BIZOMAT MAKEOS · Engineering
Overhung Pulley Shaft Bush Check (Belt Pull, Bush Loads, P, V and PV)
For a belt pulley overhung on a shaft running in two plain bushes, what load does each bush carry, and are their pressure, sliding speed and PV within the bush material’s limits?
Check of the plain (sleeve) bearings carrying an overhung pulley: the belt pull from the power, speed and pulley diameter with a belt tension factor, the reactions at the near and far bushes from the overhang and bush spacing, and the projected-area pressure, sliding velocity and PV value of each bush (as the plain bearing PV tool), against the limits of the bush material.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power through the pulley | kW | Power transmitted by the belt. |
| Shaft speed | rpm | Speed of the shaft. |
| Pulley pitch diameter | mm | Pitch diameter of the pulley. |
| Belt pull factor (shaft load ÷ effective pull) | Shaft load as a multiple of the effective belt pull (about 1.5 for V-belts, 2 or more for flat belts). | |
| Overhang (near bush centre to pulley centre) | mm | Distance from the centre of the bush nearest the pulley to the pulley centre. |
| Spacing between bush centres | mm | Distance between the two bush centres. |
| Bushes | ||
| Shaft diameter in the bushes | mm | Diameter of the shaft in the bushes. |
| Bush length | mm | Length of each bush. |
| Largest pressure for the material | MPa | Highest projected-area pressure the bush material allows. |
| Largest sliding speed for the material | m/s | Highest sliding speed the bush material allows. |
| Largest PV for the material | MPa·m/s | Highest PV the bush material allows. |
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: Power through the pulley
- What it is
- The power transmitted through the belt and pulley at the running condition being checked.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Belt pull, bush loads, pressure and PV all rise in proportion to power.
What this means: Shaft speed
- What it is
- The rotational speed of the pulley shaft, which also sets the sliding speed in the bushes.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 700 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- At a set power, higher speed lowers bush pressure and raises sliding speed in proportion, so PV does not change.
What this means: Pulley pitch diameter
- What it is
- The pitch diameter of the pulley, where the belt’s effective pull is taken to act.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pulley lowers the belt pull and the bush loads for the same torque.
What this means: Belt pull factor (shaft load ÷ effective pull)
- What it is
- The shaft load from the belt divided by the effective (driving) pull, allowing for belt tension on both sides, from the belt maker.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Overhang (near bush centre to pulley centre)
- What it is
- The distance along the shaft from the centre of the bush nearest the pulley to the centre of the pulley.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer overhang raises the loads on both bushes.
What this means: Spacing between bush centres
- What it is
- The distance between the centres of the two bushes that support the shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Wider bush spacing lowers the loads on both bushes.
Bushes
What this means: Shaft diameter in the bushes
- What it is
- The shaft journal diameter running in the bushes, used for the projected bearing area and the sliding speed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Bush length
- What it is
- The length of each bush in contact with the shaft; both bushes are taken to have the same length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pressure and PV fall in inverse proportion to bush length.
What this means: Largest pressure for the material
- What it is
- The highest projected-area pressure the bush material allows, from the bush maker’s data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The tool checks the near bush, which carries the larger load, against this limit.
What this means: Largest sliding speed for the material
- What it is
- The highest sliding speed at the bore surface the bush material allows, from the bush maker’s data.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 1000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest PV for the material
- What it is
- The highest product of pressure and sliding speed the bush material allows, from the bush maker’s data; it limits the heat generated.
- Units and format
- Enter a number in MPa·m/s: MPa·m/s. The form accepts 0.000001 MPa·m/s to 10000 MPa·m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.6 MPa·m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Torque = 9549 P ÷ n; effective pull = 2T ÷ D_p; shaft load = factor × effective pull.
- Near bush R₁ = F (L_b + a) ÷ L_b; far bush R₂ = F a ÷ L_b.
- P = R ÷ (d L); V = π d n; PV (as the plain bearing PV tool).
- Example: the belt loads the shaft with 613.88 N; the near bush carries 859.44 N at PV 1.05 MPa·m/s.
Limitations
- Steady belt load; start-up and shock raise the pull.
- Uniform bush pressure; shaft deflection concentrates load at the bush end near the pulley.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check bronze or polymer bushes on a pulley shaft
- Find the bush length needed for a belt drive
- Check a speed or power increase on a bushed shaft
Who it is for
- Maintenance engineers
- Design engineers
- Machine designers
What you get
- Torque, effective pull and shaft load
- Bush reactions
- P, V and PV of each bush
Interpreting the result
- A short overhang and widely spaced bushes keep the near bush load close to the belt pull itself.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2314–2337, 2473–2490. Topic reference; no source tables or recommended settings are reproduced.
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Open the Overhung Pulley Shaft Bush Check (Belt Pull, Bush Loads, P, V and PV) calculator