Analysis and Experimental Validation of an HTS Magnetic Suspension and Linear Synchronous Propulsion Prototype

Transcription

1 Analysis and Eperimental Validation of an HT Magnetic uspension and Linear ynchronous Propulsion Prototype Jianun Jin a,*, Luhai Zheng a, Youguang Guo b, Wei Xu b,*, and Jianguo Zhu b 1 Center of Applied uperconductivity and Electrical Engineering, University of Electronic cience and Technology of China, Chengdu 11731, China Faculty of Engineering and Information Technology, University of Technology ydney, ydney, PO Bo 13, W 7, Australia Abstract The electromagnetic design, performance analysis and eperimental measurements of a high temperature superconducting (HT) magnetic suspension and propulsion system using an HT linear synchronous motor (HTLM) drive have been carried out. Different magnetiation methods have been employed to study the magnetic flu trapping characteristics of the HT bulk magnets to validate the HT technology for the HTLM application. Three different types of permanent magnet guideways (PMGs) for the HT magnetic suspension have been developed, and their field distribution characteristics have also been analyed by using an equivalent current sheet (EC) method and verified by practical measurements. The levitation forces based on the three PMGs have been calculated and compared. An optimal PMG has been obtained as to provide the largest levitation force and better ratio (levitation force) / (permanent magnet volume). Based on comprehensive numerical analysis and eperimental testing of a prototype, typical performances of the HTLM have been obtained, including the thrust characteristics versus the frequency, phase current and air-gap length, which would benefit the electromagnetic design and the control scheme development for the HTLM. PAC: 5.5.Ly Keywords: High temperature superconductors, HT linear synchronous motor, HT magnetic levitation, Pulse magnetiation, Field-cooled magnetiation, Trapped field attenuation 1. Introduction Various kinds of high temperature superconducting (HT) suspension and linear propulsion systems using HT tapes or HT bulk magnets have been developed. These suspension systems can be categoried as the electro-dynamic (repulsion) suspension (ED) using HT coil magnets [1-], the electro-magnetic (attraction) suspension (EM) using HT coils [5, ], and the HT magnetic (repulsion) suspension using field-cooled HT bulks [7-9]. Among them, the HT magnetic suspension system is the simplest in structure using HT bulks on the moving low temperature vessels and permanent magnet guideways (PMGs) as the track, and has the capabilities of self-levitation and self-guidance without using any feedback control. The HT linear motors developed so far can be mainly classified according to their principle and structure as the HT linear reluctance motor (LRM) with ordinary copper windings on the primary (stator) and ero-field-cooled (ZFC) HT bulk poles on the secondary (mover) [1,11], the HT linear synchronous motor (HTLM) with ordinary copper windings on the primary and HT bulk or coil magnets on the secondary [1-,1-15 1], and the HTLM or linear induction motor (LIM) with HT windings on the primary [1 17,1]. These HT linear motors can be further divided into single-sided, double-sided, and cylindrical types according to their structures. Compared to the conventional linear motors, the HT linear motors have a number of potential advantages, such as small sie, high thrust, low weight, and high efficiency because of using ero-resistance HT tapes or strong-pinning HT bulks with high trapped magnetic fields. A compound model of an HT magnetic suspension and HT linear synchronous propulsion system has been proposed and developed. The system is driven by a long-primary single-sided HTLM with HT bulk magnet secondary, and the secondary mover is levitated by the HT magnetic suspension systems on both sides of the HTLM. The propulsion system can run with stable thrust without any sliding friction, and have the self-levitation and self-guidance functions in both static and dynamic operating states. As the results of using HT both for propulsion and suspension, the thrust of the compound HTLM system is higher than the systems using conventional linear motors or HT LRM for propulsion because of HT bulk magnets having higher trapped magnetic fields. To validate the performance characteristics of the prototype, a thrust measurement system has been developed to measure the lock-mover thrust of the HTLM, where the amplitude of which is the maimum thrust F em_ma. In this work, the F em_ma characteristics have been obtained by measuring the amplitude of the lock-mover thrust under various conditions. The levitation force, F Lev, and the guidance force, F Gui, are two principal performance indicators for the HT magnetic suspension system. While F Gui depends on the trapped flu in the HT bulk, F Lev is linearly proportional to the gradient of the magnetic field of PMG. Therefore it is important to design a PMG with high magnetic field gradient. Three types of PMGs have been designed for the HT magnetic suspension system, and their magnetic field distribution characteristics have been analyed and compared both by equivalent current sheet (EC) models and measurements so as to obtain the optimum PMG for the HT magnetic suspension system. It indicates that the EC method could provide a general method for the calculation of the field distribution of a PMG.. The ystem Fig.1 illustrates schematically the developed HT magnetic suspension and propulsion system with an HTLM drive, where the HTLM is located in the middle between two HT magnetic suspension sub-systems. Three types of PMGs are designed, as shown in Fig., with urface mounted (#1), Flu concentration (#), and (c) Halbach array PMGs (#3), respectively, where the arrows indicate the magnetiation directions of the dfeb permanent magnets (PMs). The values of, w, w 3 and occurring in these figures are listed in Table 1. The primary (stator) and the secondary (mover) of the HTLM are made of three-phase copper windings and magnetied YBCO(13) HT bulk magnets, respectively, and the magnets are fied in cryogenic vessels with alternating and poles along the longitudinal direction, and same poles along the transverse direction to reach the suitable stator width. Main parameters of the HTLM are listed in Table 1.

2 econdary HT bulk magnets for propulsion Primary iron core PMG Cryogenic vessels HT bulks for levitation and guidance Three-phases primary copper windings Fig. 1. chematic illustration of the HT magnetic suspension and propulsion system with an HTLM drive. PM w Pole pitch (τ) 5 mm umber of slots (Q) 7 Pair poles (p) Air gap Length (g) 5 mm HT bulk magnet length (l s) 3 mm HT bulk magnet width (w s) 3 mm HT bulk magnet height (h s) 15 mm Trapped magnetic flu intensity (B trap).5 T econdary Relative permeability (μ r). umber of HT bulk magnets along longitudinal direction umber of HT bulk magnets along transverse direction 5 Operational Maimal thrust (F em_ma) 1 k parameters Force constant /A 3. Levitation and Guidance Forces 3.1 PMG Models The EC method, which models a PM by a pair of current sheets of infinitesimal thickness, is used to derive the three different PMG models by ignoring the back iron. Fig.3 illustrates the sheet current directions corresponding to the three PMGs shown in Fig.. The magnetic flu density at a given point (, ) can be obtained by summing up the contributions of each current sheet, which is calculated by the Biot-avart law. Iron h Fe w Iron w w 3 F E D C B A PM PM w w 3 (c) Fig.. chematic structures of PMGs. urface mounted PMG (#1), Flu concentration PMG (#), and (c) Halbach array PMG (#3). Table 1 Main dimensions of transversal section of the PMGs 1 mm w 3 mm PMs width (w -) mm #1 PMG height () 5 mm oft iron width (w ) mm height (h Fe) mm mm w 9 mm PMs w 3 37 mm # PMG width (w -) 5 mm height () mm oft iron width () mm height () mm 1 mm #3 PMG w mm w 3 mm mm Table 1 Main parameters of the HTLM Part Item Value Width 15 mm Height 1 mm Primary Length mm tooth length (l t) 1 mm tooth width (w t) 15 mm C A E F D A B B J I H G w w w 3 C (c) Fig. 3. EC models of PMGs: urface mounted PMG (#1), Flu concentration PMG (#), and (c) Halbach array PMG (#3). For the Halbach array PMG with current sheets as shown in Fig.3(c), the flu density due to current sheet A can be obtained by integrating the contributions of elemental currents di= M d, where M is the magnetiation intensity of PM, and d an infinitesimal length along the Z direction, as the following µ ( M ) w1 w1 B _A = arctan arctan (1) π µ ( M ) ( + w1 ) + B _A = ln () π ( w1 ) + where μ is the permeability of vacuum. imilarly, the magnetic flu density at point (, ) generated by other current sheets can also be calculated, and the total flu density D

3 generated by all current sheets at a given point (, ) can be derived as B (kgs) B (kgs) mm w1 w1 w1 w1 w3 w B = arctan + arctan + arctan arctan + arctan arctan π hpm + hpm + w3 w w3 w w3 w arctan + arctan arctan + arctan + arctan arctan + h + h + h + h + pm pm pm pm + + pm pm pm + + pm + ( w ) + ( w1 ) + ( w1 ) + ( w ) + w h w h w h w h ln ln ln ln B mm ( + w1) + w1 hpm ( w) + w hpm = ln + ln + ln ln π ( w1 ) + w1 + + hpm ( w3 ) + w3 + + hpm ( 3 ) ( ) ( ) ( ) ( ) ( ) + w3 + + hpm hpm pm 1 + w + + ln ln arctan + arctan + arctan + w + + w + + h w w w hpm hpm hpm arctan + arctan arctan + arctan arctan w1 w1 w1 w w The magnetic flu density distributions for the surface mounted PMG. h=mm (#1) and flu concentrated PMG (#) can also be obtained using this. h=mm method. Fig. plots the calculated and measured transversal. h=mm distributions (along the ais) of B and B at the height =.1 m from the upper surface of the #1 and # PMGs, respectively. The PMG. filed was measured by sweeping a Hall probe along the transversal. - direction. It can be seen that the theoretical results are consistent with. - the eperimental measurements, where the small error is mainly. - caused by ignoring the influence of the soft iron on the flu density distribution. This validates the accuracy of the models built by the Distance (m) EC method. Based on the EC model described in Eqs.(3) and (), the. h=mm h=mm transversal distributions of flu density components B and B of the. h=mm Halbach array PMG are shown in Figs. 5 and, respectively. As. shown, the amplitudes and gradients of the magnetic flu densities. decrease as h increases, and the generated B and B have been. - substantially improved compared to the cases of #1 and # PMG Distance (mm). 3. Fig. 5. Transversal distributions of flu density at different heights () of the Halbach array PMG (#3). B along the ais at different heights. B. along the ais at different heights (). #1 (umerical calculated) #1 (Measured) # (umerical calculated) # (Measured) Distance (mm) #1 umerical calculated #1 Measured # umerical calculated # Measured Distance (mm) Fig.. Calculated and measured flu density distributions of PMGs (#1 and #). B along the ais at = 1 mm. B along ai at = 1mm. B (kgs) B (kgs) 3. Levitation and guidance forces Based on the magnetic flu density distributions of the PMGs, the levitation and guidance forces, between a rectangle HT bulk and the PMG can be calculated as follows F = J B ddd y Lev Gui (3) () hs ls δ ws δ ls ws c (5) hs ls δ ws δ ls ws c () F = J B ddd y where h s, l s, and w s are the height, length and width of the HT bulk, respectively, δ the depth of field penetration calculated by δ = B B λµ J [19], B trap the trapped magnetic flu density ( ) trap c in the HT bulk, λ the agaoka coefficient determined by the configuration of a sample, and J c the critical current density. For the three types of PMGs, the F Lev of them are calculated as listed in Table 3, and the ratios of F Lev / V pm are also calculated respectively, where V pm is the volume of PM used in the PMG. From Table 3, the Halbach array PMG (#3) has the biggest F Lev and F Lev / V pm. o the Halbach array PMG can provide the optimum system performance with better ratio (levitation force) / (PM volume) or ewtons per cubic centimeter. However, the flu concentration PMG (#) uses less PMs and is readily to assemble to eperiment, and selected here for the practical prototype.

4 Table 3 Levitaion forces of the three PMGs PMG F Lev (/m) V pm (cm 3 /m) F Lev/V PM # # # Model of HTLM Fig. plots the flu linkage distribution on a longitudinal section of the HTLM obtained by the Mawell/Ansoft TM D finite element analysis. As shown, the majority of magnetic flu flows along the iron core in the primary or stator because of the high permeability, and the flu path is in a reasonably regular pattern. According to the empirical value, the relative permeability of HT bulk magnet μ r is set to be.. Considering the reluctances of the HT bulk magnets and air gaps and neglecting the magnetic reluctance of the primary iron core, the magnetic flu linkage of one coil due to one pole-pair HT bulk magnets can be obtained approimately as F Hc hs ψ C = = R hs g t tot + + µµ r s l ws µ ( ls+ lt) ( ws+ wt) µ ws hs (7) B hs( ls+ lt) ( ws+ wt) lswh s s = hs( ls + lt) ( ws + wt) hs + µ rglswh s s + µt r ls( ls + lt) ( ws + wt) where F is the magnetomotive force of magnetic circuit, R tot the total magnetic reluctance, H c the magnetic field intensity of HT bulk magnet, τ the pole pitch, g the air gap length, l s, w s, and h s the length, width and height of the HT bulk magnet, and l t and w t the length and width of stator-tooth, respectively. ubstituting the parameters listed in Table 1 into Eq.7, it can get the value of ψ sc as. mwb. g l s 1# # 3# # h s Maimum thrust () 3 1 U/f = U/f = 3 U/f = Trapped magnetic flu density B trap (T) Fig. 7. Maimum thrust versus trapped magnetic flu density for different U/f. 5. Magnetiation Characteristics of HT Bulk Magnet Fig. shows the measured magnetic flu trapping characteristics of HT bulk magnets obtained by the field-cooled (FC) magnetiation method with a DC magnet, and the ZFC magnetiation methods with a DC magnet and a pulse magnetier, respectively. As shown in the figure, in all three cases, the B trap of the HT bulk magnet increases linearly with the eternal magnetic flu density, B et, before saturation. The amplitude of B et obtained by using the ZFC pulse magnetiation is about twice as that by the ZFC DC magnetiation, and four times as that by the FC DC magnetiation. The results are very useful to select the appropriate methods to obtain HT bulk magnets for different practical applications. For the low-field magnetiation, although the FC DC magnetiation is feasible, it is favorable to choose the ZFC pulse magnetiation for its higher magnetiation field and lower cost. The trapping magnetic flu characteristics by ZFC pulse magnetiation for three HT bulk samples (BU 1, BU and BU 3) having different qualities are given in Fig. 9. It can be seen that the quality of HT bulk has substantial influence on the magnetic flu trapping capability. The optimum value of pulse B et for saturation magnetiation with maimum trapped flu B trap_ma increases with the quality of HT bulk, and finally reaches a steady value of 1.1 T for the samples used. An optimum B et can hence be found to magnetie the HT bulks. 1. l t Fig.. Flu linkage of the HTLM. The root means square (RM) value of the back electromotive force (EMF) can be determined by E = πk 1 ψcvs τ, and then the electromagnetic thrust F em by P 3PE U ( X tsinθ + R1cosθ) E em R1 Fem = = v s t f ( R1 + Xt ) () = 3PE U R1 + Xt sin( θ + f) ER 1 t f ( R1 + X t ) where P em is the electromagnetic power, v s the synchronous velocity equal to τf, f the frequency, 1 the number of turns of winding, k the winding factor, R 1 the phase resistance, X t the synchronous reactance, P the number of pole pairs, U the phase voltage, φ the load shift angle, and φ = arctan R1 Xt. When the load angle θ = 9 - φ, the maimum electromagnetic thrust can be obtained as ( + ) 3pE U R X E R 1 t 1 em _ ma = F ( 1 + t ) t f R X Fig.7 illustrates the F em_ma versus the trapped flu density B trap of the HT bulk magnets by different ecitations of U/f when f = 5 H. It is shown that F em_ma can reach 3. k if B trap = 3 T and U/f=. (9) B trap / B trap_ma... FC DC magnetiation ZFC DC magnetiation ZFC pulse magnetiation B trap_ma=kgs Eternal magnetic flu density B et (T) Fig.. Comparison of HT bulk magnetic flu trapping characteristics within different magnetiation methods. 1. BU 1.9 BU BU 3 B trap / B trap_ma..3 B trap_ma=kgs Pulse eternal magnetic flu density B et (T) Fig. 9. Trapped magnetic flu density versus pulse B et for different samples. After trapping magnetic flu, it is also important to understand the flu distribution characteristics of the HT bulk magnets for practical applications. An analytical model of the magnetic field distribution at an arbitrary point (r, ) for a disk-shaped HT bulk magnet with a constant J c is built by []

5 a r s s K( k) + E( k ) ( ) (, µ J R D+ as + r + c s ) π ( ) d d = s s as + r + s B r a (1) where ( ) k = ar s a s + r + s 1, K and E are of the first and second kind complete elliptic integrals, R and D the radius and thickness of the disk-shaped HT bulk magnet, respectively. In the case of r =, the magnetic field B () can be simplified as ( ) µ J R+ R + + D c R+ R + B ( ) = ( + D) ln ln (11) + D For an HT bulk sample with a diameter of mm, Fig.1 shows the magnetic flu density versus the distance from the upper surface of HT bulk magnet along the ais line. As shown, a higher J c would result in a higher B trap. When J c = 1 A/m, the maimum central B trap can reach 1.1 T at 77 K. B (kgs) 1 1 J c =1 A/m J c =11 A/m J c =1 7 A/m Distance (mm) Fig. 1. B () versus distance () for different J c where the diameter of HT bulk f = mm.. Eperimental Verification Fig. 11 shows the prototype of an HTLM with HT bulk magnet secondary (mover) for the HT magnetic suspension and propulsion system. The machine is controlled by the technique of space vector pulse width modulation (VPWM). The locked-rotor thrust of the HTLM can be measured by using a pulling force sensor connected to one side of the mover, and the load connected to the other side of the mover as shown in Fig. 1. The range of the pulling force sensor is - matched the output voltage of 1-5 V. In practical thrust measurements, PMs are used to form an equivalent magnetic circuit for the tests. Fig. 11. Prototype of the HTLM for an HT magnetic suspension and propulsion system. y Load Primary stator econdary mover with HT bulk magnets Fig. 1. Thrust measurement system for the HTLM. Pulling sensor Fig.1 3 illustrates the locked-mover thrusts measured in two cases: f = H, U/f = 15, air gap length g = 1. mm, and f = 1 H, U/f = 1, g = 13. mm. The waveforms of the locked-mover thrusts are nearly sinusoidal, and the their amplitudes are the maimum thrusts F em_ma. Hence, the maimums in two ecitations are 9.9 and 1.9, respectively. Because the force of gravity of the applied load is 15., the maimum opposite pulling force of the sensor to measure is thus limited to 15.. This is why the inverse maimum thrusts shown in Fig.1 3 are smaller than the positive amplitudes. Locked-mover thrust () Locked-mover thrust () Time (s) Time (s) Fig Locked-mover thrust, f = H, U/f = 15, g = 1 mm, f = 1 H, U/f = 1, g = 13 mm. Based on the control platform developed by LabVIEW TM, the stator phase currents have been measured with different f and U/f as shown in Fig. 13. In these testing, the PWM period T s is set to.5 s, the dead time 1 μs, and the DC Bus voltage V. As seen from this figure, the stator phase current I increases with f initially, and then decreases after reaching the maimum I ma, where the frequency is defined the optimum frequency f o. It can be seen that I ma increases as U/f grows up, while f o could decrease. Fig.1 15 shows the measured F em_ma versus f under different U/f when the g = 1. mm. From the figure, F em_ma increase with f initially and then decrease after reaching their peak values of 5. and 3.5 at U/f = 5, at f = 13 H, and U/f = 1, at f = 11 H, respectively,. Fig.15 depicts the measured F em_ma versus air gap length g under different f and U/f. As shown, F em_ma decreases linearly as the g increases. In order to operate the system at the rated thrust, it is necessary to keep the length of air gap of the HT magnetic suspension at a constant value. Fig.1 7 plots the measured F em_ma, versus I. As shown, F em_ma increases almost linearly with I. Eperiment agrees well with simulation based on the magnetic circuit method ecept for a few points. These errors are mainly caused by the magnetic saturation in the primary stator iron core. Current (A) 1 1 U/f=5 1 U/f=1 U/f= U/f= Frequency (H) Fig. 13. tator phase current versus frequency with different U/f.

6 Maimum thrust ()_ U/f=5 U/f= Frequency (H) Fig Maimum thrust versus frequency with different U/f (g = 1 mm). F em_ma () U/f=1,f=H U/f=1,f=11H Air gap length (mm) Fig. 15. Maimum thrust versus air gap length with different f and U/f. F em_ma () Measured Magnetic circuit calculated 1 1 Current (A) Fig Maimum thrust versus phase current with g = 1 mm, f = 5 H. 7. Conclusions An HT magnetic suspension and HTLM propulsion system has been developed in this paper. Three types of PMGs are were firstly analyed by using the equivalent current sheet method respectively, and then the levitation force are calculated based on them having the results show that the Halbach array PMG can provide the largest levitation force and best ratio (levitation force) / (permanent magnet volume). That is to say, the Halbach array PMG can provide the optimum system performance. The magnetiation characteristics of HT bulk based on the different methods have been eprimental studied, and the conclusions form a reference to select an optimal magnetiation method to obtain HT bulk magnets. The numerical model of the HTLM has been built up and the eperiments validation for its thrust performance have been comprehensively carried out with the results show that the maimum thrust of the HTLM increases linearly with phase current, decreases linearly with the air gap length, and increases with the frequency initially and then decreases with it after reaching its peak value, which reflect the characteristics of HTLM and the developed control system, and it benefits the optimal electromagnetic design and the control scheme development of an HTLM for the HT magnetic suspension application. References [1]. Kusada, M. Igarashi, K. emoto, T. Okutomi,. Hirano, K. Kuwano, T. Tominaga, M. Terai, T. Kuriyama, K. Tasaki, T. Tosaka, K. Marukawa,. Hanai, T. Yamashita, Y. 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7 Fig. 1. chematic illustration of the HT magnetic suspension and propulsion system with an HTLM drive. Fig.. chematic structures of urface mounted PMG (#1), Flu concentration PMG (#), and (c) Halbach array PMG (#3). Fig. 3. Current sheet models, urface mounted PMG (#1), Flu concentration PMG (#), and (c) Halbach array PMG (#3). Fig.. Calculated and measured distributions of B and B along the X ais at h = 1 mm or = 1mm of the surface mounted and flu concentration PMGs. Fig. 5. Transversal distributions of flu density B and B along the X ais at different heights (). at different heights () of the Halbach array PMG (#3): B and B Fig.. Flu linkage of the HTLM. Fig. 7. Maimum thrust versus trapped magnetic flu density for different U/f. Fig.. HT bulk magnetic flu trapping characteristics comparison within different magnetiation methods. Fig. 9. Trapped magnetic flu density versus pulse B et for different samples. Fig. 1. B () versus distance () for different critical current density J c where the diameter of HT bulk f = mm. Fig. 11. Prototype of the HTLM for an HT magnetic suspension and propulsion system. Fig. 1. Thrust measurement system for the HTLM. Fig. 13. Locked-mover thrust, f = H, U/f = 15, g = 1 mm, f = 1 H, U/f = 1, g = 13 mm. Fig. 13. tator phase current versus frequency with different U/f. Fig Maimum thrust versus frequency with different U/f (g = 1 mm). Fig. 15. Maimum thrust versus frequency with different air gap lengths (U/f = 1). air gap length under different U/f and f. Fig Maimum thrust versus phase current at different frequencies ( under g = 1 mm, f = 5 H. Table 1 Main dimensions of transversal section of the PMGs Table. Main parameters of the HTLM Table 3 Levitaion forces of the three PMGs