This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu’s equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant for these algebraic equations. The validity of this research is proven by comparing the stability chart with the time responses of the vibration model suggested by prior research. This research shows that the waviness in the ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2
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e-mail: ghjang@hanyang.ac.kr
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January 2003
Technical Papers
Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness
G. H. Jang,
e-mail: ghjang@hanyang.ac.kr
G. H. Jang
PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea
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S. W. Jeong
S. W. Jeong
PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea
Search for other works by this author on:
G. H. Jang
PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea
e-mail: ghjang@hanyang.ac.kr
S. W. Jeong
PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea
Contributed by the Tribology Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for presentation at the ASME/STLE Tribology Conference, Cancun, Mexico October 27–30, 2002. Manuscript received by the Tribology Division February 22, 2002 revised manuscript received June 18, 2002. Associate Editor: J. A. Tichy.
J. Tribol. Jan 2003, 125(1): 91-101 (11 pages)
Published Online: December 31, 2002
Article history
Received:
February 22, 2002
Revised:
June 18, 2002
Online:
December 31, 2002
Citation
Jang, G. H., and Jeong , S. W. (December 31, 2002). "Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness ." ASME. J. Tribol. January 2003; 125(1): 91–101. https://doi.org/10.1115/1.1504090
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