Novel Bearingless Switched-Reluctance Motor Characterized by One-Dimensional Electromagnetic Radial Force Equations

A bearingless switched-reluctance motor (BSRM) has the combined characteristics of a switched-reluctance motor and a magnetic bearing. The BSRM developed by the NASA Glenn Research Center (refs. 1 and 2) incorporates a hybrid rotor configuration wherein a cylindrical-shaped portion of the rotor is used for levitation and a scalloped section is used for rotation. The asymmetric geometry of the rotor engenders a complex three-dimensional magnetic field topology in and around the rotor and would require complex mathematical analysis to completely describe the radial magnetic field affecting the rotor. However, we began our analysis with a one-dimensional approach, in an effort to reduce the mathematical complexity of the electromagnetic radial force derivation, and we found that it provided a good prediction of the forces. Each rotor segment (circular lamination stack and castellated lamination stack) was treated as an independent entity, and accordingly, the general one-dimensional radial electromagnetic force equation,

F = dw(x)/dg(x) = (A_o/2μ_o)(d/dx)[B²(x)g(x)]

(1)

was developed for each rotor segment. The function w(x) represents the magnetic energy stored in the gap g(x) between the stator and a rotor segment; A_o is the common cross-sectional area between the stator and rotor pole; μ_o is the permeability of free space; and B(x) is the magnetic field function. Determining a suitable mathematical form of the B(x) function was critical in obtaining the correct electromagnetic radial force impinging on the hybrid rotor. The electromagnetic radial forces on each rotor segment were subsequently summed to obtain the total levitation magnetic radial force on the rotor. The analysis was done with the nonrotating rotor poles aligned with the appropriate stator poles to achieve the maximum levitated electromagnetic radial force loads on the rotor. Two magnetic circuit geometries, approximating the complex topology of the electromagnetic fields existing in and around the hybrid rotor, were employed in formulating the electromagnetic radial force equations.

The graph shows that the theoretical and experimental results are in very close agreement. Hence, we have developed a very valuable analysis tool for designing future motors of this type for different mission applications. A pending publication (ref. 3) will give a complete description of the levitated and nonlevitated magnetic field and force characteristics of the motor and its rotor.

Theoretical and experimental levitation radial forces.

References

1. Morrison, Carlos R.: Bearingless Switched Reluctance Motor. U.S. Patent 6,727,618 B1, Apr. 27, 2004.
2. Morrison, Carlos R.: Improved Bearingless Switched-Reluctance Motor. NASA Tech Briefs, vol. 27, no. 10, 2003, pp. 68-70.
3. Morrison, Carlos R.; Siebert, Mark W.; and Ho, Eric J.: Electromagnetic Radial Forces in a Hybrid Magnetic-Bearing Switched-Reluctance Motor. NASA/TP--2007-214818 (to be published in IEEE Trans. Magnetics), 2007.

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