Characteristics of Dynamic Response of Balanced and ... - IEEE Xplore

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 23, NO. 3, JUNE 2013

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Characteristics of Dynamic Response of Balanced and Unbalanced High-Tc Superconducting Maglev System Donghui Jiang, Guangtong Ma, Yuanyuan Xu, Jun Zheng, Zigang Deng, Suyu Wang, and Jiasu Wang

Abstract—Understanding the characteristics of dynamic response of a high-Tc superconducting (HTS) maglev vehicle subject to different operating conditions is of utmost importance for advancing its application in the further transportation system. Based on a reduced HTS maglev model, this paper experimentally reproduced the balanced and unbalanced conditions of on-board passengers/freight by loading and unloading the weight to the model at different locations, namely, at the central location of the model for balanced condition and at the front of the model for unbalanced condition. Making recourse to the B&K vibration analyzer (3560C) and laser displacement acquisition equipment, the dynamic signals, i.e., acceleration, displacement, and resonant frequency of the model subject to respective balanced and unbalanced condition were sampled and analyzed. It was found that, the distribution of on-board weight affects the dynamic response of the model significantly and as expected, the unbalanced distribution does harm to the stability and thus the carrying capability of the maglev vehicle. Index Terms—Dynamic response, high-Tc superconductors (HTSC), maglev vehicle, resonant frequency (RF).

I. I NTRODUCTION

M

ORE AND more attention has been attracted to explore the application of high-Tc superconducting (HTS) maglev technology in the field of transportation system [1]–[3] and others [4], [5]. To realize the application of HTS maglev vehicle, with HTS containers levitated above a permanent magnet guideway (PMG), the characteristics of dynamic response of such system subject to different operating conditions must been well understood and its influence to achieve a reliable maglev vehicle should be clarified. One of the important operating conditions encountered frequently in use is that, the passengers/freight are usually nonuniformly distributed, which necessitates the studies on the characteristics of dynamic response of the unbalanced HTS maglev vehicle. Differing from the pioneering studies concerning the dynamic properties of the HTS maglev system with uniformly distributed mass

Manuscript received October 8, 2012; accepted November 28, 2012. Date of publication December 13, 2012; date of current version January 17, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 51007076, the Fundamental Research Funds for the Central Universities under Grant SWJTU11ZT34, and the Cultivation Foundation for Excellent Doctoral Dissertation of Southwest Jiaotong University. The authors are with the Applied Superconductivity Laboratory, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2012.2234173

[5]–[10], we designed and fabricated a reduced HTS maglev model with two cryostats to substitute the full HTS maglev vehicle system, and then reproduced the unbalanced condition as well as balanced counterpart (for comparison) of on-board passengers/freight by loading and unloading the weight to the model at different locations, namely, at the front of the model for the unbalanced condition and at the central location of the model for the balanced counterpart. II. B RIEF I NTRODUCTION OF E XPERIMENTAL S ETUP The pictures of the experimental scenario are presented in Fig. 1. The experimental setup is mainly composed of three components: The HTS maglev model, with a dimension of 0.8 m in length, 0.6 m in width and 0.35 m in height, embraces two rectangular cryostats symmetrically attached to its base (The details of the cryostat and of the PMG can be found elsewhere [1]), in addition to the B&K vibration analyzer (3560C) and laser displacement acquisition equipment to sample and analyze the dynamic signals of the model under considered conditions. The experimental procedure for the unbalanced condition is identical to that of the balanced condition except the anchored position of the weight, namely, at the front of the model for the unbalanced condition and at the central location of the model for the balanced condition, as shown clearly in Fig. 1(a) and (b). The detailed procedure to perform the experiment is as follows: The model was initially placed at a field-cooling height (FCH) of 40 mm above the center of the PMG, and then released from this position to its levitation position where the equilibrium between the gravity of the model and the vertical force exerted on the cryostat achieves. After an impulse force provided by a special hammer was applied to the model in either vertical or lateral direction, the B&K vibration analyzer started to record and analyze the dynamic signals, viz., acceleration, displacement and resonant frequency, in the respective direction through six piezoelectric accelerometers anchored at points A ∼ F marked in Fig. 1(a) and (b). The sampling interval was set to 20 ms, and the frequency band was of 0 ∼ 800 Hz. Meanwhile, the vertical displacement was measured in points A ∼ D by four Charge-coupled Device (CCD) laser displacement sensors from LK-G Series of KEYENCE Company. With an interval of 60 s, the measurement procedure were repeated identically after the weight of the model were loaded continuously by approximate 5 kg at a time, until the maximum load of ∼25 kg was imposed because the cryostats nearly touch

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Fig. 2. Time-evolution of the acceleration of the HTS maglev model at point E in the vertical direction after an impulse force was applied to this point.

Fig. 1. Experimental scenario for measuring the dynamic signals of a reduced HTS maglev model. (a) Top view of experimental setup; (b) B&K vibration analyzer (3560C) and laser displacement acquisition equipment. The accelerometers were placed at point A, B, C, D, E and F. The laser displacement sensors recorded the displacement of point A, B, C and D.

the upper surface of the PMG under the unbalanced condition. Subsequently, the unloading procedure was performed with decreasing the weight of the model by approximate 5 kg at a time. III. R ESULTS AND D ISCUSSION Fig. 2 shows the time-evolution of the acceleration of the HTS maglev model at point E with an impulse force applied to this point vertically. This figure clearly indicates that, the dynamic response of the model behaves as a typical underdamping oscillation with respect to the equilibrium position, whose characteristic equation can be represented as x ¨ + 2ξωn x˙ + ωn2 x = 0 c ξ= √ (2 mk) k ωn = m

(1) (2)

(3)

where x is the vertical/lateral displacement of the model, ξ the damping coefficient and ωn natural frequency respectively. Through FFT analysis and double integration, the frequency evolution of the model was obtained and illustrated in Fig. 3. The characteristic parameters such as the resonant frequency (RF) can be observed in the vertical/lateral direction and the vibrating frequency of the model is within the low frequency region. One can clearly find from Fig. 3, the RF of unbalanced condition in both directions is lower than that of balanced condition, showing the nonuniformity of weight can influence the dynamic response of the HTS maglev system seriously

Fig. 3. Displacement against frequency response (frequency domain) at point E after an impulse force in the (a) vertical direction and (b) lateral direction was applied to this point during the unloading procedure with the weight of load is ∼15 kg. The frequency domain is obtained through applying Fast Fourier Transform (FFT) for time domain data, then the acceleration signal is integrated to the displacement signal. The whole process could be completed automatically through the Pulse soft of the B&K vibration analyzer.

JIANG et al.: DYNAMIC RESPONSE OF BALANCED AND UNBALANCED HIGH-Tc SUPERCONDUCTING MAGLEV

Fig. 4. Variation of the resonant frequency with respect to the weight of load with impulse force applied (a) vertically and (b) laterally.

and this finding therefore necessitates the investigation of the characteristics of the dynamic response under the unbalanced condition. The relationship between the RF and weight of load was also depicted in Fig. 4. As shown in this figure, the RF of both conditions decreases as the load continually increases regardless of the direction of the impulse force. This finding indicates that the load affects obviously the dynamic stability of the HTS maglev system and the RF presets hysteretic characteristics for the weight of load which is analogous to force hysteresis in terms of displacement of PMG/HTSC system due to the fluxpinning property of HTSC [11]. According to (3), one can see clearly that, the RF is closely related with the mass and stiffness of the HTS maglev model. When the model was forced downward by increasing the load, more current is induced due to the enhancement of the external field to provide a higher Lorentz force to equilibrate the total gravity of the model. Thus, the dynamic stiffness increases [12]. Though the mass of the whole model increases, the ratio of the stiffness to the mass of model decreases all the time. Therefore, the RF decreases with the increase of load during the loading, and increases with decrease of load during the unloading. The variation of the

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Fig. 5. Variation of the levitation height (LH) with respect to the weight of load with impulse force applied (a) vertically and (b) laterally.

dynamic stiffness during the unloading case can be understood similarly to that of the loading case. However, compared to the balanced condition, the RF of the unbalanced condition shows a higher change for both directions. For the case of vertical direction, the RF of the unbalanced condition drops from 13 Hz of no load to 7 Hz of maximum load of ∼25 kg, implying a frequency variation of 6 Hz. In contrast, the frequency variation for the balanced condition is merely 2.5 Hz, from 12.5 Hz of no load to 10 Hz of maximum load of ∼25 kg. For the case of lateral direction, the RF of the unbalanced condition varies from 13 Hz of no load to 6.5 Hz of maximum load of ∼25 kg, accordingly from 13 to 8.5 Hz for the balanced condition, indicating a higher RF change happens for the unbalanced condition. This phenomenon reveals that, the unbalanced distribution of the onboard weight will bring a higher impact on the dynamic stability of the HTS maglev model than the balanced distribution. The conspicuous distinctions between unbalanced and balanced condition are reflected in the change of levitation height (LH) of the HTS maglev model. Fig. 5 gives the measured LH of the HTS maglev model against the weight of load. One can see from this figure, for the unbalanced condition, the LH

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at point B and D increases with the increase of the load, but the LH at point A and C decreases with the increase of the load until the load reaches to its maximum value, i.e., ∼25 kg, a pitching angle was therefore produced. In contrast, for the balanced condition, the LH at point A ∼ D decreases with the increase of load, which implies that the bottom of the cryostat still remains parallel to the surface of the PMG. Due to the pitching angle, the HTSC will induce opposite current with the reduction of external field and leads to the decrease of the Lorentz force in the rising side of cryostat, and consequently the dynamic stiffness of this part decreases. Therefore, the summated stiffness of the unbalanced condition is lower than that of the balanced load and the RF of the unbalanced condition for both directions decreases more obviously than that of the balanced condition with identical load. The lowest LH of unbalanced condition is only 2.7 mm, but the lowest LH of balanced condition remains 24.3 mm when the load reaches to the maximum value, as showed in Fig. 5. Thus the LH of unbalanced condition limits the carrying capacity of the vehicle because of this slant. However, the vehicle still continues to carry more loads due to enough LH under balanced condition. So, the disadvantage of the unbalanced condition is that it obviously influences the carrying capacity of the vehicle and should be suppressed as low as possible in the practical running. Additional finding from Fig. 4 is that, the vertical RF of the unbalanced condition is still smaller than its initial value when the load is completely removed. In contrast, the vertical RF of the balanced condition almost returns to its initial value, indicating a reversible process and being consistent with our previous finding concerning the lateral reversible range [13]. Fig. 5 also indicates that, for the unbalanced condition, the LH of the four points is incapable of returning to the beginning positions due to the hysteretic behavior of HTSC, causing a residual pitching angle which influences the dynamic performance. Unlikely, the model can almost return to the beginning position for the balanced condition. The lateral RF of both conditions increases slightly after the loads were completely removed. The fluxes are trapped constantly during loading and unloading procedure and the trapped fluxes are considered to be responsible mainly for the lateral behavior [14], thus the lateral force is enhanced and the lateral RF is higher than the initial value.

IV. C ONCLUSION To investigate the characteristics of dynamic response of unbalanced and balanced HTS maglev vehicle, a reduced HTS maglev model was firstly fabricated, and then, the dynamic

signals, i.e., acceleration, displacement and RF, of the model was sampled and analyzed on the basis of the B&K vibration analyzer and laser displacement acquisition equipment. Our findings indicate that, compared to the balanced condition, the unbalanced distribution of the weight will deteriorate the dynamic response of the HTS maglev system and thus possible approach, such as pre-load [15], [16], should be used to improve the dynamic properties of the HTS maglev system. R EFERENCES [1] J. S. Wang, S. Y. Wang, Y. W. Zeng, H. Y. Huang, F. Luo, Z. P. Xu et al., “The firstman-loading high temperature superconducting Maglev test vehicle in the world,” Phys. C, vol. 809–814, pp. 378–381, 2002. [2] L. Schultz, O. de Haas, P. Verges, C. Beyer, S. Röhlig, H. Olsen, L. Kühn, D. Berger, U. Noteboom, and U. Funk, “Superconductively levitated transport system—The supratrans project,” IEEE Trans. Appl. Supercond., vol. 15, no. 2, pp. 2301–2305, 2005. [3] G. G. Sotelo, D. H. N. Dias, O. J. Machado, E. D. David, R. de Andrade, Jr., R. M. Stephan, and G. C. Costa, “Experiments in a real scale MagLev vehicle prototype,” J. Phys., Conf. Ser., vol. 234, p. 032054, 2010. [4] F. N. Werfel, U. Floegel-Delor, R. Rothfeld, T. Riedel, B. Goebel, D. Wippich, and P. Schirrmeister, “Superconductor bearing, flywheels and transportation,” Supercond. Sci. Technol., vol. 25, p. 014007, 2012, (16 pp). [5] J. R. Hull, “Superconducting bearings,” Supercond. Sci. Technol., vol. 13, pp. R1–R15, 2000. [6] T. Sugiura and H. Fujimori, “Mechanical resonance characteristics of a high-Tc superconducting levitation system,” IEEE Trans. Appl. Supercond., vol. 32, no. 3, pp. 1066–1069, 1996. [7] T. Sugiura, M. Tashiro, Y. Uematsu, and M. Yoshizawa, “Mechanical stability of a high-Tc superconducting levitation system,” IEEE Trans. Appl. Supercond., vol. 7, no. 2, pp. 386–389, 1997. [8] L. Kuehn, M. Mueller, R. Schubert, C. Beyer, O. de Haas, and L. Schultz, “Static and dynamic behavior of a superconducting magnetic bearing using YBCO bulk material,” IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 2079–2082, 2007. [9] Z. Deng, J. Zheng, H. Song, L. Liu, L. Wang, Y. Zhang, S. Wang, and J. Wang, “Free vibration of the highttermperature superconducting maglev vehicle model,” IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 2071– 2074, 2007. [10] M. Komori and G. Kamogawa, “Basic study of a magnetically levitated conveyer using superconducting magnetic levitation,” IEEE Trans. Appl. Supercond., vol. 15, no. 2, pp. 2238–2241, 2005. [11] E. H. Brandt, “Friction in levitated superconductors,” Appl. Phys. Lett., vol. 16, no. 53, pp. 1554–1556, 1988. [12] W. Wang, J. Wang, W. Liu, J. Zheng, Q. Lin, S. Pan, Z. Deng, G. Ma, and S. Wang, “Characteristic study of high-Tc superconducting maglev under side-loading,” Phys. C, vol. 468, pp. 188–191, 2009. [13] G. T. Ma, J. S. Wang, Q. X. Lin, M. X. Liu, Z. G. Deng, X. C. Li, H. F. Liu, J. Zheng, and S. Y. Wang, “Lateral restorable characteristics of the high-Tc superconducting maglev vehicle above the permanent magnet guideway,” Phys. C, vol. 469, pp. 1954–1957, 2009. [14] P. Vanderbemden et al., “Remagnetization of bulk hightemperature superconductors subjected to crossed and rotating magnetic fields,” Supercond. Sci. Technol., vol. 20, pp. S174–S183, 2007. [15] H. Konishi, M. Isono, H. Nasu, and M. Hirose, “Suppression of rotor fall for radial-type high-temperature superconducting magnetic bearing,” Phys. C, vol. 392–396, pp. 713–718, 2003. [16] G. T. Ma, Q. X. Lin, J. S. Wang, S. Y. Wang, Z. G. Deng, Y. Y. Lu, M. X. Liu, and J. Zheng, “Method to reduce levitation force decay of the bulk HTSC above the NdFeB guideway due to lateral movement,” Supercond. Sci. Technol., vol. 21, p. 065020, 2008, (5 pp).