Silphenix GmbH is an engineering and consulting firm in Switzerland specializing in high-speed electrical machines, magnetic bearings, and electromagnetic field analysis. One project focus is compact high-speed flywheel systems for day storage of solar photovoltaic energy on the order of 0.5 to 5 KWh usable energy. An important constraint for energy day storage is extremely low loss per day (e.g. 1% per hour). This means that the idling losses have to be less than 5 W and 50 W for 0.5-kWh and 5-kWh units, respectively. Minimizing the idling losses requires not only operation in a vacuum environment, but also low bearing losses (magnetic bearings), low eddy current losses (reluctance machine), and low drag losses (cylindrical rotor surface).

Design tools used were the field analysis programs MAGNETO 2D and AMPERES 3D from Integrated Engineering Software (IES) that enabled modeling of both magnetic bearings and the reluctance machine. Particular features of these programs are the exceptional ease of geometric modeling and the interactive use of the two programs to create the geometric model and the currents in the stator coils. Using a parametric solver mode, the force value's axial rotor position with respect to the magnetic bearings, and the torque values versus the rotor angle are obtained.

#### Magnetic Bearings

The passive magnetic bearing (dual ring pair), as shown in Figure 1, consists of two ring pairs with repulsive magnetization in both radial and axial directions. For a horizontal orientation of the motor axis, the forces have been computed with the parametric solver mode of AMPERES for an axial rotor displacement dz between -5.0 mm and +5.0 mm. In the axial center position, the radial force F(y) is positive, providing a restoring force compensating for the rotor weight. The axial force F(z) near the center position is zero, while at the dz = -0.5 mm point, F(z) = -39.4 (N), indicating axial instability that has to be confined mechanically in both directions (e.g. with a flat precision-ground steel disk inserted at the end of the rotating axis against a small stationary steel sphere on both ends). Therefore, the actual mechanical bearing losses depend on a low axial destabilization force Fz obtained by manually adjusting the axial air gap and the optimum material choice (e.g. high-grade ceramics) for both the disk and the sphere.

Alternatively, an axial active magnetic bearing can be used that requires low power for stabilization. The radial restoring force Fy for a radial displacement of -0.5 mm is 19.4 Newton. For a rotor mass of 1 kg (9.81 N), the radial restoring force is reduced to 9.7 Newton. If a higher radial restoring force was needed, the geometry of rings or the number of ring pairs could be altered.

#### Reluctance Motor

The choice of a reluctance motor was made due to the inherent low eddy current losses and the absence of both permanent magnets and rotor coils. The geometry of stator, rotor, and the coils was successfully modeled using MAGNETO and AMPERES interactively. The torque was calculated with MAGNETO, yielding torque values for a rotor length of 1,000 mm. For a rotor length of 15 mm, the torque values are normalized by a factor of 15/1,000. The torque can also be computed with AMPERES, which requires more computing time; however, the results obtained with either program are within comparable limits.

The rotor and stator have salient poles of unequal numbers, as shown in Figure 2. The torque is generated through the physical phenomenon of reducing magnetic reluctance. When one stator coil pair is energized, a rotor torque is generated, as shown in Figure 3. The nearest rotor pole is pulled from the nonaligned position (e.g. -30 deg) towards the aligned position (0 deg). When the three stator coil pairs are connected to a 3-phase variable frequency current source, the rotor follows the rotating field. The phenomenon of magnetic reluctance can be visualized by pictorially replacing the field lines (Figure 3) with rubber bands, which exert a maximum restoring torque (i.e. maximum reluctance) on the rotor in the non-aligned position (e.g. -30 deg), and a zero torque in the center position (i.e. minimum reluctance).

#### Cylindrical Rotor Surface

Special attention had to be given to minimize the drag losses of the rotor with its four salient magnetic poles, as shown in Figure 4. In order to obtain a smooth cylindrical rotor surface, four sectorial elements were integrated into the salient rotor. The five rotor elements can be fastened with the two supporting discs and 12 screws into a compact cylindrical rotor with a cylindrical surface; however, in order keep the radial stress of the rotor within its design limits, several layers of carbon filaments (0.3 mm radially) were added to the cylindrical surface, reducing the actual air gap to 0.7 mm, which is still within the radial operation range of the magnetic bearing.

The rotor geometry was modeled with MAGNETO in 2D, as shown in Figure 4. The holes for the axis and the rotor mounting screws were added. Next, the 2D rotor elements are loaded with AMPERES 3D. The volumes of all rotor parts with the four sectorial sections, two mounting disks, the hub for the rotor axis, and the mounting holes were then generated using the “sweep mode” of AMPERES, as shown in Figure 4. Furthermore, the “object mode” allows a total or partial exploded view of the reluctance motor. The model of the reluctance motor is shown in Figure 5. When all the components of the reluctance motor were completed with AMPERES, all the data were transferred as drawings and step-mode files to the machine shop.

All the supporting structures for the stator and the magnetic bearings were designed using MAGNETO and AMPERES interactively. The assembly of system components was greatly facilitated using the object-mode of AMPERES. This mode allows a number of useful options (e.g. display of all the motor and magnetic bearing components, or an exploded view of the motor components). In particular, individual system components can be singled out and modified, if necessary.

An opto-electronic sensor above the magnetic bearing was added to measure the rpm during run down, since no electric stator signals were available. The radial air gap of only 0.7 mm requires an excellent dynamic rotor balancing and a fine adjustment of the axial rotor position.

This article was written by Dr. Hans K. Asper of Silphenix GmbH, Meilen, Switzerland using software from Integrated Engineering Software, Winnipeg, Manitoba, Canada. For more information on the products used in this application, visit here .