Hydrodynamic journal-bearing lubrication model
A mechanical-engineering study of pressure, load capacity, film thickness, attitude angle, friction, power loss, leakage, and operating-parameter effects in a hydrodynamic journal bearing.

Project definition
Problem statement
A hydrodynamic journal bearing supports a rotating shaft through pressure generated inside a converging lubricant film. Its load capacity and losses change strongly with speed, clearance, viscosity, bearing proportions, and journal position.
The engineering problem is to calculate those relationships with a transparent numerical model and verify that the main findings are stable across grid refinement and an independent limiting solution.
Project objectives
- Solve the steady finite-length Reynolds equation for the lubricant-film pressure field.
- Calculate load capacity, attitude angle, minimum film thickness, friction, power loss, side leakage, and a temperature-rise screening value.
- Compare speed, eccentricity ratio, lubricant viscosity, radial clearance, and bearing length-to-diameter ratio.
- Measure numerical convergence across five spatial grids.
- Verify a short-bearing case against an independent analytical pressure solution.
Project structure
Project components
Bearing configuration
Validates geometry, lubricant properties, operating conditions, study levels, and numerical grids.
Pressure solver
Builds and solves the sparse finite-difference Reynolds equation with the declared half-film boundary.
Performance calculation
Integrates the pressure and shear results into load, attitude, friction, power, leakage, and film-thickness measures.
Parametric study
Runs the reference case and 26 controlled variations of the principal design and operating inputs.
Verification
Compares five grids and checks a short bearing against an analytical limiting solution.
Evidence pipeline
Writes complete CSV, JSON, figure, test, document, and container evidence.
Methodology
Project workflow
- 01Define the bearing
The released configuration sets the shaft, bearing, lubricant, speed, eccentricity, and spatial grid.
- 02Solve the film pressure
The finite-difference model calculates the positive hydrodynamic pressure over the declared film region.
- 03Calculate performance
Pressure and shear are converted into the retained engineering quantities.
- 04Vary the inputs
Each parameter is changed in a controlled series while the remaining reference values stay fixed.
- 05Check the evidence
Grid convergence, analytical verification, tests, tables, figures, and limitations support the final interpretation.
Demonstration scenario
The 100 mm reference journal at 1500 rpm and eccentricity ratio 0.65 supports 21.402 kN with 7.990 MPa maximum pressure and 26.25 micrometres minimum film thickness. The short-bearing verification has 2.801 percent relative L2 error, and the finest-grid load change is 0.187 percent.
Engineering
Tools and method
- Tools
- The project uses Python, NumPy, SciPy, Pandas, Matplotlib, Jupyter for subject analysis, simulation, and results.
- Lubrication theory
- A steady, incompressible, isoviscous finite-length Reynolds-equation model with a fixed half-film cavitation boundary.
- Numerical method
- Python, NumPy, and SciPy assemble and solve the structured sparse finite-difference system.
- Analysis
- Pandas, JSON, CSV, and Matplotlib retain the parameter matrix, verification results, and figures.
- Verification
- Five spatial grids, a short-bearing analytical comparison, 47 tests, dependency checks, repository validation, and a Linux container run.
Testing
Evaluation
Evaluation measures
- Hydrodynamic pressure distribution and maximum pressure
- Load capacity and attitude angle
- Minimum lubricant-film thickness
- Friction coefficient and power loss
- Side leakage and temperature-rise screening value
- Grid convergence and short-bearing analytical error
Project boundaries
- The model is steady, laminar, isoviscous, incompressible, and smooth-surface.
- The fixed half-film boundary does not enforce lubricant mass conservation in the cavitated region.
- Elastic deformation, misalignment, turbulence, starvation, surface texture, wear, and transient journal motion are outside the retained model.
- The temperature-rise value is an adiabatic screen, not a thermohydrodynamic solution.
- Results support engineering study and comparison, not bearing certification or permission to operate machinery.
Included
- 01Complete Python source code
- 02Reference case and 26 controlled parametric cases
- 03Five-level grid-convergence study and short-bearing verification
- 04CSV and JSON results with five labelled result figures
- 0583-page project report in PDF and editable Word formats
- 0617-page setup and usage guide in PDF and editable Word formats
- 0754 annotated references and three attributed literature images
- 0847 automated tests with 99.54 percent branch-aware coverage
Project record
No information is collected on this page.
- Permanent project ID
- GP-ME-09EC65A
- Catalogued
- 21 Aug 2026
- Completed
- 28 Aug 2026
- Verified
- 28 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.