KEVOS® MAKEOS · Mechanics
Gyroscopic Couple and Bearing Reactions
What gyroscopic couple does this spinning rotor exert when its axis is turned, and what load does it put on the bearings?
Gyroscopic couple of a spinning rotor whose axis precesses (turns) at a given rate, from the rotor’s moment of inertia, spin speed and precession speed, and the resulting pair of bearing reactions.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Rotor | choice | Shape used to estimate the moment of inertia, or enter it. |
| Rotor mass | kg | Mass of the rotor. |
| Rotor outer radius | m | Outer radius of the rotor. |
| Moment of inertia (entered) | kg·m² | Polar moment of inertia of the rotor about its spin axis. |
| Spin speed | rpm | Speed of the rotor about its own axis. |
| Precession speed (axis turning rate) | rpm | Rate at which the spin axis itself is turned (for example a slewing or turning rate). |
| Bearing span | mm | Distance between the two bearings carrying the rotor. |
Method and formulas
- Angular momentum H = J ω_s.
- Gyroscopic couple = J ω_s Ω_p, about the axis perpendicular to both the spin and precession axes.
- Each bearing carries ± couple ÷ span, in opposite directions.
- Example: a 20 kg disc at 3000 rpm turned at 10 rpm exerts 131.59 N·m.
Limitations
- Steady precession at right angles to the spin axis.
- Add the gyroscopic reactions to the weight and other bearing loads.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check bearing loads on a spindle mounted on a slewing or turning machine
- Estimate gyroscopic loads on vehicle or ship rotors
- Size a gyroscopic stabiliser
Who it is for
- Design engineers
- Mechanical engineers
- Engineering students
What you get
- Gyroscopic couple
- Bearing reaction pair
- Angular momentum
Interpreting the result
- The couple grows with both speeds; slowing the turning rate is often the easiest way to reduce it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2998. Topic reference; no source tables or recommended settings are reproduced.
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