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Fig. 1. The lifting platform driven by LIMs in stereo garage If taking the car from stereo garage, the LIMs are connected with power supply, and then drive the crossbeam moving toward to the car carrying plate. When the crossbeam Car carrying plate LIMs Electromagnets Crossbeam is close to the car carrying plate, the electromagnets are supplied with DC current to attract the car carrying plate. After that, the crossbeam runs in the opposite direction driven by LIMs, so that the car carrying plate with car is taken out to the lifting platform. Finally, the car is sent to the first floor along with the lifting platform moving down. The process of storing car is just opposite. That is to say, depending on back and forth movement of LIMs, the car can be rapidly moved. In this application, two features of LIM should be noticed, one is the velocity and the other is primary length. Apparently, the stroke of LIMs is almost equal to the width of car, so the running velocity cannot be high due to limited stroke and large weight. That is to say, the rating velocity of LIMs is low. Considering the pole pitch of LIM with traditional overlapping windings, the frequency of power supply is also low. Therefore, the LIM should be designed at low frequency and full voltage. The primary length cannot be longer than the width of crossbeam. Since the width of crossbeam should be as small as possible for reducing both width and weight of the lifting platform, the primary length is also limited. Therefore, the primary width of LIM is direct proportional to the thrust force. In this case, it becomes too large if only one LIM is adopted. For decreasing the primary width per LIM, even number of LIMs are adopted, such as 2, 4, 8, 10 etc., and they are symmetrically mounted below crossbeam in two groups. Fig.1 shows four LIMs. According to the application requirement, the rated velocity, voltage and starting thrust force per designed LIM are 0.8m/s, 380V and 666N respectively. III. LONGITUDINAL MOVING MECHANISM DRIVEN BY LIMS The former stereo garage only has two parking spaces in longitudinal direction of one layer, so the lifting platform doesn’t need move. It is not suitable to huge stereo garage due to limited parking spaces. In order to enlarge the car parking capacity, the lifting platform should be moved in longitudinal direction, called lognitudinal moving mechanism. It also can be driven by LIMs. In order to simplify manufacture, the same LIMs of crossbeam can be adopted. The lognitudinal moving mechanism driven by LIMs is mounted on top of lifting platform. Fig.2. shows the simple diagram.
It only shows four parking spaces in lognitudinal direction of one layer, it can have more in actual application, such 4, 6, 8, 10 etc. Fig.2 The simple diagram of lognitudinal moving mechanism In each side, there are several LIMs, which operate in parallel. All primaries are fixed on the top of lifting platform frame together, while the long secondary is mounted on stationary frame of stereo garage. When LIMs are supplied with power supply, the lifting platform is driven to move in longitudinal direction. During the process of storing or taking car, the lognitudinal moving mechanism and the lifting platform can work together to find the parking spaces as soon as possible. After that, the crossbeam is driven to move the car. IV. ANALYSIS MODEL AND PERFORMANCE The equivalent circuit is erected to design this LIM, which can consider the transverse effect, static lognitudinal effect, dynamic lognitudinal effect and secondary back-iron loss [7]. Since the width of crossbeam is given, the primary length is fixed, and then the pole pitch and pole number are obtained. According to the required velocity 0.8m/s2, the suitable frequency of power supply is 11.5Hz. At this frequency, the voltage is full value, 380V. Based on the analytical model, the other structure parameters, such as primary width, primary height, tooth width and slot height, are investigated at starting conditions with full voltage, which starting thrust force is kept 666N. The primary width is important because it deeply affects the current density. Along with primary width increasing, the starting current almost keeps constant, but the number of turns per phase decreases. Apparently, the conductor area becomes bigger and bigger if the slot filling factor is fixed. Therefore, the current density decreases along with the increasing of primary width, shown in Fig.3. Fig. 3. The relationship between primary width and current density The primary height includes the yoke height and slot height. If slot height is fixed, the yoke height changes along with the primary height, and affects the flux density of yoke, shown in Fig.4. As it can be seen, the flux density decreases along with the increasing of primary height. Apparently, the magnetic field of yoke is already saturated if the primary height is smaller than 5.9cm, and then rapidly decreases along with the increasing of primary height. If the lamination is assembled by bolts in primary yoke, the primary height cannot be smaller than 5.9cm, that is to say, the primary height is mainly decided by mechanical installation in this case. However, it should be noticed the primary height should be larger than 5.9cm for lamination assembled by welding. Lifting platform Parking space Parking space Parking space Parking space LIM The tooth width is decided by not only the flux density of tooth, but also the mechanical strength. When tooth width varies from 3mm to 6mm, the flux density of tooth decreases. To normal LIM with frequency 50Hz, sometimes the tooth width can be 3mm. But to this LIM, the magnetic field of tooth is very saturated, so the current rapidly increases and the thrust force significantly decreases. Therefore, the tooth width should be over than 4mm. However, due to the slot width becomes smaller and smaller, the current density of winding may be increased. Therefore, the selection of tooth width also should consider the current density and mechanism strength. The slot height, which not includes the semicircle in the bottom, also deeply affects the current density. When only slot height and conductor diameter change, the thrust force almost keeps constant, but can reach maximum at suitable value, shown in Fig.5. But current density decreases along with the increasing of slot height. Therefore, the optimal slot height can be selected. Fig. 5. Current density and thrust force at different slot height After the investigation of important structure parameters, the design of LIM is completed. Fig.6 shows the thrust force at different slip. As it can be seen, the thrust force decreases along with the slip decreasing, moreover, the change is almost linear. However, the currents almost not change, which is different to normal LIM. The starting thrust force and current are 666N and 11.4A respectively. The equivalent circuit method calculates the performance of LIM based on the method of lumped parameter circuit. Since they are used to calculate static performance, the finite element (FE) method also should be adopted to analyze dynamic performance of this LIM. In the same time, the effectiveness of equivalent circuit method can also be validated. V. FEM MODEL AND ANALYSIS Fig.7 shows the FE model of this designed LIM. In this model, the end windings are considered by the effective impedance, which is calculated in the former equivalent circuit method. The secondary width is wide enough that the transverse effect can be ignored. Fig. 7. The FE model of designed LIM In this model, the velocity of primary is assumed zero and phase windings are supplied with the three phase symmetrical starting currents 11.4A, 11.5Hz, which is obtained by former equivalent circuit method, the locked thrust force is obtained, shown in Fig.8. As it can be seen, the average thrust force is 654.5N, so the error between two methods is near 1.8%, that is to say, the former results obtained by equivalent circuit method are believable. However, the thrust ripple is big due to the end effect, which cannot be obtained by former equivalent circuit method. This model also can be changed to apply the voltage source. The velocity of primary is still assumed zero, but the three phase windings are supplied with 380V, 11.5Hz three phase symmetrical voltage. The locked thrust force and phase currents are obtained, shown in Fig.9. As it can be seen, the average thrust force is 700N, so the error between two methods is near 5.1%. The three phase currents are asymmetrical and have a lot of harmonic components.