Thermomagnetic optimization of solenoidal magnetostrictive actuators

Magnetostrictive materials often rely on magnetic fields generated through the use of a solenoidal coil. However, the field-generating coil also acts as a source of heat causing thermally induced strains in the magnetostrictive drive element. To insure that the useful magnetostrictive strains are large in comparison with the thermally induced strains, the solenoid may be optimized. This paper presents a simple one dimensional (1-D) magnetic model useful for predicting the magnetic field inside the magnetostrictive drive rod. The advantage of this model is that it can be evaluated very quickly, making it well suited for use in optimization algorithms. A figure of merit is presented that weighs the energy stored in the coil against the power that must be dissipated to maintain the field. With the magnetic model and cost function, the solenoid may be sized to maximize the volume averaged field in the magnetostrictive element per unit of volume averaged dissipated heat in the solenoidal coil. While previous work addressed field/power optimization at the center of air-cored solenoids, the work presented here considers optimization of the average field along a rod of permeable magnetostrictive material. The results indicate that coil quality decreases rapidly if the coil is thinner than optimal, but decreases rather slowly for a thicker than optimal coil.