Elastohydrodynamic Lubrication (EHL) Solver Program Using MATLAB

For researchers and engineers dealing with elastohydrodynamic lubrication problems, MATLAB serves as a powerful computational tool. EHL problems typically involve calculating pressure distribution and thickness variations of thin oil films between contacting surfaces, which are crucial in the design of mechanical components like gears and bearings.

### Problem Background Elastohydrodynamic Lubrication (EHL) studies the mechanical behavior of lubricant films under high-pressure contact conditions. It combines characteristics of elastic deformation (Elasto-) and fluid dynamics (Hydrodynamic), requiring simultaneous solution of both Reynolds Equation and elastic deformation equations.

### Numerical Solution Approach Reynolds Equation: Describes pressure distribution within the lubricant film, typically requiring consideration of viscosity-pressure relationships (e.g., Barus equation) and density variations. Elastic Deformation Equation: Computes surface deformation using elastic half-space theory or finite element methods. Load Balance: Ensures total pressure in the contact area matches external applied loads.

In MATLAB implementation, the Finite Difference Method (FDM) can discretize Reynolds equation, combined with iterative methods like Newton-Raphson for solving nonlinear systems. The elastic deformation computation can be accelerated using Fast Fourier Transform (FFT) algorithms to enhance求解效率.

### Program Implementation Recommendations Grid Generation: Employ fine mesh grids to improve computational accuracy, particularly near high-pressure contact zones. Pressure-Viscosity Relationship: Implement Barus or Roelands equations to model viscosity variations with pressure. Boundary Conditions: Set appropriate inlet/outlet pressure conditions, typically using zero-pressure or Reynolds boundary conditions. Convergence Criteria: Establish reasonable iteration stopping conditions based on pressure error thresholds or load balance tolerances.

### Extended Applications The EHL solver program can be further extended to analyze Thermal EHL (TEHL) or transient EHL problems by incorporating energy equations or time-stepping methods.

MATLAB's matrix computation capabilities and rich toolboxes (optimization, FFT) make it an ideal platform for solving EHL problems, particularly during algorithm verification and rapid prototyping stages. Key functions like fftn for multidimensional FFT and fsolve for nonlinear equation solving can significantly streamline the implementation process.