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Research Papers: Hydrodynamic Lubrication

A Bubble Dynamics Based Approach to the Simulation of Cavitation in Lubricated Contacts

[+] Author and Article Information
Thomas Geike, Valentin L. Popov

Institute of Mechanics, Technische Universität Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany

Note that the central pressure is negative. A value above the classical value means a (negative) value with magnitude smaller than the classical value.

J. Tribol 131(1), 011704 (Dec 02, 2008) (6 pages) doi:10.1115/1.2991290 History: Received January 24, 2008; Revised August 29, 2008; Published December 02, 2008

The negative squeeze lubrication problem is investigated by means of numerical simulations that account for the dynamics of vaporization. The model is based on bubble dynamics, governed by the Rayleigh–Plesset equation, and the Reynolds equation for compressible fluids. Unlike most existing simulation models our model can predict tensile stresses in the fluid film prior to its rupture, which is in accordance with experimental evidence.

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Figures

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Figure 1

Normal separation of (a) circular and (b) square plates as studied experimentally among others by Hays and Feiten (4), Parkins and May-Miller (5), and Chen (6)

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Figure 2

Bubble growth according to Eq. 3 for β=103 (top) and β=108 (bottom). Numerical solution for different initial conditions R̃0; (solid lines) complete Eq. 3; (points) Eq. 3 with neglecting the first and fourth terms, i.e., the inertia and surface energy term.

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Figure 3

Bubble dynamics based simulation model of the negative squeeze film behavior

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Figure 4

Time history of pressure distribution for α0=10−8 (top) and α0=10−3 (bottom); h¯0=10−2, V¯=10−4, n¯0=109, ϕ=3×10−8, ρ¯vap=0, p¯v=0, and 0≤t¯≤0.1

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Figure 5

Normal force F¯ as a function of time t¯ for different initial vapor fractions α0=10−8–10−4; n¯0=109 (top) and n¯0=107 (bottom); h¯0=10−2, V¯=10−4, ϕ=3×10−8, ρ¯vap=0, and p¯v=0

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Figure 6

Central pressure p¯C=p¯(r¯=0) and central vapor fraction αC=α(r¯=0) as a function of time t¯ for α0=10−8, n¯0=109, h¯0=10−2, V¯=10−4, ϕ=3×10−8, ρ¯vap=0, and p¯v=0

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Figure 7

Difference in mixture density between a simulation with our model and a simulation with the cavitation algorithm by Boedo and Booker (12) at r¯=0.01 over longer time intervals (t¯≤100). In this time interval (nondimensional) density drops from 1 to 0.5; α0=10−5, V¯=10−4, h¯0=10−2, n¯0=109, ϕ=3×10−8, ρ¯vap=0, and p¯v=0.

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Figure 8

Central pressure p¯C for periodic surface separation; h¯=h¯m−h¯a cos(2πf¯t¯) with h¯m=10−2, h¯a=5.28×10−3 and f¯=T̑reff=4.4×10−8; ϕ=1.1×10−8, n¯0=107; (dash-dot) α0=4×10−5, (solid line) α0=10−6, and (dashed line) α0=10−8

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