考虑结构周期性的高温超导磁浮永磁轨道不平顺谱

吕涛; 邵天洋; 陈嵘; 高文君; 王平; 陈律铭; 李艳

doi:10.3969/j.issn.0258-2724.20250095

考虑结构周期性的高温超导磁浮永磁轨道不平顺谱

doi: 10.3969/j.issn.0258-2724.20250095

吕涛^{1, 3,},
邵天洋^{1, 2},
陈嵘^{1, 2},
高文君⁴,
王平^{1, 2},
陈律铭³,
李艳^4, ,

1.
西南交通大学高速铁路线路工程教育部重点实验室，四川成都 610031
2.
西南交通大学土木工程学院，四川成都 610031
3.
西南交通大学-利兹学院，四川成都 611756
4.
成都西南交通大学设计研究院有限公司，四川成都 610031

详细信息

作者简介:
吕涛（1987—），男，副教授，博士，研究方向为铁路轨道动力学，E-mail：t.lyu@swjtu.edu.cn

通讯作者:
李艳（1984—），女，高级工程师，博士，研究方向为新型轨道交通系统及车轨耦合关系，E-mail： liyan_0712@163.com

中图分类号: U237
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- 文章访问数: 68
- HTML全文浏览量: 35
- PDF下载量: 20
- 被引次数: 0
出版历程
- 收稿日期: 2025-03-11
- 修回日期: 2025-07-05
- 网络出版日期: 2026-03-16

Track Irregularity Spectrum of High-Temperature Superconducting Maglev Permanent Magnet Considering Structural Periodicity

LÜ Tao^{1, 3
,},
SHAO Tianyang^{1, 2},
CHEN Rong^{1, 2},
GAO Wenjun⁴,
WANG Ping^{1, 2},
CHEN Lümin³,
LI Yang^{4
, ,}

1.
MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China
2.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
3.
SWJTU-Leeds Joint School, Chengdu 611756, China
4.
Southwest Jiaotong University Chengdu Design Institute Co., Ltd, Chengdu 610031, China

摘要

摘要:
为给高温超导钉扎磁浮系统提供较为符合实际的几何不平顺轨道谱，开展考虑结构周期性的高温超导磁浮永磁轨道不平顺谱研究. 为实现包含结构周期性的永磁轨道不平顺谱表征和反演，首先建立高温超导磁浮桥梁、永磁轨道有限元模型，对其施加磁浮列车移动荷载获取最不利荷载作用位置并提取该点位移作为动态不平顺；其次，考虑桥梁徐变上拱造成的永磁轨道变形，叠加列车荷载下周期性动态不平顺结果形成轨道周期性不平顺样本；进一步，考虑永磁轨道拼装随机误差，基于白噪声滤波法得到永磁轨道随机几何不平顺样本，与周期性不平顺叠加，形成永磁轨道不平顺谱；采用4阶多项式和洛伦兹函数对永磁轨道不平顺谱进行拟合，并基于逆傅里叶变换反演拟合谱，以检验拟合算法的有效性；最后，分析列车速度变化对永磁轨道不平顺拟合谱的影响. 结果表明：列车荷载速度变化对永磁轨道不平顺谱的影响主要集中在波长3～100 m范围内；当速度接近与桥梁共振的临界速度时，永磁轨道拟合谱反演不平顺幅值变化较为显著. 本文得到的不平顺谱可方便地应用于高温超导磁浮车辆动力学计算中，为不同速度等级高温超导磁浮列车动力学分析与设计优化提供输入.
- 高温超导磁浮 /
- 永磁轨道 /
- 周期性不平顺 /
- 洛伦兹函数 /
- 逆傅里叶变换
Abstract:
To provide a more realistic geometric irregularity spectrum for high-temperature superconducting (HTS) pinning-type maglev systems, the irregularity spectrum of permanent magnet (PM) tracks considering structural periodicity was investigated. To achieve the characterization and inversion of the PM track irregularity spectrum that incorporates structural periodicity, a finite element model of an HTS maglev bridge and its PM track was first built. Moving loads from a maglev train were then applied to the model to identify the most unfavorable loading position, and the displacement at this point was extracted as the dynamic irregularity. Next, by considering the deformation of the PM track caused by bridge creep camber and superimposing the periodic dynamic irregularity results from train loads, a sample of periodic track irregularity was formed. Furthermore, random assembly errors of the PM track were modeled using a white noise filtering method to obtain a sample of random geometric irregularity. This was then superimposed with the periodic irregularity to form the overall PM track irregularity spectrum. The irregularity spectrum was fitted using a 4th-order polynomial and a Lorentzian function, and the fitted spectrum was inversely transformed via the inverse Fourier transform to verify the effectiveness of the fitting method. Finally, the influence of train speed on the fitted irregularity spectrum was analyzed. The results show that train speed mainly affects the PM track irregularity spectrum in the wavelength range of 3–100 m; when the speed approaches the critical resonance speed of the bridge, the amplitude of the inverse-transformed irregularity becomes significantly larger. The irregularity spectrum obtained in this study can be readily applied in the dynamics calculations of HTS maglev vehicles, serving as input for the dynamic analysis and design optimization of HTS maglev trains operating at various speed levels.
- high-temperature superconducting maglev /
- permanent magnet track /
- periodic irregularity /
- Lorentz function /
- inverse Fourier transform

HTML全文

图 1 永磁轨道/桥梁有限元模型（单位：m）

Figure 1. Finite element model of permanent magnet (PM) track/bridge (unit: m)

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图 2 单节列车荷载分布及模拟示意

Figure 2. Load distribution and simulation of single section train

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图 3 不同位置荷载作用点动态位移最大幅值

Figure 3. Maximum amplitude of dynamic displacement at different loading points

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图 4 桥梁跨中竖向挠度曲线（9跨为例）

Figure 4. Vertical deflection curves of bridge mid span (with 9 spans as examples)

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图 5 9跨梁永磁轨道动态位移

Figure 5. Dynamic displacement of 9-span bridge PM track

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图 6 永磁轨道动态位移谱

Figure 6. Dynamic displacement spectrum of PM track

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图 7 轨道梁周期性成分、轨道板周期性成分

Figure 7. Periodic components of bridges and track slabs

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图 8 桥梁徐变上拱

Figure 8. Bridge creep camber

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图 9 叠加周期性不平顺

Figure 9. Superimposing periodic irregularity

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图 10 永磁轨道随机、周期不平顺样本

Figure 10. Random and periodic irregularity samples of PM track

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图 11 多项式拟合永磁轨道不平顺功率密度谱

Figure 11. Polynomial fitting of power density spectrum of PM track irregularity

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图 12 融合周期性谱峰拟合结果

Figure 12. Fitting results of periodic spectral peak

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图 13 拟合曲线反演结果

Figure 13. Fitting curve inversion results

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图 14 不同速度永磁轨道动态位移谱

Figure 14. Dynamic displacement spectrum of PM track at different speeds

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图 15 不同速度永磁轨道不平顺谱拟合结果

Figure 15. Fitting results of PM track irregularity spectrum at different speeds

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表 1 模型材料参数取值

Table 1. Model material parameter values

构件名称	物理量	数值
永磁轨道	弹性模量/Pa	2×10¹¹
	密度/（ kg•m⁻³）	7850
	泊松比	0.3
轨道板	混凝土等级	C60
	弹性模量/Pa	3.65×10¹⁰
	密度/（ kg•m⁻³）	2500
	泊松比	0.2
轨道梁	混凝土等级	C40
	弹性模量/Pa	3.3×10¹⁰
	密度/（ kg•m⁻³）	2500
	泊松比	0.2
桥墩	混凝土等级	C40
	弹性模量/Pa	3.3×10¹⁰
	密度/（ kg•m⁻³）	2500
	泊松比	0.2
支座	刚度/（ N·m⁻¹）	4×10¹⁰
支座	阻尼/（N·s·m⁻¹）	1.2×10⁵

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表 2 4阶多项式拟合参数

Table 2. 4th order polynomial fitting parameters

参数	a₀	a₁	a₂	a₃	a₄
拟合值	−0.6289	0.6996	2.5598	1.5480	0.3580

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表 3 周期性谱峰拟合参数值

Table 3. Periodic spectral peak fitting parameter values

谱峰	$\varphi $	$\gamma $
1	300.0	0.00059
2	208.0	0.00058
3	88.0	0.00050
4	30.0	0.00040

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表 4 不同速度谱峰拟合参数

Table 4. Fitting parameters of spectral peaks at different velocity

速度/（km•h⁻¹）	谱峰	$ \varphi $	$\gamma $
100	1	250.0	0.00060
	2	80.0	0.00052
	3	35.0	0.00051
	4	3.5	0.00050
200	1	248.0	0.00060
	2	75.0	0.00052
	3	38.0	0.00051
	4	4.0	0.00048
300	1	252.0	0.00059
	2	78.0	0.00050
	3	36.0	0.00049
	4	3.8	0.00048
400	1	260.0	0.00059
	2	80.0	0.00051
	3	40.0	0.00050
	4	4.2	0.00048
500	1	255.0	0.00060
	2	81.0	0.00051
	3	38.0	0.00050
	4	5.0	0.00050
600	1	258.0	0.00061
	2	80.0	0.00050
	3	40.0	0.00050
	4	4.6	0.00049

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表 5 不同速度随机谱拟合参数

Table 5. Fitting parameters of random spectrum at different speed

速度/（km•h⁻¹）	a₀	a₁	a₂	a₃	a₄
100	−0.6289	0.6996	2.5598	1.5480	0.3580
200	−0.6287	0.6971	2.5462	1.5477	0.3610
300	−0.6276	0.7239	2.6614	1.6748	0.3991
400	−0.6286	0.7127	2.6354	1.6913	0.4134
500	−0.6302	0.6893	2.5677	1.6524	0.4081
600	−0.6287	0.7073	2.6156	1.6864	0.4140

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