Plate Clutch Torque (Uniform Wear)
Transmissible torque T = µ·F·n·R_mean for disc clutches and brakes.
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The engineering
Uniform wear is the honest assumption for a broken-in clutch: pressure redistributes until p·r is constant, the mean radius becomes the simple average, and the torque comes out a few percent *lower* than the new-clutch 'uniform pressure' model predicts. Design to the worn number — the clutch spends its life there, and the optimism of the fresh-lining calculation is exactly the margin you'll lose first.
The n multiplier is why motorcycles hide a dozen plates in an oil bath: each pair of mating faces is another friction surface working under the same spring force. The number that bites in service is µ under heat — organic linings fade hard past ~250 °C, so a clutch that holds rated torque on the bench can slip on the third hill start of the afternoon.
Where this math comes from
The first automobiles clutched with leather-faced cones — Karl Benz's Patent-Motorwagen of 1885 among them — which grabbed viciously, wore fast, and demanded adjustment by feel. Multi-plate discs running in oil, developed around 1905 by pioneers including Henry Selby Hele-Shaw, traded peak grip for smoothness and survivability, establishing the geometry this card computes.
The 1920s Borg & Beck single dry plate — woven asbestos (now organic or ceramic) on a sprung hub — became the template for nearly every manual transmission since. The uniform-wear analysis itself settled into the machine-design canon through the great textbooks, where it remains a rite of passage between statics and real machines.
- 1885Karl Benz (circa)Cone clutch on the first automobiles.
- 1905H. S. Hele-Shaw (circa)Multi-plate oil-bath clutch developed.
- 1925Borg & Beck (circa)Single dry-plate clutch standardizes the modern form.
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