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1 International Journal of Scientific Innovations and Sustainable Development, Volume 6, Number 1, 216 CONSTRUCTIONAL FEATURES AND PERFORMANCE ANALYSIS OF 3-PHASE LINEAR INDUCTION MOTOR Okpo, Ekom Enefiok and Nkan, Imo Edwin Department of Electrical and Electronic Engineering, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria ABSTRACT A Linear Induction Motor LIM commonly used in propulsion has attracted much attention compared with the rotating induction machine drive system. The constructional features and principle of operation of LIM were reviewed. The LIM performance in rail system and other applications were studied as well. Forces of LIM, equivalent circuit, thrust and efficiency have direct bearing with the performance of LIM. MATLAB User Interactive Program was used to evaluate the LIM parameters to obtain the best design parameters. Certain factors like aluminum thickness and number of poles in LIM were varied, plotted and analyzed. The best performance parameters, measured in terms of thrust and efficiency, were selected. Keywords: Linear Induction Motor [LIM], Single-Sided Linear Induction Motor [SLIM], Double-Sided Linear Induction Motor [DLIM], Alternating Current [AC], Finite Element [FE], Levitation INTRODUCTION A linear induction motor (LIM) is an alternating current (AC), asynchronous linear motor that works by the same general principles as other induction motor but is typically designed to directly produce motion in a straight line[7]. Characteristically, linear induction motors have a finite primary or secondary length, which generates end-effects, whereas a conventional induction motor is arranged in an endless loop. Despite their name, not all linear induction motors produce linear motion; some linear induction motors are employed for generating rotations of large diameters where the use of a continuous primary would be very expensive. They also, unlike their rotary counterparts, can give a levitation effect. As with rotary motors, linear motors frequently run on a three-phase power supply and can support very high speeds. However, there are end-effects that reduce the motor's force, and it is often not possible to fit a gearbox to trade off force and speed. Linear induction motors are thus frequently less energy efficient than normal rotary motors for any given required force output. LIMs are often used where contactless force is required, where low maintenance is desirable, or where the duty cycle is low. Their practical uses include magnetic levitation, linear propulsion, and linear actuators. They have also been used for pumping liquid metals [1]. The history of linear electric motors can be traced back at least as far as the 184s to the work of Charles Wheatstone at King s College in London [6], but Wheatstone's model was too inefficient to be practical. A feasible linear induction motor is described in US patent (195; inventor Alfred Zehden of Frankfurt-am-Main), and is for driving trains or lifts. German engineer Hermann Kemper built a working model in In the late 194s, professor Eric Laithwaite of Imperial College in London developed the first full-size working model [1]. CONSTRUCTION A linear electric motor's primary typically consists of a flat magnetic core (generally laminated) with transverse slots that are often straight cut with coils laid into the slots, with each phase giving an alternating polarity so that the different phases physically overlap. The secondary is frequently a sheet of aluminium, often with an iron backing plate. Some LIMs are double sided with one primary on each side of the secondary, and, in this case, no iron backing is needed. Two types of linear motor exist: a short primary, where the coils are truncated shorter than the secondary, and a short secondary, where the conductive plate is smaller. Short secondary LIMs are often wound as parallel connections between coils of the same phase, whereas short primaries are usually wound in series. The primaries of transverse flux LIMs have a series of twin poles lying transversely side-by-side with opposite winding directions. These poles are typically made either with a suitably cut laminated backing plate or a series of transverse U-cores. [1] Correspondence Author: Okpo, Ekom Enefiok okpoekom@yahoo.com 176

2 Constructional Features and Performance Analysis of 3-Phase Linear Induction Motor PRINCIPLES OF OPERATION The principle of operation of a LIM is the same as that of a rotary induction motor. A linear Induction motor is basically obtained by opening the rotating squirrel cage induction motor and laying it flat. This flat structure produces a linear force instead of producing rotary torque from a cylindrical machine. LIMs can be designed to produce thrust up to several thousands of Newtons. The winding design and supply frequency determine the speed of a LIM.[7] The basic principle of LIM operation is similar to that of a conventional rotating squirrel-cage induction motor. Stator and rotor are the two main parts of the conventional three phase rotary induction motor. The stator consists of a balanced polyphase winding which is uniformly placed in the stator slots along its periphery. The stator produces a sinusoidally distributed magnetic field in the air-gap rotating at the uniform speed 2ω/p, with ω representing the network pulsation (related to the frequency f by ω= 2πf) and p the number of poles. The relative motion between the rotor conductors and the magnetic field induces a voltage in the rotor. This induced voltage will cause a current to flow in the rotor and will generate a magnetic field. The interaction of these two magnetic fields will produce a torque that drags the rotor in the direction of the field. This principle would not be modified if the squirrel cage were replaced by a continuous sheet of conducting material. [7] In this electric motor design, the force is produced by a linearly moving magnetic field acting on conductors in the field. Any conductor be it a loop, a coil, or simply a piece of plate metal, that is placed in this field will have eddy currents induced in it thus creating an opposing magnetic field in accordance with Lenz's law. The two opposing fields will repel each other, creating motion as the magnetic field sweeps through the metal. n = 2f /p..1 where f is supply frequency in Hz, p is the number of poles, and is the synchronous speed of the magnetic field in revolutions per second. The travelling field pattern has a velocity of: v = 2tf..2 where v is velocity of the linear travelling field in m/s, and t is the pole pitch. For a slip of s, the speed of the secondary in a linear motor is given by v = (1 s)v.3 Electromagnetic field analysis of electromechanical devices is usually performed to achieve information about their stationary and dynamic performances. In many applications, a two-dimensional finite element analysis enables to predict with sufficient approximation device performances. Unfortunately, some core struc-tures or some behaviour conditions cannot be simulated by an equivalent 2D domain and only a 3D FE analysis provides and accurate model of the electromagnetic problem.[5] In particular one of the main problems usually encountered in the analysis of linear induction motor is represented by end effects. The eddy currents induced in the conducting plate create a counter mmf which opposes the passage of the slot leakage flux. Thus the leakage reactance of the linear motor is decreased and more flux is concentrated in air gap, resulting in an increase of the developed thrust. [5] APPLICATIONS More than 2 urban transportation lines that are propelled by linear induction motors. [4] (LIMs) are commercialized worldwide, e.g., the linear metro in Japan, then Vancouver light train in Canada, and the Guangzhou subway line 4.The typical LIM drive system, shows that the LIM hung below the redirector supplied by the inverter on the vehicle. The secondary is flattened on the railway track, and it usually consists of an aluminum sheet that is 5 1 mm thick and a 2-mmthick back iron that acts as the return path for the magnetic flux. Compared with rotary induction machine (RIM) drive systems, the LIM system has the following merits. First, it can achieve direct propulsive thrust, independent of the friction between the wheels and rail, and can safely be operated, even in rainy or snowy weather. Second, it has a smaller turning radius for its special bogie technique, smaller cross-sectional area for its omission of a gear box, larger acceleration, and stronger climbing ability due to its direct electromagnetic force. Hence, it offers a flexible line choice and reduced construction cost, which is particularly favorable for subway systems. Third, it has lower noise and less maintenance without a gear box because of the non adherent driving. 177

3 International Journal of Scientific Innovations and Sustainable Development, Volume 6, Number 1, 216 Hence, it is an attractive mode of transportation in large cities. However, as the LIM primary moves, a new flux is continuously developed at the primary entrance side, whereas the air-gap flux quickly disappears on the exit side. An eddy current in a direction counter to the primary current will be induced in the secondary sheet, and it correspondingly affects the air-gap flux profile along the longitudinal direction. This phenomenon is called the longitudinal end effect. It can decrease air-gap average flux linkage (mutual inductance) and increase relevant copper loss as its speed goes up. Due to extensive research, many papers are currently available with regard to the LIM longitudinal end-effect analysis brought by the sudden generation and disappearance of the air-gap penetrating flux density. [4] The LIM has excellent acceleration and deceleration as well as ability to climb gradients.[3] Moreover, Linear motors produced and improved are nowadays used in mechatronic systems whose examples are; High-speed transport and catapult, Industry transport systems, Batching systems, Vertical transport systems, Semiconductors and electronics industry, Explosion localizing systems, Industry robots and machine-tools, Protection and control systems of power energetic, Medical instruments, Computer engineering.[6] MODELLING OF A LINEAR INDUCTION MOTOR From the induction motor principle, we obtain a linear motor if we imagine cutting and unrolling the motor, as shown in Fig. 1, causing the motor to have a linear motion. Fig. 1 Process of unrolling a conventional motor to obtain a LIM Instead of rotating flux, the primary windings now create flux in a linear fashion. The primary field interacts with the secondary conductors and hence exerts a force on the secondary. Generally, the secondary is made longer than the primary to make maximum use of the primary magnetic field [7]. As stated earlier, there should be relative motion between the conductor and the magnetic lines of flux, in order for a voltage to be induced in the conductor. That s why induction motors, normally operate at a speed Vr that is slightly less than the synchronous velocity Vs. Slip is the difference between the stator magnetic field speed and the rotor speed. Slip is the relative motion needed in the induction motor to induce a voltage in the rotor, and it is given by S =..4 The LIM synchronous velocity Vs is the same as that of the rotary induction motor, given by v = =2fτ..5 where, R is the stator radius of the rotary induction motor, as shown in Fig 2. It is important to note that the linear speed does not depend upon the number of poles but only on the pole pitch. Fig. 2 Radius of a rotating induction motor and length of a LIM 178

4 Constructional Features and Performance Analysis of 3-Phase Linear Induction Motor The parameter τ is the distance between two neighboring poles on the circumference of the stator, called pole pitch, defined as [7] τ = 6 The stator circumference of the rotary induction motor, 2πR, in (3.3) is equal to the length of the LIM stator core, Ls as shown in figure 2.Therefore, the pole pitch of a LIM is τ = =.7 If the velocity of the rotor is Vr, then the slip of a LIM can be defined as S = 8 The air-gap shown in Fig. 2[b] is the clearance between the rotor wall and the LIM Stator in a PCP-LIM system. Forces in LIM The main forces involved with the LIM are thrust, normal force, and lateral force, as shown in Fig 3. This project is interested in thrust and its relation to other variable parameters. The normal force is perpendicular to the stator in the z-direction. Lateral forces are undesirable forces which are developed in a SLIM because of the orientation of the stator. Fig 3. Forces in a LIM Thrust Under normal operations, the LIM develops a thrust proportional to the square of the applied voltage, and this reduces as slip is reduced similarly to that of an induction motor with a high rotor resistance. The amount of thrust produced by a LIM is as follows: F = 9 where Po is the mechanical power transmitted to the rotor or the output power and Vc is the linear speed of the rotor. Normal Forces In a double-sided linear induction machine (DLIM) configuration, the reaction plate is centrally located between the two primary stators. The normal force between one stator and the reaction plate is ideally equal and opposite to that of the second stator and hence the resultant normal force is zero. Therefore, a net normal force will only occur if the reaction plate (secondary) is placed asymmetrically between the two stators. This force tends to center the reaction plate.in a SLIM configuration, there is a rather large net normal force between the primary and secondary because of the fundamental asymmetrical topology. At synchronous speed, the force is attractive and its magnitude is reduced as the speed is reduced. At certain speeds the force will become repulsive, especially at high-frequency operation. Lateral Forces As shown in Fig 3., lateral forces act in the y- direction, perpendicular to the movement of the rotor. Lateral forces make the system unstable. These occur due to the asymmetric positioning of the stator in a LIM. Generally, small displacements will only result in very small lateral forces. These forces are a matter of concern in high frequency operation (>>5Hz) where they increase in magnitude. A set of guided mechanical wheel tracks is sufficient to eliminate a small lateral force. 179

5 International Journal of Scientific Innovations and Sustainable Development, Volume 6, Number 1, 216 Equivalent Circuit Model For the analysis and design of a LIM having negligible end-effects, the perphase conventional equivalent circuit shown in Fig 4 may be used. The circuit components are determined from the LIM parameters. The LIM performances to be determined are thrust and efficiency. The approximate equivalent circuit of a LIM is presented as shown in Fig.4. This circuit is on a per phase basis. The core losses are neglected because a realistic airgap flux density leads to moderate flux densities in the core and hence, rather low core losses. Skin effect is small at rated frequency for a flat linear induction motor with a thin conductive sheet on the secondary. Therefore, equivalent rotor inductance is negligible [7]. The remaining non-negligible parameters are shown in Fig 4 and are discussed below. Fig. 4 Per-phase Equivalent Circuit Model of LIM i) Per-phase stator resistance R 1 This is the resistance of each phase of the LIM stator windings. R1 is calculated from R = ρ..1 where, ρw is the volume resistivity of the copper wire used in the stator winding, lw is the length of the copper wire per phase, and Awt is the cross-sectional area of the wire. The length of the copper wires lw is calculated from l = N l..11 Where l = 2(w + l 12 is the mean length of one turn of the stator winding per phase and lce is the length of end connection given by l = τ.13 ii) Per-phase stator-slot leakage reactance X1 The flux that is produced in the stator windings is not completely linked with the rotor conductors. There will be some leakage flux in the stator slots and hence stator-slot leakage reactance X1. This leakage flux is generated from an individual coil inside a stator slot and caused by the slot openings of the stator iron core. In a LIM stator having open rectangular slots with a double-layer winding, X1 can be determined from X = [ ] 14 Where λ = ( )..15 kp is the pitch factor. Also, λ =.3(3k 1)...16 And λ = ( ).17 iii) Per-phase magnetizing reactance Xm The per-phase magnetizing reactance, Xm, is shown in Fig 4 and is given by X =.18 where kw is the winding factor, ge is the equivalent air gap and Wse is the equivalent stator width given as W = W + g.19 iv) Per-phase rotor resistance R2 The per-phase rotor resistance R2 is a function of slip, as shown in Fig. 4. R2 can be calculated from the goodness factor G and the per-phase magnetizing reactance Xm as R =.2 18

6 Constructional Features and Performance Analysis of 3-Phase Linear Induction Motor where the goodness factor is defined as G = ( 21 ) ρr is the volume resistivity of the rotor conductor outer layer, which is aluminum here. From the equivalent circuit shown in Fig. 4, the magnitude of the rotor phase current I2 can be seen to be I = I.22 ( ) By substituting the value of R2 from (2), the rotor phase current I2 becomes I = () Thrust and Efficiency As explained earlier, the input power to the stator windings is utilized in producing useful mechanical power which is exerted on the rotor and to account for the rotor copper losses. In terms of the equivalent circuit components, the mechanical power developed by the rotor is the power transferred across the air-gap from the stator to the rotor minus the rotor copper loss or P = mi mi R = mi R.24 Also, the electromagnetic thrust generated by the LIM stator is F =..26 This is the most general form of expressing electromagnetic thrust for a LIM determined from the rotor phase current I2. However, considering the per-phase LIM equivalent circuit as shown in Fig.4, where the core losses are neglected, Fs can be expressed in terms of stator phase current I1. Substituting (23) into (26), the SLIM electromagnetic thrust becomes F =..27 [ () ] The LIM input active power is the summation of the output power and the copper losses from the stator and rotor, P = P + mi + mi R.28 Substituting (24), and (27) into (28) yields P = F V + mi R 29 The efficiency of the LIM is found by calculating the ratio of (24) and (29), i.e. η = 3 DESIGN AND ANALYSIS The design parameters for the LIM under study are as shown in table 1. Table 1: Design Parameters of LIM Rated slip 1% or.1 Allimunium thickness.1m Target trust 1 Number of phases 3 Line-line voltage 415V Supply frequency 5Hz Number of poles 4 Width of the stator.5m 15m/s MATLAB USER INTERACTIVE PROGRAM was used to analyze the performance of the machine using the expressions and parameters, the performance curve of LIM, evaluated in terms of thrust and efficiency as a function of rotor velocity as shown in figures 5 and 6 181

7 International Journal of Scientific Innovations and Sustainable Development, Volume 6, Number 1, Thrus t = 15 Thrust = Figure 5: Thrust versus Rotor Velocity at rated Slip of 1%.7 x = 15 Efficiency =.646 (64.6%) E ff ic ie n c y Figure 6: Efficiency versus Rotor Velocity at rated Slip of 1% From user interactive program of MATLAB, the performance of the are plotted as shown in figures 5 and 6 using the design parameters of table 1. It is seen that the LIM has a thrust of N and efficiency of 64.6% at the rotor velocity of 15m/s and rated slip of 1% with target thrust of 1N. Evaluation of performance of LIM by changing parameters From the design parameters of LIM at rated slip of 1% and a target thrust of 1N, performance of LIM is evaluated by varying certain parameters like aluminum thickness and number of poles. Based on this evaluation, the best possible values for these parameters are obtained. Effect of Aluminum Thickness on Performance of LIM The effect of varying the thickness of the aluminum sheet on the rotor of LIM on its performance, from 1mm to 4mm in steps of 1mm is shown in figures 7 and 8. The goodness factor of LIM is given in equation 21, where the thickness of aluminum sheet on the rotor, d, plays significant role in the performance. The performance indicators thrust and efficiency of LIM, at various thickness of aluminum sheet at rated rotor velocity, is tabulated in table

8 Constructional Features and Performance Analysis of 3-Phase Linear Induction Motor T hrus t Different Alluminium thickness Thickness =.1 Thickness =.2 Thickness =.3 Thickness = = 15 Thrust = Figure 7: Thrust versus Rotor Velocity at rated Slip of 1% at different alimunum thickness x1 2.7 Different Alluminium thickness.6 Rotor Velocity = 15 Efficiency =.646 (64.6%) E fficiency Thickness =.1 Thickness =.2 Thickness =.3 Thickness = Figure 8: Efficiency versus Rotor Velocity at rated Slip of 1% at different alimunum thickness Table 2: Thrust and Efficiency obtained at different aluminum thickness Different Thrust (N) Efficiency (%) Aluminium thickness (mm) As the thickness of Aluminum sheet is increased, the magnitude of thrust also increases. The efficiency thus not has significant impact with an increase in the aluminum thickness. It can be seen that various aluminum thicknesses have almost the same efficiency. It is seen from the figure 7 and table 2 that the magnitude of thrust at rated rotor velocity is maximum when the thickness of aluminum is 3mm. The thrust develop is N at an efficiency of % at rated slip of 1% and target thrust of 1N. Hence, a value of 3mm is the best value which yields maximum thrust at reasonable efficiency. Effect of Changing Number of Poles on Performance End effect is reduced by increasing the number of poles in LIM. End-effect loss is shared by a large number of poles, resulting in a better performance. The characteristic curve with respect to changing the number of poles is shown in figures 9 and 1. The result obtained from the plot is tabulated in table 3 183

9 International Journal of Scientific Innovations and Sustainable Development, Volume 6, Number 1, Different number of poles No of poles = 2 No of poles = 4 No of poles = 8 No of poles = 6 Th ru s t Rotor = 15 Thrust = Figure 9: Thrust versus Rotor Velocity at rated Slip of 1% at different number of poles.7 x1 2 Different number of poles.6 E ffic ien c y No of poles = 2 No of poles = 4 No of poles = 6 No of poles = 8 = 15 Efficiency =.5461 (54.6%) Figure 1: Efficiency versus Rotor Velocity at rated Slip of 1% at different number of poles Table 3: Thrust and Efficiency obtained at different number of poles Number of poles Thrust (N) Efficiency (%) It is observed that efficiency decreases with the increase in number of poles while the thrust increases the increase in the number of poles. However, with the number of poles at 8, the machine has a thrust of N and relatively average efficiency of 54.6%, at target thrust of 1N and rated slip of 1% CONCLUSION It is seen from the figure 7 and table 2 that the magnitude of thrust at rated rotor velocity is maximum when the thickness of aluminum is 3mm. The thrust develop is N at an efficiency of % at rated slip of 1% and target thrust of 1N. Hence, a value of 3mm is the best value which yields maximum thrust at reasonable efficiency. With the number of poles at 8, the machine has a thrust of N and relatively average efficiency of 54.6%, at target thrust of 1N and rated slip of 1%, which is the best design for the LIM. 184

10 Constructional Features and Performance Analysis of 3-Phase Linear Induction Motor REFERENCES Linear Induction Motor-Wikipedia, the free encyclopepia. Armando, J. S. (211). Modeling of Linear Induction Machines for Analysis and Control, Florida Atlanta University, Baco Ranton, Florida. Chan-Bae, P., Lee, H. and Lee, J. (212). Performance Analysis of the Linear Induction Motor for the Deep- Underground High-speed GTX, Journal of Electrical Engineering and Technology Vol. 7, No. 2, pp Xu, W., Sun, G., Wen, G., Wu, Z. and Chu, P. (212). Equivalent Circuit Derivation and performance Analysis of a Single-Sided Linear Induction Motor Based on Winding Function Theory, IEEE Transactions on Vehicular Technology, Vol. 61, No. 4. Manna, M. S., Marwaha, S. and Marwaha, A. (211). Performance Optimization of Linear Induction Motor by Eddy Current and Flux Density Distribution Analysis, Journal of Engineering Science and Technology Vol. 6, No. 6, pp Roma, R., Lisauskas, S. and Batkauskas V. (27). Application and Analysis of Linear Induction Motors in Mechatronic Systems, Doctorial School of Energy and Geotechnology, Kuressaare, Estonia. Bhamidi, S. P. (25). Design of a Single-Sided Linear Induction Motor Using Interactive Computer Program, University of Missouri, Columbia. PANA/217/4/I.S. Udofia/panafricanjournal@yahoo.com/ /Cashregistered/