KEVOS® MAKEOS · Power Transmission
Conveyor Gravity Take-Up Plan (Slack Side Tension, Sag Tension, Counterweight, Travel)
For a belt conveyor with a gravity take-up, how heavy must the counterweight be to stop slip and limit belt sag, and how much take-up travel does the belt need?
Plan of a gravity take-up for a belt conveyor: the load per metre, effective pull and the slack side tension needed to drive without slip (as the conveyor drive sizing tool), the tension needed to keep belt sag between carrying idlers within a percentage of their spacing, the take-up tension as the larger of the two, the counterweight mass for a take-up that carries both belt runs, and the travel for belt stretch over the belt length plus a splice allowance, against the travel available.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Throughput | t/h | Material carried per hour. |
| Belt speed | m/s | Belt speed. |
| Conveyor length (centres) | m | Length between terminal pulley centres. |
| Lift (positive up) | m | Lift. |
| Belt and idler moving mass per metre (both runs) | kg/m | Belt and rotating idler mass per metre, both runs. |
| Overall friction factor | Overall friction factor. | |
| Drive pulley friction coefficient | Friction between belt and drive pulley. | |
| Wrap on the drive pulley | ° | Wrap on the drive pulley. |
| Drive pulley diameter | mm | Drive pulley diameter. |
| Drive efficiency | % | Drive efficiency. |
| Power margin | % | Power margin. |
| Take-up | ||
| Belt mass per metre (one run) | kg/m | Mass per metre of the belt itself (one run). |
| Carrying idler spacing | m | Spacing of the carrying idlers. |
| Largest sag (% of idler spacing) | % | Largest sag between idlers as a share of the spacing (about 1–2%). |
| Belt stretch allowance | % | Permanent and elastic stretch of the belt to allow for. |
| Splice and fitting allowance | mm | Extra travel for splicing and fitting the belt. |
| Take-up travel available | mm | Travel of the take-up carriage. |
Method and formulas
- Effective pull T_e and slack side tension T₂ = T_e ÷ (e^{μθ} − 1) (as the conveyor drive sizing tool).
- Sag tension = (q_L + q_b) g a ÷ (8 × sag); take-up tension = the larger of T₂ and the sag tension.
- Counterweight = 2 × take-up tension ÷ g (both runs); travel = 2L × stretch + splice allowance.
- Example: 2,097.5 N at the take-up needs 427.78 kg of counterweight and 1,500 mm of travel.
Limitations
- Take-up at or near the drive where the slack side tension is lowest; elsewhere add the resistance between the drive and the take-up.
- Sag checked on the carrying side with the belt fully loaded.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the counterweight of a gravity take-up
- Check belt sag between idlers
- Check take-up travel for a new belt
Who it is for
- Bulk handling engineers
- Maintenance engineers
- Plant engineers
What you get
- Slack side tension for no slip
- Sag tension and take-up tension
- Counterweight and travel
Interpreting the result
- On short, lightly loaded conveyors the sag limit, not slip, usually sets the counterweight.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2487–2512, 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
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