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Fig. 7-26 Calculated rotor iron losses in the radial magnetic bearing due to the sinusoi-dal current feeding in the control coil (current frequency f and rotational speed n fulfill:
f = n, with n in s-1), neglecting the biased field excited by the magnets, calculated by 2D model in JMAG (The displayed lines correlate to different amplitudes of the applied
control current.)
Additional Losses due to PWM Control
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Fig. 7-27 Scheme of the modeled voltage source inverter to feed one coil of the magnet-ic bearing, UDC: DC link voltage, R and L: resistance and inductance of the control coil,
S1~S4: switches
a) b)
c)
Fig. 7-28 Calculated waveforms and harmonics in the x coils of the inverter-fed com-bined magnetic bearing, rotational speed 24000 min-1, switching frequencyfT 16 kHz:
a) modulated voltage, b) current (fundamental amplitude ˆI1 8 03 A. , frequency
s 400 Hz
f ), c) harmonics of the current (fundamental not shown) UDC
R L
S1 S2
S3 S4
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Table 7-9 Calculated main harmonic components of the current in Fig. 7-28 c), switch-ing frequency fT 16 kHz, fundamental frequency fs 400 Hz
Rotational speed: 24000 min-1
Frequency [Hz] Current [A] Phase angle [°]
fs 400 8.03 -93.23
T 2 s
f f 15200 0.057 -167.91
fT 16000 0.216 0.056
T 2 s
f f 16800 0.0516 168.03
T s
2 f 3 f 30800 0.0176 108.08
T s
2 f f 31600 0.0423 -83.97
T s
2 f f 32400 0.0413 -96.02
T s
2 f 3 f 33200 0.0164 71.97
7.4.4.2 Additional Copper Losses
The additional copper losses are calculated analytically by using the formulas in Chapter 6.3.2. The coils in the radial actuator are wound around each pole with the pole and slot shape shown in Fig. 7-29. To simplify the calculation, the coils are assumed to lo-cate in a rectangular-shape slot as shown in Fig. 7-29. The flux leakage in the assumed rectangular-shape slot is supposed to be higher than in the real slot. Therefore, the addi-tional losses will be over-estimated, which is as the worst case.
Fig. 7-29 Section view of the radial actuator of the magnetic bearings, modeled in JMAG x coil
y coil
x y z
Conductors in a slot
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There are 60 turns of wires in each coil, which are series connected. According to the designed slot geometry in the actuator, their arrangements are shown in Fig. 7-29. 6 wires locate in the parallel direction of the slot bottom and 10 wires locate in the verti-cal direction of the slot bottom. As all the wires are series connected, no circulating cur-rent will occur. Therefore, the additional losses are only due to the skin and proximity effect.
The calculated results are shown in Table 7-10 for the rotor speed of 24000 min-1, con-sidering the current with the harmonics in Table 7-9. Compared to the DC resistive loss-es, which considers a pure sinusoidal current feeding in a DC resistance, the current harmonics and the skin and proximity effect cause 0.4 % higher additional losses, which is very small.
Table 7-10 Calculated copper losses in the coils of the radial actuator of the combined magnetic bearing, for the current harmonics in Table 7-9 (winding resistance
Rs = 0.807 at temperature = 60 °C) Rotational
speed n
Fundamental
current ˆI1 DC resistive losses PCu,DC,1
AC resistive losses PCu,AC,k
PCu,AC,k/ PCu,DC,1
24000 min-1 8.03 A 52.06 W 56.24 W 1.004
n: rotor speed,
ˆI1: amplitude of the fundamental current,
PCu,DC,1: DC resistive losses caused by fundamental current,
PCu,AC,k: sum of the AC resistive losses considering the skin and proximity effect for the current harmonics in Table 7-9.
7.4.4.3 Additional Iron Losses
The iron losses are calculated numerically in the 2D model in JMAG (Fig. 7-11, without biased field). Instead of feeding a sinusoidal control current, the current with the har-monics in Table 7-9 is fed in the control coils. The calculated iron losses are shown in Table 7-11. The result shows that the current harmonics cause 1.94 times higher iron losses in the rotor and 1.77 times higher losses in the stator of the combined magnetic bearing. As the radial magnetic bearing has a similar structure as the radial actuator in the combined bearing, and the field distribution of both magnetic bearings are compa-rable, these ratios are also suitable when estimating the additional iron losses in the radial magnetic bearing.
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Table 7-11 Calculated iron losses in the combined magnetic bearing, calculated in the 2D planer model in JMAG shown in Fig. 7-11
Rotational speed: n = 24000 min-1
Sinusoidal: feeding a sinusoidal current with the amplitude ˆI1= 8.03 A PWM: feeding the currents in Table 7-9
Sinusoidal PWM Ratio: PWM/Sinusoidal
Rotor iron 4.44 W 8.63 W 1.94
Stator iron 16.12 W 28.6 W 1.77
7.5 Dummy Set-up
To verify the levitation force of the magnetic bearings, a prototype containing the mag-netic bearings and a shaft was built. The configuration is shown in Fig. 7-30. The elec-tric machine and mechanical bearing are not mounted. The prototype and components are shown in Fig. 7-31. To load the magnetic bearings, an additional weight was hung on the shaft in order to achieve the same weight as the designed flywheel rotor.
The testing was only carried out for a static levitation, i.e. the rotor is not rotating. The testing shows that the rotor weight of 90 kg (900N) can be suspended by the magnetic bearings, but only in one axial direction. This is the case, when the prototype Fig. 7-30 is vertical positioned with the B-side on the top. If the rotor is flipped, it cannot be levi-tated. That indicates a significant asymmetric biased field of the axial magnetic bearing that can preferably produce force only in one direction. This asymmetric effect is even larger than the simulated results in Chapter 7.3.
Fig. 7-30 Configuration of the prototype for the magnetic bearing testing under atmos-pheric pressure, including a shaft and radial magnetic bearing (A-side) and a combined
magnetic bearing (B-side) without mechanical bearings or an E-machine [47]
Radial magnetic bearing Combined magnetic bearing
A B
Axial position sensor
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a) b) c)
d)
Fig. 7-31 Dummy prototype for magnetic bearing testing:
a) prototype, b) radial magnetic bearing stator (A-side), c) combined magnetic bearing stator (B-side), d) dummy rotor showing shaft and magnetic bearing rotor components A-side
B-side
B A
Additional mass
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8. Flywheel System Set-up
8.1 System Construction
The system was constructed and set up in the Institute for Electrical Energy Conversion (Institut für Elektrische Energiewandlung, EW), TU Darmstadt. The system overview without burst containment is shown in Fig. 8-1.
Fig. 8-1 Constructed flywheel system without burst containment [47] (Autodesk Inventor 2018): 1-safety bearing (top), 2-top lid, 3-radial magnetic bearing, 4-upper housing, 5-E-machine stator, 6-flywheel rotor, 7-middle housing, 8-combined magnetic bearing, 9-bottom housing, 10-safety bearing (9-bottom), 11-axial position sensor, 12-revolusion
sensor, 13-bottom plate
8. Flywheel System Set-up
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