BIZOMAT 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. |
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 transmitted
- What it is
- The power passing through this gear mesh, for example motor power reduced by any upstream losses.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All tooth forces rise in proportion to power.
- Get it right
- Use the power at this mesh, not the installed motor rating if the gear runs below it.
What this means: Speed of this gear
- What it is
- The rotational speed of the gear whose pitch diameter you enter, so that power converts into torque on that gear.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- At constant power, forces fall in proportion as speed rises.
- Get it right
- Pair the speed with the same gear as the diameter; mixing pinion speed and gear diameter gives wrong forces.
What this means: Pitch diameter of this gear
- What it is
- The pitch diameter of the same gear, where the tangential force acts. For a helical gear it is the transverse pitch diameter.
- 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
- Tooth forces fall in proportion as pitch diameter rises.
- Get it right
- Use the pitch diameter, not the tip (outside) diameter.
What this means: Normal pressure angle
- What it is
- The pressure angle of the tooth profile in the normal plane, which sets how much of the tooth force pushes the gears apart radially.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pressure angle raises the radial force; the tangential force does not change.
- Get it right
- Use the angle on the gear drawing.
What this means: Helix angle (0 = spur)
- What it is
- The angle of the teeth to the gear axis at the pitch diameter. Helical teeth create an axial thrust that the bearings must carry.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger helix angle raises the axial and radial forces.
- Get it right
- 0 means spur teeth and no axial force.
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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