Abstract
The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings. On solving the Reynolds equation, the oil film force is always obtained in polar coordinates; thus, the stiffness and dampness parameters can be easily obtained in polar coordinates. Therefore, the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study.
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Abbreviations
- C :
-
radial clearance, μm
- D :
-
journal diameter, mm
- e :
-
journal eccentricity, mm
- f ε :
-
fluid film reaction component on the eccentric direction, N
- f φ :
-
fluid film reaction component perpendicular to the eccentric direction, N
- F X :
-
fluid film reaction component on X direction, N
- F Y :
-
fluid film reaction component on Y direction, N
- h :
-
film thickness, mm
- L :
-
bearing length, mm
- m :
-
mass of rotor per each bearing, kg
- p :
-
pressure, N·m−2
- R :
-
radius of journal, mm
- W :
-
external load, N
- x :
-
coordinate of circumferential direction, mm
- y :
-
coordinate of the eccentric direction, mm
- z :
-
coordinate of axial direction, mm
- X, Y, Z :
-
Cartesian coordinates
- ε :
-
eccentricity ratio, e/C
- θ :
-
angular coordinate, °
- μ :
-
viscosity of zero shear rate, N·s·m2
- φ :
-
attitude angle, rad
- ω :
-
rotation speed of shaft, rad/s
- ω*:
-
= ω(W/mC)1/2
- ω*s :
-
non-dimensional stability threshold speed
- C*ij :
-
non-dimensional damping coefficients, i, j = X, Y
- f*ε :
-
= fε/(SW)
- f*ε :
-
= fφ/(SW)
- F*X :
-
= FX/W
- FY*:
-
= FY/W
- h*:
-
= h/c
- Kij*:
-
non-dimensional stiffness coefficients, i, j = X, Y
- p*:
-
= pC2/(μωR2)
- S :
-
= μωRL3/(WC2)
- z*:
-
= 2z/L
- gz:
-
gradient on z direction
- s:
-
stability state
- ε:
-
component on eccentric direction
- φ:
-
component perpendicular to eccentric direction
- *:
-
non-dimensional parameter
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Acknowledgments
This research is supported by science and technology research project of Hubei provincial department of education (No. Q20192603) and doctoral research fund of Hubei University of Arts and Science (No. 2059023).
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Zhuxin TIAN. He received his bachelor degree in mechanical design manufacturing and automation in 2009 from Huazhong University of Science and Technology, Wuhan, China. He has obtained his Ph.D. degree in mechatronic engineering from Huazhong University of Science and Technology in 2018. After then, he joined Hubei University of Arts and Science as a lecturer. His research interests include hydrostatic and hydrodynamic bearings.
Yu HUANG. He received his bachelor degree in machinery manufacturing process and equipment in 1993 from Huazhong University of Science and Technology, Wuhan, China. He received his M.S. and Ph.D. degrees in automotive engineering and mechanical design manufacturing and automation from Huazhong University of Science and Technology in 2000 and 2004, respectively. After then, he joined Huazhong University of Science and Technology as a lecturer. His current position is a professor and the deputy director of the National engineering research center for digitalization of manufacturing equipment. And he joined Hubei University of Arts and Science as an adjunct professor in 2019. His research areas cover high performance hydrostatic bearing, laser fine processing technology and equipment and highpower laser cutting and welding equipment.
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Tian, Z., Huang, Y. Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal bearings. Friction 9, 201–206 (2021). https://doi.org/10.1007/s40544-019-0328-9
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DOI: https://doi.org/10.1007/s40544-019-0328-9