MEC-39

Petroff bearing

Lightly loaded long journal.

Reading speed

MachinesPetroff bearing

Governing equation

\mu=\frac{2\pi^2\eta N r L}{W}\frac{r}{c}

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

where

\eta: Viscosity (Pa·s)
N: Speed (rev/s)
r: Radius (m)
L: Length (m)
W: Load (N)
c: Clearance (mm)
\mu: Friction (—)

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

\mu=\frac{2\pi^2\eta N r L}{W}\frac{r}{c}

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

$N = 1$ $\mu = 0.001$

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

\mu=\frac{2\pi^2\eta N r L}{W}\frac{r}{c}

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

$N = 1$ $\mu = 0.001$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mu}{\mathrm{d}N}

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

$N = 1.497$ $\mu^{\prime} = 0.001$

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-39 — Petroff bearing) is the form associated with Petroff bearing. Working symbols: $\eta$ , $N$ , $r$ , $L$ , $W$ , $c$ $\rightarrow$ $\mu$ . Lightly loaded long journal. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

\mu

from

\eta

N

r

L

W

c

in Mechanical via

\mu=\frac{2\pi^2\eta N r L}{W}\frac{r}{c}

Lightly loaded long 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

\eta = 0.080\,\mathrm{Pa·s}

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

r = 0.040\,\mathrm{m}

L = 0.080\,\mathrm{m}

W = 2000.000\,\mathrm{N}

c = 0.080\,\mathrm{mm}

, the governing relation

\mu=\frac{2\pi^2\eta N r L}{W}\frac{r}{c}

yields

\mu = 0.0253\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Viscosity \eta0.08 Pa·sSpeed N20 rev/sRadius r0.04 mLength L0.08 mLoad W2000 NClearance c0.08 mm

Outputs

Friction \mu0.0253 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Lightly loaded long journal. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube