Abstract
Linearized dynamic bearing coefficients are commonly used to determine the vibration response of rotors supported by journal bearings. Journal bearings can, however, behave nonlinearly, particularly in the presence of bearing wear. This work was undertaken to examine the effect of bearing wear severity on the linear and nonlinear responses of a rigid rotor at low, moderately, and highly loaded operating regime. Numerical results showed that the center of the nonlinear orbit coincides with the center of the linear orbit for all three operating regimes in non-worn bearing. However, in worn bearings, the center of the nonlinear orbit shifts away from the center of the linear orbit for all three operating regimes. The nonlinear analysis also showed that super-synchronous vibration response may occur, particularly at highly loaded operating regimes and at the maximum wear depth investigated in this work.
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Abbreviations
- c :
-
Radial clearance, m
- D :
-
Journal diameter, m
- d 0 :
-
Wear depth, m
- e :
-
Eccentricity between journal center and bearing center, m
- F x, F y :
-
X- and Y-component of fluid film journal bearing force, N
- f x, f y :
-
Non-dimensional X- and Y-component of fluid film journal bearing force
- F r, F t :
-
Radial and tangential component of fluid film journal bearing force, N
- h :
-
Fluid film thickness at non-worn region, m
- h 0 :
-
Initial fluid film thickness at non-worn region, m
- h w :
-
Fluid film thickness at worn region, m
- L :
-
Bearing length, m
- M :
-
Rotor mass, m
- m :
-
Non-dimensional rotor mass
- O b :
-
Bearing center
- O j :
-
Journal center
- P :
-
Fluid film oil pressure of non-worn region, Pa
- P w :
-
Fluid film oil pressure of worn region, Pa
- R :
-
Journal radius, m
- t :
-
Time, s
- U :
-
Unbalance force, N
- u :
-
Non-dimensional unbalance force
- W :
-
Bearing load, N
- X, Y :
-
Coordinates of the journal center
- x, y :
-
Coordinates of the journal center, normalized with respect to c
- \(\overline{x},\overline{y}\) :
-
Journal center amplitudes
- Z :
-
Axial distance in the direction of Z-axis, m
- γ :
-
Circumferential coordinate from X-axis, rad
- δ :
-
Wear depth parameter ratio
- ε :
-
Eccentricity ratio
- ε 0 :
-
Steady-state eccentricity ratio
- θ :
-
Circumferential coordinate, rad
- θ s :
-
Circumferential coordinate of the starting point of the worn region, rad
- θ f :
-
Circumferential coordinate of the final point of the worn region, rad
- μ :
-
Viscosity, Pa s
- φ :
-
Attitude angle, rad
- φ 0 :
-
Attitude angle at static equilibrium position, rad
- ω :
-
Angular speed of the rotor, rad/s
- σ :
-
Modified Sommerfeld number
- τ :
-
Non-dimensional time
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Acknowledgements
This work was supported by Tenaga Nasional Berhad (TNB) and UNITEN through the BOLD 2023 Research Grant under the project code of J510050949. The first author would also like to express his sincere gratitude to Universiti Tenaga Nasional for awarding him the UNITEN-YCU Postgraduate Scholarship to support his studies.
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This paper was presented at International Session in KSME Annual Meeting 2023, Songdo Convensia, Incheon, Korea & Online, November 1–4, 2023.
Logamurthi Raja Moorthi is a Mechanical Engineer in Tenaga Nasional Berhad, Malaysia. He is currently pursuing his Masters of Mechanical Engineering at Universiti Tenaga Nasional (UNITEN), Malaysia under the Yayasan Chancellor UNITEN scholarship fund. His field of study is in mechanical vibrations.
Jawaid I. Inayat-Hussain is an Associate Professor of the College of Engineering, Universiti Tenaga Nasional, Malaysia. He received his Ph.D. in Mechanical Engineering from Kobe University, Japan. His research interests are in the areas of rotordynamics, vibration and noise control, and machinery condition monitoring.
Azrul Abidin Zakaria is a Senior Lecturer of the College of Engineering, Universiti Tenaga Nasional, Malaysia. He received his Ph.D. in Mechanical Engineering from University of Southampton, United Kingdom. His research interests include mechanical vibrations, engineering graphics, computer aided engineering, and machine design.
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Moorthi, L.R., Inayat-Hussain, J.I. & Zakaria, A.A. Effect of bearing wear on linear and nonlinear responses of a rigid rotor supported by journal bearings. J Mech Sci Technol 38, 2741–2747 (2024). https://doi.org/10.1007/s12206-024-2204-4
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DOI: https://doi.org/10.1007/s12206-024-2204-4