Squeeze Film Force Modeling with Considering Slip and Inertia Effects Between Hydrophobic Surfaces Within Submillimeter
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ORIGINAL PAPER
Squeeze Film Force Modeling with Considering Slip and Inertia Effects Between Hydrophobic Surfaces Within Submillimeter Clearance Xueping Li1 · Bin Han1 · Xuedong Chen1 · Xinhao Luo1 · Wei Jiang1 Received: 7 January 2020 / Accepted: 7 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Squeeze film force exists but is undesirable in some engineering applications such as immersion lithography and micro-electro mechanical systems. The dynamic characteristics of such systems can be improved by adopting hydrophobic surfaces. In addition to squeeze film damping effects, slip effects are prominent and the inertial effects can be neglected with small film thickness, while inertial effects are prominent and slip effects can be neglected with large film thickness. Existing squeeze film force models that ignore inertia effects will cause unacceptable deviations between hydrophobic surfaces with clearance from dozens to hundreds of microns. In this paper, the squeeze film force model is formulated based on Navier–Stokes equations and two parameters slip boundary conditions while simultaneously considering slip and inertia effects. Experiments using different squeeze film thicknesses and squeeze amplitudes are conducted with parallelism between two specimen surfaces of less than 0.01°. The experimental results show that the slip and inertia effects are critical for accurately predicting the squeeze film force between hydrophobic surfaces under moderate film thickness. The predicted errors of the proposed model can be significantly reduced to less than 0.5% after proper fitting of the two slip parameters under all the test conditions. The method can be adopted for the identification of slip parameters and derivation of kinetic models for systems with squeeze film. Keywords Squeeze film force · Hydrophobic surface · Slip boundary conditions · Fluid inertia List of Symbols b Slip length, m f Frequency of squeeze, Hz Fin Squeeze film force in the region 0 ≤ r ≤ Rs, N Fouter Squeeze film force in the region Rs ≤ r ≤ R, N Fexp Amplitude of experimental squeeze film force, N Fpre Amplitude of predicted squeeze film force, N h Dynamic film thickness (h0 + εsin(ωt)), m ḣ Velocity of squeeze, m/s ḧ Accelerate of squeeze, m/s2 h0 Initial film thickness, m P Pressure in the film region, Pa r, z Radial and axial coordinates R Radius of the circular plate, m Rs Internal radius of slip region, m Rsm Minimum value of Rs, m us Slip velocity, m/s * Wei Jiang [email protected] 1
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Luoyu Road 1037, Wuhan 430074, China
Vr, Vz Velocity in r and z direction, respectively, m/s α Damping correction coefficient β Inertial correction coefficient γ Predicted error of squeeze film force ε Amplitude of squeeze, m η Dynamic viscosity of lubricant, Pa·s ρ Density of lubricant, kg/m3 σ Accumulated fitting error, N τco Critical surface shear stress, Pa 𝜏̃co
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