Gear counter shaft bearing load calculation
Work out the tangential, radial and axial gear forces from torque and pitch diameter, then the reaction at each bearing and its life. The Rotec AI worked template does every step with one set of inputs.
What loads a counter shaft bearing
- The gear mesh is by far the largest load. It comes from the torque and the pinion pitch diameter, not from the weights.
- Weights of the pinion, shaft and coupling add a smaller vertical load.
- The coupling adds a radial force from misalignment, in an unknown direction.
- Axial load comes from the gear only if the pinion is helical. On a spur pinion it comes from shaft growth, friction in the free bearing and coupling thrust.
The method in five steps
- Torque. T in N·m = 9,550 × power in kW ÷ speed in rpm.
- Tangential force. Ft = 2 × T ÷ d, with d the pitch diameter in metres.
- Radial and axial force. Fr = Ft × tan α ÷ cos β and Fa = Ft × tan β. A spur gear has β = 0, so Fa is zero.
- Reactions. Take moments about each bearing, with the gear forces in the plane of the mesh and the weights downward.
- Life. Convert to the equivalent load with the thrust, then L10h = (C/P)^p × 1,000,000 ÷ (60 n).
Worked example
A 2,500 kW mill drive at 124 rpm with an 810 mm pinion, 20° pressure angle, spur teeth. Pinion at 368 mm from bearing A, span 2,134 mm.
| Quantity | Value |
|---|---|
| Torque | 192,540 N·m |
| Tangential force Ft | 475,408 N |
| Radial force Fr | 173,034 N |
| Axial force from the gear | 0 N (spur) |
| Design load, bearing A (worst direction) | about 420,000 N |
| Design load, bearing B | about 120,000 N |
The lesson: the gear force is more than ten times the weights, so a small error in power, diameter or pressure angle changes the bearing life a lot.
Check the inputs
- One set of numbers. Power, speed and diameter must be the same on every sheet.
- Pressure angle must match the gear drawing.
- Axial load needs a named source and one value.
- Service factor must be stated, not buried in a formula.
Do it in Rotec AI
The licensed Load Calculator has a worked template for a gear-driven counter shaft. It takes the geometry, tries both rotation directions and every coupling direction, and gives the equivalent load and life of both bearings. A free preview shows the layout.
Related tools and guides
Questions
How do I calculate the load on a mill pinion bearing?
Find the torque from power and speed, then the tangential force Ft = 2T/d, then the radial and axial forces from the pressure and helix angles. Take moments about each bearing, add the weights and the coupling force, and use the resultant at each bearing.
Does a spur pinion give an axial load?
No. A spur pinion gives no axial force from the gear. Any axial load comes from shaft growth, friction in the free bearing or the coupling.
Why can two sheets for the same shaft give different life?
Usually because they use different inputs, such as power, diameter or axial load. Use one set of inputs on every sheet.
Results are starting points from standard engineering practice. Confirm critical selections with the bearing or lubricant maker.