空气弹簧作为新型中低速磁浮车辆中重要的悬挂部件，它的动态特性对新型中低速磁浮车辆动力学性能的影响成为了一个值得关注的问题。本文分别建立了空气弹簧的非线性模型和新型中低速磁浮车辆的动力学模型，分析了空气弹簧自身动态特性。通过两个模型进行联合仿真，分析空气弹簧的建模方法和物理参数对新型中低速磁浮车辆动力学性能的影响以及车辆在三种状态下通过不同半径曲线时的空气弹簧形态变化。通过仿真分析，得出下列主要结论：
1）在0~20Hz的激振频率下，低频段空气弹簧的垂向刚度不会随着频率而变化，而附加气室和主气室体积比的增加会明显降低空气弹簧的垂向刚度。中高频范围内，空气弹簧的垂向刚度会随着频率的增加而逐渐增加，节流孔直径的增加会使空气弹簧的垂向刚度减小，而附加气室与主气室体积比和激振幅值的增大都会使空气弹簧的垂向刚度变大。
2）当节流孔直径处于一个较小的范围内，空气弹簧位移传递比的峰值随着节流孔的直径增加而减小。而当节流孔直径大于一定数值后，位移传递比的峰值呈现逐渐增大的趋势，并且对应的频率也在逐渐向一个较低的频率平移。附加气室和主气室体积比的增加会使空气弹簧的位移传递比的峰值减小，而且位移传递比峰值对应的频率也在逐渐减小。激振幅值越大，空气弹簧位移传递比的峰值越小。
3）空气弹簧非线性模型计算出来的磁浮车辆垂向平稳性比线性模型计算出来的结果差，而当车辆通过曲线时非线性模型计算出来的车体侧滚角、空气弹簧垂向位移以及水平位移要比线性模型计算出来的结果小。
4）节流孔直径的变化会明显影响磁浮车辆直线运行时的垂向平稳性指标。只有当节流孔直径取在合理范围内时，车体前后端平稳性指标都能达到优秀。节流孔直径对车辆的曲线通过性能基本无影响。附加气室与主气室体积比越大，车辆直线运行时的垂向平稳性越好。在车辆通过曲线时，附加气室与主气室体积比的增加会使车体的侧滚角变大，同时空气弹簧的垂向位移和水平位移的幅值也会增加。
5)车辆在欠超高、均衡状态和过超高状态下通过大半径曲线时，空气弹簧的垂向位移会呈现左右对称变化，即同一悬浮架的一侧空气弹簧的压缩量等于另一侧的拉伸量，并且同一侧的三个空气弹簧具有一致性。车辆以欠超高和过超高状态通过曲线时，空气弹簧垂向位移的幅值出现在圆曲线上；以均衡状态通过曲线时，空气弹簧的垂向位移幅值出现在缓和曲线上。而车辆在三种状态下通过小半径曲线时，各个位置的空气弹簧垂向位移变化不具有对称性和一致性。
 

Airspring is an important component of secondary suspension for new generation low speed maglev, the effects of whose dynamic acteristics on the dynamics performance of maglev should be drawn much attention on. A nonlinear model for airspring and a dynamics model for new generation low speed maglev are established in this thesis, and the dynamic acteristics of airspring have been analyzed. A co-simulation is performed with these two models to analyze the effect of the modelling approaches and physical parameters of airspring on the dynamics performance of low speed maglev.
According to the above work, some conclusions can be reached. Among the frequency ranging from 0 to 20Hz, the vertical stiffness of airspring would not vary with the frequency in the range of low frequency. For high frequency the vertical stiffness increases with increasing frequency. And larger orifice diameter will decrease the vertical stiffness and the increase of ratio between auxiliary chamber volume and main chamber volume  Vr/Va and excitation amplitude will result in the increase of the stiffness.
When the orifice diameter is small, the displacement ratio peak will decrease as the orifice diameter increases. While the orifice diameter is greater than a certain value, the displacement ratio peak will start to increase as the orifice diameter increases and the eigenfrequency will move to a lower one. The displacement ratio peak and eigenfrequency will both decrease as Vr/Va  increases. And a larger excitation amplitude will lead to a vsmaller displacement ratio peak.
As the co-simulation result, it is shown that the vertical ride quality index computed by the nonlinear model is greater than the one by linear model when vehicle is running on the tangent track, and the maximum roll angle of carbody and the horizontal displacement of aispring to the contrary when vehicle is passing curves.
The vertical ride quality index significantly varies with the orifice diameter. Only when the value of orifice diameter is proper, the carbody can reach a good ride quality. The orifice diameter has little influence on curve negotiating performance of maglev vehicle. Better vertical ride quality can be reached as the Vr/Va  increases. When vehicle is passing curves, the maximum roll angle of carbody and maximum vertical and horizontal displacement of airspring will increase as the Vr/Va  increases, while the maximum longitudinal displacement to the contrary.
When the vehicle is passing large-radius curves in any superelevation condition, the variation of vertical displacement of airsprings in the same bogie will possess symmetry, which means the amount of compression on the one side is equal to the amount of stretch on the other side. At the same time, the three airsprings on the same side of vehicle will show the consistency of vertical displacement. When vehicle is passing curves in the cant deficiency and cant excess condition, the amplitude of vertical displacement of airspring occurs on the circle curve section. While the amplitude appears on the transition section when vehicle passing curve in the balance condition. There is no symmetry and consistency of vertical displacement of airspring when vehicle is passing small-radius curves.
 

[1] 张羽. 城市轨道交通2016年统计分析报告发布[N]. 中国交通报, 2017-03-30.

[2] 吴祥明. 磁浮列车[M]. 上海: 上海科学技术出版社, 2003.

[3] 周庆瑞, 金锋编. 新型城市轨道交通[M]. 北京: 中国铁道出版社, 2005.

[4] 连级三. 磁浮列车原理及技术特征[J]. 电力机车技术, 2001(03):23-26.

[5] Kemper H. Schwebebahn mit Räderlosen Fahrzeugen, die an eisernen Fahrschienen mittels magnetischer Felder entlang schwebend geführt werden: Germany Patent, 643316[P]. 1937-04-05.

[6] Nakamura S. Development of high speed surface transport system (IISST)[J]. IEEE Transactions on Magnetics, 1979,15(6):1428-1433.

[7] Suzuki S, Kawashima M, Hosoda Y, et al. HSST-03 system[J]. IEEE Transactions on Magnetics, 1984,20(5):1675-1677.

[8] Yasuda Y, Fujino M, Tanaka M, et al. The first HSST maglev commercial train in Japan[C]. Proceedings of the 18th international conference on magnetically levitated systems and linear drives (MAGLEV 2004). 2004:76-85.

[9] Park D Y, Shin B C, Han H. Korea's urban maglev program[J]. Proceedings of the IEEE, 2009,97(11):1886-1891.

[10] 刘建勋, 卜继玲. 轨道车辆转向架橡胶弹性元件应用技术[M]. 北京: 中国铁道出版社, 2012.

[11] 李芾, 戚壮. 轨道车辆空气弹簧悬挂系统应用与研究[J]. 中国铁路, 2014(4):42-47.

[12] 陈灿辉, 程海涛, 刘建勋. 轨道交通用空气弹簧的结构与应用研究[J]. 铁道机车车辆, 2010,30(6):49-53.

[13] 孔军. 空气弹簧在我国轨道车辆中的应用与发展[J]. 铁道车辆, 2002,40(3):5-8.

[14] 刘增华, 李芾, 黄运华. 空气弹簧及其在轨道车辆上的应用[J]. 电力机车与城轨车辆, 2003,26(6):24-27.

[15] 张利国, 张嘉钟, 贾力萍, 等. 空气弹簧的现状及其发展[J]. 振动与冲击, 2007,26(2):146-151.

[16] 甄亚林, 李芾, 霍芳霄. 空气弹簧发展及其研究现状[J]. 电力机车与城轨车辆, 2014(1):27-32.

[17] 郑文博. 橡胶空气弹簧的应用和发展[J]. 橡胶科技, 2010,08(8):5-9.

[18] 严隽耄, 傅茂海. 车辆工程[M]. 北京: 中国铁道出版社, 2011.

[19] 孔军. 试验型磁浮列车用空气弹簧研制[J]. 铁道车辆, 2000,38(B12):48-50.

[20] 尹力明, 赵志芬. 空气弹簧在磁悬浮列车上的应用研究[J]. 机车电传动, 2002(5):28-30.

[21] 石军, 刘少义, 许恒波, 等. 中低速磁浮列车用新型空气弹簧的研制[J]. 铁道车辆, 2012,50(7):18-21.

[22] Jack G. Ride on air: A history of air suspension[M]. New York: SAE Inc, 1999.

[23] Shearer J L. Continous control of motion with compressed air[M]. Cambridge: Massachusetts Institute of Technology, 1954.

[24] Cavanaugh R D. Air suspension and servo-controlled isolation systems[J]. Shock and Vibration Handbook, 1976,2:31-33.

[25] Kunica S. Servo-controlled pneumatic isolators-their properties and applications[C]. Mechanical Engineering. 345 E 47TH ST, New York, NY 10017: ASME-AMER Soc Mechanical Eng, 1966,88(2):72.

[26] Esmailzadeh E. Design synthesis of a vehicle suspension system using multi-parameter optimization[J]. Vehicle System Dynamics, 1978,7(2):83-96.

[27] Oda N, Nishimura S. Vibration of air suspension bogies and their design[J]. Bulletin of Jsme, 1970,13(55):43-50.

[28] Baach B I, Rivin E. Analysis of a damped pneumatic spring[J]. Journal of Sound & Vibration, 1983,86(2):191-197.

[29] Eickhoff B M, Evans J R, Minnis A J. A review of modelling methods for railway vehicle suspension components[J]. Vehicle System Dynamics, 1995,24(6-7):469-496.

[30] Toyofuku K, Yamada C, Kagawa T, et al. Study on dynamic acteristic analysis of air spring with auxiliary chamber[J]. Jsae Review, 1999,20(3):349-355.

[31] Sorli M, Quaglia G. Analysis of vehicular air suspension[J]. Turkish Journal of Earth Sciences, 1999,22:220-238.

[32] Quaglia G, Sorli M. Air suspension dimensionless analysis and design procedure[J]. Vehicle System Dynamics, 2001,35(6):443-475.

[33] Berg M. A three-dimensional airspring model with friction and orifice damping[C]. Proceedings of the 16th IAVSD symposium. Pretoria, South Africa: 2000,33(supl):528-539.

[34] Berg M. An airspring model for dynamic analysis of rail vehicles[R]. Stockholm: Department of Vehicle Engineering, Royal Insititute of Technology, 1999.

[35] Presthus M. Derivation of air spring model parameters for train simulation[D]. Luleå Tekniska Universitet, 2002.

[36] Suda Y, Wang W, Komine H, et al. Study on control of air suspension system for railway vehicle to prevent wheel load reduction at low-speed transition curve negotiation[J]. Vehicle System Dynamics, 2006,44(sup1):814-822.

[37] Docquier N. Multiphysics modelling of multibody systems: application to railway pneumatic suspensions[D]. Université catholique de Louvain, 2010.

[38] Docquier N, Fisette P, Jeanmart H. Model-based evaluation of railway pneumatic suspensions[J]. Vehicle System Dynamics, 2008,46(S1):481-493.

[39] Docquier N, Fisette P, Jeanmart H. Multiphysic modelling of railway vehicles equipped with pneumatic suspensions[J]. Vehicle System Dynamics, 2007,45(6):505-524.

[40] Pellegrini C, Gherardi F, Spinelli D, et al. Wheel–rail dynamic of DMU IC4 car for DSB: modeling of the secondary air springs and effects on calculation results[J]. Vehicle System Dynamics, 2006,44(sup1):433-442.

[41] Nieto A J, Morales A L, González A, et al. An analytical model of pneumatic suspensions based on an experimental acterization[J]. Journal of Sound & Vibration, 2008,313(1):290-307.

[42] Evans J, Berg M. Challenges in simulation of rail vehicle dynamics[J]. Vehicle System Dynamics, 2009,47(8):1023-1048.

[43] Sayyaadi H, Shokouhi N. A new model in rail–vehicles dynamics considering nonlinear suspension components behavior[J]. International Journal of Mechanical Sciences, 2009,51(3):222-232.

[44] Sayyaadi H, Shokouhi N. Effects of air reservoir volume and connecting pipes' length and diameter on the air spring behavior in rail-vehicles[J]. Iranian Journal of Science & Technology Transaction B Engineering, 2010,34(B5):499-508.

[45] Alonso A, Giménez J G, Nieto J, et al. Air suspension acterisation and effectiveness of a variable area orifice[J]. Vehicle System Dynamics, 2010,48(sup1):271-286.

[46] Facchinetti A, Mazzola L, Alfi S, et al. Mathematical modelling of the secondary airspring suspension in railway vehicles and its effect on safety and ride comfort[J]. Vehicle System Dynamics, 2010,48(sup1):429-449.

[47] Mazzola L, Berg M. Secondary suspension of railway vehicles - air spring modelling: Performance and critical issues[J]. Proceedings of the Institution of Mechanical Engineers Part F Journal of Rail & Rapid Transit, 2014,228(3):225-241.

[48] 郭荣生. 空气弹簧悬挂的振动特性和参数计算(上)[J]. 铁道车辆, 1992(5):1-6.

[49] 郭荣生. 空气弹簧悬挂的设计与计算[M]. 青岛: 四方车辆研究所, 1973.

[50] 徐庆善. 隔振技术的进展与动态[J]. 机械强度, 1994,16(1):37-42.

[51] 陆正刚. 空气弹簧振动系统阻尼特性及改进措施[J]. 铁道车辆, 1994(6):5-9.

[52] 张士义, 张先彤, 张庆春, 等. 超精密加工中的隔振技术研究[J]. 仪器仪表学报, 1995(S1):379-384.

[53] 赵洪伦, 张广世. 高速客车空气弹簧非线性横向刚度特性研究[J]. 铁道车辆, 2000,38(3):30-33.

[54] 王常魁. 空气弹簧及其在铸造生产中的应用[J]. 中国铸造装备与技术, 1985(1):28-31.

[55] 杨毅夫. 空气弹簧及其在有源悬挂中应用的探讨[J]. 中国铁道科学, 1994(4):8-15.

[56] 周永清, 朱思洪. 车辆空气悬架研究综述[J]. 轻型汽车技术, 2003(5):8-11.

[57] 应杏娟, 李郝林, 倪争技. 空气弹簧隔振器的动力特性研究[J]. 上海理工大学学报, 2006,28(2):164-168.

[58] 赵建文, 盛英, 仇原鹰. 空气弹簧参数对减振性能的影响[J]. 噪声与振动控制, 2006,42(3):22-25.

[59] 尹万建, 杨绍普, 申永军, 等. 空气弹簧悬架的振动模型和刚度特性研究[J]. 北京交通大学学报, 2006,30(1):71-74.

[60] 郑明军, 陈潇凯, 林逸. 空气弹簧力学模型与特性影响因素分析[J]. 农业机械学报, 2008,39(5):10-14.

[61] 李芾, 付茂海, 黄运华, 等. 车辆空气弹簧动力学参数特性研究[J]. 中国铁道科学, 2003,24(5):91-95.

[62] 原亮明, 宫相太, 刘爽堃, 等. 铁道车辆空气弹簧垂向动态特性分析方法的研究[J]. 中国铁道科学, 2004,25(4):37-41.

[63] 原亮明, 宫相太, 王渊, 等. 铁道车辆空气弹簧-可变节流阀垂向动态特性的研究[J]. 铁道学报, 2005,27(1):40-44.

[64] 王家胜, 朱思洪. 带附加气室空气弹簧动刚度影响因素试验研究[J]. 振动与冲击, 2010,29(6):1-3.

[65] 王家胜, 朱思洪. 带附加气室空气弹簧动刚度的线性化模型研究[J]. 振动与冲击, 2009,28(2):72-76.

[66] 马佳富, 张海军, 朱思洪, 等. 带附加气室空气弹簧等效刚度和等效阻尼高斯模型[J]. 南京农业大学学报, 2016,39(5):880-886.

[67] 陈燎, 周孔亢, 李仲兴. 空气弹簧动态特性拟合及空气悬架变刚度计算分析[J]. 机械工程学报, 2010,46(4):93-98.

[68] 张伟龙, 陈燎. 空气弹簧附加气室容积有效利用率研究[J]. 重庆交通大学学报(自然科学版), 2014,33(6):150-154.

[69] 陈灿辉, 谢建藩, 陈娅玲. 汽车悬架用空气弹簧的非线性有限元分析[J]. 汽车工程, 2004,26(4):468-471.

[70] 方松, 高红星, 池茂儒. 基于空气弹簧非线性模型的车辆振动特性研究[J]. 机车电传动, 2014(6):31-35.

[71] 罗仁, 曾京, 邬平波. 空气弹簧对车辆曲线通过性能的影响[J]. 交通运输工程学报, 2007,7(5):15-18.

[72] 戚壮, 李芾, 丁军君, 等. 高速动车组空气弹簧横向非线性动力学模型研究[J]. 中国铁道科学, 2014,35(6):111-118.

[73] 戚壮, 李芾, 黄运华, 等. 基于AMESim平台的轨道车辆空气弹簧系统气动力学仿真模型研究[J]. 中国铁道科学, 2013,34(3):79-86.

[74] 戚壮, 李芾, 黄运华, 等. 高速动车组空气弹簧垂向动态特性研究[J]. 机械工程学报, 2015,51(10):129-136.

[75] 戚壮, 李芾, 孙树磊, 等. 动车组转向架空气弹簧支撑模式研究[J]. 机车电传动, 2013(5):9-12.

[76] 张广世, 沈钢. 带有连接管路的空气弹簧动力学模型研究[J]. 铁道学报, 2005,27(4):36-41.

[77] 池茂儒, 高红星, 张卫华, 等. 基于辅助空间的空气弹簧非线性模型[J]. 中国铁道科学, 2014,35(3):83-89.

[78] 池茂儒, 高红星, 张卫华, 等. 空气弹簧频变特性研究[J]. 西南交通大学学报, 2016,51(2-3):236-243.

[79] 高红星, 池茂儒, 朱旻昊, 等. 空气弹簧模型研究[J]. 机械工程学报, 2015,51(4):108-115.

[80] Bruni S, Vinolas J, Berg M, et al. Modelling of suspension components in a rail vehicle dynamics context[J]. Vehicle System Dynamics, 2011,49(7):1021-1072.

[81] INTEC GmbH. Documentation to SIMPACK[CP]. SIMPACK version 8.9 edition.2013

[82] 龚睿. 固定节流孔流量特性的仿真分析及实验[D]. 武汉理工大学, 2014.

[83] 刘东辰, 曾京, 池茂儒, 等. 空气弹簧节流孔非线性力学模型研究[J]. 铁道车辆, 2014,52(12):9-13.

[84] Rail Delta. VAMPIRE User's Manual[CP].2003

[85] 费国忠, 彭光正, 赵彤, 等. 气管道流量特性参数理论分析与实验研究[J]. 工程设计学报, 2004,11(2):77-80.

[86] 孙忠潇. Simulink仿真及代码生成技术入门到精通[M]. 北京: 北京航空航天大学出版社, 2015.

[87] Liu Z, Long Z, Li X. Maglev Trains[M]. Springer Berlin Heidelberg: Springer, 2015.

[88] TB/T 2360-1993, 铁道机车动力学性能试验鉴定方法及评定标准[S].

[89] GB/T 5599-1985, 铁道车辆动力学性能评定和试验鉴定规范[S].

[90] 杨铭. 长沙南至机场中低速磁悬浮工程限界研究[J]. 铁道标准设计, 2017,61(3):19-23.

[91] GB 50157-2013, 地铁设计规范[S].

[92] 吴耀庭. 铁路曲线及曲线养护[M]. 北京: 中国铁道出版社, 1995.