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Abstract
A mixed elastohydrodrynamic (EHL) model for journal bearings considering an axial flow due to shaft axial motion and misalignment is developed for lubrication performance evaluation. A new, faster mixed EHL computing technology utilizing the odd–even successive overrelaxation (OESOR) parallel numerical iterative method is proposed based on the red–black successive overrelaxation (RBSOR) method to minimize the execution time prolonged by the complexity caused by the axial flow and misalignments. The multithreaded computing scheme conducted by the OpenMP directive using different meshes and threads suggests that the OESOR method exhibits better efficiency. A series of transient analyses was conducted to solve the mixed EHL model with the parallel OESOR method. The results show that the axial flow and misalignments significantly affect the average pressure, hydrodynamic and asperity contact pressure, elastic deformation, and other characteristics of the journal bearings.
Nomenclature
| A | = | Total contact area (m2) |
| C | = | Radial clearance (mm) |
| Cpr | = | Contact pressure parameter used in the asperity contact model, Cpr = πE*σ/2λz |
| Dm | = | Degree of misalignment |
| E′,E* | = | Elastic modulus (Pa), equivalent elastic modulus (Pa), E* = 2[(1 − νJ)/E′J + (1 − νB)/E′B]− 1 |
| F | = | Load (N) |
| GE | = | Influence function for elastic deformation (m/N) |
| HB, HY | = | Bearing hardness and nondimensional hardness, HY = 2(HB)λz/(πE*σ) |
| h | = | Film thickness (μm) |
| hT | = | Average gap (μm) |
| L | = | Bearing width (mm) |
| ΔL | = | Shaft axial motion amplitude (mm) |
| = | Nondimensional contact pressure for contact pressure calculation, | |
| p | = | Pressure (Pa) |
| R | = | Radius (mm) |
| Rq | = | RMS roughness (μm) |
| r, z | = | Radial and width coordinates (mm) |
| SC | = | Sommerfeld number, SC = ηUBR2/(Wc2) |
| Tθ,Tz | = | Rotation and axial movement period (s) |
| t | = | Time (s) |
| Tθ,Tz = u | = | Journal rotation velocity, u = u1 + u2, (m/s) |
| u1, u2 | = | Bearing, shaft rotation velocity (m/s) |
| v | = | z Direction of flow velocity, v = v1cos(β) + v2, (m/s) |
| v1, v2 | = | Bearing, shaft axial motion velocity (m/s) |
| w | = | r Direction of flow velocity, w = v1sin(β)cos(π − θ + ϕ), (m/s) |
| w1, w2 | = | Bearing, shaft r direction motion velocity (m/s) |
| Z | = | Asperity height (μm) |
| α | = | Contact area in the vicinity of a nodal point (m2) |
| β | = | Misalignment angle (°) |
| β′ | = | Wedge angle between the journal and bearing (°) |
| γ | = | Aspect ratio for roughness orientation |
| δ | = | Deformation (μm) |
| ϵ | = | Journal bearing eccentricity ratio at the mid-plane of the bearing |
| ϵ′ | = | Misalignment eccentricity ratio |
| ϵ′max | = | Maximum possible ϵ′ |
| η | = | Viscosity (PaS) |
| θ | = | Circumferential coordinate (rad) |
| λz | = | Autocorrelation length in the transverse direction (μm) |
| μ | = | Friction coefficient |
| ρ | = | Density (kg/m3) |
| σ | = | RMS roughness (m) |
| = | Poisson's ratio | |
| φ | = | Flow factor |
| φ | = | Attitude angle (rad) |
| ψ | = | Misalignment directional angle |
| ψ {} | = | Operator for mathematical expectation |
Subscripts
| asp | = | Asperity contact |
| B, J | = | Bearing, journal |
| c | = | Asperity contact |
| E | = | Elastic |
| nom | = | Nominal contact |
| r | = | Real contact |
| θ, z | = | Circumference and axial directions |
| s | = | Shear |