A numerical model of an oscillating squeeze film between a rubber surface and a rigid surface

Effects of permeability and surface roughness on the behavior of an oscillating viscoelastic squeeze film

“…Moreover, no solid‐solid contact occurs even during the squeezing stage of the oscillating motion. To ensure full hydrodynamic fluid film condition in the calculation, the minimum clearance was always maintained such that h min /μ≥3.92, where h min is the minimum nominal film thickness (Mustafa, 2007). The input parameters used in the calculation are as follows:Radius of the rubber block, R: 49 mm.Thickness of the rubber block, L: 29.2 mm.Dynamic viscosity of silicone oil, η: 0.116 Pa.s.Density of silicone oil, ρ: 970 kg/m 3 .Amplitude of oscillation, a: 0.3 mm.Initial nominal film thickness, h o : 1.4 mm.In Figure 4, the oscillating squeeze film pressure at the center of the rubber surface is presented as the integral average pressure across the squeeze film as a function of dimensionless time when the surface is smooth, frequency of oscillation is 20 Hz and the permeability, k is 2.63×10 −10 m 2 .…”

“…v rm is the radial velocity averaged across the film thickness at r=R. It may be determined by flow rate balance across the boundaries of the clearance gap (Mustafa et al , 2010) as: Equation 6 where h˜ denotes the arithmetic mean of the instantaneous fluid film thickness.…”

“…Pressure, p m in the porous matrix may be expressed by the following Laplace equation (Mustafa et al , 2010): Equation 7 Along with four boundary conditions as follows: Equation 8 Equation 9 The boundary condition at z=L provides the link between the pressure in the porous matrix and the fluid film pressure in the clearance gap. This pressure in the clearance gap given by equation (2) varies with time and is linked to the viscoelastic deformation, u of the rubber material through the following relation: Equation 10 The derivation of this constitutive equation for rubber using a three‐element viscoelastic model or standard linear material model is given in Mustafa (2007). Here, P is the integral averaged axial pressure in the porous matrix.…”

“…Kaneko et al (2004) found that the effect of fluid inertia on pressure and surface deformation of viscoelastic materials becomes important for oscillation of over 40 Hz. Recently, Mustafa (2007) proposed a model considering the combined effect of surface roughness, permeability and viscoelasticity for calculating the performance parameters of an oscillating squeeze film between a porous rubber block and a rigid plate. Mustafa et al (2010) have shown that at a given permeability, rough surface of rubber material contributes to good load‐carrying capacity and minimizes leakage flow.…”

“…Recently, Mustafa (2007) proposed a model considering the combined effect of surface roughness, permeability and viscoelasticity for calculating the performance parameters of an oscillating squeeze film between a porous rubber block and a rigid plate. Mustafa et al (2010) have shown that at a given permeability, rough surface of rubber material contributes to good load‐carrying capacity and minimizes leakage flow. In this paper, the effects of both surface roughness and permeability on the behavior of an oscillating squeeze film over a rubber surface are presented.…”