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How to Calculate Belt Tension During Startup (Take-up & Safety Check)

Belt conveyor failures during startup are often caused not by insufficient motor power, but by excessive belt tension.

During acceleration, additional forces act on the belt, increasing tension at the drive and take-up sections. If this is not checked properly, it can lead to:

  • Belt overstress and premature belt failure
  • Drive pulley slip
  • Excessive shaft, bearing, and gearbox loads
  • Incorrect take-up sizing

This article explains how to calculate belt tension during startup, including take-up force requirements and safety checks, using practical engineering methods.

Technical diagram of a belt conveyor showing T1 tight side and T2 slack side tension forces during acceleration

Figure 1: Conceptual diagram of belt tension distribution during startup. Note how T1 (Tight Side) increases due to acceleration, while the Take-up Unit maintains T2 (Slack Side) tension to prevent slip.
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1. Why Belt Tension During Startup Matters

Steady-state belt tension is relatively low and stable. However, during startup, the conveyor must overcome:

  • Steady running resistance
  • Acceleration force (F = m × a)
  • Additional dynamic effects at the drive pulley

These effects increase belt tension significantly for a short period. Designing only for steady-state tension can cause serious reliability problems.

2. Basic Parameters Required

Conveyor data

  • Total moving mass, mtotal (kg)
  • Equivalent mass including inertia, meq (kg)
  • Belt speed, v (m/s)
  • Acceleration time, t (s)
  • Drive pulley diameter, D (m)

Forces

  • Running resistance force, Frunning (N)
  • Acceleration force, Facc (N)

Belt & take-up

  • Belt allowable working tension
  • Take-up type (gravity or screw)
  • Wrap angle at drive pulley

3. Step 1 – Calculate Acceleration Force

During startup, the belt must accelerate the moving mass and rotating components. We use the Equivalent Mass method (see our Acceleration Time article for details).

For typical belt conveyors:

meq ≈ 1.05 to 1.20 × mtotal

Linear acceleration:

a = v / t

Acceleration force:

Facc = meq × a

This force acts in addition to steady-state running resistance.

For applications requiring precise motor acceleration analysis, full inertia reflection to the motor shaft should be performed instead of using a simplified equivalent mass.

4. Step 2 – Calculate Total Conveyor Force During Startup

Total force (Effective Tension) during startup is:

Fstartup = Frunning + Facc

Running resistance force can be calculated using standard methods described in:

How to Calculate Motor Power and Torque for a Belt Conveyor »

5. Step 3 – Calculate Tight Side and Slack Side Belt Tension

Belt tension around the drive pulley is divided into:

  • T1 – Tight side tension (carrying side)
  • T2 – Slack side tension (return side / take-up)

The effective driving force is the difference between them:

Fstartup = T1 − T2

To prevent belt slip, the ratio of tensions must satisfy the Euler–Eytelwein formula:

T1 / T2 ≤ eμθ

Where:

  • μ = friction coefficient (typically 0.30–0.35 for rubber lagging)
  • θ = wrap angle (radians)
Engineering Shortcut:
Calculate the minimum required slack-side tension to prevent slip:

T2,min = Fstartup / (eμθ − 1)

Then calculate the tight-side tension:
T1 = Fstartup + T2
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6. Step 4 – Take-up Force Requirement

The take-up system must provide at least the calculated T2.

For Gravity Take-up systems (belt wraps approximately 180° around the weight pulley):

Take-up Weight = 2 × T2

For Screw Take-up systems, apply a safety margin due to lack of constant tension:

Design Force ≈ 1.5 × T2

7. Step 5 – Belt Safety Check

Maximum belt tension during startup is approximately:

Tmax ≈ T1

Check:

Tmax ≤ Allowable belt working tension

If this condition is not satisfied, consider:

  • Increasing acceleration time (reduces Facc)
  • Increasing pulley wrap angle (reduces required T2)
  • Selecting a higher-rated belt

8. Worked Example – Startup Belt Tension

Given:

  • Total mass, mtotal = 580 kg
  • Equivalent mass, meq = 638 kg
  • Belt speed, v = 1.0 m/s
  • Acceleration time, t = 5 s
  • Running force, Frunning = 370 N
  • Friction coefficient, μ = 0.35
  • Wrap angle, θ = 180° = 3.14 rad

1. Acceleration force:

Facc = 638 × (1.0 / 5) = 127.6 N

2. Total startup force:

Fstartup = 370 + 127.6 = 497.6 N

3. Drive factor:

eμθ = e0.35 × 3.14 ≈ 3.0

4. Minimum slack-side tension:

T2 = 497.6 / (3.0 − 1) = 248.8 N

(Select T2 = 250 N)

5. Tight-side tension:

T1 = 497.6 + 250 = 747.6 N

Conclusion: Peak startup belt tension is approximately 748 N. For a gravity take-up, the required weight is 500 N (≈ 51 kg).

9. Practical Engineering Guidelines

  • Startup belt tension is often 1.3–1.8× steady-state tension.
  • Longer acceleration times significantly reduce peak belt stress.
  • Gravity take-up systems handle dynamic effects better than screw take-ups.
  • Always verify belt tension against manufacturer-rated working tension.

10. Conclusion

Belt tension during startup is a critical but often overlooked design check.

By accounting for acceleration force, pulley friction, and take-up behavior, engineers can prevent belt slip, belt overstress, and premature mechanical failures.

This completes the conveyor drive design process together with motor power, starting torque, and acceleration time calculations.

 
Starting method selection (VFD vs Soft Starter) is equally critical to gearbox life.

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