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Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support

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Abstract

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-θ-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincaré map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

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Authors and Affiliations

  1. School of Printing and Packaging Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yongfang Zhang

  2. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, China

    Yongfang Zhang & Yanjun Lü

  3. College of Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Yongfang Zhang, Yanjun Lü & Norbert Müller

  4. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Di Hei, Yanjun Lü & Quandai Wang

  5. Department of Mechnical and Electrical Engineering, Shaanxi Railway Institute, Weinan, 714000, China

    Di Hei

Authors
  1. Yongfang Zhang
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  2. Di Hei
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  3. Yanjun Lü
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  4. Quandai Wang
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  5. Norbert Müller
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Corresponding author

Correspondence to Yanjun Lü.

Additional information

This project is supported by National Natural Science Foundation of China(Grant No. 51075327), National Key Basic Research and Development Program of China(973 Program, Grant No. 2013CB035705), Shaanxi Provincial Natural Science Foundation of China(Grant No. 2013JQ7008), Open Project of State Key Laboratory of Mechanical Transmission of China(Grant No. SKLMT-KFKT-201011), Tribology Science Fund of State Key Laboratory of Tribology of China(Grant No. SKLTKF11A02), and Scientific Research Program of Shaanxi Provincial Education Department of China(Grant Nos. 12JK0661, 12JK0680)

ZHANG Yongfang, born in 1975, is currently an associate professor and a post-doctor at Key Laboratory of NC Machine Tools &Integrated Manufacturing Equipment of Ministry of Education, Xi’an University of Technology, China. She received her PhD degree from Northwestern Polytechnical University, China, in 2007. Her research interests include nonlinear dynamics of bearing-rotor system, mechatronics.

HEI Di, born in 1983, is currently a PhD candidate at Xi’an University of Technology, China. He received his master degree on mechatronics in Xi’an University of Technology, China, in 2009. His research interests include nonlinear dynamics and control, mechatronics.

LÜ Yanjun, born in 1972, is currently a professor at Key Laboratory of NC Machine Tools &Integrated Manufacturing Equipment of Ministry of Education, Xi’an University of Technology, China. He received his PhD degree on mechanical engineering in Xi’an Jiaotong University, China, in 2005. His research interests include nonlinear dynamics and control, advanced bearing and its lubrication, mechatronics.

WANG Quandai, born in 1969, is currently an associate professor at School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, China. He received his PhD degree on mechanical engineering in Xi’an Jiaotong University, China, in 2009. His research interests include advanced bearing and its lubrication, micro/nano fabrication, mechatronics.

MÜLLER Norbert, is currently an associate professor of mechanical engineering at Michigan State University, USA. He received his PhD degree from Technische Universität Dresden, Germany, in 1999. His research interests include high-speed drives and bearings, mechatronics, turbomachinery, wave rotors, micro-fabricated energy systems.

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Zhang, Y., Hei, D., Lü, Y. et al. Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support. Chin. J. Mech. Eng. 27, 358–368 (2014). https://doi.org/10.3901/CJME.2014.02.358

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  • DOI: https://doi.org/10.3901/CJME.2014.02.358

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