Hydrodynamic Bearing Oil-Flow Calculator
Estimate the axial pressure difference required to deliver oil through a finite hydrodynamic bearing clearance.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
How to use
- This calculator has one axial-flow mode. Enter shaft diameter D, bearing length L, and radial clearance c in millimetres.
- Enter signed eccentricity ratio ε with −1 < ε < 1. In this implementation positive ε increases h₀; verify that convention against your coordinate system.
- Enter positive dynamic viscosity η in Pa·s at the intended operating temperature.
- Enter the required positive oil flow Q₁ and choose its unit, then choose the pressure display unit.
- Select Calculate or edit any field to update the result. Reset example restores all supplied values and recalculates.
- Read required pressure difference first, then h₀, L/D, c/R, and the SI flow conversion. Values are rounded to two decimal places except the supporting SI flow.
- Correct red warnings before interpreting results. Check whether the calculated supply pressure, available flow, and lubricant temperature are realistic.
- Do not use this relation for grooved, starved, turbulent, thermally varying, deformable, rough, mixed-lubrication, or safety-critical bearing design without a fuller model and test evidence.
Worked example
For D=40 mm, L=40 mm, c=0.2 mm, ε=0, η=0.04 Pa·s, and Q₁=5 L/h, the result is Δp=0.27 bar, h₀=0.20 mm, L/D=1.00, and c/R=0.01. This means about 0.27 bar axial pressure difference is required under the idealized model.
Related analysis
Equations used
All calculations use SI units internally. Positive Q and positive Δp point from supply to outlet. ε is signed as defined below.
Definitions: Q₁ is entered volume flow and Cᵤ converts the selected unit to m³/s; Q is SI flow [m³/s]; D and R are shaft diameter and radius [m]; L is axial bearing length [m]; c is radial clearance [m]; η is dynamic viscosity [Pa·s]; ε is a dimensionless signed eccentricity ratio; Δp is pressure difference [Pa before conversion]; and h₀ is the displayed clearance metric [m before conversion].
Flow conversions are 1 m³/min=1/60 m³/s, 1 m³/h=1/3600 m³/s, 1 L/min=10⁻³/60 m³/s, and 1 L/h=10⁻³/3600 m³/s. Pressure conversions are 1 MPa=10⁶ Pa, 1 bar=10⁵ Pa, and 1 mbar=100 Pa.
Displayed pressure, h₀, L/D, and c/R are rounded to two decimal places using nearest-value decimal rounding.
Theory and method
The relation is a pressure-driven, finite-length axial-clearance form of the incompressible Reynolds lubrication equation. Pressure demand rises linearly with flow Q, viscosity η, and length L, but varies inversely with the cube of radial clearance c. Clearance uncertainty therefore dominates many screening estimates.
The factor 2+3ε² adjusts conductance for eccentricity and is insensitive to the sign of ε. The displayed h₀ relation is sign-sensitive: this calculator defines positive ε so h₀=c(1+ε). Many journal-bearing texts define eccentricity toward the minimum gap and write hmin=c(1−ε); reverse the entered sign if that is your convention.
Assumptions and limits
Assumes steady, laminar, isoviscous, incompressible oil flow through a uniform rigid smooth circular clearance. It omits grooves, rotation-induced circumferential pumping, cavitation, starvation, turbulence, temperature/viscosity feedback, elastic or thermal deformation, roughness, leakage paths, and mixed or boundary contact. Inputs must be finite; D, L, c, η, and Q₁ must be strictly positive; −1 < ε < 1.
References
- Hamrock, B. J. (1991), Fundamentals of Fluid Film Lubrication, NASA RP-1255, axial flow and Reynolds-equation foundations. NASA NTRS record.
- Reynolds, O. (1886), “On the Theory of Lubrication,” Philosophical Transactions of the Royal Society. doi:10.1098/rstl.1886.0005.