Magnetic shape memory alloys (MSMAs) are a class of active materials that de- form under magnetic and mechanical loading conditions. This work is concerned with the modeling of MSMAs constitutive responses. The hysteretic magneto-mechanical responses of such materials are governed by two major mechanisms which are variant reorientation and field induced phase transformation (FIPT). The most widely used material for variant reorientation is Ni2 MnGa which can produce up to 6% magnetic field induced strain (MFIS) under 5 MPa actuation stress. The major drawback of this material is a low blocking stress, which is overcome in the NiMnCoIn material system through FIPT. This magnetic alloy can exhibit 5% MFIS under 125 MPa actuation stress. The focus of this work is to capture the key magneto-thermo-mechanical responses of such mechanisms through phenomenological modeling. In this work a detailed thermodynamic framework for the electromagnetic interaction within a continuum solid is presented. A Gibbs free energy function is postulated after identifying the external and internal state variables. Material symmetry restrictions are imposed on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals whereas continuous symmetry is considered for polycrystalline materials. The constitutive equations are derived in a thermodynamically consistent way. A specific form of Gibbs free energy for FIPT is proposed and the explicit form of the constitutive equations is derived from the generalized formulation. The model is calibrated from experimental data and different predictions of magneto-thermo-mechanical loading conditions are presented. The generalized constitutive equations are then reduced to capture variant reorientation. A coupled magneto-mechanical boundary value problem (BVP) is solved that accounts for variant reorientation to investigate the influence of the demagnetization effect on the magnetic field and the effect of Maxwell stress on the Cauchy stress. The BVP, which mimics a real experiment, provides a methodology to correlate the difference between the externally measured magnetic data and internal magnetic field of the specimen due to the demagnetization effect. The numerical results show that localization zones appear inside the material between a certain ranges of applied magnetic field. Stability analysis is performed for variant reorientation to analyze these numerical observations. Detailed numerical and analytical analysis is presented to investigate these localization zones. Magnetostatic stability analysis reveals that the MSMA material system becomes unstable when localizations appear due to non-linear magnetization response. Coupled magneto-mechanical stability analysis shows that magnetically induced localization creates stress-localizations in the unstable zones. A parametric study is performed to show the constraints on material parameters for stable and unstable material responses.

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The use of high-precision automated equipment is steadily increasing due in part to the progressively smaller sizes of electronic circuits. Currently, piezoelectric transducers (piezos) dominate as the actuation device for high precision machines, but shape memory alloys (SMA) may be a viable alternative to reduce monetary costs. This work explores the implementation of a low-cost linear macro-micro positioning system. The system consists of a modified printer carriage to provide long range, macro scale linear motion (approximately 200 mm range and 200 µm precision) and a micro scale system (approximately 4 mm range and 5 µm target precision) that uses an SMA actuator. A detailed description of the design and implementation of the system is given in this research. A model of the macro-stage is then generated by first identifying and inverting a simple friction model to linearize the system, thereby allowing for modified least squares (MLS) identification of a linear model. Various controllers are attempted for the macro-stage and compared with an experimentally tuned nonlinear PD controller that is implemented in the final design. A model of the micro-stage is derived through analysis of the SMA actuator. The model for the actuator is separated into two portions, an electro-thermal model, and a hysteresis model. The hysteresis model is derived using the Preisach model, and the electro-thermal model through MLS identification. To control the micro-stage, a PI controller with antiwindup is developed experimentally. The two stages are then executed together in closed loop and the resulting coupling between the two stages is briefly examined. Experimental data used for the modelling and design is presented, along with results of the final macro-micro linear positioning system.

Shape memory alloys (SMAs) are metallic materials, which have two main stable crystalline phases: austenite, a high temperature phase and martensite, a low temperature phase. Austenite and martensite each have unique physical and mechanical properties, and transformation between these phases enables two effects known as the shape memory effect (SME) and superelasticity. When a material that displays the SME is plastically deformed at low temperature, a heat input will cause the SMA to return to its original shape before the deformation. At higher temperatures, the material displays an effect called superelasticity, where strains of up to 10% are recoverable. These characteristics of SMA allow for significant amounts of strain recovery, and enable the design of SMA actuators. The temperature in an SMA actuator is generally controlled by resistive heating, also know as joule heating, and the strain recovery capabilities are used to do work on a load, thereby creating an electro-mechanical actuator. SMA actuators have attractive properties such as high energy density, smooth and silent actuation, reduced part counts compared to traditional alternatives, and scalability down to the micromechanical level. The phase transformation in SMA actuators, however, is highly non-linear. Therefore, the use of SMA as actuators, for example in positioning systems, benefits from the development of good models to predict and control the materials. The goals of this work are to develop a model suitable for real-time implementation, and that reproduces the observed behaviour of SMA actuators. The model is then inverted and used to develop a model-based controller, used in conjunction with traditional PID control to improve the precision and robustness of SMA actuators. The modelling portion of this work consists of the development of a phenomenological SMA model. The forward model is split into three blocks: a heating block, a phase kinetics block and a mechanical block. Since joule heating is commonly used in SMA actuators to bring about an increase in temperature, the heating block presents equations to convert a current input into the temperature of the wire. The phase kinetics block equations convert the calculated temperature and applied stress to the fraction of martensite present in the SMA. Finally, the mechanical model calculates the strain in the material from the martensite fraction and the applied stress. Once the model equations are presented, experimental verification tests are shown to compare physical SMA behaviour with that predicted by the model. Each of the blocks of the forward model are then inverted in order to be used as a feedforward linearizing controller. The control section of this thesis deals with the response of two common types of SMA actuators: a constant force SMA actuator and a spring-biased SMA actuator. The response of the system to step and sinusoidal signals with period of 5 seconds is investigated using two types of controllers: a traditional PI controller and the inverse-model controller in feedforward with a PI controller in feedback. Additionally, the robustness of the system is investigated through the response of the system to transient and sinusoidal stress disturbances. The disturbance rejection is investigated on a constant force actuator both with and without the presence of a force sensor.

The use of high-precision automated equipment is steadily increasing due in part to the progressively smaller sizes of electronic circuits. Currently, piezoelectric transducers (piezos) dominate as the actuation device for high precision machines, but shape memory alloys (SMA) may be a viable alternative to reduce monetary costs. This work explores the implementation of a low-cost linear macro-micro positioning system. The system consists of a modified printer carriage to provide long range, macro scale linear motion (approximately 200 mm range and 200 µm precision) and a micro scale system (approximately 4 mm range and 5 µm target precision) that uses an SMA actuator. A detailed description of the design and implementation of the system is given in this research. A model of the macro-stage is then generated by first identifying and inverting a simple friction model to linearize the system, thereby allowing for modified least squares (MLS) identification of a linear model. Various controllers are attempted for the macro-stage and compared with an experimentally tuned nonlinear PD controller that is implemented in the final design. A model of the micro-stage is derived through analysis of the SMA actuator. The model for the actuator is separated into two portions, an electro-thermal model, and a hysteresis model. The hysteresis model is derived using the Preisach model, and the electro-thermal model through MLS identification. To control the micro-stage, a PI controller with antiwindup is developed experimentally. The two stages are then executed together in closed loop and the resulting coupling between the two stages is briefly examined. Experimental data used for the modelling and design is presented, along with results of the final macro-micro linear positioning system.

Shape memory alloys (SMAs) are metallic materials, which have two main stable crystalline phases: austenite, a high temperature phase and martensite, a low temperature phase. Austenite and martensite each have unique physical and mechanical properties, and transformation between these phases enables two effects known as the shape memory effect (SME) and superelasticity. When a material that displays the SME is plastically deformed at low temperature, a heat input will cause the SMA to return to its original shape before the deformation. At higher temperatures, the material displays an effect called superelasticity, where strains of up to 10% are recoverable. These characteristics of SMA allow for significant amounts of strain recovery, and enable the design of SMA actuators. The temperature in an SMA actuator is generally controlled by resistive heating, also know as joule heating, and the strain recovery capabilities are used to do work on a load, thereby creating an electro-mechanical actuator. SMA actuators have attractive properties such as high energy density, smooth and silent actuation, reduced part counts compared to traditional alternatives, and scalability down to the micromechanical level. The phase transformation in SMA actuators, however, is highly non-linear. Therefore, the use of SMA as actuators, for example in positioning systems, benefits from the development of good models to predict and control the materials. The goals of this work are to develop a model suitable for real-time implementation, and that reproduces the observed behaviour of SMA actuators. The model is then inverted and used to develop a model-based controller, used in conjunction with traditional PID control to improve the precision and robustness of SMA actuators. The modelling portion of this work consists of the development of a phenomenological SMA model. The forward model is split into three blocks: a heating block, a phase kinetics block and a mechanical block. Since joule heating is commonly used in SMA actuators to bring about an increase in temperature, the heating block presents equations to convert a current input into the temperature of the wire. The phase kinetics block equations convert the calculated temperature and applied stress to the fraction of martensite present in the SMA. Finally, the mechanical model calculates the strain in the material from the martensite fraction and the applied stress. Once the model equations are presented, experimental verification tests are shown to compare physical SMA behaviour with that predicted by the model. Each of the blocks of the forward model are then inverted in order to be used as a feedforward linearizing controller. The control section of this thesis deals with the response of two common types of SMA actuators: a constant force SMA actuator and a spring-biased SMA actuator. The response of the system to step and sinusoidal signals with period of 5 seconds is investigated using two types of controllers: a traditional PI controller and the inverse-model controller in feedforward with a PI controller in feedback. Additionally, the robustness of the system is investigated through the response of the system to transient and sinusoidal stress disturbances. The disturbance rejection is investigated on a constant force actuator both with and without the presence of a force sensor.

SMA belongs to a class of so-called “smart materials” which possess properties that can be controlled by application of various types of stimuli – stress, temperature, electric field or magnetic field. In particular, SMA is a smart material which undergoes a temperature- or stress-dependent phase transformation giving it the property of remembering its original shape. Once deformed (up to a certain recoverable strain), SMA returns to its original shape upon heating. In this thesis, a study of SMA models and techniques to improve the performance of SMA actuators was carried out. In general, an SMA model is required for 3 main purposes: simulation, analysis and for model-based hysteresis compensation. In this work, the reduced-order form of John Shaw’s partial-differential equation model is chosen for implementation and simulation. The reduced-order form is used because its simpler structure makes it more useful for real-time control applications. The parameters were estimated for the John Shaw model followed by its implementation in MATLAB. From the view of control applications, a limitation of the John Shaw model is the inability to reproduce the so-called ‘minor loop behavior’ which is observed when the material is subject to cycling resulting in incomplete phase transformations. Modeling minor loop behavior is particularly important in closed-loop strain (or position) control applications since achieving a specific target strain between the two (load-dependent) extremes requires partial phase transformation. Herein, the governing equations are modified to include minor loop behavior. This behavior was tested using damped signals which would be expected to trigger minor loops in the actual SMA and reasonable match is observed from the simulations. The use of SMA actuators is limited by the relatively slow response time compared to other smart materials. The conventional current saturation (CS) scheme limits the maximum current into the wire at the manufacturer-specified safe current values in order to protect the wire from damage due to overheating. However, this is a conservative limit on the maximum current and hence, the response is artificially slowed. In order to improve the response time, a model-based temperature saturation (MBTS) scheme was developed, in which current is saturated based on model-predicted temperature. The MBTS scheme allows much higher currents to be applied to the wire, while ensuring that the wire is not damaged. Based on simulations using the reduced-order John Shaw model, it is observed that better tracking occurs using the MBTS scheme in the actuation scheme as compared to the CS scheme.

Shape Memory Alloys (SMAs) have been demonstrated to be effective actuator elements in a wide range of applications, such as robotics, medicine, aerospace and automotive. Enabled by the unique thermo-mechanical properties of SMAs, these actuators offer the advantages of light weight, high power-to-weight ratio and a simple actuation mechanism compared to traditional actuator types. At the same time, the widespread adoption of the SMA actuator remains elusive as its low power efficiency and complex hysteretic behaviour often render it an impractical means of actuation. These actuators also exhibit a slow response speed and their response is highly sensitive to changes in the external environment, namely ambient temperature and mechanical stress, thus complicating their control. Position, force or temperature sensors may be used to facilitate feedback control, but at the cost of increasing the overall size and complexity of the system. The difficulties caused by the hysteretic behaviour can be largely avoided when SMA wires are used as on-off actuators, making SMAs well suited for such applications. However, they may still be subject to a wide range of dynamic operating conditions that would impact their actuation time, and achieving a consistent actuation time is often highly desirable. This thesis presents the synthesis of a nitinol SMA actuator control system which uses electrical resistance feedback to enable a fast response speed and robustness to disturbances in the external environment. A study of the resistance behaviour of SMAs is discussed first. The design of an adaptive controller and the experimental evaluation of its performance are described in detail next. The objective of the SMA actuator control system is to achieve a consistent and fast actuation time throughout the range of operating ambient temperature and stress. The control system is implemented experimentally and shown to be quite successful.

The impact of swirl (i.e., flow with axial and azimuthal velocity components) on the turbulent flow in a pipe is studied using two-component laser-Doppler velocimetry (LDV). There are practical motivations for the flow geometry. For example, previous studies demonstrate that introducing swirl in the tube bank of a paper machine headbox can significantly increase mixing, and hence increase fiber dispersion and orientation isotropy in the finished paper product. The flow characteristics in a pipe downstream of a single straight tapered fin, a single fin with 180??ist but otherwise identical geometry, and four twisted fins were therefore studied at a pipe-based Reynolds number of 80,000. Radial profiles of the mean and rms fluctuations of the streamwise and azimuthal velocity components are measured; results for the straight and twisted single fin are compared to determine the effects of fin geometry and swirl on the turbulent wake downstream of the fin. From a practical viewpoint, it is also desirable to have adjustable swirl, where swirl can either be turned on or off depending upon the type of paper product being produced. The next generation swirler concept consists of fins fabricated from two-way shape memory alloys. Using the two-way memory effect, the fins will be in their straight configuration when cold and twisted configuration (hence acting as a swirler) when hot. This study is the initial phase in developing new active control mechanisms, known as the Vortigen concept, for increasing productivity, and hence reducing wasted raw material and energy, in the pulp and paper industry.

Soft materials have attracted much scientific and technical interest in recent years. In this thesis, attention has been placed on the underpinning relations between molecular structure and properties of one type of soft matter - main chain liquid crystalline elastomers (MCLCEs), which may have application as shape memory or as auxetic materials. In this work, a number of siloxane-based MCLCEs and their linear polymer analogues (MCLCPs) with chemical variations were synthesized and examined. Among these chemical variations, rigid p-phenylene transverse rod and flat-shaped anthraquinone (AQ) mesogenic monomers were specifically incorporated. Thermal and X-ray analysis found a smectic C phase in most of our MCLCEs, which was induced by the strong self-segregation of siloxane spacers, hydrocarbon spacers and mesogenic rods. The smectic C mesophase of the parent LCE was not grossly affected by terphenyl transverse rods. Mechanical studies of MCLCEs indicated the typical three-region stress-strain curve and a polydomain-to-monodomain transition. Strain recovery experiments of MCLCEs showed a significant dependence of strain retentions on the initial strains but not on the chemical variations, such as the crosslinker content and the lateral substituents on mesogenic rods. The MCLCE with p-phenylene transverse rod showed a highly ordered smectic A mesophase at room temperature with high stiffness. Mechanical properties of MCLCEs with AQ monomers exhibit a strong dependence on the specific combination of hydrocarbon spacer and siloxane spacer, which also strongly affect the formation of ð-ð stacking between AQ units. Poisson s ratio measurement over a wide strain range found distinct trends of Poisson s ratio as a function of the crosslinker content as well as terphenyl transverse rod loadings in its parent MCLCEs.