By Dominique Bonneau, Aurelian Fatu, Dominique Souchet

This sequence offers the required parts to the improvement and validation of numerical prediction versions for hydrodynamic bearings. This ebook describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically special and every part is carefully illustrated.

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The level 3 loop consists of the search for the partition of the domain into active and inactive zones. For the stationary case presented in this section, the number of pseudo time steps (level 1 loop) is fixed at 10 and the number of thermal iterations (level 2 loop) is fixed at 5. For the first pseudo time step, the search for the first partition (level 3 loop) requires nine iterations. After this, 3 level iterations are required for each change of the time step and only one for the following temperature changes (level 2 loop).

If the calculation hypotheses are those of mixed lubrication, zones with a contact pressure that is not equal to zero can appear. In these zones, the dissipated energy must merge with the energy that results from friction between the asperities of the roughness. 26] 36 Thermo-hydrodynamic Lubrication in Hydrodynamic Bearings where f is the friction coefficient between the two solids making up the walls, u1 and u2 are the respective velocities of these walls (we assume here that there is no relative velocity in the z axial direction), h is the distance between the mean surfaces of the rough walls and pc is the contact pressure (see Chapter 3 of [BON 14b] for more details).

2. Decentered weighting functions. One-dimensional case Each function is of the form: Wi (ξ ) = N i (ξ ) + α F (ξ ) ; Wi (η ) = N i (η ) + β F (η ) ; Wi (ζ ) = N i (ζ ) + γ F (ζ ) where α, β and γ are decentering coefficients, which depend on the Péclet number Pe, and thus, respectively, on the components u, v and w of the velocity corresponding to the three directions x, y and z of the element, of the density ρF, of the specific heat Cp F, of the conductivity kF of the fluid and of the dimensions Δx, Δy and Δz of the sides of the element [HEI 77]: ⎛ α = sign ( u ) ⎜ coth ⎝ u ρ F C pF Δ x Pex 2 ⎞ − ⎟ , Pex = 2 Pex ⎠ kF ⎛ ⎜ ⎝ Pe y ⎛ Pez 2 ⎞ − ⎟, 2 Pez ⎠ β = sign ( v ) ⎜ coth γ = sign ( w) ⎜ coth ⎝ 2 − 2 Pe y ⎞ ⎟; ⎟ ⎠ Pe y = v ρ F C pF Δ y Pez = kF wρ F C pF Δ z kF where sign(u), sign(v) and sign(w), respectively, give the orientation of the flow in the directions x, y and z.

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