BIZOMAT 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). |
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: Rotor
- What it is
- How the rotor’s polar moment of inertia is found: from mass and radius for a solid disc (J = M R² ÷ 2) or a thin ring (J = M R²), or taken directly from the inertia you enter.
- Units and format
- Choose one of 3 options from the list: Solid disc; Thin ring; Enter the inertia.
- Example
- The form opens with “Solid disc” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose the thin ring only when nearly all the mass sits at the rim; for a spoked or stepped rotor, enter the inertia from CAD instead.
What this means: Rotor mass
- What it is
- The mass of the spinning rotor. It sets the inertia for a disc or ring, and it is always used for the rotor’s own weight, shared equally between the two bearings.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For a disc or ring, inertia, angular momentum and gyroscopic couple all rise in direct proportion to mass.
- Get it right
- Even when you enter the inertia directly, the mass still sets the static weight on each bearing, so keep it correct.
What this means: Rotor radius
- What it is
- The outer radius of the disc or ring, from the spin axis to the rim. It is used only with the solid disc and thin ring choices.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 10 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Inertia, and so the gyroscopic couple, grows with the square of the radius.
- Get it right
- Radius, not diameter: halve the measured outside diameter.
What this means: Rotor inertia (entered)
- What it is
- The polar mass moment of inertia of the rotor about its spin axis, for a rotor that is neither a plain disc nor a thin ring. It is used only when “Enter the inertia” is selected.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0.000001 kg·m² to 100000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.4 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The gyroscopic couple and bearing reaction are directly proportional to it.
- Get it right
- Take it about the spin axis from CAD or the maker’s data; it is ignored for the disc and ring choices.
What this means: Spin speed
- What it is
- How fast the rotor spins about its own axis (flywheel, turbine or fan speed), as distinct from the slower turning of the machine that carries it.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Angular momentum, couple and the gyroscopic reaction at each bearing rise in direct proportion to spin speed.
- Get it right
- Use the highest spin speed at which the turn or swing can happen.
What this means: Precession from
- What it is
- Where the precession (the turning of the spin axis) comes from: a vehicle following a curve, where the rate is speed ÷ turn radius, or an axis turned at a known speed, such as a slewing boom or rotating platform.
- Units and format
- Choose one of 2 options from the list: Vehicle turning (speed and radius); Turning speed of the axis.
- Example
- The form opens with “Vehicle turning (speed and radius)” selected as a worked example. Choose the option that matches your case.
What this means: Vehicle speed
- What it is
- How fast the vehicle carrying the rotor travels round the curve. Used only with “Vehicle turning”; with the turn radius it gives the precession rate.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0 m/s to 200 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The precession rate and gyroscopic couple rise in direct proportion to vehicle speed.
- Get it right
- Metres per second, not km/h: divide km/h by 3.6.
What this means: Turn radius
- What it is
- The radius of the curve the vehicle follows, from the centre of the turn to the vehicle. Used only with “Vehicle turning”.
- Units and format
- Enter a number in m: metres. The form accepts 0.1 m to 10000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The precession rate and couple are inversely proportional to the turn radius.
- Get it right
- A tighter turn is a smaller radius and gives a larger couple.
What this means: Turning speed of the axis
- What it is
- How fast the rotor’s spin axis itself swings round, for a rotor on a slewing crane, turntable or rotating platform. Used only with “Turning speed of the axis”.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 10000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The precession rate and couple rise in direct proportion.
- Get it right
- This is the slow turning of the axis, not the rotor’s own spin speed.
What this means: Bearing span
- What it is
- The axial distance between the two bearings that carry the rotor shaft. The gyroscopic couple is resisted by equal and opposite forces at these bearings.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The gyroscopic reaction per bearing is the couple divided by the span, so a longer span lowers it.
- Get it right
- Measure between the bearing centres, and enter it in millimetres.
What this means: Allowable load per bearing
- What it is
- The largest radial load one bearing may carry for your life requirement, worked out from the bearing maker’s rating. The most loaded bearing (weight share plus gyroscopic reaction) is compared with it.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A load for one bearing, not for the pair.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Gyroscopic loads
In Whirling Shafts by the Numbers
What it covers: Why a spinning rotor pushes back when its axis is turned: angular momentum, the gyroscopic couple and bearing reactions, applied to a truck-mounted mill that lifted a bearing on tight turns.
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Open the Gyroscopic Bearing Load on a Turning Rotor calculator