Calculation
Fᵤ = F₁ − F₂
Only the difference F₁ − F₂ transmits torque, while the combined span forces load the shaft and bearings.
Ingenieurmäßige Vorbemessung
Belt effective tension from span tensions
Only the difference F₁ − F₂ transmits torque, while the combined span forces load the shaft and bearings.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Effective tension Fᵤ — Tangential useful force that transmits torque and power.
- Tight-side tension F₁ — Force in the more highly loaded belt span during operation.
- Slack-side tension F₂ — Remaining force in the less highly loaded belt span.
Example
A 1,000 N tight-side tension minus 400 N slack-side tension gives 600 N effective tension.
Assumptions and limits
Steady operation with span forces at the section considered. Centrifugal tension, tensioning method and dynamic peaks are not calculated independently.
Understand Belt effective tension from span tensions
This calculator separates useful circumferential force from the larger forces carried by the two free spans of a belt drive. It finds Fᵤ from tight-side tension F₁ and slack-side tension F₂, or rearranges the balance for either missing span force.
What does this quantity describe?
Effective belt tension Fᵤ is the difference between span tensions: Fᵤ = F₁ − F₂. It acts tangentially at the pulley pitch radius and produces transmitted torque. Common pretension added to both spans raises F₁ and F₂ without increasing their difference by the same amount.
If two people pull a rope in opposite directions with 1,000 N and 400 N, the resultant is 600 N. For a belt, that difference is the tangentially useful force, although both individual forces still matter to the belt, shaft and bearings.
Formula and variables
Fᵤ = F₁ − F₂
Fᵤ = F₁ − F₂F₁ = Fᵤ + F₂F₂ = F₁ − FᵤP = Fᵤ · vM = Fᵤ · d/2
| Symbol / input | Meaning |
|---|---|
| Effective tension Fᵤ | Tangential useful force that transmits torque and power. |
| Tight-side tension F₁ | Force in the more highly loaded belt span during operation. |
| Slack-side tension F₂ | Remaining force in the less highly loaded belt span. |
Choose the inputs correctly
F₁ is the more highly loaded tight-side force and F₂ the slack-side force. Both values must describe the same operating condition, pulley and convention regarding centrifugal tension. In driving operation F₁ must be at least as large as F₂.
How to use the calculator
Select Fᵤ and enter measured span forces or values from a manufacturer calculation. To size one span, select F₁ or F₂ and enter the required effective tension plus the other span force. Then check traction, allowable belt tension and bearing load separately.
Worked example
For F₁ = 1,000 N and F₂ = 400 N, Fᵤ = 1,000 − 400 = 600 N. At v = 12 m/s this would transmit 7.2 kW; on a 200 mm pitch-diameter pulley it would produce 60 N·m.
Understand the result and units
600 N is not the maximum belt force but the useful difference. The belt must carry at least F₁, while shaft load follows from the vector combination of both span forces. A small Fᵤ with large F₁ and F₂ indicates high pretension with low force utilisation.
Forces are evaluated in newtons. Power in watts follows from newtons times metres per second; torque in newton metres follows from newtons times metres. Use identical units for both span forces.
Effective pull is not shaft load
Fᵤ acts tangentially and produces torque. The shaft instead experiences the geometric vector sum of the forces pulling along both spans. With nearly parallel spans, bearing load is on the order of F₁ + F₂ and can greatly exceed Fᵤ.
Typical applications
Use the result to derive belt-drive power and torque, interpret span-force measurements, and check how much of the force predicted by a manufacturer selection actually transmits work.
Assumptions, limits and common mistakes
This force balance is not a complete belt rating. It does not determine required friction, pretension, centrifugal tension, dynamic factors, width or service life. Product-specific manufacturer data remains authoritative.
Common mistake: Do not use F₁ + F₂ as transmitted circumferential force. Do not mix operating forces with standstill pretension values. Tight and slack sides exchange roles when power flow reverses.
Frequently asked questions
What is effective belt tension?
It is tight-side tension minus slack-side tension. Only this difference produces transmitted torque.
Is Fᵤ the maximum belt force?
No. The largest belt force is normally F₁ and may also contain a centrifugal component.
How do I calculate power from Fᵤ?
Use P = Fᵤ·v when belt speed v is known. Divide watts by 1,000 for kilowatts.
How do I calculate pulley torque?
Use M = Fᵤ·d/2 with pitch diameter d expressed in metres.
Why is there still tension on the slack side?
Pretension is required to create pulley contact pressure and traction, so the slack span does not become force-free.