Journal-Bearing Squeeze-Film/Impact Calculator

How to use

1. Enter the positive bearing length ratio L/D and journal radius R in millimetres.
2. Enter the final eccentricity ratio ε from 0 (concentric) up to, but not including, 1. Positive ε denotes radial approach toward the bearing wall.
3. Enter lubricant dynamic viscosity η in Pa·s and radial clearance ratio ΔR/R.
4. Select Calculate, or edit any field for an immediate update. Reset restores the worked-example values.
5. Read I₀ as the lubricant-film reaction impulse in N·s. I₀* is its dimensionless counterpart; the remaining metrics confirm converted geometry.
6. Correct any red validation warning before using a result. Do not use this model for cavitating, starved, compressible, thermally varying, elastic, rough, or mixed-lubrication contacts.

Input definitions

• L/D is bearing length divided by shaft diameter; it must be greater than zero.
• ε = e/ΔR is eccentricity divided by radial clearance. The sign convention is positive radial approach from the concentric position; the implemented range is 0 ≤ ε < 1.
• R is the journal radius in millimetres, equal to half the shaft diameter; it must be greater than zero.
• η is lubricant dynamic viscosity in Pa·s at the assessed operating temperature; it must be greater than zero.
• ΔR/R is radial clearance divided by journal radius; it must satisfy 0 < ΔR/R < 1.

Equations used

Let λ=L/D, s(ε)=√(1−ε), and

a(ε) = √3 · 2^3/4 · s(ε) / (2λ)

The finite-length integral is

J(ε) = 3π[√2λ + 2^1/4√3 atan(a(ε))s(ε)] / [s(ε)λ]

The implemented accumulated dimensionless impulse and dimensional impulse are

I₀* = J(ε) − J(0)
I₀ = I₀* η L D / (ΔR/R)²

Geometry is converted using D=2R, L=λD, ΔR=(ΔR/R)R, and e=εΔR. I₀* is the dimensionless accumulated impulse from the concentric position. I₀ is the dimensional impulse in N·s. All equations use SI units internally. Results are shown with six significant digits; no intermediate rounding is applied.

Theory and method

The calculation integrates the squeeze-film reaction of a finite-length hydrodynamic journal bearing as the journal moves from ε=0 to the specified positive eccentricity. It assumes an incompressible, isoviscous Newtonian lubricant, full-film Reynolds behavior, rigid smooth surfaces, and a π-film boundary condition. The rapidly increasing result as ε approaches 1 represents the idealized resistance of a narrowing full film.

The model excludes cavitation, starvation, lubricant compressibility, thermal-viscosity change, inertia, elastic deformation, surface roughness, and asperity contact. It is unsuitable near ε=1 where those effects and manufacturing tolerances can dominate. Reference: method C9.4 for a finite-length impact-loaded hydrodynamic journal bearing with π-film boundary condition.

Worked example

1. Use L/D=1, ε=0.85, R=20 mm, η=0.04 Pa·s, and ΔR/R=0.002.
2. The calculator gives I₀*=12.2426 and I₀=195.882 N·s, with D=40 mm, L=40 mm, ΔR=40 µm, and e=34 µm.
3. Interpretation: under the stated ideal full-film assumptions, the lubricant transmits approximately 196 N·s of reaction impulse while the journal moves from concentricity to ε=0.85.

Continue in TriboSolver to refine the pressure field with actual geometry, operating transients, lubricant behavior, and boundary conditions.