Tilting-Pad Slider Bearing Calculator

Estimate the load, viscous friction, and optimum pivot location of one plane Michell tilting pad.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Single-pad result

Ideal steady full-film capacity at the selected optimum geometry.

Load capacity, F—kN

Positive V points toward the trailing edge; positive pivot offset e is measured from pad centre in that direction.

Equations used

Let r=L/B. L/B is pad length perpendicular to motion divided by B; B is pad length in the sliding direction. The selected r supplies the dimensionless coefficients Ff*, h₀*, and ε.

μ = (Ff*/h₀*) (h₀/B)

F = (Ff*/μ)² η V r B

L = rB; e = εB

V is the positive relative sliding speed, η is dynamic viscosity, and h₀ is the minimum outlet film thickness. B and h₀ are converted to metres in the load equation, giving F in newtons. Ff* is the dimensionless friction number; h₀* is the dimensionless minimum-film coefficient; ε = e/B is positive toward the trailing edge. Results use full precision and display six significant digits.

Coefficient table

For r = 0.5, 0.75, 1, 1.5, and the infinite-width approximation: (Ff*, h₀*, ε) = (3, 0.16, 0.20), (2.5, 0.22, 0.15), (2.4, 0.27, 0.12), (2.2, 0.32, 0.10), and (1.8, 0.39, 0.09). L/B = 2 is not offered because no coefficient branch is defined for it.

Assumptions and limits

Steady, fully flooded, laminar, incompressible, isoviscous Newtonian lubrication; rigid plane surfaces; no slip; one pad; and a tabulated optimum compromise between minimum friction and maximum film thickness. The infinite-width option uses r=100 as the tabulated approximation. Do not use for start/stop, reversing speed, mixed or boundary lubrication, starvation, cavitation-sensitive operation, turbulence, thermal or elastic distortion, misalignment, rough surfaces, wear, or safety/life qualification.

How to use

Select the supported pad aspect ratio L/B; use the infinite-width approximation only when side leakage is negligible.
Enter B in mm, measured in the positive sliding direction, and V in m/s.
Enter operating dynamic viscosity η in Pa·s and required minimum film thickness h₀ in µm.
Select Calculate or edit any field to update the result. Select Reset to restore the worked example.
Read F as ideal single-pad normal load capacity, μ as viscous friction coefficient, and ε/e as the optimum pivot location.
Correct every warning before interpretation and independently verify units, lubricant state, geometry, and load sharing.
Do not apply the model when the film is not fully hydrodynamic or when thermal, elastic, transient, cavitation, starvation, or surface-contact effects are important.

Worked example

For L/B=0.75, B=80 mm, V=0.5 m/s, η=0.025 Pa·s, and h₀=10 µm, the table gives Ff*=2.5, h₀*=0.22, and ε=0.15. The expected output is μ=0.00142045 and F=2.3232 kN; L=60 mm and the pivot lies e=12 mm toward the trailing edge. This screens one pad carrying about 2.32 kN under the stated ideal assumptions.

Theory and method

A moving runner entrains lubricant into the converging gap beneath a freely tilting pad. Hydrodynamic pressure supports normal load, while viscous shear produces friction. The tabulated coefficient sets represent an optimized pad attitude and pivot location for each aspect ratio. Because coefficients are discrete, this calculator does not interpolate arbitrary L/B values.

References

A. G. M. Michell, Lubrication of Plane Surfaces, Zeitschrift für Mathematik und Physik 52 (1905), 123–137, is the historical plane tilting-pad basis. Osborne Reynolds, On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower’s Experiments, Philosophical Transactions of the Royal Society of London 177 (1886), 157–234, DOI 10.1098/rstl.1886.0005, supplies the thin-film lubrication framework. The discrete C9.2 coefficient table and equations above define this calculator; no DOI is claimed for Michell’s 1905 paper.

Continue in TriboSolver to refine lubricant, operating, and contact assumptions in a broader analysis workflow.