MAGNETIC BEARING ASSEMBLY

Abstract

A radial magnetic bearing assembly having an unsymmetrical stator. The assembly comprises fewer or smaller electromagnets, and thus capacity, in the two lower quadrants below the rotor in use, in comparison to the electromagnets, and thus capacity, in the two upper quadrants above the rotor in use. This creates space in the two lower quadrants that can advantageously be used to move for example instrumentation and cooling from other places of the assembly to make the bearing assembly compacter, and also to be able to put instrumentation and cooling where it is best needed, close to the rotor.

Claims

1. A radial magnetic bearing comprising: a rotor; and a stator, wherein the bearing is divided into four quadrants, two upper quadrants located above the rotor in a direction that is opposite to a direction of gravity when in use and two lower quadrants located below the rotor in the direction of gravity towards the earth when in use, the extension of the rotor being substantially perpendicular to the direction of gravity when in use, the stator comprising electromagnets in the two upper quadrants, the electromagnets in the two upper quadrants having a joint stator capacity larger than the gravity load of the rotor at the bearing, wherein static gravity is used as a static capacity in the two lower quadrants, wherein a joint stator capacity in the two lower quadrants is less than the joint stator capacity in the two upper quadrants, thereby making an area of the stator used by electromagnets in the two lower quadrants plus an available area along the stator without electromagnets in the two lower quadrants, substantially the same size as an area of the stator used by electromagnets in the two upper quadrants.

2. The radial magnetic bearing according to claim 1, wherein the joint stator capacity in the upper quadrants minus the gravity load of the rotor at the bearing, is greater than the joint stator capacity in the two lower quadrants, excluding the static capacity.

3. The radial magnetic bearing according to claim 1, wherein the stator comprises electromagnets in the two lower quadrants, and in that the joint stator capacity in the two lower quadrants due to the electromagnets is less than 50% of the joint stator capacity in the two upper quadrants due to the electromagnets in the two lower quadrants.

4. The radial magnetic bearing according to claim 3, wherein the joint stator capacity in the two lower quadrants due to the electromagnets equals approximately 30% of the joint stator capacity in the two upper quadrants due to electromagnets.

5. The radial magnetic bearing according to claim 1, wherein the bearing only comprises electromagnets in the two upper quadrants, the bearing being exclusive of any electromagnets in the two lower quadrants, wherein the bearing is only using the static capacity for the two lower quadrants, resulting in configuration where the available area along the stator in the two lower quadrants is substantially the same size as the area of the stator used by electromagnets in the two upper quadrants.

6. The radial magnetic bearing according to claim 1, each of the two upper quadrants further comprising at least two independent circuits of electromagnets, wherein the two circuits are fed by one individual current power amplifier, wherein the power amplifiers delivering the same current for each of the independent circuits of electromagnets of a same quadrant.

7. The radial magnetic bearing according to claim 6, the two upper quadrants further comprising two or more power amplifiers per quadrant, each power amplifier feeding one independent circuit of electromagnets, thereby decreasing the inductance seen by each power amplifier to increase at least one of (a) a dynamic capability and (b) a power amplifier failure tolerance of the bearing.

8. The radial magnetic bearing according to claim 1, wherein the available area in the two lower quadrants is at least in part used for instrumentation.

9. The radial magnetic bearing according to claim 8, the instrumentation further comprising at least one of: (a) a position sensor, (b) a vibration sensor, (c) a rotor temperature sensor, and (d) a speed sensor.

10. The radial magnetic bearing according to claim 1, wherein the available area in the two lower quadrants is at least in part used to place at least one auxiliary landing bearing.

11. The radial magnetic bearing according to claim 1, wherein the available area in the two lower quadrants is at least in part used to place a mechanical support in case of failure of the magnetic bearing.

12. The radial magnetic bearing according to claim 1, wherein the available area in the two lower quadrants is at least in part used to place a cooling system for the rotor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The invention will now be described in more detail for explanatory, and in no sense limiting, purposes, with reference to the following figures, in which:

[0020] FIG. 1 presents a cross section elevation view of a magnetic bearing, wherein the section is taken across a rotor of the magnetic bearing;

[0021] FIG. 2 presents a cross section elevation view of the magnetic bearing originally introduced in FIG. 1, wherein the section is taken along the rotor of the magnetic bearing;

[0022] FIG. 3 presents a basic principle of the invention by a cross section of a first embodiment of a radial magnetic bearing according to the invention, across the rotor of the magnetic bearing;

[0023] FIG. 4 presents an example of a use of space created around a stator of a radial magnetic bearing according to the first embodiment of the invention, at, for example, a first location along the rotor axis;

[0024] FIG. 5 presents an example of a use of space created around the stator of the radial magnetic bearing according to the first embodiment of the invention, at for example a second location along the rotor axis;

[0025] FIG. 6 presents a cross section of the radial magnetic bearing according to FIGS. 4 and 5, wherein the section is taken along the rotor of the magnetic bearing;

[0026] FIG. 7 presents an example of the invention by a cross section of a second embodiment of a radial magnetic bearing according to the invention, wherein the section is taken across the rotor of the magnetic bearing; and

[0027] FIG. 8 presents an example of the invention by a cross section of a third embodiment of a radial magnetic bearing according to the invention, wherein the section is taken across the rotor of the magnetic bearing.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

[0028] In order to clarify the method and device according to the invention, some examples of its use will now be described in connection with FIGS. 1 to 8.

[0029] FIG. 1 illustrates a cross section across a rotational axis of a radial magnetic bearing 100 with a rotor 102 and a stator 110. The stator is divided into four quadrants 112, 114, 116, 118, including two upper quadrants 112, 114 that are located above the rotor 102 in a direction that is opposite to a direction of gravity 130 when in use and two lower quadrants 116, 118 that are located below the rotor 102 in the direction of gravity (towards the earth) when in use. Each quadrant 112, 114, 116, 118 comprises electromagnets 122, 124, 142, 144, 162, 164, 182, 184, here illustrated as two in each quadrant 112, 114, 116, 118, that are controlled by at least one power amplifier 125, 145, 165, 185 per quadrant 112, 114, 116, 118.

[0030] The vertical static gravity load 190 at the radial magnetic bearing is W, each upper quadrant then needs to deliver a force of W/2 192, 194 so that the vertical force 190 is equal to W (vertical projection of two 45 axes) just to keep the rotor in equilibrium.

[0031] FIG. 2 illustrates a side cross section along a rotational axis of a radial magnetic bearing according to FIG. 1, rotor 202, stator 210 and electromagnets 222, 282. Also illustrated here are the sensors 252, 254, 256 and auxiliary bearing(s) 270 that are needed. As can be seen in FIG. 2 (not to scale), the extension along its axis of rotation is quite large and with that the disadvantages it brings of having both the sensors and auxiliary bearing(s) along the shaft. For example, the position of the shaft where the position sensors measure the position is not necessarily the same position of the rotor within the bearing.

[0032] FIG. 3 illustrates a basic principle of the invention by a cross section of a first embodiment of a radial magnetic bearing according to the invention, across its rotor. Here it can be seen that the stator is unsymmetrical with regard to the electro magnets 322, 324, 342, 344, 363, 383, there being fewer, or smaller or less powerful electro magnets in the two lower quadrants 316, 318 in comparison to the two upper quadrants 312, 314. This is made possible by taking into account gravity as a permanent force of the magnetic bearing.

[0033] The standard rule of design for a magnetic bearing machine is to have a four quadrant radial bearing with a load capacity equal to at least 2 times, commonly 3 times for super-critical machine, the weight of the rotor at the magnetic bearing. The possibility of the invention of using gravity as a permanent force will in this example be described for a 3 times ratio.

[0034] We assume that the vertical gravity load at the radial bearing is W 390. Each quadrant is designed to be able to deliver a maximum force (capacity of the magnetic bearing) of 3*W/2 so that the maximum vertical force is equal to 3 W (vertical projection of two 45 axes). In this configuration, each of the upper quadrants 312, 314 can deliver at its maximum a force of 3*W/2. Each upper quadrant is loaded with a gravity force of W/2 392, 394. The maximum dynamic force (usable force) that each upper quadrant is able to produce is 3*W/2W/2=2 W/2. The maximum force that must be delivered by each of the upper quadrants is the gravity force plus the needed maximum dynamic force. On the other hand the two lower quadrants 316, 318 only need to deliver a maximum force equal to the needed maximum dynamic force minus the gravity force. The required maximum force of each upper quadrant is then W/2+2 W/2=3 W/2 and the required maximum force of each lower quadrant is then (W/22 W/2)=W/2. That is to say that each of the two lower quadrants need electro magnets 363, 383 with a maximum force that is three times smaller than the maximum force of the electro magnets 322, 324, 342, 344 of each of the two upper quadrants. As the maximum force of a magnetic bearing is roughly given by its stator surface, the magnetic pole area of each of the lower quadrants can be one third of the magnetic pole area of each of the upper quadrants. Thus only 30 373, 375 of each of the bottom quadrants is needed for magnetic pole area, leaving a total of 120 372, 374, 376 in the two lower quadrants 316, 318 for other use.

[0035] As can be seen by the calculations mentioned above, this embodiment according to the invention illustrated in FIG. 3 does not jeopardize the static capacity of the system or its dynamic capacity, it can always create the same static force and the same modulation.

[0036] The only restriction of the invention is that the stator is not symmetrical and thus has to be positioned such that when in use the upper quadrants are on the upper side and thus the lower quadrants are on the bottom side of the rotor of the magnetic bearing. When in use the quadrants of the magnetic bearing have to located such that the directional vector of gravity goes between/divides the two upper quadrants and likewise between/divides the two lower quadrants.

[0037] The advantages given by this new configuration are significant, space that is not needed for the electro magnets can advantageously be used to place position sensors, auxiliary bearing(s), speed sensor(s), cooling and more. Even the use of an IR rotor temperature probe looking at the rotor becomes possible and allows measuring the temperature at the hottest part of the magnetic bearing (see for examples FIGS. 5 and 6).

[0038] FIG. 4 illustrates an example of a use of space created around a stator of a radial magnetic bearing according to the first embodiment of the invention, at for example a first location along its rotor axis. In this example, three coolers 457, 458, 459 are added in the available spaces in the two lower quadrants. It is a great benefit of this invention to enable efficient cooling of the rotor directly where the rotor losses are created.

[0039] To be able to efficiently cool a rotor directly is particularly advantageous when the rotor is running at a critical speed. In situations like this the damping synchronous force created by the magnetic bearing is at the same angular location of the rotor, creating uneven losses and subsequently uneven temperature distribution around the rotor that may create thermal unbalance. When an efficient cooling is directly applied on the rotor, thermal unbalances can be avoided or at least reduced. This is particularly advantageous when the rotor laminations are, for corrosion aspect, made of stainless steel like AISI 444 or 17-4PH. These materials have a large magnetic hysteresis cycle and the losses are very high compared with standard lamination (made of iron silicon). The application of direct cooling on the rotor lamination significantly eases the cooling efficiency. The cooling system can either be gas injection or liquid injection or any kind of cooling flow.

[0040] FIG. 5 illustrates a further example of a use of space created around a stator of a radial magnetic bearing according to the first embodiment of the invention, at for example a second location along its rotor axis. In this example, several sensors 554, 556 and auxiliary bearings 575, 576, 577 are using space in the two lower quadrants that is not being used by electro magnets of the two lower quadrants.

[0041] It can be noted that position sensors can now be placed at the force center of the bearing avoiding the non-co-location of the bearing with its position sensor, significantly easing the magnetic bearing controller design. As mentioned, use of IR rotor temperature probe looking at the rotor becomes possible and allows measuring temperature at the hottest part of the magnetic bearing, and not along a shaft.

[0042] By placing auxiliary bearings here enables giving support to the rotor/shaft when the magnetic bearing is turned off or defective at the same place along the rotor as when the magnetic bearing is active.

[0043] FIG. 6 illustrates a cross section of a radial magnetic bearing according to FIGS. 4 and 5, along its rotor. FIGS. 4, 5 and 6 represent a possible arrangement of utilizing available space around the stator of a radial magnetic bearing according to the invention.

[0044] In a further example, in case the required bearing capacity is only 2 times or less than the weight of the gravity load, the electro magnets of the two lower quadrants can be completely removed, potentially creating 180 of available space. In this case, the power amplifiers from the two lower quadrants can be used in parallel for the electro magnets of the two upper quadrants, increasing the bearing bandwidth. Each of the upper quadrants can advantageously even have more than two power amplifiers. Alternatively, the power amplifiers of the two lower quadrants can be removed/not used, thus using only one power amplifier per quadrant.

[0045] To get a better understanding how this is possible, we go slightly back and again reference FIG. 1, where a standard configuration of a radial magnetic bearing is shown. For the best dynamic capacity it is common in such a standard configuration to work in class A configuration, that is to say that a bias current equal to half of the maximum current is used and facing quadrants are working in push-pull configuration, the first quadrant 112 and the third quadrant 116, and also the second quadrant 114 and the fourth quadrant 118.

[0046] If we only consider one 45 axis (for example the first quadrant 112 and the third quadrant 116) the force F of a magnetic bearing is quadratic versus the current I and for a given geometry, we can write F=KI.sup.2. We divide this up into the individual quadrants and have: [0047] F1 is the force delivered by the upper quadrant. [0048] F2 is the force delivered by the lower quadrant. [0049] I1 is the current flowing in the electromagnets of the upper quadrant. [0050] I2 is the current flowing in the electromagnets of the lower quadrant. [0051] IM is the maximum current the power amplifiers are able to deliver. [0052] FM is the maximum force delivered by a quadrant with a current IM. [0053] U is the feeding voltage of the power amplifiers. [0054] We can calculate K as FM=K*IM.sup.2, K=FM/IM.sup.2 [0055] Working around a bias current equal to half the maximum current, for a current variation of that cannot exceed IM/2 (otherwise maximum current of the amplifier is reached)

F1=K*(IM/2+).sup.2

F2=K*(IM/2).sup.2

F1F2=4*K*IM/2*=2*K*IM*=2*FM/IM* [0056] And when =IM/2, the maximum force is obtained. [0057] Under normal operation, the bearing is loaded by the gravity and F1F2=W/2 and we can write

F1F2=W/2=2*FM/IM*=2*(2*W)/IM* [0058] Gives =IM/4 and I1=3*IM/4=0.75*IM [0059] The remaining available current is therefore IM/2IM/4=IM/4 that corresponds to the remaining available force (2*WW/2)=W/2

[0060] The electromagnets of a quadrant has an inductance value of Lc, the current modulation will create a voltage across this inductance that must not exceed the feeding voltage U. Therefore the maximum frequency up to which the remaining force can be modulated can be written:

fa=1/2*U/(Lc*IM/4)

[0061] Note that due to the class A configuration, if the force is sinusoidal, the current is sinusoidal.

[0062] Now with reference to FIG. 7, in a class B configuration according to the invention in a further embodiment, with one power amplifier 725, 745 and corresponding electromagnets 722, 724, 742, 744 in each upper quadrant 712, 714, and nothing in the two lower quadrants 716, 718. This gives a total of 180 degrees of available space, both lower quadrants.

[0063] Having nothing in the two lower quadrants we get:

F1=K*(I1).sup.2=FM/IM.sup.2*(I1).sup.2 [0064] F2 does not exist.

[0065] Under normal operation, each upper quadrant of the bearing is loaded by gravity and then F1 needs to be F1=W/2 and we thus get:

FM/IM.sup.2*(I1).sup.2=((2*W)/IM.sup.2)*(I1).sup.2=W2

and I1=IM/2=0.7*IM

[0066] The remaining available force is always the same (2*WW/2)=W/2, but to modulate this remaining force, the current is not anymore sinusoidal and will go up to full current then down to zero, approaching a square wave. The maximum voltage across the inductance is then driven by the above calculated I1. Therefore the maximum frequency up to which the remaining force can be modulated can be written:

fb=1/2*U/(Lc*IM/2)

[0067] To compare both frequencies,

fb/fa={1/2*U/(Lc*IM/2)}/{1/2*U/(Lc*IM/4)}=1/22=0.35

[0068] FIG. 8 illustrates an example of the invention by a cross section of a still further embodiment of a radial magnetic bearing according to the invention, across its rotor. In the embodiment the radial magnetic bearing is in a class B configuration, with two power amplifiers 885, 825, 845, 865 per upper quadrant, and nothing in the lower quadrants. In this case, the power amplifiers from the two lower quadrants can be used in parallel for the electromagnets 822, 824, 842, 844 of the two upper quadrants, increasing the bearing bandwidth.

[0069] The same calculation applies but as the magnetic circuit is shared in two identical parts and each of the power amplifiers is seeing an inductance Lb half of the class A inductance Lc.

[0070] To compare both frequencies,

fc/fa={1/2*U/(Lc*IM/22)}/{1/2*U/(Lc*IM/4)}=1/2=0.7

[0071] Each of the upper quadrants can advantageously have even more than two power amplifiers per upper quadrant. For example if the concept is extended to 3 power amplifiers per upper quadrant the inductance each power amplifier sees would be Lc/3.

[0072] Dynamic calculations have been done on a 46 MW compressor, running 4200 rpm in super critical conditions. The aim is to have the maximum margin versus API 617 (American Petroleum Institute standard dealing with Axial and Centrifugal Compressor and Expander-compressor for Petroleum, Chemical and Gas Industry Services) regulation that requests to be able to handle at least 2 (new revision) to 4 times (old revision) the API unbalance. Most of the time and as for this example, the force requested by the bearing is less than the gravity load and the proposed configuration according to the invention is even further beneficial.

[0073] Under one time API unbalance, (API 617) it has been calculated that the maximum force to modulate at 4200 rpm was 1750 N. To compare the benefit between all configurations, the maximum number of time API unbalance the bearing can handle before reaching the saturation voltage (300V) of the power amplifiers is tabulated.

[0074] The B class with 4 amplifiers (2 per quadrant) as per FIG. 8 is able to handle 23% more unbalance than the A class with 4 amplifiers as per FIG. 1.

TABLE-US-00001 Class B Class B2 Class A (2 amps) (4 amps) (4 amps) N API 4.32 8.07 6.50 Rotor mass 9500 9500 9500 kg Bearing inductance 0.264 0.264 0.264 H API unbalance force 1750 1750 1750 N MCS 4200 4200 4200 rpm Fmax 65899 65899 65899 N Imax 30 30 30 A Fbal 7560 14123 11375 N Static load 32949 32949 32949 N I1 nominal 21.2 21.2 22.5 A I1 max under unbalance 23.5 25.4 25.1 A I1 min under unbalance 18.6 16.0 10.1 A Quadratic sum of current (no 900 900 1125 A.sup.2 unbalance) Nampli/Quadrant 1 2 1 Total number of amplifiers 2 4 4 Calculated voltage 300 300 300 V

[0075] We can see that the best configuration is given by the proposed arrangement according to FIG. 8 with an unbalance margin increase by 24%

[0076] There is also an improvement in losses. Rotor losses are barely proportional to the forces applied around the bearing by the four quadrants, i.e. to the quadratic sum of the currents; we can see a reduction of the rotor losses by 25%. The stator losses are mainly ohmic losses. They are also proportional to the square of the current per quadrant. There is therefore also a benefit of 25%. In addition, manufacturing costs are reduced as there are fewer electromagnets needed and there might be no need to install stator lamination.

[0077] All embodiments according to the invention have a number of advantages over traditional radial magnetic bearings by the space made available in the two lower quadrants. The free space given by the removed parts of the bearing may be used for other purpose like cooling, draining, junction boxes installation, interconnection location, easy access for inspection, sensors and more, improving the compactness and the maintainability of the magnetic bearing.

[0078] The invention is based on the basic inventive idea of taking into account gravity as a permanent force that is usable for magnetic bearings, thus being able to create a more compact magnetic bearing including sensors and auxiliary bearing(s). The invention is not restricted to the above-described embodiments, but may be varied within the scope of the following claims.

[0079] FIG. 1 illustrates a cross section of a magnetic bearing, across its rotor: [0080] 100 Radial magnetic bearing [0081] 102 Rotor [0082] 110 Stator [0083] 112 First quadrant, an Upper quadrant, [0084] 114 Second quadrant an Upper quadrant, [0085] 116 Third quadrant a Lower quadrant, [0086] 118 Fourth quadrant a Lower quadrant, [0087] 122 First electromagnet of the first quadrant [0088] 124 Second electromagnet of the first quadrant [0089] 125 Power amplifier [0090] 130 Direction of gravity [0091] 142 First electromagnet of the second quadrant [0092] 144 Second electromagnet of the second quadrant [0093] 145 Power amplifier [0094] 162 First electromagnet of the third quadrant [0095] 164 Second electromagnet of the third quadrant [0096] 165 Power amplifier [0097] 182 First electromagnet of the fourth quadrant [0098] 184 Second electromagnet of the fourth quadrant [0099] 185 Power amplifier [0100] 190 W, vertical static gravity load of the rotor at the radial magnetic bearing [0101] 192 W/2 force needed from first quadrant so that the upper quadrants total equal W [0102] 194 W/2 force needed from second quadrant so that the upper quadrants total equal W

[0103] FIG. 2 illustrates a cross section of a magnetic bearing according to FIG. 1, along its rotor: [0104] 202 Rotor [0105] 210 Stator [0106] 222 Electromagnet of an upper quadrant [0107] 252 Position sensor [0108] 254 Position sensor [0109] 256 Sensor [0110] 270 Auxiliary bearing [0111] 282 Electromagnet of a lower quadrant

[0112] FIG. 3 illustrates a basic principle of the invention by a cross section of a first embodiment of a radial magnetic bearing according to the invention, across its rotor: [0113] 312 First quadrant, Upper quadrant [0114] 314 Second quadrant, Upper quadrant [0115] 316 Third quadrant, Lower quadrant [0116] 318 Fourth quadrant, Lower quadrant [0117] 322 First electromagnet of the first quadrant [0118] 324 Second electromagnet of the first quadrant [0119] 325 Power amplifier [0120] 342 First electromagnet of the second quadrant, [0121] 344 Second electromagnet of the second quadrant, [0122] 345 Power amplifier [0123] 363 Electromagnet of the third quadrant [0124] 365 Power amplifier [0125] 370 A 90 degree sector, a full quadrant, [0126] 372 A 30 degree available sector of the third quadrant [0127] 373 A 30 degree sector used by the electromagnet of the third quadrant [0128] 374 A 60 degree available sector in part in both the third and the fourth quadrants [0129] 375 A 30 degree sector used by the electromagnet of the fourth quadrant [0130] 376 A 30 degree available sector of the fourth quadrant [0131] 383 Electromagnet of the fourth quadrant [0132] 385 Power amplifier [0133] 390 W, vertical static gravity load of the rotor at the radial magnetic bearing [0134] 392 W/2 force needed from first quadrant so that the upper quadrants total equal W [0135] 394 W/2 force needed from second quadrant so that the upper quadrants total equal W

[0136] FIG. 4 illustrates an example of a use of space created around a stator of a radial magnetic bearing according to the first embodiment of the invention, at for example a first location along its rotor axis: [0137] 457 First cooler [0138] 458 Second cooler [0139] 459 Third cooler

[0140] FIG. 5 illustrates an example of a use of space created around a stator of a radial magnetic bearing according to the first embodiment of the invention, at for example a second location along its rotor axis: [0141] 554 First sensor [0142] 556 Second sensor [0143] 575 First mini auxiliary bearing [0144] 576 Second mini auxiliary bearing [0145] 577 Third mini auxiliary bearing

[0146] FIG. 6 illustrates a cross section of a radial magnetic bearing according to FIGS. 4 and 5, along its rotor: [0147] 603 Rotor/Shaft [0148] 611 Stator [0149] 622 Electromagnet of an upper quadrant [0150] 652 Sensor/Cooler/ . . . [0151] 676 One mini auxiliary bearing

[0152] FIG. 7 illustrates an example of the invention by a cross section of a second embodiment of a radial magnetic bearing according to the invention, across its rotor: [0153] 712 First quadrant, an upper quadrant [0154] 714 Second quadrant, an upper quadrant [0155] 716 Third quadrant, a lower quadrant [0156] 718 Fourth quadrant, a lower quadrant, [0157] 722 First electromagnet of the first quadrant [0158] 724 Second electromagnet of the first quadrant [0159] 725 Power amplifier for the first and second electromagnet of the first quadrant [0160] 742 First electromagnet of the second quadrant [0161] 744 Second electromagnet of the second quadrant [0162] 745 Power amplifier for the first and second electromagnet of the second quadrant

[0163] FIG. 8 illustrates an example of the invention by a cross section of a third embodiment of a radial magnetic bearing according to the invention, across its rotor: [0164] 822 First electromagnet of the first quadrant [0165] 824 Second electromagnet of the first quadrant [0166] 825 Power amplifier for the second electromagnet of the first quadrant [0167] 842 First electromagnet of the second quadrant [0168] 844 Second electromagnet of the second quadrant [0169] 845 Power amplifier for the first electromagnet of the second quadrant [0170] 865 Power amplifier for the second electromagnet of the second quadrant [0171] 885 Power amplifier for the first electromagnet of the first quadrant.