Drive pulley traction calculator (T1 / T2)
Minimum slack-side tension to avoid drive slip, from effective tension, friction coefficient and wrap angle.
Result
How it works
A drive pulley can only transmit tension if the belt does not slip. The capstan (Euler–Eytelwein) relation links the tight-side tension T1 and slack-side tension T2 at the point of slip to the friction coefficient and the wrap angle.
From the effective tension Te = T1 − T2 you can find the smallest T2 that still transmits Te. Your take-up must keep the real slack-side tension above this value with margin.
Formula
T1 / T2 = e^(μ·θ) T2,min = Te / (e^(μ·θ) − 1) T1 = T2 + Te θ in radians = degrees × π / 180
| Symbol | Meaning | Unit |
|---|---|---|
| Te | Effective tension the drive must transmit | kN |
| μ | Friction coefficient between belt and pulley surface (verified) | — |
| θ | Wrap angle of the belt on the drive pulley | degrees |
| T1 | Tight-side tension | kN |
| T2 | Slack-side tension | kN |
Worked example
Inputs: Effective drive tension Te = 12 kN; Verified friction coefficient μ = 0.35 ratio; Actual drive wrap angle θ = 210 degrees.
μ = 0.35 and θ = 210° are illustrative inputs for this example only. They are not recommended values. Use the friction coefficient for your lagging and conditions, and the wrap angle measured on your drive.
- θ = 210 × π / 180 = 3.665 rad; μθ = 0.35 × 3.665 = 1.283
- e^(μθ) = 3.607
- T2,min = 12 / (3.607 − 1) = 4.603 kN
- T1 = 4.603 + 12 = 16.603 kN
Assumptions and limits
- Ideal capstan relation at impending slip with constant friction. It is not the required take-up tension.
- Start-up and braking, wet or contaminated lagging, belt sag limits and the full conveyor tension profile can each require a higher T2.
- The calculator has no default friction coefficient or wrap angle on purpose. Enter values you have verified for your pulley and lagging.
- Friction coefficients above 1 and wrap angles above 360° are outside this screening tool.
Screening estimate, not a design approval. Verify measured inputs, current standards, manufacturer limits and site procedures before purchasing, cutting or installation. Isolate and lock out equipment before any hands-on measurement.
Questions
How can I stop drive pulley slip?
Raise slack-side tension (take-up), increase wrap angle with a snub pulley, improve lagging friction, or keep the lagging clean and dry. Find the actual cause first.
Is T2,min the take-up tension I should set?
No. It is the theoretical slip limit. The required take-up tension must also satisfy sag, start-up and other conditions, plus a margin.
Source notes
- Capstan (Euler–Eytelwein) belt-friction relation; radians used internally.
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