One-dimensional Analytical Constant Parameter Linear Electromagnetic-magnetomechanical Models of a Cylindrical Magnetostrictive (terfenol-d) Transducer

A method is presented for including motional and eddy current effects when analytically modeling electrical impedance functions of cylindrical magnetostrictive transducers. To approximate eddy current effects, one-dimensional analytical constant parameter linear electromagnetic models of a cylindrical magnetostrictive transducer are developed. Maxwell's equations are solved for the magnetic field strength as a function of radial position. Closed form expressions for magnetic flux as a function of radial position are then derived, from which transducer electrical impedance functions are formulated. Two different physical models of the transducer are considered. The first model results in the classic eddy current solution for a rod in a wound wire solenoid. The second physical model includes the effects of a conducting external cylindrical housing. Motional effects are incorporated into the electromagnetic models via the magnetomechanical model, which is a frequency and load dependent, complex valued expression for the "dynamic magnetic permeability" of the magnetostrictive material within the transducer. The functional form for this dynamic magnetic permeability is derived by comparing the transduction equations for the magnetostrictive material with those for the transducer containing the material. Electrical impedance functions for both physical models are compared with an experimental measurement for a particular magnetostrictive transducer (using Terfenol-D) in its low signal linear range of operation. The second physical model was found to offer the better simulation of the experimental measurement of the transducer's electrical impedance, with errors in magnitude or phase of less than ±5% for excitation frequencies between 100 and 10 000 Hz (the as-run mechanical resonant frequency was 8800 Hz). Experience has shown that measured material parameters typically yield simulations of electrical impedance functions within ±10%. Predictions of electrical impedance 1-D Analytical Electromechanical Models 2 D. L. Hall and A. B. Flatau functions for Terfenol-D transducers, calculated based on estimated or published Terfenol-D parameters, can be in error by well over 40%. Thus, the accuracy of model results seem to be controlled primarily by the accuracy with which magnetostrictive material parameters are known.