Friction

, Volume 4, Issue 4, pp 324–334

Optical analysis of ball-on-ring mode test rig for oil film thickness measurement

  • Yaoguang Zhang
  • Wenzhong Wang
  • Shengguang Zhang
  • Ziqiang Zhao
Open Access
Research Article

DOI: 10.1007/s40544-016-0127-5

Cite this article as:
Zhang, Y., Wang, W., Zhang, S. et al. Friction (2016) 4: 324. doi:10.1007/s40544-016-0127-5

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.

Keywords

film thickness measurement optical interference optical matrix rolling bearing high speed 

Nomenclature

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

Mi

OTM of the air medium between lens and image surface

Mlens

OTM of the lens

Ma

OTM of the air medium between the lens and the ring in the uncorrected system

Mr

OTM of the outer surface of the ring

Mo

OTM of the glass medium of ring

Mc

OTM of the cylindrical lens

Ma1

OTM of the air medium between the ring and the cylindrical lens in the corrected system

Ma2

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

di

distance between the image surface and the lens

da

distance between the lens and the ring in the uncorrected system

dax

da for the object-image relationship in the x direction to hold

day

da for the object-image relationship in the y direction to hold

do

thickness of the glass ring

dc

thickness of the cylindrical lens, the curvature of which is ignored

da1

distance between the ring and the cylindrical lens in the corrected system

da2

distance between the lens and the cylindrical lens in the corrected system

mij

the element at the ith row and jth column of M

L

width of the homogeneous medium layer

n1, n2

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)

Rc

radius of the cylindrical lens, Rc > 0 for convex (center of curvature after interface)

Copyright information

© The author(s) 2016

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Yaoguang Zhang
    • 1
  • Wenzhong Wang
    • 1
  • Shengguang Zhang
    • 1
  • Ziqiang Zhao
    • 1
  1. 1.School of Mechanical EngineeringBeijing Institute of TechnologyBeijingChina

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