Field homogeneity improvement of maglev NdFeB magnetic rails from joints
© Li et al. 2016
Received: 9 October 2015
Accepted: 2 March 2016
Published: 25 March 2016
An ideal magnetic rail should provide a homogeneous magnetic field along the longitudinal direction to guarantee the reliable friction-free operation of high temperature superconducting (HTS) maglev vehicles. But in reality, magnetic field inhomogeneity may occur due to lots of reasons; the joint gap is the most direct one. Joint gaps inevitably exist between adjacent segments and influence the longitudinal magnetic field homogeneity above the rail since any magnetic rails are consisting of many permanent magnet segments. To improve the running performance of maglev systems, two new rail joints are proposed based on the normal rail joint, which are named as mitered rail joint and overlapped rail joint. It is found that the overlapped rail joint has a better effect to provide a competitive homogeneous magnetic field. And the further structure optimization has been done to ensure maglev vehicle operation as stable as possible when passing through those joint gaps. The results show that the overlapped rail joint with optimal parameters can significantly reduce the magnetic field inhomogeneity comparing with the other two rail joints. In addition, an appropriate gap was suggested when balancing the thermal expansion of magnets and homogenous magnetic field, which is considered valuable references for the future design of the magnetic rails.
KeywordsMagnetic rail Joint Field homogeneity Maglev
In 2014, a new generation of the high temperature superconducting (HTS) maglev indoor experiment platform in enclosed tubes has been successfully developed in Southwest Jiaotong University. It is composed of a HTS maglev vehicle named as Super-Maglev, evacuated tubes whose vacuum degree is adjustable, and a circular Halbach-type magnetic rail. The HTS maglev has the development potential in the area of urban and cargo transportation for its advantages of high speed, low noise, riding comfort and safety (Ma et al. 2003).
Magnetic rail is one of the core components in the HTS maglev system, which is used to provide magnetic field source to the whole levitation system. By employing the Halbach-type magnetic rail (Jing et al. 2007; Deng et al. 2009), a strong magnetic field with high gradient in distribution can be achieved for providing stable suspension (Wang et al. 2001; Sotelo et al. 2011; Deng et al. 2015). Magnetic field is particularly required to be as homogeneous as possible along the running direction, so that a friction-free movement can be achieved in theory. In fact, the longitudinal magnetic field above the magnetic rail is usually not sufficiently homogeneous as excepted for the practical applications, the main obstacle is that the long distance rails are assembled by lots of short rail segments (Okano et al. 2004). There are joint gaps between every adjacent segment. Those joint gaps are the major factor affecting the magnetic field inhomogeneity. The inhomogeneous magnetic field has been verified as a kind of external disturbance for the maglev vehicle, and is a non-ignorable factor that directly affects the riding comfort and the running safety (Lin et al. 2011; Sun et al. 2016).
Enormous work has been done to explore the influence of magnetic field inhomogeneity due to joint gaps. Okano et al. (2004) and Lin et al. (2011) calculated the magnetic field inhomogeneity between two segments of the conventional unimodal magnetic rail and put forward some improvement countermeasures. The cost of the Halbach-type magnetic rail is just about 38 % of that of conventional unimodal magnetic rail per kilometer (Wang et al. 2002 and Del-Valle et al. 2011), while the levitation efficiency (N/cm3) is about 2.85 times larger (Deng et al. 2008), and thus has been widely used or reformed for the maglev applications (Guo et al. 2010; Deng et al. 2013; Boughrara et al. 2013). But until recently, the method to improve magnetic field homogeneity of the Halbach-type magnetic rail with joint gaps is so limited that it is necessary to optimize the Halbach-type magnetic rail joint to guarantee the riding comfort of the HTS maglev vehicle. In this paper, the magnetic field inhomogeneity over normal rail joint which was employed in the present Maglev system was evaluated. Two rail joints, the mitered rail joint and the overlapped rail joint, have been proposed aiming at improving the longitudinal homogeneity of the applied magnetic fields. The simulation results show the effectiveness of the new rail joints, especially for the overlapped rail joint, and the further optimized rail joint has better performance.
Coordinate systems of these three rails were set up as shown in Fig. 3. The origins of the coordinate system are established on the bottom of the geometric center of the gaps. X-axis is perpendicular to the running direction and Y-axis parallels to the running direction of the magnetic rail and its direction is from left to right. Z-axis is along the vertical direction.
Magnetic field of the normal rail joint
Comparison on magnetic fields of three different rail joints
From the above analysis, it points out that the magnetic field above the normal rail joint is not homogeneous, and this magnetic field inhomogeneity will affect running performance of the levitated vehicle. Therefore, the mitered rail joint and the overlapped rail joint are put forward to improve the magnetic field to ensure the vehicle operate stable in a comparatively homogeneous magnetic field, as shown in Fig. 3b, c, respectively.
Realizing an appropriate structure parameter is a significant way to improve homogeneity of magnetic field above a rail with certain joint gap. In order to improve the magnetic field as homogeneous as possible, structure optimizations of the mitered rail joint and the overlapped rail joint are further explored.
The mitered rail joint
In Fig. 3b, it is seen that rail structure varies with the change of θ. Therefore, taking rail structure into account, magnetic field distributions above mitered rail joint with θ of 15°, 30°, 45°, 60° and 75° have been discussed.
The overlapped rail joint
The Overlapped height
Change ratio of overlapped rail joint with different rail structures
Upper joint gap (%)
Bottom joint gap (%)
The lapped length
Suitable size of the joint gap
PMs have the basic property of thermal expansion at high temperature, which may lead to the deformation and influence the operation performance of the maglev vehicle. Thus it is necessary to maintain a suitable size of the joint gap. In order to determine the most suitable size of the joint gap between two magnetic rail segments, the thermal expansion size of a magnetic rail was calculated. The coefficient of NdFeB’s thermal expansion is 4 × 10−6/°C. The formula of linear expansion is α = △L/L × △T, where α refers to coefficient of thermal expansion, △L length change of the object, △T temperature variation, L initial length of the object. Through this formula, with 35° temperature change (the common temperature variation from winter to summer in Chengdu), a Halbach rail of 1 meter long will increase 0.14 mm in summer compared to that in winter. Based on the above analysis and the magnetic field change ratio, it is suitable to have a joint gap around 1 mm.
Change ratio of different rail joints with a 1 mm joint gap
Normal rail joint
Mitered rail joint
(θ = 30°)
Overlapped rail joint (h 1:h 2 = 1:2)
To ensure the best performance of the maglev vehicle running above a long distance magnetic rail, two new rail joints, mitered rail joint and overlapped rail joint, have been put forward to obtain a comparatively homogeneous magnetic field, and structure parameter optimization was conducted. The simulation results show that mitered rail joint and overlapped rail joint are possible to obtain a comparatively homogeneous magnetic field than normal rail joint; the reason is that the rail with special joint shape always has magnets to compensate the magnetic field intensity above the joint gaps. The further optimizations show that overlapped rail joint can significant improve performance of the maglev vehicle when the ratio h 1/h 2 is 1:2. Considering the thermal expansion of magnets, the joint gap within 1 mm is suggested. The overlapped rail joint with optimized parameter does improve the performance of HTS Maglev system.
For further study, a small-size overlapped rail joint construction is planned to verify the function in improving the field homogeneity.
YJL performed the simulation analysis and drafted the manuscript. RXS, ZC, YS, HW, ZDY, and FC participated the simulation work. QD, CYD, JZ and ZGD conceived of the study. All authors read and approved the final manuscript.
This work was partially supported by National Natural Science Foundation in China (51307147 and 51375404), the Fundamental Research Funds for the Central Universities and the State Key Laboratory of Traction Power at Southwest Jiaotong University (2015TPL_Z02 and 2016TPL_T09).
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Boughrara K et al (2013) Magnetic field distribution and levitation force calculation in HTSC-PMG maglev vehicles. Prog Electromagn Res B 55:63–86View ArticleGoogle Scholar
- Del-Valle N et al (2011) Magnet guideways for superconducting maglevs: comparison between Halbach-type and conventional arrangements of permanent magnets. J Low Temp Phys 162(1–2):62–71View ArticleGoogle Scholar
- Deng ZG et al (2008) High-efficiency and low-cost permanent magnet guideway consideration for high-Tc superconducting Maglev vehicle practical application. Supercond Sci Technol 21:115018View ArticleGoogle Scholar
- Deng ZG et al (2009) Performance advances of HTS maglev vehicle system in three essential aspects. IEEE Trans Appl Supercond 19(3):2137–2141View ArticleGoogle Scholar
- Deng ZG et al (2013) An efficient and economical way to enhance the performance of present HTS Maglev systems by utilizing the anisotropy property of bulk superconductors. Supercond Sci Technol 26(2):025001View ArticleGoogle Scholar
- Deng ZG et al (2015) Levitation performance of rectangular bulk superconductor arrays above applied permanent magnet guideways. IEEE Trans Appl Supercond 25(1):3600106Google Scholar
- Guo F et al (2010) Structural parameter optimization design for Halbach permanent Maglev rail. Phys C 470(3):1787–1790View ArticleGoogle Scholar
- Jing H et al (2007) A two-pole Halbach permanent magnet guideway for high temperature superconducting maglev vehicle. Phys C 463–465:426–430View ArticleGoogle Scholar
- Lin QX et al (2011) Study of magnetic field inhomogeneity due to different positional deviations of a permanent magnet guideway. J Supercond Nov Magn 24(5):1473–1478View ArticleGoogle Scholar
- Ma KB et al (2003) Superconductor and magnet levitation devices. Rev Sci Instrum 74(12):4989–5017View ArticleGoogle Scholar
- Okano M et al (2004) Magnetic rail construction for a low loss superconducting magnetic levitation linear guide. IEEE Trans Appl Supercond 14(2):944–947View ArticleGoogle Scholar
- Sotelo GG et al (2011) Experimental and theoretical levitation forces in a superconducting bearing for a real-scale maglev system. IEEE Trans Appl Supercond 21(5):3532–3540View ArticleGoogle Scholar
- Sun RX et al (2011) Study on the magnetic field inhomogeneity of a halbach permanent magnet guideway due to different defects. IEEE Trans Appl Supercond 26(1):3600107Google Scholar
- Wang JS et al (2001) Levitation force of a YBaCuO bulk high temperature superconductor over a NdFeB guideway. IEEE Trans Appl Supercond 11(1):1801–1804View ArticleGoogle Scholar
- Wang JS et al (2002) The first man-loading high temperature superconducting maglev test vehicle in the world. Phys C 378–381:809–814View ArticleGoogle Scholar