V-Belt Force-Deflection Tensioning
How to actually SET the tension the other belt tiles assume. Span is the tangent between the sheaves, t = sqrt(C^2 - ((D-d)/2)^2); deflect its midpoint 1/64 in per inch of span and read the force. The elegant part: at that deflection the span cancels out of the statics, so the force is exactly one sixteenth of the static tension no matter the drive size - 5.5 lb of force IS 88 lb per belt. A 32 in center on 12 and 4 in sheaves spans 31.75 in and wants a 1/2 in deflection. New belts get about 1.3x the range because an unseated belt sheds tension in the first day. Over-tensioning buys no capacity at all - only the tight-slack DIFFERENCE transmits power - it just puts hundreds of pounds of side load into the bearings, whose life falls as the cube of it. The recommended force range is the belt maker's proprietary table and is an input here, not built in.
Formula and source
span t = sqrt(C^2 - ((D - d)/2)^2); deflection = t/64; static tension T = 16 F (from F = 4 T x deflection / t at deflection = t/64); wrap on the small sheave theta = 180 - 2 asin((D - d)/(2C)) deg; static shaft side load = 2 T n sin(theta/2).
Force-deflection tensioning as published by the V-belt manufacturers - Carlisle/Timken (reproduced in Greenheck Fan Application FA/127-11), Gates, TB Wood's, and Bestorq all give the same 1/64 in of deflection per inch of span. The span and wrap expressions are plane geometry and the tension relation is statics; neither is a table lookup.
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