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Magnetostrictive materials optimised by multi-physics simulation

Comsol : 14 May, 2014  (Application Story)
Materials that demonstrate different responses to varying external stimuli are known as "smart materials,’ and their discovery has led to the creation of products that perform on a whole new level. These engineered materials are developed to perform smarter and more efficiently than their predecessors, allowing materials to be designed based on the products and environments in which they will be used. Using Comsol, Etrema researchers were able to find a design that was optimised for the competing requirements of both the AC and DC magnetics.
Magnetostrictive materials are engineered smart materials that change shape when exposed to a magnetic field and they have proven crucial for the production of transducers, sensors and other high-powered electrical devices. 
Engineers at Etrema Products design devices using magnetostrictive materials for defence and other industry applications including sensors, loudspeakers, actuators, SONAR, and energy harvesting devices. The unique properties of magnetostrictive materials - their ability to mechanically respond to magnetic fields and their characteristic nonlinearity - make designing these devices a challenge. Multi-physics simulation can be used to accurately represent the material properties and complex physics interactions within such devices, facilitating the production of the next generation of smart products.
Magnetostriction occurs at the magnetic domain level as magnetic regions realign in response to variation in either magnetic or mechanical energy, causing a change in a material’s shape or magnetic state (Fig 1). For example, iron elongates by 0.002% when exposed to a strong magnetic field, and nickel contracts by 0.007% under that same field. Terfenol-D -  a “giant magnetostrictive material" -  demonstrates deformations 100 times that of iron and was first developed by the US Navy in the 1970s. Etrema is currently its sole commercial producer.
Etrema designs magnetostrictive transducers (Fig 2) using Terfenol-D. These devices convert magnetic energy into mechanical energy and are critical components of many larger, more complex systems. To accurately model these complex devices, Etrema uses Comsol Multiphysics.
1 (above right): Magnetostrictive materials change their physical shape in response to an applied magnetic field and vice versa.
2 (below left): Diagram of a magnetostrictive transducer showing the magnetic and mechanical components of the device.
3 (below right): Closely packed SONAR array, which includes a magnetostrictive transducer at its core. From left to right: a single magnetostrictive SONAR transducer; the transducer packaged with power electronics; and the full array, made up of 18 transducer elements.
Simulations include permanent magnets and coils, the magnetic fields created by these coils, stress and modal analyses of structural mechanics components, as well as heat transfer in the device to mitigate heat generated by eddy currents and hysteresis. Fully coupled models are used to evaluate the overall electro-mechanical characteristics of these transducers. “When we first began to expand our engineering process to model such devices, our modelling techniques consisted of a system of disjointed methods that included hand calculations, equivalent circuits, and single-physics modelling,” says Senior Engineer Julie Slaughter. “However, our decision to move toward a devices and systems approach coincided with the advent of multi-physics finite element analysis and we adopted Comsol as our modelling tool for systems-based modelling. This greatly improved our understanding of transducers and their design.” 
Firstly, models are created to analyse individual physics; then, multi-physics simulations are built to determine how the physics interact with one another. This approach allows for both a targeted look as well as a complete picture of the physics interactions taking place within their devices. An overview of this design process can be seen in the design of a close-packed SONAR source array, which includes a magnetostrictive transducer at its core (see Fig 3). Not only are there many different material properties that need to be analysed and optimised, but the transducer also contains a combination of electrical, magnetic, and structural physics that interact within the device.
Deformation within the transducer was analysed using a single-physics model in which static loads were used to estimate fatigue and determine if the pre-stressed bolts and Terfenol-D core would hold up against the system’s strain. The initial transducer design demonstrated severe bending at the mechanical interface between the transducer and the load, however further load analysis and structural optimizations allowed the transducer to be redesigned with reduced deformation and stress (see Fig 4). The model was also used to detect undesirable modes of vibration in the operating bandwidth that could affect overall performance.
Single-physics models were developed to evaluate the DC and AC magnetics separately. “We matched the electrical requirements of the transducer with the available power amplifiers, and evaluated electrical losses due to eddy currents and air gaps within the device,” says Slaughter.
Permanent magnets were integrated into the transducer design to magnetically bias the material to enable bidirectional motion and minimize nonlinear behaviour and frequency-doubling effects. “Stray magnetic fields in close proximity with the electronics can cause problems with noise and corrupted signals,” Slaughter explains. “We had to carefully consider the design of the transducer’s magnetic circuit as well as the placement of key electrical components to avoid stray magnetic flux that can interfere with the electronics.” Using Comsol, Etrema researchers were able to find a design that was optimised for the competing requirements of both the AC and DC magnetics.
The models for this design demonstrated that the magnetic fields mainly stay confined to the magnetic components, thereby reducing the exposure of the electronics to the magnetic fields.
4 (above left): The initial transducer design shows severe bending in the mechanical interface to the load. Right: The redesigned model demonstrates reduced deformation.
5 (below right): Magnetic fields generated from a 1-ampere input to the coil. Displacements are calculated using the maximum current input.
The next step in Etrema’s design process was to create fully coupled multi-physics models. “When setting up our multi-physics models, we use coupled equations, where strain is a function of stress and also of the magnetic field,” says Slaughter. “This is the basis of implementing coupled magnetostriction in Comsol.” Using this process, Slaughter and her team determined how the magnetic and mechanical domains would interact within the device and ultimately predicted how the magnetostrictive material would behave (Fig 5).
“For the coupled linear magnetostrictive model, our simulations showed that the device would perform largely as expected, with few adjustments needed in either the mechanical or magnetic aspects of the design,” she continues. “The magnetic fields remained confined to the magnetic circuit, and deformations remained minimal.” 
These multi-physics models were further validated using experimental data. “The models of impedance and displacement were very similar to experimental results,” says Slaughter. At Etrema, both single physics models and fully coupled multi-physics simulations have proven to be powerful tools for transducer design, evaluation, and optimisation. The construction of single-physics models allows for design diagnosis prior to the development of multi-physics models, where attributing an undesired interaction to a certain physics type is more straightforward.
Coupled models then further describe the way the individual physics will interact in the real world. Although Etrema focuses on magnetostrictive materials, all transducer technologies involve coupled multi-physics interactions, including piezoelectric, electrostatic, and electromagnetic effects, and each can benefit from the use of multi-physics simulations. Finite element models can be used at different stages of product development: During design development, for the evaluation of existing products, and when it is necessary to troubleshoot performance issues.
Smart Materials Backgrounder
The term smart materials refers to a class of materials that are highly responsive and have the inherent capability to sense and react according to changes in the environment. The common characteristic of all smart materials is the ability to react mechanically to external stimuli.
Smart materials largely respond in one of two ways - either electrostrictively or magnetostrictively. The terms identify how they are told to move - either electrically or magnetically. Other smart materials, such as Shape Memory alloys, react to changes in temperature.
Early smart material applications started with magnetostrictive technologies. This involved the use of nickel as a sonar source during World War II to find German U-boats by Allied forces. Although limited by its power density and strain capabilities, nickel is still used today in cleaning baths at ultrasonic frequencies.
Piezoceramics, the other main type of smart materials, were initially discovered by Pierre and Jacques Curie. They identified the response that crystals of sugar and Rochelle salt made when subjected to mechanical stress. This development in 1880 began the work in what is now a $600 million dollar industry today. Their initial success, and the corresponding converse effect of strain production by the application of an applied electric field, led the way to the first serious applications of piezoceramic materials, which began during World War I. In addition to nickel sonar transducers, work began in France on the development of an ultrasonic submarine detector that would emit a high frequency "chirp" and measure depth by timing the return echo. The success of sonar then stimulated intense research and development into a variety of piezoelectric formulations and shapes.
However, piezoceramic materials do have limitations - namely fatigue and ageing. Therefore, in the 1960s, the Naval Ordnance Laboratory began work on new materials that would be able to send out stronger sonar signals. By this time, considerable work had been done by the Ames Laboratory in rare earth separation and processing to prepare high purity rare earth metals. This led to an alliance between the Naval Ordnance Laboratory and Ames Laboratory, which developed a processing technique to produce these "giant magnetostrictive" materials in research quantities. This feat, and subsequent patent activity, led to the birth of Terfenol-D.
Terfenol-D is an alloy of terbium, dysprosium, and iron and has the largest room temperature magnetostriction of any known material. The name Terfenol-D comes from the metallic elements; terbium (TER), iron (FE), Naval Ordnance Labs (NOL), and Dysprosium (-D). NOL, now known as Naval Surface Warfare Center - Carderock Division (NSWC-CD), developed and named the material. Terfenol-D was developed for higher power sonar that would also have greater bandwidth and greater reliability. ETREMA holds patents and licenses to many Terfenol-D applications, including the exclusive worldwide licenses to manufacture all types of Terfenol-D materials.
Terfenol-D is a solid-state transducer capable of converting very high energy levels from one form to another. In the case of electrical-to-mechanical conversion, the magnetostriction of the material generates strains 100 times greater than traditional magnetostrictives, and 2-5 times greater than traditional piezoceramics. The material has a high Curie temperature (380C), which enables magnetostrictive performance greater than 1000ppm from room temperature to 200C. By adjusting the stoichiometry of the alloy, this temperature range can be extended down to cryogenic temperatures.
Author: Alexandra Foley
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