Balance a flywheel because an off-centre mass pulls on the bearings with a force of mass × offset × ω², which rises with the square of the speed: a 500 kg wheel with its centre of mass 1 mm off the axis pulls with 12.3 kN at 1,500 rpm, 2.5 times its own weight, and the pull rotates with the wheel. Find the heavy side on level knife edges, correct it by removing metal opposite or adding a bolted weight, and then raise the speed in steps while watching for vibration.
Part of Flywheel Energy Storage
Finding and correcting the uneven mass distribution of a flywheel, and checking the result at speed.
Unbalance Force Grows With The Square Of Speed
If the wheel’s centre of mass is offset from the axis by a distance e, the offset mass whirls round the axis and the bearings must supply the centripetal force F = m × e × ω².
- At 300 rpm (ω = 31.4 rad/s): F = 500 × 0.001 × 31.4² = 493 N.
- At 1,500 rpm (ω = 157.1 rad/s): F = 500 × 0.001 × 157.1² = 12,337 N (12.3 kN), or 1.26 tonnes-force.
Five times the speed gives 25 times the force. Compare it with the wheel’s weight, 500 × 9.81 = 4,905 N: at 1,500 rpm the bearings carry 2.5 times the static load, and the load direction turns once every revolution, 25 times a second. That hammers bearing races, loosens bolts and fatigues the shaft. Blade Balancing makes the same point for wind rotors: static balance removes the bulk of the trouble.
How Much Correction A Millimetre Needs
A correction weight m_c at the rim radius r_c balances an offset when m_c × r_c = m × e:
m_c = 500 × 0.001 ÷ 0.6 = 0.83 kg at the rim.
So a wheel of this size is sensitive to a weight of under a kilogram at the rim. A casting with a blowhole or a cored rim with uneven wall thickness can be off by far more.
An accepted target is the ISO balance quality grade G6.3, which sets e × ω at or below 6.3 mm/s. This figure is quoted from memory; check it against a standard if you can. At 157.1 rad/s it allows e = 6.3 ÷ 157.1 = 0.040 mm and a residual force of 500 × 0.00004 × 157.1² = 494 N, 4% of the 1 mm case.
Static Balance Method
- Mount the wheel on its own shaft, then lay the shaft across two hardened, polished, level knife edges or two free-running bearings, as for Flywheel. Check the edges are level with a water level or spirit level.
- Release the wheel gently and let it settle. The heavy side finishes at the bottom.
- Turn the wheel 90 degrees and release again. If the same spot always ends at the bottom, that is the heavy spot; mark it.
- Fix a trial weight on the opposite rim, in a bolted clamp, and repeat. Adjust the trial weight until the wheel stays at any angle you put it.
- Weigh the trial weight and convert to a permanent correction: remove the same moment of metal at the heavy spot by drilling shallow holes, or bolt a weight through the rim opposite. Never rely on tape, wire or glue, which will leave at speed.
- Repeat step 2 to 4 after the correction until the wheel stops at random angles.
Why Static Balance Is Not Enough Above A Few Hundred Rpm
A static test only places the centre of mass on the axis. A wheel can be statically balanced and still have a heavy spot at one face and a light one opposite, which makes a rocking couple when it spins. The corpus Flywheel page says static balance is enough below 200 to 300 rpm and that a higher speed needs dynamic balancing on a machine. A thin disc keeps couple unbalance small, but this page has no sourced figure for how thin, and no balancing-machine method. Treat a wheel above 300 rpm as having an unknown residual couple and allow for it by running up slowly.
Staged Run-Up Test
- Run the wheel in its pit, with the lid closed and everyone outside the plane of rotation.
- Spin to about 10% of the target speed and hold for a minute. Watch the frame from a safe position for movement: a pointer fixed to the frame near the shaft end, or a coin stood on edge on a bearing housing, shows vibration without anyone touching the machine.
- Raise the speed in steps of about 10% of the target, holding one minute at each, and stop if the vibration grows faster than the speed does.
- If the vibration rises to a peak at one speed and then falls, you have crossed a resonance of the frame and shaft. Pass through it without dwelling, and do not hold the wheel near it in normal use.
- After any repair, new weights or bearing change, repeat from step 1.
Common Mistakes
- Taping on temporary weights. The weight leaves at speed as a projectile.
- Balancing the wheel without its shaft and key. The shaft and keyway change the mass distribution; mount them first.
- Trusting a good result at low speed. Force goes as speed squared; a quiet wheel at 300 rpm can be 25 times noisier at 1,500.
- Forgetting wear. A wheel that vibrates after months may have lost a weight or cracked.
Safety
A wheel that shakes cannot be stopped quickly
A vibrating wheel only grows worse if the cause is a loosening bolt or a cracking spoke, and a 500 kg wheel at 1,500 rpm needs far longer than a moment to stop (see Speed Limiting). Stop the drive at the first unexplained vibration and let the wheel coast down with nobody near it. Do not approach until it has fully stopped, and inspect the rim and spokes for cracks before any restart.
What’s Next
- Learn next: Bearings & Friction — the bearings that take the unbalance force
- Combine with: Housing — where the run-up test takes place