Noether Symmetry of Automotive Electromagnetic Suspension Systems and Its Application

CUI Xin-bin; FU Jing-li

doi:10.21656/1000-0887.380060

Volume 38 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(12): 1331-1341

CUI Xin-bin, FU Jing-li. Noether Symmetry of Automotive Electromagnetic Suspension Systems and Its Application[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1331-1341. doi: 10.21656/1000-0887.380060

Citation:

PDF( 2226 KB)

Noether Symmetry of Automotive Electromagnetic Suspension Systems and Its Application

doi: 10.21656/1000-0887.380060

CUI Xin-bin¹,
FU Jing-li²

¹School of Mechanical Engineering & Automation, Zhejiang Sci-Tech University,Hangzhou 310018, P.R.China;²School of Sciences,Zhejiang Sci-Tech University,Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China（11472247;11272287）

Received Date: 2017-03-15
Rev Recd Date: 2017-04-12
Publish Date: 2017-12-15

Abstract

Abstract

The Noether symmetry of vehicle vibration systems with electromagnetic suspension was studied, and the conserved quantity of the system was given. Furthermore, with the conserved quantity, the symmetry solution of the system was obtained. In the form of energy, the Lagrangian equations under different vibration modes were built. With the chosen displacement coordinates as the generalized coordinates, the Noether symmetries of the system under different vibration modes were studied, the corresponding Noether identities, Killing equations and generalized Noether theorems were given. The conserved quantity of the system was applied so that a new method for solving vehicle vibration system responses was proposed. Then this method was used in the calculation of a specific vehicle vibration system, and the displacement response curves and velocity response curves of the system in the cases of swerving, braking, accelerating and so on can be obtained. The calculation results agree well with the empirical data.
- electromagnetic suspension,
- Lagrangian equation,
- Noether symmetry,
- conserved quantity

FullText(HTML)

References(19)

References

[1]	Thompson A. Design of active suspensions[J]. Proceedings of the Institution of Mechanical Engineers,1970,185(1): 553-563.
[2]	Sharp R S,Crolla D A. Road vehicle suspension system design-a review[J]. Vehicle System Dynamics,1987,16(3): 167-192.
[3]	喻凡, 张勇超. 馈能型车辆主动悬架技术[J]. 农业机械学报, 2010,41(1): 1-6.(YU Fan, ZHANG Yong-chao. Technology of regenerative vehicle active suspensions[J]. Transactions of the Chinese Society for Agricultural Machinery,2010,41(1): 1-6.(in Chinese))
[4]	Gysen B L J, Paulides J J H, Janssen J L G, et al. Active electromagnetic suspension system for improved vehicle dynamics[J]. IEEE Transactions on Vehicular Technology,2010,59(3): 1156-1163.
[5]	Gysen B L J, Paulides J J H, Janssen J L G, et al. Design aspects of an active electromagnetic suspension system for automotive applications[J]. IEEE Transactions on Industry Applications,2008,45(5): 1589-1597.
[6]	黄昆, 张勇超, 喻凡. 电动式主动馈能悬架综合性能的协调性优化[J]. 上海交通大学学报，2009,43(2): 226-230.(HUANG Kun, ZHANG Yong-chao, YU Fan. Coordinate optimization for synthetical performance of electrical energy-regenerative active suspension[J]. Journal of Shanghai Jiaotong University,2009,43(2): 226-230.(in Chinese))
[7]	ZHANG Yong-chao, CAO Jian-yong, ZHANG Guo-guang, et al. Robust controller design for an electromagnetic active suspension subjected to mixed uncertainties[J]. International Journal of Vehicle Design,2013,63(4): 423-449.
[8]	梅凤翔. 分析力学[M]. 北京: 北京理工大学出版社, 2013.(MEI Feng-xiang. Analytical Mechanics [M]. Beijing: Bejing Institute of Technology Press, 2013.(in Chinese))
[9]	邱家俊. 机电分析动力学[M]. 北京: 科学出版社, 1992.(QIU Jia-jun. Electromechanical Analytical Dynamics [M]. Beijing: Science Press，1992.(in Chinese))
[10]	梅凤翔. 李群和李代数对约束力学系统的应用[M]. 北京: 科学出版社, 1999.(MEI Feng-xiang. Application of Lie Groups and Lie Algebras to Constrained Mechanical Systems [M]. Beijing: Science Press, 1999.(in Chinese))
[11]	方建会. 二阶非完整力学系统的Lie对称性与守恒量[J]. 应用数学和力学, 2002,23(9): 982-986.(FANG Jiang-hui. Lie symmetries and conserved quantities of second-order nonholonomic mechanical system[J]. Applied Mathematics and Mechanics,2002,23(9): 982-986.(in Chinese))
[12]	梅凤翔. 具有可积微分约束的力学系统的Lie对称性[J]. 力学学报, 2000,32(4): 466-472.(MEI Feng-xiang. Lie symmetries of mechanical system with integral differential constraints[J]. Acta Mechanica Sinica,2000,32(4): 466-472.(in Chinese))
[13]	翟晓阳, 傅景礼. 汽车车体振动系统的对称性与守恒量研究[J]. 应用数学和力学, 2015,36(12): 1285-1293.(ZHAI Xiao-yang, FU Jing-li. Study on symmetries and conserved quantities of vehicle body vibration systems[J]. Applied Mathematics and Mechanics,2015,36(12): 1285-1293.(in Chinese))
[14]	Scherpen J M A, Klaassensi J B, Ballini L. Lagrangian modeling and control of DC-to-DC converters[C]// Proceedings of the INTELEC’〖STBX〗99 . Copenhagen, 1999: 99CH37007, 31-14.
[15]	Scherpen J M A, Jeltsema D, Klaassensi J B. Lagrangian modeling and control of switching networks with integrated coupled magnetics[C]//Proceedings of the 39th IEEE Conference on Decision and Control . Vol4. 2000: 4054-4059.
[16]	Stramigioli S.Modeling and IPC Control of Interactive Mechanical Systems—A Coordinate-Free Approach [M]. London: Springer, 2001.
[17]	谢煜, 傅景礼, 陈本永. 压电堆叠作动器的对称性求解[J]. 应用数学和力学, 2016,37(8): 778-790.(XIE Yu, FU Jing-li, CHEN Ben-yong. Solution of symmetries for piezoelectric stack actuators[J]. Applied Mathematics and Mechanics,2016,37(8): 778-790.(in Chinese))
[18]	FU Jing-li, CHEN Li-qun. On Noether symmetries and form invariance of mechanico-electrical systems[J]. Physics Letters A,2004,331(3/4): 138-152.
[19]	Preumont A. Mechatronics: Dynamics of Electromechanical and Piezoelectric Systems [M]. Netherlands: Springe, 2006.