Water-Lubricated Slide Bearing Calculator

How to use

1. Use the single steady, fully flooded submerged-bearing mode.
2. Enter all ten required values in the displayed units. Every entered value must be finite; F, D, L, ΔD, n, η, ρ, and c must be greater than zero, while μ and Qf may be zero.
3. Select a unit for forced flow and for the natural-leakage result. Edit any field or select Calculate to update all six outputs; select Reset to restore the worked example.
4. Interpret ΔT as an adiabatic screening temperature increase, Q as natural side leakage, N as friction power, P·V as a load-speed severity metric, Cq as a dimensionless flow coefficient, and L/D as bearing slenderness.
5. Correct every warning before use. A high ΔT, PV value, or low natural flow requires supplier data and a more detailed thermal-hydrodynamic check.
6. Do not use this model for dry starts, starved flow, mixed or boundary lubrication, turbulence, cavitation, shaft/bearing deformation, roughness contact, wear life, groove-pressure design, transient duty, or final safety decisions.

Worked example

For F=6500 N, μ=0.2, D=132 mm, L=160 mm, ΔD=0.4 mm, n=190 rpm, η=0.001 Pa·s, ρ=1000 kg/m³, c=4180 J/(kg·K), and Qf=0 L/min, the calculator returns ΔT=13.4 K, Q=109.722 L/h, N=1707.14 W, P·V=0.4 MPa·m/s, Cq=0.725, and L/D=1.21. The result indicates that natural leakage alone is predicted to carry the friction heat with a 13.4 K adiabatic rise; verify that rise and PV against the actual bearing material and water supply.

Equations used

All dimensional equations use SI units internally. R is shaft radius [m], cᵣ is radial clearance [m], and ω is angular speed [rad/s]: R=D/2, cᵣ=ΔD/2, and ω=2πn/60. D and L are converted from millimetres. The correlation fixes the dimensionless eccentricity ratio at ε = 0.999 and defines:

γ = √(1−ε²)

λₘ = √{2(2+ε²)(1+γ) / [4γ²+4γ−γε²]}

λₑ = 1−exp(−2L/D)

Zₑ = 1−tanh[λₑ(L/D)]/[λₑ(L/D)]

Zₘ = 1−tanh[λₘ(L/D)]/[λₘ(L/D)]

Cqe = π(1+ε)−πεZₑ(ε+1)(ε+2)/(2+ε²)

Cqm = π(1−ε)+πεZₘ(ε−1)(ε−2)/(2+ε²)

Cq = (Cqe−Cqm)/(2π)

Q = Cqω(L/D)2R²cᵣ

P·V = [F/(LD)]ωR

N = μFωR

ΔT = N/[(Q+Qf)ρc]

γ is the positive dimensionless auxiliary eccentricity factor; because 0<ε<1, 0<γ<1. λₘ is a positive dimensionless fixed-eccentricity auxiliary factor. λₑ is a dimensionless length-ratio auxiliary factor in the open interval (0, 1) for L/D>0. Zₑ and Zₘ are dimensionless finite-length correction factors in the open interval (0, 1) for finite L/D>0. Cqe and Cqm are positive dimensionless auxiliary flow-coefficient terms; Cq is the resulting positive dimensionless natural-leakage coefficient. The e and m subscripts distinguish the two algebraic branches retained by the audited correlation; they are labels, not user-selectable operating modes.

F is positive bearing load; μ is the non-negative friction coefficient; Qf is additional forced flow; ρ is water density; c is specific heat; Q is natural side leakage; N is friction power; and ΔT is the adiabatic temperature rise. Positive flow is heat-carrying water through the bearing. η is recorded but does not enter this fixed flow/heat correlation. No intermediate quantity is rounded. Display rounding follows the correlation interface: L/D, P·V, N, and ΔT to two decimals; Cq and Q to three decimals.

Theory and method

The model combines a finite-length hydrodynamic leakage correlation at the fixed near-contact eccentricity ε=0.999 with projected-area PV, Coulomb-style friction power, and a steady adiabatic water energy balance. Its dimensionless λ, Z, and Cq terms are sequential algebraic corrections for finite bearing length; the e/m suffixes only identify the two retained equation branches. Natural side leakage is governed by geometry, clearance, and speed; added forced flow changes only the heat balance. This is a screening model for a fully flooded submerged bearing, not a coupled thermal-hydrodynamic solution.

Assumptions include steady incompressible flow, a rigid smooth circular shaft and bearing, fixed ε, uniform entered friction coefficient, and complete conversion of friction power into the combined water stream. The model omits viscosity influence in the leakage correlation, external heat transfer, turbulence, cavitation, starvation, grooves and supply pressure, elastic/thermal distortion, roughness, contaminants, wear, and mixed lubrication.

Hydrodynamic basis: O. Reynolds, “On the Theory of Lubrication” (1886), doi:10.1098/rstl.1886.0005. For coupled film, pressure, and temperature analysis, Continue in TriboSolver and independently validate geometry, water properties, boundary conditions, and material limits.