ISEF 2007 - XIII International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Prague, Czech Republic, September 13-15, 2007
Squirrel-Cage Induction Motor with Intercalated Rotor Slots of Different Geometries V. Fireţeanu POLITEHNICA University of Bucharest, EPM_NM Lab., Bucharest, Romania
[email protected] Abstract – This paper deals with a particular design of squirrel-cage rotor slots and copper bars of high power induction motors able to ensure high values of both starting torque and breakdown torque. The innovation consists in a rotor with two different geometries of slots, respectively of bars cross-section shape. Along the rotor periphery, bars with cross-section of rectangular shape are followed by bars of stepped shape cross-section and vice-versa
Introduction A good design of classical induction motors with respect to the electromagnetic torque must answer two contradictory requirements, respectively high value of starting torque and high value of breakdown torque. In case of squirrel-cage induction motors, these characteristics are very dependent on the rotor slot geometry [1], [2]. Starting from the results presented in the reference [3] this paper studies a new configuration of the squirrel cage able to realize a good compromise between a high value of motor starting torque and a high value of breakdown torque. A three-phase squirrel-cage induction motor with rated power Pn = 500 kW, synchronous speed 750 rpm, supplied at 6 kV, 50 Hz is studied. Two shapes in Figure 1 of the rotor bars cross-section, rectangular shape and respectively stepped shape are considered. Independently of the value of h2/a2 and h1/h2 parameters, the rotor bars have the same cross-section area.
Simulation Results Analysis Starting torque, breakdown torque and energetic parameters
a)
b)
Fig. 1. Slot geometries and different shapes of rotor bars cross-section a) rectangular shape; b) stepped shape
In case of rectangular shape of bar cross-sections, Fig. 1a, the increase of ratio h2/a2 between the bars height and thickness ensures the increase of per unit starting torque (Mp/Mn), Fig. 2, and the decrease of per unit breakdown torque (Mmax/Mn).
Fig. 2. Starting torque (Mp/Mn) and breakdown torque (Mmax/Mn) versus ratio h2/a2
The two electromagnetic torque – slip characteristics (M-s) in Fig. 3, correspond to the lower (h2/a2)min and upper (h2/a2)max values which characterize the rectangular bars crosssection geometry, Fig. 1a, considered in this study. These values correspond to an almost square bar, with a2 = 15 mm and h2 = 14.92 mm, respectively, a deep rectangular bar, with a2 = 4 mm and h2 = 55.93 mm. In case of stepped shape bars, Fig. 1b, the height h1 of the upper bar step is the parameter of bar cross-section geometry and h2 is the total height of the stepped bar. The upper step of the bar has the thickness, a1 = 3 mm and the lower step has square Fig. 3. Electromagnetic torque versus slip for rectangular bars shape. The dependence of starting torque Mp on the ratio (h1/h2) in Fig. 4 relieves an optimal shape of stepped bars for the value (h1/h2)opt = 18/31.03 = = 0.58. After this value, both starting torque and breakdown torque decrease.
Fig. 4. Starting torque (Mp/Mn) and breakdown torque (Mmax/Mn versus (hl/h2) for stepped shape bars
The (M-s) characteristics in Fig. 5 correspond to the minimum value (h1/h2)min = 10/23.92 = 0.418 and to the optimal value (h1/h2)opt . The comparison of these curves with those in Fig. 3 shows the following: - if the almost square shape bars, with the ratio (h2/a2)min = 14.92/15 = 0.994 are replaced with bars of stepped shape crosssection with (hl/h2)min = 10/23.92 = 0.418, the starting torque increases with 58.4 % and to the breakdown torque diminishes with 41.3 %; - if the deep rectangular bars with (h2/a2)max = 55.92/4 =13.98 are replaced with stepped bars of optimal cross-section, with Fig. 5. Electromagnetic torque versus slip for (hl/h2)opt = 0.58, the starting torque increases stepped shape bars with 32.6 % and the breakdown torque increases also with 9.2 %. Both starting torque and breakdown torque increase when changing the deep rectangular shape bars with optimal stepped shape bars. The high value of the starting torque in Fig. 5, corresponding to the ratio (h1/h2)opt = 18/31.03 = = 0.58 in case of stepped shape bars, and the high value of breakdown torque corresponding to the value (h2/a2)min = 14.92/15 in case of rectangular bars, suggest the idea of an innovative squirrel-cage, where the (h1/h2)opt Fig. 6 Squirrel-cage rotor with intercalated bars bars are intercalated with (h2/a2)min bars. It results the rotor geometry in Fig. 6, called squirrel-cage with intercalated slots of different geometries. The (M-s) characteristic for the new rotor geometry in Fig. 7 and the values of starting and breakdown electromagnetic torques, Table 1, reflect a compromise between high values of starting torque, which can be obtained with stepped shape bars – green colour in Figs. 6 and 7, and high values of breakdown torque that characterise the rectangular bars of almost square shape – magneta colour in the same figures. In case of the new rotor with intercalated bars the starting torque increases with 91.6 % and the breakdown torque decreasees with only 21.6 % with Fig. 7. Electromagnetic torque versus slip for respect the rotor variant with almost intercalated rotor bars square bars ((h2/a2)min). In comparison
with with rotor variant with stepped bars with (h1/h2)opt , the starting torque of the new rotor variant decreases with 26.6 % but the breakdown torque increases with 45.3 %. As waited, the starting current, the rotor Joule losses and the motor energetic parameters efficiency and power factor, Table 1, have values between those obtained when all rotor slots have only one of the two geometries in Fig. 6. Table 1. Motor characteristics Rotor bars geometry Mmax/Mn Ip/In Pj2/Pn Mp/Mn Rectangular bars with (h2/a2)min 0.545 2.958 6.101 1.164 Stepped bars with (h1/h2)opt 1.423 1.597 4.187 1.278 Intercalated bars : rectangular bars (h2/a2)min + 1.044 2.320 5.167 1.216 stepped bars(h1/h2)opt
Fig. 8. Magnetic field lines for motor rated load operation: rotor with intercalated bars, rectangular bars (h2/a2)min + stepped bars(h1/h2)opt
η [%] 95.43 95.15
cosϕ 0.859 0.804
95.30
0.833
The magnetic field lines for rated load operation of the motor with intercalated bars and the chart of current density in rotor bars at motor start-up are presented in Fig. 8, respectively Fig. 9. For rated load operation, the Joule effect generates 0.704 kW in each rectangular bar and 0.783 kW in each stepped shape bar of the new rotor variant. When the rotor contains only rectangular bars with (h2/a2)min , this power is 0.745 kW/bar and when the rotor contains only stepped
bars with (h1/h2)opt , 0.749 kW/bar. For motor start-up, the Joule power is 5.85 kW in each rectangular bar and 11.09 kW in each stepped shape bar of the new rotor variant. When the rotor contains only rectangular bars with (h2/a2)min this power is 4.93 kW/bar and when the rotor contains only stepped bars with (h1/h2)opt , this power is 12.7 kW/bar. Time variation and harmonics of electromagnetic torque at rated load
Fig. 9. Chart of current density in rotor bars for motor start-up: intercalated bars, rectangular bars (h2/a2)min + stepped bars(h1/h2)opt
The time variation of electromagnetic torque for rated load operation of the new motor with intercalated bars is presented in Fig. 10, where the numerical values corresponds to the half on the motor, which was considered for the electromagnetic field computation domain. The mean electromagnetic torque
of the motor, Fig. 10 a), has the value 3247.24 x 2 = = 6494.5 Nm. The most important harmonics of the electromagnetic torque, Fig. 10 b), with amplitudes of around 30 Nm have the frequency 300 Hz and respectively 700 Hz.
a)
b)
Fig. 10. Time variation and harmonics of the electromagnetic torque at motor rated load
Transient time variation of motor velocity The three curves in Fig. 11 ilustrate the transient variation of velocity for motor no-load start in cases : rotor with rectangular bars with (h2/a2)min , rotor with stepped bars with (h1/h2)opt and the new rotor with intercalated bars. The time of motor start in 6.30 seconds in the first case, 5.08 seconds in the second case and 5.18 seconds in the third case.
Rotor with rectangular bars with (h2/a2)min
Rotor with stepped bars with (h1/h2)opt
Fig. 11. Transient time variation of velocity at motor start-up
New rotor with intercalated bars
The three curves in Fig. 12 show the transient variation of velocity when double of rated load is applied after no-load start of the motor in three previously defined cases. Since in the second case stepped bars with (h1/h2)opt , the breakdown torque is not high enough, when apply a charge double with respect rated one, the motor is not able to reach a new steady state operation regime, with a lower value of the rotor speed that hapens in the first and the third case of rotor bar cross-section geometry.
Rotor with rectangular bars with (h2/a2)min
Rotor with stepped bars with (h1/h2)opt
Fig. 12. Transient time variation of velocity at motor start-up
New rotor with intercalated bars
References [1] M. Brojboiu, Concerning the influence of the rotor bar geometry on the induction motor performances, Proc. of 5th TELSIKS’01 International Conference, Sept. 2001. [2] J. L. Kirtley Jr., Designing Squirrel Cage Rotor Slots with High Conductivity, Proc. of ICEM’04 Conference, Sept. 2004. [3] O.A. Turcanu, T. Tudorache, V. Fireteanu., Influence of Squirrel-Cage Bar Cross-Section Geometry on Induction Motor Performances, Proc. of SPEEDAM’06, May 2006. [4] V. Fireteanu, T. Tudorache, O.A. Turcanu, Optimal Design of Rotor Slot Geometry of Squirrel-Cage Type Induction Motors, Proc. of IEMDC’06 Conferrence, May 2007.
