BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Throughput
- What it is
- The mass of material the belt carries each hour at the design rate.
- Units and format
- Enter a number in t/h: t/h. The form accepts 0.000001 t/h to 100000 t/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 t/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More throughput raises the load per metre, the effective pull and the take-up tension.
- Get it right
- Enter tonnes per hour; use the peak rate the conveyor must handle.
What this means: Belt speed
- What it is
- The linear speed of the belt surface.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 20 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- At a fixed throughput a faster belt carries less load per metre.
- Get it right
- Enter metres per second, not metres per minute.
What this means: Conveyor length (centres)
- What it is
- The horizontal length of the conveyor between the centres of the head and tail pulleys.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 10000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction pull and the belt stretch travel both rise with length.
- Get it right
- Measure centre to centre of the terminal pulleys.
What this means: Lift (positive up)
- What it is
- The height the material is raised from the loading point to discharge. A conveyor running downhill has a negative lift.
- Units and format
- Enter a number in m: metres. The form accepts -500 m to 1000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More lift adds directly to the effective pull.
- Get it right
- Use a negative value for a decline; if the pull becomes negative the tool says the drive must brake.
What this means: Belt and idler moving mass per metre (both runs)
- What it is
- The mass per metre of the belt on both runs plus the rotating parts of the carrying and return idlers, used for friction pull.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0.000001 kg/m to 10000 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kg/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Include both belt runs and idler rolls; take idler roll mass from the idler catalogue.
What this means: Overall friction factor
- What it is
- An overall friction factor that lumps idler rolling resistance, belt flexing and material movement into one coefficient on the moving mass.
- Units and format
- Enter a plain number with no unit. The form accepts 0.005 to 0.2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.025 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The friction part of the effective pull rises in direct proportion.
- Get it right
- Take it from a belt conveyor design standard or the belt supplier for the installation conditions.
What this means: Drive pulley friction coefficient
- What it is
- The friction coefficient between the belt and the drive pulley face, which limits how much pull the pulley can transmit before slipping.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.35 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction lowers the slack side tension needed to stop slip.
- Get it right
- Use a value for the lagging and conditions; wet or bare pulleys grip less.
What this means: Wrap on the drive pulley
- What it is
- The angle of drive pulley surface the belt is in contact with.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 90° to 480°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More wrap lowers the slack side tension needed to stop slip.
- Get it right
- A snub pulley increases the wrap; measure the arc of contact, not the snub position.
What this means: Drive pulley diameter
- What it is
- The diameter of the drive pulley. It is listed with the drive data but no result of this tool uses it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It does not change any result here; check the pulley diameter against the belt maker’s minimum separately.
What this means: Drive efficiency
- What it is
- The share of motor power that reaches the drive pulley after gearbox and coupling losses. It is used for the motor power figure.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself; take it from the gearbox maker’s data.
What this means: Power margin
- What it is
- Extra power you add on top of the calculated motor power to cover starting, surges and uncertainty.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 200%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself; it affects only the motor power figure, not the take-up results.
Take-up
What this means: Belt mass per metre (one run)
- What it is
- The mass per metre of the belt alone on one run, used with the material load to find the tension needed to limit sag.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0.000001 kg/m to 10000 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the belt maker’s data sheet for the belt type and width.
What this means: Carrying idler spacing
- What it is
- The centre-to-centre spacing of the carrying idler sets along the loaded run.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 10 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tension needed for the sag limit rises in direct proportion to idler spacing.
- Get it right
- Use the largest spacing on the carrying side, as sag is worst there.
What this means: Largest sag (% of idler spacing)
- What it is
- The largest belt sag you accept between carrying idlers, as a share of the idler spacing. It keeps material from spilling and the belt from flapping.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.2% to 10%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller allowed sag needs proportionally more tension.
- Get it right
- Type the percentage itself; take the limit from the belt maker or design standard.
What this means: Belt stretch allowance
- What it is
- The total belt stretch, elastic and permanent, the take-up must absorb, as a share of belt length.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 10%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Travel needed rises in direct proportion to the stretch allowance.
- Get it right
- Take it from the belt maker’s data for the carcass type; textile belts stretch more than steel cord.
What this means: Splice and fitting allowance
- What it is
- Extra take-up travel kept for making a splice and fitting the belt, added to the stretch travel.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Allow for the length the splice method uses; ask the belt fitter.
What this means: Take-up travel available
- What it is
- The travel the gravity take-up carriage has from its highest to its lowest position, compared with the travel needed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the usable carriage travel between the stops, not the tower height.
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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