) This repository consists of both data files and MATLAB software files. The experimental setup for this data and software is a linear shape memory alloy (SMA, Flexinol HT) wire actuated under a constant bias mass and the same SMA wire coupled to a steel beam resulting in a bending structure. The experimental data is the electrical input power and visual marker data captured by a high speed camera for various tests run (to be explained in the following sections). The software files then simulate the SMA response using the electrical power data as an input into the model. The resulting model results are then compared to the experimental visual marker data to assess the accuracy of the model. For the linear SMA model, the root mean squared error for the various input waveforms was an average of 0.003 strain. For the unimorph SMA, the root mean squared error of the configuration was an average of 1.38 mm. ## Description of the data and file structure The data set includes data for both a linear and morphing SMA actuator. **Linear SMA Data** The linear SMA data set includes: 1. lengthWireMat\_step1.mat 2. lengthWireMat\_sine1.mat 3. lengthWireMat\_trap2.mat 4. powerMat\_step1.mat 5. powerMat\_sine1.mat 6. powerMat\_trap2.mat The files beginning with "lengthWireMat\_" contain the length of the SMA wires captured by the high speed camera (at 100 Hz). The files beginning with "powerMat\_" contain the time vector for the electrical power in the first column, the voltage reading from the power supply in the second column, and the current reading from the power supply in the third column. This data is recorded by the power supply itself. Three electrical waveforms were tested: a sinusoidal input (sine1), a step input (step1), and a trapezoidal input (trap2). **Unimorph SMA Data** The unimorph SMA data set includes: 1. expX\_metalCCS\_small\_test2.mat 2. expY\_metalCCS\_small\_test2.mat 3. expX\_metalCCS\_big\_test2.mat 4. expY\_metalCCS\_big\_test2.mat 5. powerMat\_metalCCS\_small\_test2.mat 6. powerMat\_metalCCS\_big\_test2.mat The files beginning with "expX\_" contain the X coordinates of the SMA unimorph actuator captured by the high speed camera (at 100 Hz). The files beginning with "expY\_" contain the Y coordinates of the SMA unimorph actuator captured by the high speed camera (at 100 Hz). There are a total of 11 markers on each actuator located at 10 mm intervals along the length. The files beginning with "powerMat\_" contain the time vector for the electrical power in the first column, the voltage reading from the power supply in the second column, and the current reading from the power supply in the third column. This data is recorded by the power supply itself. There are two different actuators tested in this work (labeled "big\_test2" and "small\_test2"). This refers to the offset distance between the SMA wire and the beam (big = 1.00 mm and small = 0.675 mm). The rest of the attributes of the actuators are the same. ## Code/Software The code was run on MATLAB 2022b. The Hybrid Equations Toolbox was used to implement the hybrid dynamical equations (Ricardo Sanfelice (2023). Hybrid Equations Toolbox (https://github.com/pnanez/HyEQ\_Toolbox/releases/tag/3.0.0.76), GitHub. Retrieved November 5, 2023.) **Linear SMA Software** The software files used specifically for the linear data include: 1. mainSMALinear.m 2. smaMaterialModelLinear.m 3. delFunLin.m The main .m file is used to run the MATLAB model and the calls the other functions. The "smaMaterialModelLinear" contains the hybrid model for the linear SMA model to model the continuous and discrete states. The "delFunLin.m" is a function that calculates the derivatives of the states. **Unimorph SMA Software** The software files used specifically for the linear data include: 1. mainSMABending.m 2. smaMaterialModel.m 3. delFun.m 4. twoDBeamSMA.m The main .m file is used to run the MATLAB model and the calls the other functions. The "smaMaterialModel" contains the hybrid model for the unimorph SMA model to model the continuous and discrete states. The "delFun.m" is a function that calculates the derivatives of the states. **Mutual Functions** The following functions are used by both the linear and unimorph model: 1. smaVariableStructure.mat (imports various material properties and simulation parameters) 2. seriesFun.m (function for series addition of material properties) 3. strainFun.m (function for strain calculation) **Implementation** In order to run the model, run the "main" files. These files are set up to pull the experimental data from a folder (change if pulled from the same directory)