Abstract
The instability of kinematic pairs made with permanent magnets (passive magnetism) significantly restricts their technical use. On the other hand, they show very good tribological properties: null friction and wear. In previous works, it has been verified that by using Mathieu Functions any instability of the levitated member may be removed if one of the two members is subjected to a parametric excitation. In this paper, the problem is discussed directly utilizing the nonlinear equation of motion of the levitated member, and it is confirmed that it may be stable.
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References
Earnshaw, S.: On the nature of molecular forces which regulate the constitution on luminiferrous ether trans. Cambridge Philos. Soc. 7, 97–112 (1842)
Bassani, R., Villani, S.: Passive magnetic bearing: conic-shaped bearing. Proc. Instn. Mech. Engrs. 213, 151–161 (1999)
Bassani, R.: A stability space of a magneto-mechanical bearing. ASME, J. Dyn. Syst. (in press)
Bassani, R.: Stability of permanent magnets bearings under parametric excitations. Trib. Trans. 48, 457–463 (2005)
McLachlan, N.W.: Theory and Application of Mathieu Functions, p. 401, Oxford, Claredon (1947) Oxford: Claredon Press
Bassani, R.: Permanent magnetic levitation and stability. Find. Trib. Micro-Macro, Kluver 547–554 (2001)
Bassani, R.: Earnshow S. (1805–1888) and magnetic stability. Meccanica 41, 375–389 (2006)
Bassani, R., Di Puccio, F., Ciulli, E., Mugolino, A.: Study of conic permanent magnet bearings. I° AIMETA International Tribology Conference 447–454 (2000)
Bassani, R.: Stabilità dei corpi in campi potenziali. DCMN, Università di Pisa, RL 524, 4 (1991)
Coey, J.M.D.: Rare-Hearth Iron Permanent Magnets, p. 522, Claredon, (1996)
Lemarquaud, G., Yonnet, J.P.: Classification des suspensions magnètiques. RGE 6, 31–34 (1990)
Tokoro, H., Uchida, K.: High energy product Nd-Fe-B sintered magnets produced by wet compacting process. IEEE Trans. Mag. 37, 2463–3466 (2001)
Newland, D.E.: Mechanical Vibration Analysis and Computation, p. 583, Longman, Harbow and Wiley, New York (1989)
Szempliñska-Stupnicka, V.: The Behavior of Nonlinear Vibrating Systems, Vol. I°, p. 251, Kluver A.P., (1990)
Zuillinger, D.: Standard Mathematical Tables and Formulae, p. 812, CRC, (1996)
Bassani, R., Ciulli, E.: Passive magnetic bearings. Low instability and possibile stability. Proceedings of the World Tribology Congress 2005-63546, Washington DC, (September 2005)