KEVOS® MAKEOS · Mechanics
Gyroscopic Bearing Load on a Turning Rotor
When the machine carrying this spinning rotor turns or swings, what gyroscopic couple acts, and what total load does each bearing then carry?
Bearing loads on a rotor whose axis is turned while it spins (a vehicle turning, a swinging boom or a rotating platform): rotor inertia for a disc, a ring or an entered value, angular momentum, the precession rate from a turn radius and speed or from an entered turning speed, the gyroscopic couple and the equal and opposite bearing reactions over the bearing span (as the gyroscope precession tool), the static weight share on each bearing, and the largest bearing load against your allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Rotor | choice | How the rotor inertia is found. |
| Rotor mass | kg | Mass of the rotor (also used for its weight on the bearings). |
| Rotor radius | m | Outer radius of the disc or ring. |
| Rotor inertia (entered) | kg·m² | Polar inertia of the rotor if entered directly. |
| Spin speed | rpm | Spin speed of the rotor. |
| Precession from | choice | Whether the axis turns because the vehicle turns, or at a given turning speed. |
| Vehicle speed | m/s | Speed of the vehicle round the turn. |
| Turn radius | m | Radius of the turn. |
| Turning speed of the axis | rpm | Turning speed of the rotor axis. |
| Bearing span | mm | Distance between the two bearings of the rotor. |
| Allowable load per bearing | N | Allowable radial load per bearing (from the bearing rating and your life requirement). |
Method and formulas
- Disc J = M R² ÷ 2; ring J = M R²; angular momentum H = J ω_s (as the gyroscope precession tool).
- Precession rate Ω = v ÷ R_turn for a turning vehicle, or 2π n_p ÷ 60.
- Gyroscopic couple T = H Ω; bearing reaction = T ÷ L, adding to one bearing and subtracting from the other; static share = M g ÷ 2.
- Example: the couple is 62.832 N·m, adding 209.44 N to one bearing; the most loaded bearing carries 307.51 N.
Limitations
- Steady precession with the spin and precession axes at right angles.
- Rotor unbalance and shock loads must be added separately.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check bearings of a flywheel or fan on a vehicle or crane
- Find the extra bearing load on a turning machine
- Compare rotor speeds for gyroscopic load
Who it is for
- Design engineers
- Vehicle engineers
- Machine designers
What you get
- Inertia, angular momentum and precession rate
- Gyroscopic couple and bearing reactions
- Largest bearing load against the allowable
Interpreting the result
- Gyroscopic load rises with both spin speed and turning rate: a faster rotor on a tighter turn sees much more.
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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