Design and Voltage Supply of High-Speed Induction - Aaltodoc

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82 Stator core of AMB Rotor Fig. 7.1 A picture of a 2D FEM model to approximate the end ring inductance. The inductances given by the 2D FEM were about four times bigger than calculated from Eq. 7.3 for the rotor constructions compared in Chapter 5. The model is not accurate but increasing the value of the inductance from the values given by Foelsch’s method can be justified. Using a higher value for the end ring inductance decreases the possibility of overestimating the motor characteristics. This is one example showing that for an accurate modeling a true 3D FEM should be used. 7.2 Modeling of the flux fringing in the air gap Stator end winding End rind Half of a stator core The flux fringing in the air gap is another problem for a 2D FEM model. The model assumes that there are no axial flux components, if the 2D plane is set as a cross section of the motor. In reality the flux fringes, especially at the air gap region. Thus the modeled flux density needed to calculate the electromagnetic torque is incorrect. Also, the magnetizing current goes wrong because of the incorrect air gap reluctance. Usually, this problem is solved by calculating an effective core length. The length of the motor is increased so that the average flux density is correct. The filling factors of core parts are decreased so that the flux density in the iron stays as it is. Often, such a rule of thumb is used so that the length of the motor is increased with the value of the air gap at the each end of the core (Richter 1951). For example, a stator core of 100 mm with an air
gap of 1 mm would yield an effective length of 102 mm. More accurate solutions are discussed in the literature. Flack and Knight (2000) discuss several methods that can be used to model the radial ventilation ducts for large induction motors, from Carter’s correction factor approach to full 3D models. The results were interesting as they pointed out that an analytical equation based on Carter’s correction factor could yield almost the same results as a 3D FEM. In the high-speed motors considered in this study, the flux fringing effect is strong. This is because the motors are relatively short compared to the air gap. For the copper coated rotor, this is especially important, as the iron-to-iron air gap is even larger. This was seen in Table 2.3. In addition, the use of a radial cooling duct in the stator doubles the flux fringing regions. Usually, the effective length is calculated so that the average flux density of the fringed flux, normal to the stator and rotor surface, corresponds to the constant flux density in the region where the flux has only the normal component: l eff ( B n) ∫ ⋅ dl 3D = Bdl l ∫ 2D 2D , (7.4) where n is the unit vector normal to the integration path. This definition for the effective length should give a good estimation for an air gap permeance and the magnetization reactance. Estimation of torque per slip characteristic is important for solid steel rotors. A low slip operation is needed in order to avoid extensive saturation and iron loss in the rotor. The problem in the calculation of effective length is that the magnetization reluctance and the torque cannot be correct at the same time. The air gap torque depends on the square of the flux density (Arkkio 1987): l Te = rBrBϕ dS , (7.5) 0 ( ) ∫ eff r − r s r Sag where µ0 is the permeability of vacuum and rs and rr are outer and inner radii of the air gap, respectively. Br and Bϕ are radial and tangential components of magnetic flux density, respectively. The linear averaging gives values which are too large for leff. If a more accurate estimation for the air gap torque is needed, the effective length has to be calculated as proportional to the average of the square of the flux density: l eff = 3D ( B n) ∫ ⋅ ∫ 2D B 2 2 dl dl l 2D 83 (7.6)
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El 108 ACTA POLYTECHNICA SCANDINAVI
Page 3 and 4:
PREFACE This thesis is the result o
Page 5 and 6:
5 Comparison of rotors for 60 kW 60
Page 7 and 8:
LIST OF SYMBOLS a Number of paralle
Page 9 and 10:
Rn Resistance of a parallel conduct
Page 11 and 12:
1 INTRODUCTION The need for high ro
Page 13 and 14:
Conventional (high-speed) drive Hig
Page 15 and 16:
Chapter 5 reports the comparison of
Page 17 and 18:
Some penetration depth values are c
Page 19 and 20:
2.2 Stator windings for high-speeds
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⎛ π ⎞ sin⎜ν ⎟ ⎛ π ⎞
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Table 2.3 Air gap characteristics o
Page 25 and 26:
Cooling of the stator could need ax
Page 27 and 28:
f sw N p = (2.9) fs The switching f
Page 29 and 30:
3 ROTOR CONSTRUCTIONS Starting from
Page 31 and 32: and eddy-currents traveling on the
Page 33 and 34: support the squirrel cage winding,
Page 35 and 36: 3.1.3 Rotor loss and friction loss
Page 37 and 38: Table 3.1 High-speed induction moto
Page 39 and 40: critical speeds are passed relative
Page 41 and 42: Table 3.2 The free-free natural fre
Page 43 and 44: Table 3.3 The free-free natural fre
Page 45 and 46: 4 COMPARISON OF ROTORS FOR 65 KW 30
Page 47 and 48: Temperature [ºC] 110 109 108 107 1
Page 49 and 50: Temperature rise [K] 120 100 80 60
Page 51 and 52: improve the laminated design, more
Page 53 and 54: The copper coated solid steel rotor
Page 55 and 56: As reported in Lähteenmäki et al.
Page 57 and 58: Temperature rise [K] 100 80 60 40 2
Page 61 and 62: 6. The rest of the loss is defined
Page 63 and 64: Temperature rise [K] 100 80 60 40 2
Page 65 and 66: 5.2.7 About the mechanical robustne
Page 67 and 68: 6.1 Comparison of PAM and PWM for 6
Page 69 and 70: h d = , (6.2) I I h, PAM where Ih,P
Page 71 and 72: Fig. 6.4 Phase-to-phase voltage and
Page 75 and 76: Machines loss [W] 12000 10000 8000
Page 77 and 78: considerably higher than expected.
Page 79 and 80: In order to improve the performance
Page 81: l = + , (7.2) sλs 2leλ e l wλ w
Page 85 and 86: Table 7.1 Calculated effective leng
Page 87 and 88: Input current [A] 170 160 150 140 1
Page 89 and 90: 8 CIRCULATORY CURRENTS IN A STATOR
Page 91 and 92: Table 8.1 Circulatory current loss
Page 93 and 94: Fig. 8.4 Strand currents in the two
Page 95 and 96: 8.2 Impedance of the circulatory cu
Page 97 and 98: Because Φ l is approximately at th
Page 99 and 100: Table 8.2 Circulatory current loss
Page 101 and 102: Power loss [W] 3500 3000 2500 2000
Page 103 and 104: k cc 600 500 400 300 200 100 0 0 50
Page 105 and 106: 9 OPTIMIZATION OF SOLID STEEL ROTOR
Page 107 and 108: whole solution space determined by
Page 109 and 110: the average time saving is 39 %. Th
Page 111 and 112: Fig. 9.3 Cross sections of the 16,
Page 113 and 114: Height of bar slot [mm] 8 6 4 2 0 R
Page 115 and 116: The different rotor topologies were
Page 117 and 118: possible. The coating practically v
Page 119 and 120: Table 9.3. Optimization results for
Page 121 and 122: Fig. 9.11 Initial (left) and opt. (
Page 123 and 124: high-speed induction machine. Accor
Page 125 and 126: Foelsch K. 1936. Magnetfeld und Ind
Page 127 and 128: Pyrhönen J. and Kurronen P. 1994.
Page 129 and 130: APPENDIX 129
Page 131 and 132: currents in the solid iron flow mor
Page 133 and 134:
where the C sw E is the loss coeffi
Page 135 and 136:
B. CALCULATION OF THERMAL CHARACTER
Page 137 and 138:
Axial cooling duct Frame R fr3 Stat
Page 139 and 140:
Linear equalities Ax = b, (C3) wher
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