MEC-05

Petroff bearing friction

f = 2π² (μ N / P) (r/c) for a lightly loaded journal.

Reading speed

BearingsPetroff 1883ISO 7902

Governing equation

f=2\pi^2\dfrac{\mu N}{P}\dfrac{r}{c}

$N \in \left[1, 80\right]$

where

\mu: Viscosity (Pa·s)
N: Rotation speed (rev/s)
P: Specific pressure (kPa)
r/c: Radius/clearance (—)
f: Friction coefficient (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

f=2\pi^2\dfrac{\mu N}{P}\dfrac{r}{c}

$N \in \left[1, 80\right]$

$N = 1$ $f = 0.002$

Along the curve

②

Domain of the variable — blue

N_{\min} = 1,\quad N_{\max} = 80

$N \in \left[1, 80\right]$

$N = 1$ $N = 1$

Along the curve

③

Response curve — green

f=2\pi^2\dfrac{\mu N}{P}\dfrac{r}{c}

$N \in \left[1, 80\right]$

$N = 1$ $f = 0.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f}{\mathrm{d}N}

$N \in \left[1, 80\right]$

$N = 1.497$ $f^{\prime} = 0.002$

Along the curve

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-05 — Petroff bearing friction) is the form associated with Petroff 1883 · ISO 7902. Working symbols: $\mu$ , $N$ , $P$ , $r/c$ $\rightarrow$ $f$ . Petroff assumed Couette shear in a concentric oil film; torque is viscosity times speed times (r/c).

Purpose

Purpose: compute

f

from

\mu

N

P

r/c

in Mechanical via

f=2\pi^2\dfrac{\mu N}{P}\dfrac{r}{c}

f = 2π² (μ N / P) (r/c) for a lightly loaded journal. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.080\,\mathrm{Pa·s}

N = 20.000\,\mathrm{rev/s}

P = 400.000\,\mathrm{kPa}

r/c = 500.000\,\mathrm{—}

, the governing relation

f=2\pi^2\dfrac{\mu N}{P}\dfrac{r}{c}

yields

f = 0.0395\,\mathrm{—}

. Long bearing, concentric, SI: N in rev/s, P in Pa. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Viscosity \mu0.08 Pa·sRotation speed N20 rev/sSpecific pressure P400 kPaRadius/clearance r/c500 —

Outputs

Friction coefficient f0.0395 —

Reading speed

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Narration of this film

Long bearing, concentric, SI: N in rev/s, P in Pa.

Petroff assumed Couette shear in a concentric oil film; torque is viscosity times speed times (r/c).

Reading speed

Watch on YouTube