A low cost linear induction motor for laboratory experiments

Transcription

1 A low cost linear induction motor for laboratory experiments J. Atencia, A. García Rico and J. Flórez Department of Electrical, Electronics and Control Engineering, Escuela Superior de Ingenieros Industriales, (Universidad de Navarra), San Sebastián, Spain Abstract In this paper we present a linear induction motor (LIM) prototype for education. LIMs allow easy identification and study of the different concepts and parameters of the electromagnetic circuit that they have in common with other types of electrical machine. Some experiments are presented that highlight the proposed approach. Keywords linear electric machines; linear induction machines; modelling There is a wide bibliography for the different applications of linear electrical machines in industry. Normally they are used in special applications or where the task requires a dynamic performance that rotary machines are unable to give.1 4 A linear motor can be obtained by cutting a rotary motor along its radius from the centre axis of the shaft to the external surface of the stator core and rolling it out flat. This particular geometry makes them suitable for special industrial applications that can be found in transportation systems, manufacturing processes, pumping of liquid metals, etc.5 Progress in power electronics and a.c. variable speed drives has had a strong impact on the development of linear induction drives. Linear electric machines are direct drives, they allow accelerations, velocity and position-accuracy far better than their rotary counterparts; however, they are usually more expensive.6 As well as the industrial benefits, this paper observes some advantages of linear motors in the field of education. This type of electrical machine allows undergraduate students of electrical engineering courses to identify easily and to understand the different concepts and parameters of the electromagnetic circuit that can be found in common with any other types of electrical machine. In this paper, a low cost way to develop a laboratory linear induction machine prototype is presented. The main objective of the design is to build up a low cost prototype that is easy to handle, manipulate and test. The purpose of this prototype is not centred on achieving a great dynamic performance of the machine but on highlighting the electromagnetic effects that are involved. The main components of the linear motor are described, and some possibilities of the design are discussed. A laboratory experiment for undergraduate students is presented in order to make them more familiar with the electromagnetic concepts, and to show how to work and experiment with electric machines. The performed tests are based on the conventional tests for rotary machines, and have some variations and a broader perspective on electrical devices. These tests show the students how

2 118 J. Atencia, A. García Rico and J. Flórez to learn to identify the different electromagnetic parameters such as leakage reactances, mutual reactance and their relation with the electromagnetic fluxes and with the phenomenon of electromagnetic induction. Design of a LIM Design considerations The purpose of this prototype is for use and testing in a laboratory. The construction and subsequent tests will provide valuable information on this type of electrical machine, and the results, once extrapolated, could serve to design industrial prototypes. This requires some special characteristics that must be taken into account before calculating the different main parameters of the device. $ A low performance motor is targeted. High dynamic performance is not needed in order to study the characteristics of the linear motor in relation to its geometry. Actually, a high performance motor for laboratory testing has some disadvantages, such as the extra protection needed, higher cost, and greater difficulties of working with it. $ As a first approach, an oscillating movement gives enough information to study the motor. The basic electronics should at least generate this type of movement. However, it would also be interesting to supply the motor from a commercial regulator to generate more complex types of movements. Therefore, the primary voltage and demanded currents must be compatible with the supply characteristics of a standard regulator. $ The guides, travel and main dimensions of the prototype must be designed to fit in a laboratory and must have an open structure. This last need is important for testing; for instance in order to introduce probes or sensors inside the machine. $ A common sense need is that everything must be as simple as possible, in order to achieve a low cost construction and to avoid problems of mounting and of manipulating the geometry of the linear machine. Table 1 shows some chosen values of different parameters of the machine. TABLE 1 Type of machine Supply voltage Maximum currents Maximum travel Maximum velocity Maximum acceleration Natural cooling Specifications of the prototype Three-phase asynchronous 220 V 5 A 2 m 5 m/s 10 m/s2

3 Low cost LIM for laboratory experiments 119 Construction of the prototype Figure 1 shows the prototype reported here. It corresponds to a three-phase linear induction motor with aluminium sheet over the secondary iron. Figure 2 shows the linear motor, with its most important components. The basic considerations for developing the prototype are the following. Fig. 1 L IM prototype. Fig. 2 Prototype structure.

4 120 J. Atencia, A. García Rico and J. Flórez Primary windings There is a wide spectrum of types of winding for linear motors. For the design of this prototype, a double-layer, full pitch winding has been chosen (Fig. 3). This distribution of windings is simple but very effective, and has been used widely for rotary machines. The winding has two layers, full pitch coils and (2p+1) poles with half-filled end slots. The prototype has been designed with four pairs of poles per phase, in order to limit the phase-current asymmetries.7 Primary iron Figure 4 shows the structure of the primary iron of the laboratory prototype. It is highly recommended to use a laminated core in the primary in order to reduce magnetic losses. A preliminary value of the physical magnitudes may be obtained using the rotary machine expressions.8 The nominal velocity is a function of the nominal electrical frequency and of the pole pitch. The value for the nominal velocity at 50 Hz is 5 m/s (Table 1). Therefore the pole pitch must be t=n sinc /(2f )=50 mm (1) Fig. 3 T wo poles machine windings. Fig. 4 A view of the primary iron.

5 Low cost LIM for laboratory experiments 121 Since it is a full pitch coil winding of a three-phase machine, the slot pitch is t = t =16.7 mm (2) s 3 The primary part has open slots, because they are a great advantage from the construction point of view, and do not present a great problem for holding the windings. The slot width b s and tooth width b t (Fig. 5) are, as in rotary machines, approximately equal. However, for mechanical reasons, the width of the slots has been set to b s =10 mm and b t =6.7 mm. It is interesting to design the slots as short as possible to minimise the magnetic saturation of the teeth. The dimensions of the slots are lower-limited for thermo-mechanical reasons the coils must fit inside them and the heat of the windings must be withdrawn. Once the width of the slot has been set, the maximum current density per active slot area determines the slot height. With a maximum current density per active slot area of 3.5 A/mm for natural cooling,9 the height of the slot is h s =35 mm. The factor h s /b s is 3.5, which is a reasonable value for open slots.10 The height of the back iron, h c, can be estimated from the total flux that goes through a pole pitch. This magnetic flux returns through the back iron, so there is a direct relation between both measures. h # b 2t g c b p c For laboratory purposes the value of the airgap flux density b g =0.5 T is reasonable. It is also possible working with 0.7 T as in rotary machines, but then the attraction forces between primary and secondary will be too high. In the back iron the flux density b c should not be higher than 1.7 T, in order to avoid extra losses and hot points.7 Setting b c =1 T, then h c #15 mm. With the special geometry of the linear motor, the total length of the machine can be calculated as follows: length=tω(number of poles per phase+1)+b t (4) (3) Fig. 5 Open slot structure of the primary iron.

6 122 J. Atencia, A. García Rico and J. Flórez Therefore length=50 mmω(8+1)+7mm=457 mm The thrust that the linear machine is able to develop depends on the width of the machine, and the number of poles. Normally, the relation between the primary width and pole pitch is at least about 2.47 in rotary machines, to keep the proportion of leakage flux of the end coils low. In this case, the width of the prototype has the same value as the pole pitch, to keep the total force low without having to reduce the whole engine. Figure 6 shows the main dimensions of the primary part of the prototype. Secondary electrical circuit The easiest way to build a secondary electrical circuit is using an aluminium plate (Fig. 2). It is cheap, and easy to handle. If the thickness of the aluminium is small the conducting plate will get hot if it is too big, the airgap would be large and the efficiency of the machine low. A good choice for the prototype is 1.5 mm. The plate may be a little bit wider than the primary iron, to allow the current closing its path outside the active area. Secondary iron The secondary iron length must be at least the primary length plus the length of travel. The secondary iron is as wide as the primary iron, to maximise the linkage flux. If the same induction level in both irons (primary and secondary) is targeted, the secondary iron must be as high as the back iron of the primary. In the secondary part, a solid core can be tolerated and is preferred to a laminated one, because of simplicity and price. Support and guidance There are two different forces held exclusively by the armature: an attractive force between both irons, due to the presence of a magnetic field between them, and a repulsive force between the primary iron and the aluminium. This Fig. 6 Main physical values of the primary part.

7 Low cost LIM for laboratory experiments 123 repulsive force occurs because of the Eddy currents generated in the aluminium by the magnetic flux of the primary iron (Fig. 7). With the same levels of current, the maximum value of the attractive resultant takes place and at low frequencies ( less Eddy currents). Therefore the structure must be designed to support the maximum force, that means when the machine is supplied with d.c. currents. One advantage of designing a prototype with low attractive forces involved is that the structure that must hold the primary and secondary can be simpler. The structure has two different parts the carriage and the stationary part with the rails. The carriage is not attached vertically to the structure it just lies on the rails supported by four wheels. In this way it is easy to take the motor apart and to introduce sensors, or just to inspect the inner parts of the motor. The primary iron is held only by the front and the rear part of the primary holder (Fig. 4), and is not totally covered by it to allow rapid measures of temperature in different parts of the geometry. Between the rails and the aluminium sheet, there are two holes along the track (Fig. 2). This is very helpful for introducing instrumentation in the motor and for testing. Instrumentation End position sensors Electrical detectors are needed in order to limit the working area of the machine. Opto-electronic detectors are preferred, because the capacitive and inductive ones are more sensitive to magnetic fluxes. The limit switches may also be used to change the sense of motion. In this way it is very easy to make the motor move and oscillate through a long period of time, and study its performance, as a first approach to the controlled movement. Position The accuracy in positioning is determined by the kind of the detector (Fig. 8). For a 1.5 m travel, a low cost choice is to use a rotary encoder fixed to the moving unit, with a pulley and a thin but resistant cable tied to the ends of the armature (Fig. 9). This possibility is interesting if the absolute reference position is not important but the velocity is. After some oscillations, the motor should be moved to a start point to reset the position measure. Another choice is to use a screw instead of a pulley. In this case, the absolute reference is always known, and the accuracy of the position depends on the tolerance of the diameter of the screw. The thread must exert a very small force to turn the shaft of the encoder. Therefore, only one turn of the thread around the pulley (or the screw) is needed. The resolution of the system depends on the resolution of the encoder and on the diameter of the pulley.

8 124 J. Atencia, A. García Rico and J. Flórez Fig. 7 A view of the primary part.

9 Low cost LIM for laboratory experiments 125 Fig. 8 Detail of the position detector system. Fig. 9 Position detector system. Magnetic field The magnetic field may be measured either with a teslameter, or with low cost instrumentation such as Hall sensors and searching coils. Hall sensors measure magnetic field density in a range from d.c. to khz, and they are suited for measuring in discrete points in space. A single searching coil detects variations in the magnetic field that goes through it, reporting a voltage proportional to the gradient of this variation: e= d dt W (4) The ends of the primary iron and the distribution of the primary windings produce asymmetries in the magnetic field along the length of the motor. Each

10 126 J. Atencia, A. García Rico and J. Flórez pole of the machine has its particular level of magnetic flux, therefore just one searching coil does not reflect the whole magnetic linkage between the primary and secondary parts of the electric machine. One coil for each pole of the machine is introduced in the airgap, and all of them connected in series like a primary winding (Fig. 10). Together, they provide a unique searching winding, which give a measure of the total average flux that takes place in the airgap. The searching winding has the same structure and connections between coils as a primary phase winding. Finally, several such searching windings are introduced into different parts of the geometry in order to be able to study the whole averaged electromagnetic map of the machine. Though searching coils only measure alternative fields, the implementation is very simple, low cost and easy to prepare. Tests The main purpose of the study is to find an easy and precise way to determine the lumped parameters of an equivalent circuit of a linear machine. The differences between the conventional tests for rotary machines and those for linear machines are introduced and discussed. The equipment used for the following tests consists of some searching windings, a three-phase power meter, and a tester to measure voltage and currents. The searching windings (Fig. 11) allow indirect measures of magnetic fluxes (Fig. 12) and induced voltage. These measures can be used to obtain the parameters of the equivalent circuit of the machine, and to study different aspects of the flux path. Equivalent circuit of the linear induction machine The electromagnetic performance of linear machines is similar to that of their rotary counterparts. Important differences may arise in high-speed performance. However, these differences may be neglected from the point of view of the equivalent circuit,7,11,12 as the range of velocities of these kinds of LIM and in particular this prototype, are designed for low speed operation (v<3 m/s). In conclusion, the equivalent circuit of rotary machines (Fig. 13) is also valid for this prototype. Fig. 10 Connection of a searching winding.

11 Low cost LIM for laboratory experiments 127 Fig. 11 Searching windings. Fig. 12 Searching windings and flux paths. Fig. 13 Single-phase equivalent circuit of the linear induction motor prototype.

12 128 J. Atencia, A. García Rico and J. Flórez Tests for determining the lumped parameters of the LIM The conventional tests for rotary machines are the stand still test and the no-load test. As linear motors have a special geometry, they present some difficulties in performing these tests. $ The stand still test of the linear machines does not present any main difference or additional problem to the stand still test of rotary machines. $ The no-load test of rotary machines is not available with this kind of prototype, as the travel length is quite short and there is not enough time to reach steady state. The no-load test may be modified, testing the machine without aluminium in the secondary. This test is similar to the secondary open circuit test for slip ring machines and it implies no movement, so it is reasonable for linear machines. With these two tests, the modified no-load test and stand still test, two phasor equations can be obtained. V 1 and I 1 are easily obtained from the measure of a tester and a power meter. (V 1 ) no load test =(I 1 ) no load testa R 1 +X 1 j+ R c X m R c +X m j j B (5) (V 1 ) stand still test =(I 1 ) stand still testar 1 +X 1 j+ R c X m R c +X m j (R 2 j X 2 ) A R c X m R c +X m j +X 2B j+r 2B (6) There are six unknown parameters R 1, X 1, R 2, X 2, R c and X m referred to the primary, and four scalar equations. Therefore, two more equations are needed to solve the system. These two extra equations can be obtained if the module and the angle of E referred to V 1 are known. E represents the inducted voltage in the primary windings and in the secondary conductors due to the airgap ( linkage) flux in the equivalent circuit (Fig. 13). Actually this equivalent circuit is a simplified model of the electromagnetic phenomenon that takes place inside the real machine. It can be seen in Fig. 12 that the flux that reaches the aluminium is not the same as the flux that goes through the teeth (primary flux), so the induced voltage in both circuits is not the same. Using the searching windings, the induced voltages in different parts of the magnetic circuit can be measured (Fig. 14). However, we must decide which one of the different measures of the searching windings is better suited for finding the value of E in the simplified model of Fig. 13. Once the module and angle of voltage E are determined, two more equations to determine the six lumped parameters are easily proposed.

13 Low cost LIM for laboratory experiments 129 Set up of the prototype to perform the different measurements In order to make all the measurements a three-phase power meter, a tester and an oscilloscope are needed. With the power meter and tester, the supply voltage and current can be measured. The oscilloscope is needed to determine the module and angle of the voltage E referred to V 1. The searching windings have the same structure and connections between coils as a primary phase winding. The only difference is that the searching windings have single-turn coils, and the phase windings have multi-turn coils. This means that the module of the voltage measured in the searching coils must be scaled to introduce it in the equivalent circuit referred to the primary. As each coil has only one turn, the transformation factor is E equivalent circuit E searching winding = n 1 with n turns per primary winding. With the oscilloscope, it is possible to measure the angle between the E searching winding and the supply voltage V 1 as follows. $ If the phase A is taken as the V 1 reference voltage, all the searching windings must be perfectly aligned with the phase A winding. $ A terminal of every searching winding must be connected to the primary neutral (Fig. 14). $ One probe of the oscilloscope measures the voltage V A and it serves as the reference angle measure. The other probe is used to measure the voltage of a searching winding. The angle between both signals is the angle of E searching winding of the equivalent circuit. The correct alignment of the searching windings with phase A is very important, because if they are not well aligned, the angle measured doesn t reflect the electrical angle between signals. To avoid this error, the searching windings 1 and 2, Fig. 11, must be mounted in the same slots of the armature as phase A. Searching windings 3 and 4 are more difficult to align because they are on the secondary, and phase A is on the armature of the move unit. (7) Fig. 14 Equivalent circuit with a searching winding.

14 130 J. Atencia, A. García Rico and J. Flórez The correct alignment of windings 3 and 4 is performed by supplying only phase A, and measuring the induced voltage on searching winding 3. Both windings are well aligned when the inducted voltage reaches its maximum, as the primary moves along the secondary. Once the maximum is found, the carriage must be fixed, and all three phases can be supplied again in order to start testing. Lumped parameters calculation using E obtained from searching winding 2 Considering E = n 2 1 E searching winding 2 the method may proceed as follows: $ No load test. As mentioned before, this test is similar to the secondary open circuit test for slip ring machines. With the value of the module and angle of E 2, the parameters R 1, X 1, R c and X m can be easily obtained. (R 1 +X 1 j)= (V 1 ) no load test (E 2 ) no load test (I 1 ) no load test (8) R X c m R +X j j= (E 2 ) no load test (9) (I ) c m 1 no load test $ Stand still test (with aluminium sheet). The machine must be clamped and supplied with the primary voltage raised in steps until the primary current reaches its nominal value. It is the same test as for rotary machines. With the measured values of I and, the parameters R, X, R and X c m from the previous test, R and X are obtained. 2 2 ) 1 stand still test (R +X j)= A(V (R +X j) B R X c m (I ) 1 1 (R +X j) j 1 stand still test c m 2 2 (R +X j)+ R c X m 1 1 (R +X j) j (V 1 ) (10) stand still test (I ) c m 1 stand still test Though now it is not necessary to measure the value of (E ) to find 2 stand still test the parameters, its value may be used to verify the results. Lumped parameters calculation using E obtained from searching winding 3 Another choice may be made, assuming E 3 =(n/1) Esearching window 3 (Fig. 12). In the no-load test (without aluminium sheet) it is quite difficult to use the searching winding 3 and to place it in the same place as in the stand still test. In order to avoid the need for E in the no-load test to determine the six unknown parameters, the method may be slightly modified either in the calculations or in the order of the tests. $ Stand still test (with aluminium sheet). The machine must be held stationary,

15 Low cost LIM for laboratory experiments 131 and supplied with the primary voltage raised in steps until the primary current reaches its nominal value. It is the same test as for rotary machines. This time with the known values of E 3, V 1 and I 1, the parameters R 1 and X 1 can be calculated. (R 1 +X 1 j)= (V 1 ) stand still test (E 3 ) stand still test (I 1 ) stand still test (11) $ No-load test. Using only V 1 and I 1, and the parameters calculated before, R 1 and X 1, the unknown R c and X m can be easily obtained. R c X m R c +X m j j= (V 1 ) no load test (I 1 ) no load test (R 1 +X 1 j) $ Finally, with R 1, X 1, R c and X m and again using the results obtained in the stand still test, R 2, X 2 are obtained. ) 1 stand still test (R +X j)= A(V (R +X j) B R X c m (I ) 1 1 (R +X j) j 1 stand still test c m 2 2 (R +X j)+ R c X m 1 1 (R +X j) j (V 1 ) stand still test (I ) c m 1 stand still test (13) Discussion of some other induced voltages in the searching windings Besides the calculation of the parameters of the equivalent circuit, the induced voltages in the searching windings may be analysed to explore the characteristics of the magnetic circuit. The meaning of E sw2 and E sw3 has already been pointed out. E sw2 is proportional to the flux in the teeth of the primary, and E sw3 proportional to the secondary flux. $ If E sw2 is taken as the airgap induced voltage, (which is proportional to the linkage flux) then the voltage E sw1 reflects the linkage flux plus the slot leakage flux (Fig. 15). In the equivalent circuit, it should be E =E 1 (n/1)e sw1 (Fig. 13) if all the coils of the primary windings are concentrated at the top of the slots. Actually, the primary coils support a smaller flux, because a part of it closes over them inside the slot8 and, for this reason, X 1 cannot be obtained from the impedance of (E 1 E 2 )/I 1. $ E sw4 shows the amount of field that crosses the iron vertically and produces Fig. 15 Slot leakage flux.

16 132 J. Atencia, A. García Rico and J. Flórez the linkage field. The difference between E sw4 and E sw5 gives the order of magnitude of the flux that goes through the secondary iron but does not produce thrust (it is outside the active zone of the machine) (Fig. 16). $ With the value of E sw5 we can quantify and compare the amount of field that goes from the primary iron through the aluminium and reaches the secondary iron, against the part that passes through the aluminium but does not reach the secondary iron, and goes back to the primary iron through the air. Conclusions The proposed tests may be a good help for student s understanding of concepts regarding the different tests and performance of electric machines. The laboratory prototype, besides its low cost, presents some other advantages compared to rotary machines. $ It is easier to handle and modify in order to achieve different configurations such as squirrel cage secondary, different geometries of conductive sheet in the secondary, etc. $ The main components are easier to identify. $ Its open structure allows the use of searching coils or windings in the airgap (Fig. 17) and some other places to analyse the different leakage fluxes and the linkage flux. $ Linear machines show a different geometry with a modified electromagnetic circuit to rotary machines. This fact helps the students to obtain a more general and comprehensive understanding of the electromagnetic phenomenon that takes place inside electromachinery. Fig. 16 L inkage flux and leakage flux driven through the secondary iron.

17 Low cost LIM for laboratory experiments 133 Fig. 17 Airgap of the linear machine. Acknowledgements The authors wish to express their gratitude to the Basque Government for the financial support of the project EL00198 on linear machines. J. Atencia also wishes to express his gratitude to the Asociación de Amigos de la Universidad de Navarra for his scholarship. References 1 A. Gastli, Compensation for the effect of joints in the secondary conductors of a linear induction motor Ref IEEE T rans. Magn., 13(2) (1998), H. S. Hahn and J. L. Sanders, Performance analysis of a LIM-based high-speed tool delivery system for machining, Int J. Prod. Res., 32(1) (1994), Jin Sang-Baeck and H. Dong-Seok, A method of optimal design of single-sided linear induction motor for transit, IEEE T rans. Magn., 33(5) (1997), P. Van den Braembussche, J. Swevers and V. Van Brussel, Accurate tracking control of linear synchronous motor machine tool axes, Mechatronics, 6(5) (1996), S. A. Nasar, I. Boldea and Z. Deng, Forces and parameters of permanent magnet linear synchronous machines, IEEE T rans.magn., 23(1) (1987), G. W. McLean, Review of recent progress in linear motors, IEE Proc. B, 135(6) (1988), S. A. Nasar and I. Boldea, Linear electric actuators and generators (Cambridge University Press, Cambridge, 1997). 8 M. G. Say, Alternating Current Machines (Pitman, 1976). 9 J. F. Gieras, Linear induction drives, Monographs in Electrical and Electronic Engineering (Oxford University Press, Oxford, 1994).

18 134 J. Atencia, A. García Rico and J. Flórez 10 A. García Rico and L. Ormazabal, Cálculo automático de máquinas asíncronas, Lecturing Notes. Publicaciones ESII, Universidad de Navarra, S. Nonaka, Equations for calculation of equivalent circuit parameters of single-sided linear induction motors, Proc. Int. Conf. on Electrical Machines (ICEM96), Sept. 1996, Vigo, Spain, Vol. 2 (1996), pp S. Nonaka, Investigation on equations for calculation of secondary resistance and secondary leakage reactance of single-sided induction motors, Electr. Eng. Japan (USA), 122(1) (1998),