This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a “law of approach” to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is demonstrated that the model accurately characterizes the magnetic hysteresis in the material, as well as the strains and forces output by the transducer under conditions typical of engineering applications.
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References
1.
Brown, W. F., “Irreversible magnetic effects of stress,”Phys. Rev., 75(1):147-154, January 1949.
2.
Bozorth, R. M. and H. J. Williams, “Effect of small stresses on magnetic properties,”Rev. Mod. Phys., 17(1):72-80, January 1945.
3.
Birss, R. R., C. A. Faunce and E. D. Isaac, “Magnetomechanical effects in iron and iron-carbon alloys,”J. Phys. D: Appl. Phys., 4:1040-1048, 1971.
4.
Pitman, K. C., “The influence of stress on ferromagnetic hysteresis,”IEEE Tans. Magn., 26(5), September 1990.
5.
Jiles, D. C., “Theory of the magnetomechanical effect,”J. Phys. D: Appl. Phys., 28:1537-1546, 1995.
6.
Spano, M. L., A. E. Clark and H. T. Savage, “Effect of stress on the magnetostriction and magnetization of rare earth-Fe1.95 alloys,”IEEE Trans. Magn., MAG-19(5):1964-1966, September 1983.
7.
Clark, A. E., H. T. Savage and M. L. Spano, “Effect of stress on the magnetostriction and magnetization of single crystal Tb0.27Dy0.73Fe2,”IEEE Trans. Magn., MAG-20(5), 1984.
8.
Calkins, F. T., M. J. Dapino and A. B. Flatau, “Effect of prestress on the dynamic performance of a Terfenol-D transducer,” in Proc. of SPIE Smart Structures and Materials, Vol. 3041, pp. 293-304, San Diego, CA, March 1997.
9.
Hall, D. L., “Dynamics and vibrations of magnetostrictive transducers,” Ph.D. dissertation, Iowa State University, Ames, IA, 1994.
10.
Duenas, T. A., L. Hsu and G. P. Carman, “Magnetostrictive composite material systems analytical/experimental,” in Adv. Smart Materials Fundamentals and Applications, Boston, MA, 1996.
11.
Dapino, M. J., R. C. Smith and A. B. Flatau, “An active and structural strain model for magnetostrictive transducers,” in Proceedings of SPIE, Smart Structures and Materials 1998, Vol. 3329, pp. 198-209, San Diego, CA, March 1998.
12.
Dapino, M. J., R. C. Smith and A. B. Flatau, “Structural-magnetic strain model for magnetostrictive transducers,”IEEE Trans. Magn., 36(3)545-556, 2000.
13.
Jiles, D. C. and D. L. Atherton, “Ferromagnetic hysteresis,”IEEE Trans. Magn., MAG-19(5):2183-2185, 1983.
14.
Jiles, D. C. and D. L. Atherton, “Theory of the magnetization process in ferromagnets and its application to the magnetomechanical effect,”J. Phys. D: Appl. Phys., 17:1265-1281, 1984.
15.
Jiles, D. C. and D. L. Atherton, “Theory of ferromagnetic hysteresis,”J. Magn. Magn. Mater., 61:48-60, 1986.
16.
Clark, A. E., “High power rare earth magnetostrictive materials,” in Procs. Recent Advances in Adaptive and Sensory Materials and Their Applications, pp. 387-397, Lancaster, PA, Technomic Publishing Co., Inc., 1992.
17.
Jiles, D. C.Introduction to Magnetism and Magnetic Materials, Chapman & Hall, London, First edition, 1991.
18.
Bozorth, R. M., Ferromagnetism, D. Van Nostrand, Inc., 1968.
19.
Cullity, B. D., Introduction to Magnetic Materials, Addison-Wesley, Reading, MA, 1972.
20.
Chikazumi, S., Physics of Magnetism, R. E. Krieger Publishing, Malabar, FL, 1984.
21.
Jiles, D. C. and D. L. Atherton, “Theory of ferromagnetic hysteresis,”J. Appl. Phys., 55(6):2115-2120, 1984.
22.
Jiles, D. C., J. B. Thoelke and M. K. Devine, “Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis,”IEEE Trans. Magn., 28(1):27-35, 1992.
23.
Craik, D. J. and M. J. Wood, “Magnetization changes induced by stress in a constant applied field,”J. Phys. D: Appl. Phys., 4:1009, 1971.
24.
Sablik, M. J. and R. A. Langman, “Approach to the anhysteretic surface,”J. Appl. Phys., 79(8):6134-6136, 15 April 1996.
25.
Sablik, M. J. and D. C. Jiles, “Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis,”IEEE Trans. Magn., 29(3), 1993.
26.
Delince, F., A. Genon, J. M. Gillard, H. Hedia, W. Legros and A. Nicolet, “Numerical computation of the magnetostriction coefficient in ferromagnetic materials,”J. Appl. Phys., 69(8):5794-5796, 1991.
27.
Agayan, V., “Thermodynamic model for ideal magnetostriction,”Physica Scripta, 54:514-521, 1996.
28.
Mason, W. P., Electromechanical Transducers and Wave Filters, D. Van Nostrand, Toronto, 1942.
29.
Claeyssen, F., R. Bossut and D. Boucher, “Modeling and characterization of the magnetostrictive coupling,” in Power Transducers for Sonics and Ultrasonics, B. F. Hamonic, O. B. Wilson and J.-N. Decarpigny, Eds., pp. 132-151, Toulon, France, Springer-Verlag, June 1990.
30.
Sherman, C. H. and J. L. Butler, “Analysis of harmonic distortion in electroacoustic transducers,”J. Acoust. Soc. Am., 98(3):1596-1611, 1995.
31.
Claeyssen, F., N. Lhermet and R. L. Letty, “Design and construction of a resonant magnetostrictive motor,”IEEE Trans. Magn., 32(5):4749-4751, 1996.
32.
James, R. D. and D. Kinderlehrer, “Theory of magnetostriction with applications to TbxDy1-xFe2,”Philosophical Magazine B, 68(2):237-274, 1993.
33.
Calkins, F. T., “Design, analysis and modeling of giant magnetostrictive transducers,” Ph.D. dissertation, Iowa State University, Ames, Iowa, 1997.
34.
Dapino, M. J., F. T. Calkins and A. B. Flatau, “Statistical analysis of Terfenol-D material properties,” in Proceedings of SPIE, Smart Structures and Materials 1997, Vol. 3041, pp. 256-267, San Diego, CA, March 1997.
35.
Chen, W., J. Frank, G. H. Koopmann and G. A. Lesieutre, “Design and performance of a high force piezoelectric inchworm motor,” in Proc. of SPIE Smart Structures and Materials, Newport Beach, CA, March 1999. To be published.
36.
Butler, J. L., Application Manual for the Design of ETREMA Terfenol-D Magnetostrictive Transducers, ETREMA Products, Inc., Ames, IA, 1988.
