Recent Developments of Electrical Drives - Part 30 docx

II-12. Field-Circuit Finite Elements Models 283 0 0,2 0,4 0,6 0,8 1 1,2 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 current [A] calculated A1e s1t + A2e s2t A1e s1t A2e s2t measured time [s] Figure 16. Decomposition of measured current curve vs. time into exponential components for DC voltage 23.82 V. 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 0 0,04 0,08 0,12 0,16 0,2 0,24 current [A] calculated A1e s1t + A2e s2t A1e s1t A2e s2t measured time [s] Figure 17. Decomposition of measured current curve vs. time into exponential components for DC voltage 32.49 V. 0 1 2 3 4 5 6 7 8 0 0,03 0,06 0,09 0,12 0,15 0,18 time [s] measured polynomial A2e s2t calculated polynomial + A2e s2t current [A] Figure 18. Decomposition of measured current curve vs. time into exponential components for DC voltage 138 V. 284 Kom ˛ eza et al. Table 3. Values of solution coefficients obtained from measured curves DC supply Steady-state U s (V) current (A) A 1 (A) A 1 /U s () −s 1 (1/s) A 2 (A) A 2 /U s () −s 2 (1/s) 13.41 0.58 0.18 0.0134 18.3 0.4481 0.0334 335.9 23.31 1.01 0.34 0.0146 22.4 0.7883 0.0338 385.3 32.49 1.48 0.515 0.0159 13.3 1.1 0.0339 341.2 138.01 6.18 4.8 0.0348 422.0 In Fig. 21 the relative permeability curves vs. time is shown: a—average for both stator and rotor core, b—average for one tooth pitch. The average value changes significantly and the permeability distribution is also different. The second important reason for the observed effect is a very well known skin effect in the rotor bars. As can be expected the current density distribution in the rotor bar changes consider- ably during the time (Fig. 22). The resulting value of equivalent rotor bar resistance and inductance changes too (Figs. 23–25). It should be emphasized that all described changes occur during the initial period when the stator current is compensated by rotor current. The main flux and magnetizing current do not grow as they occur in the final period when stator current goes to a constant value Figure 19. Relative permeability for time 0.005 s. II-12. Field-Circuit Finite Elements Models 285 Figure 20. Relative permeability for time 0.01 s. and rotor current disappears. According to these results, it should be clear why constant parameter equivalent circuits, sometimes used especially by Matlab Simulink users, are not usable for transient simulation of induction machines. Therefore noticeable growth of scientific reports according to adjustable parameters can be observed. 0 20000 40000 60000 80000 100000 120000 0 0,002 0,004 0,006 0,008 0,01 time [s] b a relative permeability Figure 21. The relative permeability curves vs. time. (a) Average for both stator and rotor core. (b) Average for one tooth pitch. 286 Kom ˛ eza et al. 0,0E+0 4,0E+6 8,0E+6 1,2E+7 1,6E+7 2,0E+7 0 0,002 0,004 0,006 0,008 0,01 0,012 0,01 0,005 0,004 0,003 0,002 0,001 0,0001 current density [A/m 2 ] height [m] 0,0005 Figure 22. Current density distributions vs. bar height at different time instants for DC voltage equal 138 V. 0,0E+0 5,0E-5 1,0E-4 1,5E-4 2,0E-4 2,5E-4 3,0E-4 0 0,002 0,004 0,006 0,008 0,01 resistance [ Ω] time [s] Figure 23. Equivalent resistance of the rotor bar vs. time. 0,0E+0 1,0E-7 2,0E-7 3,0E-7 4,0E-7 5,0E-7 6,0E-7 0 0,002 0,004 0,006 0,008 0,01 inductance [H] time [s] Figure 24. Equivalent inductance of the rotor bar vs. time. II-12. Field-Circuit Finite Elements Models 287 0 100 200 300 400 500 600 700 0 0,02 0,04 0,06 0,08 time [s] bar current [A] Figure 25. Rotor bar current vs. time for DC supply voltage 138 V. Starting test with sinusoidal supplying voltages The examination of the motor characteristics during starting is the most important method for comparisonofthe field-circuitdynamic model ofthe motor withthe measurements. This test makes possible to compare all electromechanical quantities with the measurement. The solution of the mechanical transient equation due to moment of inertia value is not very sensible to torque higher frequency components. Therefore the speed vs. time curves, calculated using different methods, are very similar to the measuredone. A similar situation can be observed for the current because of a significant value of magnetization current and the stator windings impedance. The most important is of course the torque characteristic vs. time (Figs. 26–28). Conclusion The presented paper has shown methods that can be used to verify the validity of the created field-circuit model for simulating transients occurring during the starting of the induction -100 100 300 500 700 900 1100 1300 1500 1700 0 0,02 0,04 0,06 0,08 0,1 0,12 time [s] measured calculated rotor speed [rpm] Figure 26. Rotor speed vs. time during starting. 288 Kom ˛ eza et al. -8 -6 -4 -2 0 2 4 6 8 10 0 0,04 0,06 0,08 0,1 0,12 current [A] time [s] measured calculated 0,02 Figure 27. Current vs. time during starting. -2 0 2 4 6 8 10 12 0 0,02 0,04 0,06 0,08 0,1 0,12 t s calculated measured time [s] torque [Nm] Figure 28. Torque vs. time during starting. motor feed from an inverter. After verification this model can be successfully used for the analysis and optimization of the induction motor feed from an inverter. References [1] M. Dems, K. Kom ˛ eza, “Circuit and Field-Circuit Analysis of Induction Motor with Power Controller Supply”, International XIII Symposium Microdrives and Servomotors, MIS’2002, Krasiczyn, Poland, September 15–19, 2002, Tom II, Vol. 2, pp. 453–458. [2] M. Dems, K. Kom ˛ eza, Electromechanical transient processes of the induction motor with power controller supply, Electromotion, Vol. 10, No. 1, pp. 19–25, 2003. [3] M. Dems,K. Kom ˛ eza, “Simulationsof ElectromagneticField Distribution in anInduction Mo- tor withPower Controller Supply”, Proceedingsof theXXII InternationalAutumn Colloquium ASIS 2000. [4] K. Kom ˛ eza, M. Dems, “The Comparison of the Starting Characteristics of an Induction Motor for Frequency and Soft Starter Starting”, Proceedings of the 8thPortuguese-Spanish Congress on Electrical Engineering, Portugal, July 3–5, 2003. II-12. Field-Circuit Finite Elements Models 289 [5] M. Dems, K. Kom ˛ eza, “A Comparison of Circuit and Field-Circuit Models of Electromechan- ical Transient Processes of the Induction Motor with Power Controller Supply”, Proceedings COMPUMAG’2001, Lyon-Evian, France, July 2–5, 2001, pp. 206–207. [6] PC OPERA-2D—version 10.5,Software forElectromagneticDesign from VECTORFIELDS, 2005. [7] S. Wiak,K. Kom ˛ eza, M. Dems,“Electromagnetic Fieldand Parameters Modelling ofInduction Motors by Means of FEM”, Proceedings 32 Spring. International Conference MOSIS’98, Ostrava, Czech Republic, May 5–7, 1998, Vol. 3, pp. 275–281. [8] M. Dems, K. Kom ˛ eza, Influence of mathematical model simplifications on dynamic calcula- tions ofinduction motors,Zeszyty Naukowe Politechniki L  ´odzkiej, Elektryka, wrzesie´n, L ´od´z, 2005. [9] M. Dems, J. Zadro˙zny, J. Zadro˙zny Jr., “Comparison of Simulation Methods of Small Induc- tion Motor Electromechanical Transients”, International XII Symposium Micromachines and Servodrives, MIS’2000, Kamie´n ´ Sl c aski, Poland, September, 2000. [10] K. Kom ˛ eza, M. Dems, S. Wiak, Analysis of the influence of the assumption of equivalent saturation on starting currents in induction motor, COMPEL Int. J. Comput. Math. Electr. Electron. Eng., Vol. 19, No. 2, pp. 463–468, 2000. III-1.1. DESIGN AND MANUFACTURING OF STEEL-CORED PERMANENT MAGNET LINEAR SYNCHRONOUS MOTOR FOR LARGE THRUST FORCE AND HIGH SPEED Ho-Yong Choi 1 , Sang-Yong Jung 2 and Hyun-Kyo Jung 1 1 Electromechanics Labratory, School of Electrical Engineering, Seoul National University, Korea Shillim-Dong, Kwanak-Gu, Seoul, Korea 2 Namyang R&D Center, Hyundai Motor Company, Hwasung-Si, Kyunggi-Do 445-706, Korea plate@elecmech.snu.ac.kr Abstract. Design characteristics of steel-cored PMLSM (Permanent Magnet Linear Synchronous Motor) are presented. Particularly, dynamic constraints resulted from repeated short-stroke travel are applied to the design criteria determining the machine specification. In addition, distinctive unde- sirable feature of detent force in steel-cored PMLSM and its notable minimizing methods based on manufacturing feasibility are considered. The designed machine is manufactured and tested for the verification. Introduction In thesedays, linearmachine is widely usedin industrial fieldbecause of itsbetter character- istics,such ashighaccelerationandspeed,largethrustforce,andsoon.Torealizesufficiently large thrust force and power density, steel-cored permanent magnet linear synchronous mo- tor is superior to air-cored motor. However, steel-cored motor has some demerits such as large normal force and force ripples caused by the high detent force. The normal force problem can be overcome by the LM (Linear-Motion) guide or the bearing system and the detent force reduction method should be considered during the machine design procedure. The magnetic saturation from large operation currents for the high speed operation can be a problem and proper steel-core design is also required [1,2]. Many linear applications require high acceleration and velocity with the short-stroke movement. In such applications, general design strategies considering the steady-state con- dition are not agreeable because linear motor operates mostly under the accelerating or decelerating circumstances on short travel displacements [3]. In addition, since the servo- capability responding to various motional profiles is recently regarded to be necessary, new plans considering dynamic constraints under the maximum input voltage and current should be made for better efficiency in machine sizing. Generally, capability of steel-cored S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 295–306. C  2006 Springer. 296 Choi et al. PMLSM is defined by maximum input voltage and current, which expresses the maximum thrust force accordingto thespecified mover velocity [4].Thiscapability, directly connected to a motor size, must be at least larger than the required motional profiles. Accordingly, dy- namic constraints can be induced from arelation between such different dynamic capability and required motional profiles under the limited input voltage and current. These dynamic constraints express the admissible design range from which the design variables meeting the required trajectory can be obtained after all [5–7]. In this paper, steel-cored permanent magnet linear synchronous motor for large thrust force and high speed operation is designed and tested. The required maximum thrust force of the motor is 15,000 N and the maximum speed is 4 m/s. The continuous thrust force is 3,000 N under input voltage of 220 V and maximum peak current of 300 A. Finite element analysisis appliedin themachine designprocedure andsome optimizationmethod isusedto minimize the detent force problem. The machine is manufactured and tested forverification of the designed model’s validity. Design of steel-cored PMLSM Steel-cored PMLSM Fig. 1 shows the moving-coil type steel-cored PMLSM with the magnetic combination of four poles and three coils which shows better operation in control. Self-bonded wires are much convenient to be attached to the core simply with a voltage of 5 to 6 V or thermal heating. Hall-sensors and incremental encoders are used for feedback control system, and Cable-Veyor, LM guide, and Shock-Absorber must be equipped. In addition, steel-cored Figure 1. Steel-cored PMLSM (moving coils, four poles + three coils). III-1.1. Design and Manufacturing of Steel-Cored PMLSM 297 PMLSM has been much advanced from coreless one, and getting widely used mainly due to its large force productivity. Capability and required motional profile PMLSM with limited input voltage (V max ) and current (I max ) has dynamic capability as follows, which is induced with commands as i d = 0 (force maximization). F e,max = 3 2 K e min  C 1 + √ C 2 −C 3 R 2 s + (π/τ) 2 L 2 s v 2 , I max  , (1) where, C 1 ≡−R s  K e v +  2L s 3K e  m da dt + Ba  , C 2 ≡   π τ  2 L 2 s v 2 + R 2 s  V 2 max , C 3 ≡  π τ  2 L 2 s v 2  K e v +  2L s 3K e  m da dt + Ba  2 , τ :Pole pitch [m], K e : EMF constant [V/(m/sec)] R s :Resistance [], L s : Synchronous Inductance [H] Equation (1) indicates the maximum thrust force at specified velocity under the max- imum input voltage and current, and also includes the time-varying component, such as acceleration (a) and jerk (J = da/dt), available in dynamic analysis. Proposed dynamic capability has more meaning in linear machine than the conventional static capability under the acceleration and jerk set to be zero, which has been conventional approaches to the design process until now. In Fig. 2, motional profiles of trapezoidal acceleration mode, most common in actual operation, andits relevantForce-Speed curveare shown. Force-Speed characteristics, which are obtained at each time interval, can be summarized as follows. F e (v) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ m  2a max t 1 v + Bv + F l (0 <v≤ v 1 ) ma max + Bv + F l (v 1 <v≤ v 2 ) m  2a max (v max − v) t 1 + Bv + F l (v 2 <v≤ v max ) (2) where, v 1 = (a max /2)t 1 ,v 2 = a max (t 1 /2 + t 2 ) Figure 2. Motional profiles of trapezoidal acceleration and Force-Speed curve. . V. 0,0E+0 5,0E-5 1,0E-4 1,5E-4 2,0E-4 2,5E-4 3,0E-4 0 0,002 0,004 0,006 0,008 0,01 resistance [ Ω] time [s] Figure 23. Equivalent resistance of the rotor bar vs. time. 0,0E+0 1,0E-7 2,0E-7 3,0E-7 4,0E-7 5,0E-7 6,0E-7 0. efficiency in machine sizing. Generally, capability of steel-cored S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 295 306 . C  2006 Springer. 296 Choi et al. PMLSM. Labratory, School of Electrical Engineering, Seoul National University, Korea Shillim-Dong, Kwanak-Gu, Seoul, Korea 2 Namyang R&D Center, Hyundai Motor Company, Hwasung-Si, Kyunggi-Do 44 5-7 06, Korea plate@elecmech.snu.ac.kr Abstract.