This paper identifies an abstraction that is found in the equations that describe the 3D interaction between cuboidal permanent magnets and applies this to the magnetic design of a gravity compensator. It shows how the force between magnets and its position-sensitivity, important design parameters for magnetically levitated 6-DoF gravity compensators, may be translated into the magnetic domain and verifies this with 3D analytical models. With this information, a number of basic gravity compensator topologies is derived. These topologies are subsequently investigated in more detail, with specific focus on combining a high force with low position sensitivity.
1. Ibrahim, R. A., "Recent advances in nonlinear passive vibration isolation," Journal of Sound and Vibration, Vol. 314, 371-452, 2008. doi:10.1016/j.jsv.2008.01.014
2. Robertson, W. S., M. R. F. Kidner, B. S. Cazzolato, and A. C. Zander, "Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation," Journal of Sound and Vibration, Vol. 326, 88-103, May2009. doi:10.1016/j.jsv.2009.04.015
3. Janssen, J. L. G., "Extended analytical charge modeling for permanent-magnet based devices: Practical application to the interactions in a vibration isolation system,", Ph.D. thesis,Eindhoven University of Technology, Eindhoven, The Netherlands,2011.
4. Nagaya, K. and M. Sugiura, "A method for obtaining a linear spring for a permanent magnet levitation system using electromagnetic control," IEEE Trans. on Magn., Vol. 31, 2332-2338, May1995. doi:10.1109/20.376226
5. Akoun, G. and J.-P. Yonnet, "3D analytical calculation of the forces exerted between two cuboidal magnets," IEEE Trans. on Magn., Vol. 20, 1962-1964, Sept.1984. doi:10.1109/TMAG.1984.1063554
6. Bancel, F., "Magnetic nodes," J. of Appl. Phys., Vol. 32, 2155-2161, Jun.1999.
7. Janssen, J. L. G., J. J. H. Paulides, E. A. Lomonova, F. Bölöni A. Tounzi, and F. Piriou, "Analytical calculation of interaction force between orthogonally magnetized permanent magnets," Sensor Letters, Vol. 7, 442-445, Aug.2009. doi:10.1166/sl.2009.1049
8. Allag, H. and J.-P. Yonnet, "3D analytical calculation of interactions between perpendicularly magnetized magnets: Application to any magnetization direction," Sensor Letters, Vol. 7, 486-491, Aug.2009. doi:10.1166/sl.2009.1094
9. Furlani, E. P., Permanent Magnet and Electromechanical Devices:Materials, Analysis And Applications, 6th edition, Academic Press, London,2001.
10. Ravaud, R. and G. Lemarquand, "Magnetic field produced by a parallelepipedic magnet of various and uniform polarization," Progress In Electromagnetic Research, Vol. 98, 207-219, 2009. doi:10.2528/PIER09091704
11. Yonnet, J.-P. and H. Allag, "Three-dimensional analytical calculation of permanent magnet interactions by `magnetic node' representation," IEEE Trans. on Magn., No. 99, 1,2011.
12. Janssen, J. L. G., J. J. H. Paulides, and E. A. Lomonova, "Analytical force and stiffness calculations for magnetic bearings and vibration isolation," Computer Field Models of Electromagnetic Devices, 1st edition,502-511, IOS Press, Amsterdam,2010.
13. Puppin, E. and V. Fratello, "Vibration isolation with magnet springs," Review of Scientific Instruments, Vol. 73, 4034-4036, Nov.2002.
14. Choi, K. B., Y. G. Cho, T. Shinshi, and A. Shimokohbe, "Stabilization of one degree-of-freedom control type levitation table with permanent magnet repulsive forces," Mechatronics, Vol. 13, 587-603, 2003. doi:10.1016/S0957-4158(02)00032-6
15. Choi, Y.-M., M. G. Lee, D.-G. Gweon, and J. Jeong, "A new magnetic bearing using halbach magnet arrays for a magnetic levitation stage," Review of Scientific Instruments, Vol. 80, No. 045106, 1-9, 2009.
16. Janssen, J. L. G., J. J. H. Paulides, E. A. Lomonova,B. Delinchant, and J.-P. Yonnet, "Design study on magnetic springs with low resonance frequency," Proc. of the LDIA 2011 Symp., Vol. 19, 1-6, Eindhoven, the Netherlands,2011.