**Projects
**

__Passive
electromagnetic suspension for rotor applications:__

Non-contact suspensions help to avoid noise, friction and wear. Permanent magnets permit to obtain important levitation forces and stiffnesses, but a suspension realized only with permanent magnets is inherently unstable. In combining permanent magnets and induced (eddy) currents, total stability can be achieved, without need for electrical supply or control system.

Here, we discribe the design, the (predicted) behaviour and the experimental tests and results of an electrodynamic suspension including both permanents magnets and short-circuited coils.

The structure of the electrodynamic suspension is done in Fig. 1 . The nominal rotational speed is 11 000 rpm . An overview of the system physical functioning is given below, and is followed by a description of the system’s elements.

Figure 1: Suspension structure .

The structural support is composed of an aluminium axle and an external cylinder body, also in aluminium. While the axis remains stationary, the cylinder is rotating ( the rotor).

Two identical, symmetrical electrodynamic sets (both a Halbach array and a short-circuited coil) are installed along the rotation axis. Two touch-down bearings ensure positioning and stability for low-speed conditions. Note that these bearings, thanks to a radial air-gap of 1 mm, let a place enough for electrodynamic stabilization.

As proposed by the physician Klaus
Halbach in 1985, a *Halbach array * of magnets, which alows to obtain a
concentration of the magnetic field. The structure proposed here contains 24 magnets in a
six-pole-pairs distribution, as shown in Fig. 2. Only NdFeB magnets are used
for the Halbach array; these high-performance magnets have a remanence of about
1.2 T.

Figure 2: Halbach structure.

The Halbach arrays are fixed to the rotor and create a rotate magnetic field. The magnetic field turns at the rotor speed and the field frequency is the rotor speed multiplied by the number of magnetic pole-pairs. It is, for the six-pole-pairs structure, the magnetic speed is six times the mechanical one.

The short-circuited conductors (Fig.
3),
fixed to the stator, *see* the Halbach magnetic field. Each conductor goes
all along the coil support and returns at the diametrally opposite side. Then,
when the rotor is centered, the same voltage is induced at both sides of each
conductor and no current results. It means, no drag forces and no electric
losses are presented in centered, nominal position. For a shifted rotor, the
induced voltages at each side are different in magnitude, and a finite current
will flow within the loop. The value of this current depends on the circuit
impedance. The 36 conductors (for each coil) have been realised with HF- Litz
wire (Ø 0.1 mm x 120 conductors), in order to avoid parasitic eddy currents.

Figure 3: Short-circuited coils.

**
System Operation :**

The Halbach array produces a magnetic
field, with a sinusoidal space distribution, in close proximity to the coils.
When the rotor turns, the *spatial* field distribution becomes a* time*
field distribution, which induces a sinusoidal voltage. An induced current
appears in the coils, defined by the ratio between the induced voltage and the
coils’ impedance. As noted, when rotor is centered, there is no current in the
coils.

If the coils impedance is purely resistive, the angle between voltage and current is zero. However, if the coils' impedance is mainly inductive, this angle brings close to 90°. As shown in the planar representation of the system (Fig. 4b), in order the impedance of the coil be predominantly inductive, a ferromagnetic core should be added to the coils.

a) Impedance purely resistive, **I**
= I (j _{0}), a drag force is created ( no
lift force).

b) Impedance mainly inductive, **I** @
I (j _{0} + 90°), a lift force is created (
no drag force).

Figure 4: Halbach field, induced current and resulted force.

Because the inductance grows with the rotational speed, drag and lift forces vary with speed too, as shown in Fig. 5. A critical, minimal speed is required to obtain a good lift-to-drag ratio.

Figure 5: Drag and lift forces vs. speed.

Magnetic saturation can play an interesting role in the bearing behavior, providing that the circuit inductance does not remain constant. Consider the RL coil circuit, where the inductance has a ferromagnetic core. When the magnetic saturation appears in the core, the inductance (and so, the global impedance) decreases and, for a constant voltage supply, the current increases. By increasing the current value, the magnetic saturation can help in increasing the Lorentz force.

The structure above presented ensures the *radial*
stability of the rotor. Both the *axial* and *angular* stability and
weight support must be provided by another non-contact system. Permanent
magnet bearings seem ideal for this application; the electrodynamic bearings
compensate their inherent instability. For example, the bearing shown in Fig. 6
can support the rotor weight, without modifying the global stiffnesses balance.

Figure 6: Weight support bearing.

The magnetic forces and stiffnesses can be measured and calculated, respectively, for several values of mechanical speed and radial shift. It is obvious that a repelling force (between coils and magnets) must be created, following as near as possible the shifted direction.

The stiffness gives important information about the quality of the system stability. Stiffness can be defined as:

(1)

For a 2D system, the global behavior for stiffness can be expressed by:

(2)

The different stiffnesses can be calculated from the forces analysis.

The suspension presented above uses electrodynamic forces for the centering action. An external permanent magnet bearing must ensure angular and axial stability, as well as weight support. In this case electrodynamic forces stabilize two degrees of freedom ( DOF ), which is not quite advantageous. Therefore, we propose a new structure, where electrodynamic forces ensure only the axial stabilization. The remaining DOF are stabilized by permanent magnet bearings (Fig: 7).

Figure 7: Improved suspension (electrodynamic axial stabilisation).

An electrodynamic suspension for total levitation has been presented. Both the physical description and the different parts of the system were discussed. A novel, improved structure is at present under study. Electrodynamic forces will be used for stabilizing only one degree of freedom.