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An Improved Interference Method for Measuring Lubricant Film Thickness Using Monochromatic Light

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Abstract

Optical interferometry is one of the most important methods used to measure lubricant film thickness. Based on the principle of relative optical interference intensity and using monochromatic light, this paper proposes an improved interference method to measure lubricant film thickness. First, a universal formula for calculating lubricant film thickness is deduced according to the basic principle of relative optical interference intensity. Then, based on the actual curve describing the relationship between the light intensity and film thickness, the accuracy of the interference method for monochromatic light is improved. The methods used to calibrate the inference order are also discussed. This paper uses the proposed method to measure the lubricant film thickness of base oil. The proposed method was validated through measurements and compared to the calculation results from the Hamrock–Dowson formula and another measurement method. Finally, a fitting formula for calculating the film thickness was derived for the light loading and high-velocity conditions.

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Abbreviations

\(H_{\text{c}}^{*}\) :

Dimensionless central film thickness in the Hamrock–Dowson formula

\(H_{\hbox{min} }^{*}\) :

Dimensionless minimum film thickness in the Hamrock–Dowson formula

\(E'\) :

General modulus of elasticity of two contacting surfaces, \(\frac{1}{{E^{\prime}}} = \frac{1}{2}\left( {\frac{{1 - \mu_{1}^{2} }}{{E_{1} }} + \frac{{1 - \mu_{2}^{2} }}{{E_{2} }}} \right)\), where E 1 and E 2 are the moduli of elasticity of the two contacting materials and μ 1 and μ 2 are the Poisson’s ratios of the two contacting materials

f :

Friction force between a glass disk and a steel ball

\(I_{\hbox{max} }^{k}\), \(I_{\hbox{min} }^{k}\) :

Maximum and minimum intensities in the half-order k range

G * :

Material parameter in the Hamrock–Dowson formula

H :

Lubricant film thickness

h c :

Dimensional central film thickness

h l=0, h l=1 :

Film thickness of the dark fringe order l = 0, 1

h m=0 :

Film thickness of the bright fringe order m = 0

I :

Vector sum of the two amplitudes for two interfering light beams

I 1, I 2 :

Corresponding light intensity for two wavelengths of light at the same location in an interference image

I max :

Maximum light intensity in an interference pattern

I min :

Minimum light intensity in an interference pattern

\(\overline{I}\) :

Relative light intensity

I 0 :

Light intensity when the lubricant film thickness is zero

\(\overline{I}_{0}\) :

Relative light intensity when the lubricant film thickness is zero

k :

Sequence number of the thickness range defined as the half-order and determined by dividing the thickness–intensity curve at the peak or valley

l :

Dark fringe order

m :

Bright fringe order

n d :

Refractive index of the lubricant

R x :

Equivalent contact radius in the x axis direction

U :

Entrainment velocity, U = (u 1 + u 2)/2

U * :

Speed parameter in the Hamrock–Dowson formula

u 1, u 2 :

Velocities of the two contacting surfaces

W :

Contact load

W * :

Load parameter in the Hamrock–Dowson formula

α :

Pressure–viscosity coefficient of the lubricant

ε :

Ellipticity of the contact

η :

Kinetic viscosity of the lubricant under ambient temperature and pressure

λ :

Wavelength of the incident light

φ 0 :

Phase difference caused by the reflection of the coated film and steel ball

φ 1, φ 2 :

Initial phase of two interfering light beams

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Acknowledgements

This research was supported by the Science and Technology Planning Project of Guangdong Province (Grant No. 2015A030401103) and the National Natural Science Foundation of China (Grant No. 51575190).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Guangdong University of Petrochemical Technology, Maoming, 525000, China

    Yingjun Chen

  2. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510640, China

    ** Huang

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  1. Yingjun Chen
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  2. ** Huang
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Correspondence to Yingjun Chen.

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Chen, Y., Huang, P. An Improved Interference Method for Measuring Lubricant Film Thickness Using Monochromatic Light. Tribol Lett 65, 120 (2017). https://doi.org/10.1007/s11249-017-0903-z

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