6. E-Machine Design
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6. E-Machine Design
A high-speed E-machine is responsible for the kinetic and electric energy conversion in a flywheel system. It is used as a motor for the charge of the flywheel and as a generator for the discharge. The basic requirements for electric machines in flywheels are:
- High robustness;
- High efficiency;
- No cooling problems for the rotor.
A permanent magnet (PM) machine is chosen in our design based on the comparison in Table 1-6 for the commonly used E-machines in the flywheel systems. The reluctance machine is not considered in our design, due to the low power factor for synchronous reluctance machine (SynRM) and the high torque ripple for the switching reluctance machine (SRM). The induction machine has high robustness with high efficiency. The drawback is high rotor losses. As our system operates in vacuum, the high rotor losses in the induction machine lead to high rotor temperature without effective cooling, which is not acceptable. Compared to reluctance machine and induction machine, PM machine has low rotor losses, high power density and high efficiency. Therefore, it is used in our system. A proper design is required dealing with the typical downsides of the PM ma-chine: the rotor mechanical strength, the rotor losses and the demagnetization problems, etc.
6.1 E-machine Design Overview
Design Specifications and Operating Characteristics
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According to the specifications, the operating characteristics of the machine is defined in Fig. 6-1. The E-machine should provide a constant power PN in the speed range of nmin … nmax. The power is positive if the machine operates as a motor and negative as a generator. Two operating points OP1 and OP2 are defined for the operations at nmin and nmax, respectively. As the induced voltage increases in proportional to speed, terminal voltage reaches the limit of the inverter Us,max at nmax. Therefore, for the operation be-tween nmin and nmax, the flux is weakened by applying negative current in d-axis. The torque Mmax decreases for increasing speed, while the power is constant. For the speed lower than nmin, the machine operates with constant torque.
Table 6-1 E-machine design specifications
Parameters Symbol Value Unit
Maximum speed nmax 24000 min-1
Minimum speed nmin 12000 min-1
Nominal output voltage (r.m.s.) of inverter UAC 396 V Max. phase voltage (r.m.s., Y connection) Us, max 228.6 V
Inverter switching frequency fT 12 kHz
Rated output power (motor) PN 28 kW
Max. current (r.m.s.) Imax 50 A
Operation duty type Continuous duty
0 n
P
Motor nmax
Generator
0 nmin
OP1 OP2
U, M
Us,max
Mmax
PN
Fig. 6-1 Operating characteristics of the E-machine, PN = 28 kW, nmin = 12000 min-1, nmax = 24000 min-1, Us, max: max. terminal voltage, M: torque
E-machine Preview 6.1.2
The proposed design is a 4-pole PM machine with surface mounted rotor magnets, shown in Fig. 6-2. The main parameters are shown in Table 6-2. The detailed design parameters can be found in Chapter 6.2.
6. E-Machine Design
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Fig. 6-2 Section view of the E-machine geometry, 1/2 model in JMAG (with surface mounted magnets and bandage)
Table 6-2 E-machine main dimensions and design parameters
Parameter Symbol Value
Stator inner diameter dsi 130 mm
Stator outer diameter dso 190 mm
Shaft diameter dsh 90 mm
Iron stack length LFe 90 mm
Air gap length 1 mm
Bandage thickness hB 3 mm
Magnet dimension lmbmhm 22.5 mm×4.9 mm×3.2 mm Segmentation per pole cmzm 18 (circumferential)×4 (axial)
Air gap flux density B,1 0.45 T
Thermal loading A J 2181 A/cm·A/mm2
Material
Bandage Carbon fiber HTS5631+epoxy resin Magnet VACOMAX 225 (Sm2Co17)
Iron sheet NO 20
Cooling Water cooled with jacket on the stator outer surface Main critical considerations for the machine design are as follows:
1) Rotor mechanical strength
The magnets are glued on the surface of a laminated rotor iron package and fixed with a carbon fiber bandage on the outer surface. Compared to interior PM machine with magnets buried in the rotor iron, this configuration is more endurable for high velocity.
The potential failure is the bandage damage due to high tensile stress in circumferential direction. Even though carbon fiber bandage has very high tensile strength (2615 MPa for the used material HTS5631+epoxy resin), a big safety factor (>3) should be re-served as the strength will decrease for high temperatures. A temperature of 141 °C should not be exceeded for safe operation. Chapter 6.5 presents the detailed stress cal-culation in the bandage.
Rotor bandage
Stator iron Stator winding Segmented
magnets Rotor iron
Shaft
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2) Rotor losses and thermal limit in vacuum
The magnets are segmented in both radial and axial direction to reduce eddy current losses, which are the dominant heat sources on the rotor. As the rotor operates in vacu-um, the heat is dissipated by radiation, which relies on the emissivity of the surface ma-terial and the surface area. A rough estimation of the rotor temperature in vacuum is necessary in order to determine the permissible rotor losses for the given temperature limit of 141 °C.
A rough thermal calculation is done by assuming a homogeneous rotor located in an enclosed containment as shown in Fig. 6-3.
Fig. 6-3 Simplified rotor contour for a rough calculation of the rotor radiative heat transfer
The emissivity of the containment inner surface is assumed to be s = 0.95, which is the value for a black-painted surface. A constant temperature of 60 °C is assumed for the containment. This is also reasonable for a water cooled stator based on the thermal analysis in Chapter 9. According to the calculation in Chapter 9, the rotor steady state temperature is almost homogeneous distributed. A rotor temperature r and emissivity
r are assumed on the rotor surface. The radiative heat transfer from the rotor to the stator is calculated by
4 4
r s
rad
r s
r r r sr s s
1
1 1
(T T ) P
A A F A
,
(6-1)
where the subscript s denotes the stator inner surface, r denotes the rotor outer surface.
Fsr is the facing factor depending on the position of the two surfaces. Fsr = 1 for a body in an enclosed containment. A is the surface area, T is the absolute temperature (in K) on the surface (The corresponding celsius temperature is denoted by in °C), σ is Stef-an-Boltzmann constant, σ = 5.67×10−8 W/(m2 ∙ K4), and is the surface emissivity.
Ø260
Ø80
160
600
Ø80
6. E-Machine Design
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Fig. 6-4 shows the temperatures for different emissivity r on the rotor surface. If an emissivity r = 0.242 is assumed for a grinded steel rotor surface [49], at the tempera-ture of 141 °C, the radiative heat transfer of 86 W can be calculated from (6-1). That means the rotor losses should be no higher than 86 W to obtain a rotor temperature lower than 141 °C. An efficient radiative heat transfer can be realized by an increased emissivity, e.g. on a black-painted rotor surface.
Fig. 6-4 Calculated rotor radiative heat transfer versus rotor temperatures for different rotor surface emissivity r, calculated for an enclosed stator with constant temperature
s = 60 °C and emissivity s = 0.95 on the inner surface.
3) Efficiency and loss calculation
Loss calculation is important concerning efficiency and thermal performance. The loss calculation (in Chapter 6.3) is performed in numerical program JMAG, taking the addi-tional losses due to inverter feeding into account.
4) Demagnetization
The irreversible demagnetization of the magnets should be always avoided for safety, even when failure occurs in the inverter. The demagnetizing performance of the ma-chine is analyzed in Chapter 6.4.3 in case of a three phase short circuit, which is regard-ed as the most dangerous failure. The usregard-ed magnet material is VACOMAX 225 (Sm2Co17). With an almost linear demagnetizing curve, it has a good anti-demagnetizing performance, even at a high temperature of 300 °C.
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