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The first group of the stage design concepts use active magnetic suspension in all degrees of freedom. In these designs, the stage’s motion is along y-axis, and all other degree of freedom of the stage are actively suspended via magnetic bearings.

Figure 3-7: Design concept 1 of magnetically-levitated linear stage with all-DOFs actively controlled.

Group I: Design Concept 1

Fig. 3-7 shows a design concept of a magnetically-levitated linear stage using active magnetic suspension in all degrees of freedom. When the stage is driven by hystere- sis motors, the stage secondaries are made of magnetically-semi-hard material with relatively large permeability. There are four stators configured around the moving stage, interfacing with the stage secondaries. The normal surfaces of the secondary are configured at an angle with the horizontal plane. Here, each stator is able to control its total normal force, total thrust force, and the torque to the secondary in the pitch direction. With all these forces and torques, all degrees of freedom of the stage can be actively controlled.

Below we discuss the winding pattern for the stator that can implement the con- trol for required torques and forces. The winding of each stator has two possible configurations. Figure 3-8 shows the first winding configuration. Here, the stator winding consists of a series of lumped coils, and each coil is driven by independent power amplifiers. By controlling the currents in each coil, the total normal force, total thrust force, and total torque in 𝑥-direction on the stage secondary can be con- trolled independently. This winding pattern requires a relatively large number of

𝑇

𝐹

𝐹

x

y

z

Stator

Figure 3-8: Stator winding configuration using independently-controlled lumped coils.

Figure 3-9: Stator winding configuration using double multi-phase windings and the corresponding air-gap flux distribution.

independent power amplifiers, especially for linear stages with long transportation distance.

The other possible winding pattern uses multiple-winding type linear bearingless motor configuration, shown in Figure 3-9. In this winding configuration, two sets of multi-phase windings are configured in the same stator, as shown in Figure 3-9. Here the windings (𝐴, 𝐵, 𝐶) shown with large circles are the motor windings, and the windings (𝑢, 𝑣, 𝑤) shown with small circles are the torque control windings. The wavelength of the torque control winding magneto-motive force is twice of that of the motor winding. The same phase in each set of winding are connected in series, and there are in total six independent currents in this stator. The bottom plot in Figure 3-

9 shows the air-gap fluxes generated by the two sets of windings. Here the blue lines show the motor flux, the red lines show the torque control flux. The forces and torques generated by this stator is briefly discussed below. The total normal force 𝐹𝑧 and

total shear force 𝐹𝑦 can be controlled via the amplitude and phase, or 𝑑- and 𝑞-axis,

of the motor winding excitation. The torque about 𝑥-axis can be controlled by the interaction between the motor flux and the torque control flux. For example, for flux distribution in Figure 3-9, the torque control flux intensifies the fluxes in the yellow region, and attenuates the flux in the blue region, which generates controlling torque about the 𝑥-axis in Figure 3-9. This design resembles the winding pattern of rotary bearingless motors with multiple windings [63], where the suspension flux steers the motor air-gap flux in a rotating frame for torque generation. Note that this winding pattern can only be applied for those linear motors operating in synchronous mode and has a relatively large 𝑑-axis flux, for example linear reluctance motors and linear hysteresis motors. In these circumstances, the interaction between the 𝑞-axis motor flux and the torque control flux has small amplitudes, and therefore the generated disturbance forces and torque can be rejected by feedback control.

With such stator designs, there exists several stage configurations to implement motion and active suspension in all degrees of freedom. Figure 3-10 shows several example configurations. Among these configurations, design concept 1 shown in Fig- ure 3-7 allows a simple design for the separating channel between the stator and the stage, and allows a mechanically stiff stage design, which is favorable for our target application.

Group I: Design Concept 2

Figure 3-11 shows a linear stage design concept uses a combination of regular linear motors and flux steering magnetic bearings. Here, two stage secondaries are config- ured on the two wings of the moving stage. Four regular linear motor stators are configured on both top and bottom of the moving stage, interfacing with the stage secondaries. The stator’s winding uses regular three-phase winding. The winding of the top and bottom stators can be connected to reduce the number of independent

(a)

(b)

Figure 3-10: Alternative configurations of stage design concept 1 with all-DOFs ac- tively controlled.

Figure 3-11: Design concept 2: magnetically-levitated linear stage with regular linear motors and flux steering magnetic bearings.

currents. These stators generate motor fluxes shown by the red lines in Figure 3-11, which interact with the stage secondaries and thereby generates thrust force in 𝑦- direction. The normal forces generated by the motor fluxes are largely canceled out by top and bottom motors when the stage is centered.

In addition to the motor stators, two rows of magnetic bearings with E-shaped cores are configured on the two sides of the moving stage, as shown in Figure 3-11. Each magnetic bearing has two coils wrapping around the top and bottom arms of the E-shaped core, as shown by coil A and coil B in Figure 3-11. The current in each coil is independently controlled. There are two kinds of magnetic fluxes generated by the E-shaped magnetic bearing. The common-code current in coil A and coil B generates lateral control flux, as shown by the blue flux lines in Figure 3-11. This flux generates normal forces on the left and right edges of the moving stage, which can control the 𝑥-directional suspension of the moving stage. With at least two magnetic bearings configured along the moving stage, the 𝜃𝑧-directional magnetic suspension can also

be controlled. This flux will also flow across the motor air gaps, however it does not generate net force to the stage when the stage secondary is centered vertically. In addition, the differential current in coil A and coil B generates vertical control flux, as shown by the green flux lines in Figure 3-11. This flux steers the motor flux and vertical control flux to generate vertical control force on the moving stage. For example, in Figure 3-11, the vertical control fluxes intensify the motor fluxes in the top air gaps, and weaken the motor fluxes in the bottom air gaps, thereby generates vertical suspension force pointing upwards, which can be used to compensate the weight of the stage, and to control its 𝑧- and 𝜃𝑦-directional suspension. With multiple

E-shaped magnetic bearings interfacing with the moving stage simultaneously, the stage’s suspension in 𝜃𝑥-direction can also be actively controlled. As a result, this

stage configuration is able to actively control all degrees of freedom of the moving stage.

The stage design concept 2 shown in Figure 3-11 presents a relatively simple stage design, and here the suspension of the stage in different degrees of freedom are largely decoupled, which allows a simple control design. The main drawback of this stage is that its vertical suspension force relies on a non-zero motor flux. As a result, the currents in the motor windings cannot be zero even when no motion is required. This fact makes the stage less efficient in power consumption when carrying the gravity load.

z y x Coil B Coil A Motor flux phase A Suspension flux Air gap 1 Air gap 2

Figure 3-12: Design concept 1: magnetically-levitated linear stage with connected C-shaped core stator design.