Differential band brake
Belt tensions, shaft load and actuating force for a differential (two-lever) band brake, which can be configured bi-directional, self-energising, or as a one-way clutch.
Circumferential force, T₁−T₂ = M/r666.67 N
Band tension ratio, T₁/T₂ = exp(μα)2.85
Band tension, T₁1027.09 N
Band tension, T₂360.43 N
Shaft load, F_a1371.34 N
Actuating force, F_i = (T₂b₂−T₁b₁)/a0.47 N
Method & references
- Euler-Eytelwein capstan friction formula: T₁/T₂ = exp(μα).
- If b₂T₂ = b₁T₁ the brake is self-locking in one direction (F_i=0) and free-wheeling in the opposite direction — the differential arrangement can be used as a one-way clutch.
The computation is a literal port of the original client-side JavaScript from /calculators/e3_5e.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.