Calculator Inputs
Example Data Table
Each case below is calculated by the same engine used in the form, so the numbers stay consistent.
| Case | Scenario | Power | Speed mode | v | Belt | μ | Wrap | Tc | T1 | T2 | ΔT |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Example A | Default preset values (flat belt with centrifugal tension). | 5.00 kW | Pulley + RPM | 10.472 m/s | Flat | 0.300000 | 180.000° | 21.93 N | 804.227 N | 326.762 N | 477.465 N |
| Example B | Lower power, smaller pulley, no centrifugal tension. | 3.00 kW | Pulley + RPM | 7.069 m/s | Flat | 0.250000 | 170.000° | 0.000000 N | 810.370 N | 385.957 N | 424.413 N |
| Example C | V-belt with groove angle and centrifugal tension. | 10.00 kW | Pulley + RPM | 15.708 m/s | V-belt | 0.350000 | 200.000° | 49.35 N | 695.872 N | 59.25 N | 636.620 N |
| Example D | Direct belt speed entry for quick checks. | 2.20 kW | Direct speed | 8.500 m/s | Flat | 0.300000 | 160.000° | 0.000000 N | 456.221 N | 197.397 N | 258.824 N |
| Example E | Known slack-side tension (T2) to back-calculate T1. | 1.50 kW | Direct speed | 6.000 m/s | Flat | 0.280000 | 175.000° | 0.000000 N | 352.781 N | 150.000 N | 202.781 N |
Formula Used
- Belt speed (from pulley): v = π · D · N / 60
- Power to tension difference: ΔT = (T1 − T2) = P / v
- Flat belt tension ratio: T1/T2 = e^(μθ)
- V-belt effective friction: T1/T2 = e^(μθ / sin(β/2))
- Centrifugal tension: Tc = m · v²
- With centrifugal correction: (T1 − Tc) / (T2 − Tc) = e^(μ′θ)
- Pulley torque: τ = (T1 − T2) · (D/2)
Notes: θ is in radians, D is in meters, N is RPM, P is in watts, and tensions are in newtons.
How to Use This Calculator
- Enter power and select the correct unit.
- Choose a belt speed source and fill those fields.
- Set μ and wrap angle based on your drive condition.
- Enable centrifugal tension when belt speed is high.
- Optionally provide T1, T2, or Ti to back-check results.
- Use width, thickness, and stress to see design warnings.
- Download CSV for spreadsheets or PDF for reporting.
Belt Tension Guide
Power and belt speed
Belt drives transmit power by creating a tension difference. If power is 5 kW and belt speed is 10 m/s, the required ΔT is P/v = 5000/10 = 500 N. Raising speed lowers ΔT, which can reduce peak loading on the belt.
Finding belt speed from pulley data
When belt speed is unknown, use v = πDN/60. With a 200 mm pulley at 1000 rpm, D = 0.20 m and v ≈ 3.1416×0.20×1000/60 ≈ 10.47 m/s. This is why small diameter, high‑rpm pulleys quickly increase speed.
Friction and wrap angle ratio
The friction model links tensions by T1/T2 = e^(μθ). For μ = 0.30 and θ = 180° (π rad), ratio ≈ e^(0.30π) ≈ 2.57. If wrap rises to 210° (3.665 rad), the ratio becomes e^(0.30×3.665) ≈ 3.00, allowing the same power with lower slack tension. Typical dry rubber-on-cast-iron μ ranges from 0.25 to 0.40, while oily surfaces can drop below 0.15. Use measured conditions whenever possible for accurate design and safer sizing.
V-belt groove advantage
V-belts multiply effective friction using μ′ = μ/sin(β/2). With μ = 0.35 and groove angle β = 34°, sin(17°) ≈ 0.292, so μ′ ≈ 1.20. The higher μ′ greatly boosts T1/T2 for compact drives.
Centrifugal tension at high speed
At high speed the belt develops Tc = m v². For m = 0.20 kg/m and v = 10.5 m/s, Tc ≈ 0.20×110.25 ≈ 22 N. Tc reduces the “usable” friction margin because (T1−Tc)/(T2−Tc) must satisfy the exponential ratio.
Initial tension and slip control
Initial tension Ti sets the average belt load: T1 = Ti + ΔT/2 and T2 = Ti − ΔT/2. If Ti is too low, T2 can approach zero and the belt may flap or slip. If Ti is too high, bearing loads and belt stress rise.
Strength and design checks
A simple stress check uses allowable force = width×thickness×stress. With 50 mm width, 6 mm thickness, and 8 MPa allowable, capacity is 50×6×8 = 2400 N. With a safety factor 1.5, design limit is 1600 N; compare this to T1 for maintenance and troubleshooting decisions.
FAQs
1) What do T1 and T2 mean?
T1 is the tight-side belt tension leaving the driving pulley, and T2 is the slack-side tension returning. Power transfer depends on the difference ΔT = T1 − T2, not the absolute values alone.
2) How do I choose the friction coefficient μ?
Use manufacturer data when available. As a rule of thumb, clean dry contact may be around 0.25–0.40, while dust, oil, or glazing can reduce μ below 0.15. If unsure, test or derate conservatively.
3) What wrap angle should I enter?
Enter the belt contact angle on the driving pulley. Typical drives are near 180°, while idlers can increase wrap to 200–220°. Higher wrap increases the allowable tension ratio and reduces the required slack tension.
4) When should I include centrifugal tension?
Include it for high belt speeds or heavier belts, because Tc = m v² grows rapidly with speed. Tc reduces the effective friction margin and can change the feasible tension range, especially above about 15–20 m/s.
5) Why do I get a non-positive T2?
It usually means the chosen initial tension is too low for the required ΔT, or the power/speed inputs are inconsistent. Increase Ti, increase speed, improve wrap or μ, or reduce transmitted power.
6) How does the strength check work?
The tool estimates allowable force from width×thickness×allowable stress (MPa = N/mm²), then divides by the safety factor. Compare that design limit to T1; if T1 is higher, select a stronger belt or redesign the drive.