Hydrodynamic Behavior of the Sliding Surface with Semicircular Pores: Theoretical and MATLAB Considerations

2. Model And Basic Equations

Cross-section of the two opposite surfaces with hemispherical pores on the lower surface are shown in Fig.1; each pore has radius r₀ and the gap between surfaces equals h0.

Figure 1.

Semicircular pore cell geometry

Assuming that the pores are arranged regularly and the distance 2r₁ between pores (see Figure 1) is sufficiently large so that the interaction between the pores can be neglected, only one pore with the adjoining part, called the control cell, can be studied. The hydrodynamic lubrication is described by the Reynolds equation, which in its dimensionless form is

• X=x/r₀,

• H=h/h₀,

• P=p/Λ,

• Λ=6μur₀/h₀².

Here and hereinafter:

• P = p/Λ - dimensionless hydrodynamic pressure;

• p - dimensional hydrodynamic pressure;

• u- dimensional velocity of sliding surface, along coordinate x;

• r₀ - dimensional pore radii;

• r₁ – control cell dimension;

• h₀ - dimensional minimal clearance (gap) between surfaces;

• X=x/r₀ - dimensionless coordinate;

• x - dimensional coordinate;

• H – dimensionless local film thickness;

• h – dimensional local film thickness;

• W=w/(Λr₀) - dimensionless load support;

• Λ=6μur₀/h₀²;

• μ - dimensional dynamic viscosity of lubricating film;

• w- dimensional load support along x-direction;

• Ψ= r₀/ h₀ - pore radii to gap value ratio;

• ξ = r₁/r₀ – control cell dimension to pore radii ratio;

• max – maximal value;

• cav – cavitation threshold.