Abstract
There are few experimental results available on film thickness at speeds above 5 m/s and they are almost all based on the optical ball-on-disc test rig. In contrast to the contacts in a rolling bearing, in which the lubricant in the oil reservoir distributes symmetrically, ball-on-disc contact shows asymmetry of lubricant distribution due to centrifugal effects. In order to closely imitate the contact occurring between the ball and the outer ring of a ball bearing, this study proposes an experimental model based on ball-on-glass ring contact. An optical matrix method is used to analyze the optical system, which is composed of a steel ball-lubricant-chromium-coated glass ring. Based on the optical analysis, the measurement system is improved in order to obtain a high quality interference image, which makes it possible to measure the film thickness at high-speeds conditions.
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Abbreviations
- x, x′:
-
coordinates in the radial direction of the ring at which the ray intersects with the input and output planes
- α, α′:
-
angles of the projections of rays onto the xz plane with the optical axis at the input and output planes
- y, y′:
-
coordinates in the axis direction of the ring at which the ray intersects with the input and output planes
- β, β′:
-
angles of the projections of rays onto the yz plane with the optical axis at the input and output planes
- M :
-
optical transfer matrix (OTM) of an optical system
- M i :
-
OTM of the air medium between lens and image surface
- M lens :
-
OTM of the lens
- M a :
-
OTM of the air medium between the lens and the ring in the uncorrected system
- M r :
-
OTM of the outer surface of the ring
- M o :
-
OTM of the glass medium of ring
- M c :
-
OTM of the cylindrical lens
- M a1 :
-
OTM of the air medium between the ring and the cylindrical lens in the corrected system
- M a2 :
-
OTM of the air medium between the lens and the cylindrical lens in the corrected system
- S :
-
OTM of the uncorrected system
- C :
-
OTM of the corrected system
- d i :
-
distance between the image surface and the lens
- d a :
-
distance between the lens and the ring in the uncorrected system
- d ax :
-
da for the object-image relationship in the x direction to hold
- d ay :
-
da for the object-image relationship in the y direction to hold
- d o :
-
thickness of the glass ring
- d c :
-
thickness of the cylindrical lens, the curvature of which is ignored
- d a1 :
-
distance between the ring and the cylindrical lens in the corrected system
- d a2 :
-
distance between the lens and the cylindrical lens in the corrected system
- m ij :
-
the element at the ith row and jth column of M
- L :
-
width of the homogeneous medium layer
- n 1, n 2 :
-
refractive index of glass K9 and air
- ρ:
-
radius of the sphere, ρ > 0 for convex (center of curvature after interface)
- f :
-
focal length of lens, f > 0 for convex/positive (converging) lens
- R :
-
radius of the ring, R > 0 for convex (center of curvature after interface)
- R c :
-
radius of the cylindrical lens, Rc > 0 for convex (center of curvature after interface)
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Acknowledgement
The work was supported by the National Natural Science Foundation of China (Nos. 51675046 and 51275045) and the National Key Basic Research (973) Program of China (No. 2011CB706602).
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Yaoguang ZHANG. He received his bachelor degree in Automation School in 2014 from Beijing University of Posts and Telecommunications, Beijing, China. Now he is a Ph.D. student in School of Mechanical Engineering in Beijing Institute of Technology, Beijing, China. His current research interests include elastohydrodynamic lubrication film thickness measurement and lubricant performance considering limiting shear stress at very high speed.
Wenzhong WANG. He received his Ph.D. degree in mechanical engineering from Tsinghua University, China, in 2003, and then he worked in State Key Laboratory of Tribology as a postdoc research fellow. He joined School of Mechanical Engineering at Beijing Institute of Technology from 2006. His current position is a professor and director of Department of Machine Design. His research areas cover modeling of lubricated contact problem, contact model for inhomogeneous and function gradient materials, dynamics of rolling bearing, and thermal analysis.
Shengguang ZHANG. He received his bachelor degree in School of Mechanical Engineering in 2011 from Beijing Institute of Technology, Beijing, China. Now he is a Ph.D. student at the same university. His research focuses on the modeling analysis of lubricated contact problem considering the effect of material inhomogeneity. His research interests also include the dynamic modeling analysis of rolling bearings and the measurement of lubrication film thickness by optical interferometry method.
Ziqang ZHAO. He received his Ph.D. degree in mechanical engineering from Beijing Institute of Technology, China, in 2009. He joined School of Mechanical Engineering at Beijing Institute of Technology from 2009. His current position is a lecturer. His research areas cover dynamic theory and experiment of gear transmission system and rolling bearing, numerical simulation of lubrication, thermal analysis, and mechanical design and so on.
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Zhang, Y., Wang, W., Zhang, S. et al. Optical analysis of ball-on-ring mode test rig for oil film thickness measurement. Friction 4, 324–334 (2016). https://doi.org/10.1007/s40544-016-0127-5
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DOI: https://doi.org/10.1007/s40544-016-0127-5