MEC-42

Clutch torque

Uniform-pressure disk clutch.

Reading speed

MachinesClutch torque

Governing equation

T=\tfrac12\mu F(R_o+R_i)n

$F \in \left[200, 10000\right]$

where

\mu: Friction (—)
F: Axial (N)
R_o: Outer R (mm)
R_i: Inner R (mm)
n: Faces (—)
T: Torque (N·m)

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

T=\tfrac12\mu F(R_o+R_i)n

$F \in \left[200, 10000\right]$

$F = 200$ $T = 11.4$

Along the curve

②

Domain of the variable — blue

F_{\min} = 200,\quad F_{\max} = 10000

$F \in \left[200, 10000\right]$

$F = 200$ $F = 200$

Along the curve

③

Response curve — green

T=\tfrac12\mu F(R_o+R_i)n

$F \in \left[200, 10000\right]$

$F = 200$ $T = 11.4$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}T}{\mathrm{d}F}

$F \in \left[200, 10000\right]$

$F = 261.6$ $T^{\prime} = 0.057$

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-42 — Clutch torque) is the form associated with Clutch torque. Working symbols: $\mu$ , $F$ , $R_o$ , $R_i$ , $n$ $\rightarrow$ $T$ . Uniform-pressure disk clutch. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

T

from

\mu

F

R_o

R_i

n

in Mechanical via

T=\tfrac12\mu F(R_o+R_i)n

Uniform-pressure disk clutch. 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 = 0.300\,\mathrm{—}

F = 2000.000\,\mathrm{N}

R_o = 120.000\,\mathrm{mm}

R_i = 70.000\,\mathrm{mm}

n = 2.000\,\mathrm{—}

, the governing relation

T=\tfrac12\mu F(R_o+R_i)n

yields

T = 114.00\,\mathrm{N·m}

. 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

Friction \mu0.3 —Axial F2000 NOuter R R_o120 mmInner R R_i70 mmFaces n2 —

Outputs

Torque T114.00 N·m

Reading speed

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Narration of this film

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

Uniform-pressure disk clutch. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube