MEC-41

Lewis gear bending

Spur-tooth bending with form factor Y.

Reading speed

MachinesLewis gear bending

Governing equation

\sigma=F_t/(b m Y)

$F_t \in \left[100, 8000\right]$

where

F_t: Tangential (N)
b: Face (mm)
m: Module (mm)
Y: Lewis Y (—)
\sigma: Stress (MPa)

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

\sigma=F_t/(b m Y)

$F_t \in \left[100, 8000\right]$

$F_t = 100$ $\sigma = 5.556$

Along the curve

②

Domain of the variable — blue

F_t_{\min} = 100,\quad F_t_{\max} = 8000

$F_t \in \left[100, 8000\right]$

$F_t = 100$ $F_t = 100$

Along the curve

③

Response curve — green

\sigma=F_t/(b m Y)

$F_t \in \left[100, 8000\right]$

$F_t = 100$ $\sigma = 5.556$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\sigma}{\mathrm{d}F_t}

$F_t \in \left[100, 8000\right]$

$F_t = 149.7$ $\sigma^{\prime} = 0.056$

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-41 — Lewis gear bending) is the form associated with Lewis gear bending. Working symbols: $F_t$ , $b$ , $m$ , $Y$ $\rightarrow$ $\sigma$ . Spur-tooth bending with form factor Y. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

\sigma

from

F_t

b

m

Y

in Mechanical via

\sigma=F_t/(b m Y)

Spur-tooth bending with form factor Y. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

F_t = 1200.000\,\mathrm{N}

b = 20.000\,\mathrm{mm}

m = 3.000\,\mathrm{mm}

Y = 0.300\,\mathrm{—}

, the governing relation

\sigma=F_t/(b m Y)

yields

\sigma = 66.67\,\mathrm{MPa}

. 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

Tangential F_t1200 NFace b20 mmModule m3 mmLewis Y Y0.3 —

Outputs

Stress \sigma66.67 MPa

Reading speed

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Narration of this film

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

Spur-tooth bending with form factor Y. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube