Cement plant
Counter shaft and pinion bearings: how to work out the loads
A step-by-step method for the radial and axial load on a mill pinion counter shaft, and what to check before trusting the result.
The shaft
A counter shaft sits between a coupling and a pinion that meshes with a girth gear. Two bearings carry it, usually one located and one free.
The method
| Step | Formula | Note |
|---|---|---|
| Torque | T = 9,550 × P ÷ n (N·m) | P in kW, n in rpm |
| Tangential force | Ft = 2 × T ÷ d | d = pinion pitch diameter, in metres |
| Radial force | Fr = Ft × tan α ÷ cos β | α = pressure angle (20° common). β = helix angle, 0 for a spur gear |
| Axial force | Fa = Ft × tan β | Zero for a spur gear |
| Reactions | Moments about each bearing | Weights act down, gear forces act in the plane of the mesh |
| Service factor | Multiply the gear force | State it. A factor of two is not a default |
Worked sizes
For 2,500 kW at 124 rpm the torque is about 192.5 kN·m. On an 810 mm pinion the tangential force is about 475 kN, and at 20° the radial force is about 173 kN. The coupling and the weight of the shaft and pinion are small next to that.
Check before you trust the result
- Same power, speed and pinion diameter on every sheet.
- The pressure angle matches the gear drawing.
- Axial load has a named source and one value.
- The weights and gear forces are in the right planes before they are added.
- No hard-coded numbers in formulas, and all reactions positive where they should be.
Lubrication and monitoring (typical practice)
- Large oil-lubricated trunnion bearings commonly use ISO VG 680 or 1000 oil with EP additive, held at about 40 to 50 °C.
- Offline filtration to ISO 18/16/13 or better is a common target.
- Overall vibration below about 4.5 mm/s is healthy, above about 11.2 mm/s calls for a shutdown inspection (ISO 10816 guide).
- Check backlash and girth gear alignment at planned intervals, by laser where possible.
Takeaway. The method is short. The risk is in the inputs, so make every sheet use the same ones.
Put it to work in the tool