V-Belt Force-Deflection Tensioning
How to actually SET a V-belt's tension, by deflecting the span at its midpoint.
Example
You enter
- Center distance (in) 32
- Large sheave pitch diameter (in) 12
- Small sheave pitch diameter (in) 4
- Measured deflection force (lb) 5.5
- Maker's recommended min force (lb) 4.8
- Maker's recommended max force (lb) 7.2
- Belt condition used
- New-belt factor 1.3
- Number of belts 2
You get
- Belt span 31.75 in
- Deflection (in) 0.496078
- Static tension at the measured force 88 lb per belt
- Target min force (lb) 4.8
- Target max force (lb) 7.2
- Status IN RANGE
- Wrap angle (deg) 165.638
- Shaft load (lb) 349.239
Checked against published worked examples from: V-belt manufacturers' field procedure (Carlisle, Gates, TB Wood's, Bestorq).
Details, formula, and sources
ScopeSpan 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 or tablespan 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).
Source and editionForce-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.
Free accessThe 1/64-per-inch rule and the procedure are published free in manufacturer application guides and fan-industry bulletins. The recommended force VALUES are section- and drive-specific manufacturer tables and are entered by the user rather than reproduced here.
What governsEstimate. AHJ and licensed professional govern.
API field namescenter_distance_in, large_sheave_dia_in, small_sheave_dia_in, measured_force_lb, rec_min_force_lb, rec_max_force_lb, belt_condition, new_belt_factor, belt_count, span_in, deflection_in, static_tension_lb, target_min_force_lb, target_max_force_lb, status, wrap_angle_deg, shaft_load_lb
- Deflection rule 1/64 in of deflection per 1 in of belt spanCarlisle/Gates/TB Wood's/Bestorq published field procedure
- Tension from force T = 16 F, derived from midspan statics at deflection = t/64statics, not a table
- Recommended force range user-entered from the belt maker's table; not reproducedstated scope limit
- New-belt factor 1.3 default, editable; the manufacturer's figure governscommonly published run-in allowance
- Small-deflection approximation the 1/64 slope is shallow enough that sin(angle) is taken as the tangentstated scope limit