KEVOS® MAKEOS · Gears
Gear Tooth Forces
What tangential, radial and axial forces does this gear mesh put on the shafts?
Tangential, radial (separating) and axial (thrust) tooth forces of a spur or helical gear from power, speed and pitch diameter, for shaft and bearing loads.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power transmitted | kW | Power through the mesh (motor power × any upstream efficiency). |
| Speed of this gear | rpm | Speed of the gear whose pitch diameter is entered. |
| Pitch diameter of this gear | mm | Pitch diameter of the same gear. |
| Normal pressure angle | ° | Normal pressure angle. |
| Helix angle (0 = spur) | ° | Helix angle; 0 for spur gears. |
Method and formulas
- T = 9549 × P ÷ n (N·m); Ft = 2T ÷ d.
- Radial Fr = Ft tan αn ÷ cos β; axial Fa = Ft tan β.
- Total F = √(Ft² + Fr² + Fa²); pitch-line velocity = π d n ÷ 60 000.
- Example: 15 kW at 1450 rpm on an 80 mm gear gives Ft = 2,469.6 N and Fr = 898.88 N.
Limitations
- Friction and dynamic loads are not included; apply application and dynamic factors from your rating method.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find bearing loads from a gear mesh
- Size shafts carrying gears
- Check the thrust a helical gear puts on its bearings
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Torque
- Tangential, radial and axial force
- Total tooth force
- Pitch-line velocity
Interpreting the result
- Use the forces with the gear position on the shaft to find bearing reactions.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2195–2200. Topic reference; no source tables or recommended settings are reproduced.
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