Couple a flywheel to its generator by sizing the machine to the power you want to draw, not to the energy stored: a 500 kg wheel gives up about 463 Wh between 1,500 rpm and 750 rpm, so a 2.8 kW generator empties it in 10 minutes and a 0.46 kW one in an hour. The torque for a fixed power doubles as the wheel slows to half speed, and a motor-and-generator round trip returns only 72 to 81% of the energy put in, so decide between one reversible machine and two separate ones before you build.
Part of Flywheel Energy Storage
The link between the spinning wheel and the electrical or mechanical load: power, torque, efficiency and the three ways to connect them.
Power Is Set By The Machine, Not The Wheel
The energy is in the wheel; the rate at which it comes out is set by the generator and the load. For the 500 kg wheel of this series, 617 Wh at 1,500 rpm and 154 Wh at 750 rpm, the usable energy between those speeds is 617 − 154 = 463 Wh = 1.67 MJ.
| Draw | Time to use 463 Wh | Torque at 1,500 rpm | Torque at 750 rpm, same power |
|---|---|---|---|
| 0.46 kW | 1 h | 2.9 N·m | 5.9 N·m |
| 2.8 kW | 10 min | 17.7 N·m | 35.4 N·m |
| 167 kW | 10 s | 1,060 N·m | 2,120 N·m |
Working, middle row: power 2,780 W ÷ ω 157.1 rad/s = 17.7 N·m; at half speed ω = 78.5 rad/s gives 2,780 ÷ 78.5 = 35.4 N·m. The bottom row is far beyond any village generator and is shown to make the point: the wheel can in principle deliver enormous power, and the machine and the load are what limit it.
Efficiency: What A Round Trip Returns
Motor-Generator Duality gives 85 to 90% for each machine, 72 to 81% combined. To refill 463 Wh of the wheel you must put in 463 ÷ 0.90 = 514 Wh to 463 ÷ 0.85 = 545 Wh of electricity; on discharge you get back 463 × 0.85 = 394 Wh to 463 × 0.90 = 417 Wh. The ratio 394 ÷ 545 = 72% to 417 ÷ 514 = 81% matches the corpus range. Bearing and air losses (see Bearings & Friction) come on top while the wheel sits charged.
Three Ways To Couple
- One reversible machine on the wheel shaft. Simplest and cheapest. Needs its terminal voltage managed across the speed range; see Motor-Generator Set.
- Separate motor and generator on one shaft. Each can be sized for its own job, and the generator can be an alternator that does not need to motor. Costs two machines and two sets of bearings.
- Mechanical drive from a prime mover with a take-off. A flywheel on a mill or turbine shaft smooths torque with no electrical machine at all; see Clutch & Gearing.
Sizing The Coupling
Generator Coupling gives torque in ft·lb as HP × 5,252 ÷ rpm and advises multiplying by 2 to 3 for shock and starting loads. In SI the torque is P ÷ ω. The middle row above, 17.7 N·m, becomes 35 to 53 N·m for coupling selection. Always size for the torque at the lowest wheel speed you will draw to, since torque rises as speed falls. Align the shafts, or use a flexible coupling or belt; a wheel is a heavy, stiff shaft and does not forgive misalignment.
Common Mistakes
- Sizing the generator by the energy stored. The energy tells you how long it can run, not how big it must be.
- Forgetting that torque rises as the wheel slows. A coupling that is fine at full speed slips or breaks at half.
- Counting the energy stored as the energy returned. Multiply by 0.75 for the usable speed range and again by the two machine efficiencies.
Safety
A disconnected generator does not stop the wheel
If the load trips off, the wheel keeps its 2.2 MJ and the generator output rises with speed if it is still being driven; if the wheel is being driven by a prime mover, removing the load lets it overspeed. Keep a load, a brake, or a speed limit in place whenever the wheel is connected to a source of power; see Speed Limiting and Load Control.
What’s Next
- Learn next: Motor-Generator Set — one reversible machine on the shaft
- Combine with: Variable Speed Drive — handling the 2-to-1 speed range