# Formula for optimizing a Flywheel Design

1. Mar 28, 2015

### MaterSammichM

I tinker with single cylinder 4-stroke (kart) racing engines a good deal. Flywheel design for optimum weight has always amazed me. Does anyone have formulas for optimizing the design? It's more than just saying "x" pounds is best, because the actual shape of the flywheel, width and thickness of the rim, and how close the mass is to the center of rotation matter also. Can anyone recommend a good book? I know I = 0.5m*r^2 is good for the MOI, but that's far from the total equation. Designing an engine from scratch.

2. Mar 29, 2015

### OldEngr63

At its minimum MMOI, the flywheel must add enough energy storage so that the entire moving assembly (flywheel, crank, con rod, piston) will have enough kinetic energy to make it to the top of the compression stroke. With too little stored energy, the piston will never reach TDC, the cylinder will not fire, and the engine will not run.

Additional flywheel MMOI beyond the minimum serves two purposes:
1) to smooth the output torque from the engine;
2) to influence the torsional vibration response for the overall engine/drive line system.

The flywheel must be designed not to be overstressed at max engine rpm, which means that you have to pay attention to centrifugal stresses in the rotating disk. Weight can be reduced by thinning the center section while leaving a heavier rim, but you really should only work on this after you have a target MMOI for the system. The MMOI is the critical property for the flywheel.

While MMOI = (1/2)*M*R^2 is correct for a simple, flat disk, it is not correct for a more complex flywheel with multiple thicknesses. If you have a thin center and a heavy rim, you must calculate MMOI for each part separately and then add them.

3. Mar 30, 2015

### Kishan Majethia

Will it not increase centrifugal stresses by increasing rim mass and reducing mass at center?

4. Mar 30, 2015

### OldEngr63

Without a doubt, increasing the rim thickness will increase centrifugal stress. The whole problem is one of not exceeding the allowable stress, not one of avoiding all stress. We want to obtain the desired MMOI with a minimum mass, and that calls for a thick rim and an thin center. Stress is a part of the picture under any design scenario, but that is acceptable. That is why we use steel rather than pot metal for the flywheel.

5. Apr 3, 2015

### MaterSammichM

wouldn't the amount of compression that the piston is fighting against also be a factor?

6. Apr 3, 2015

### billy_joule

Yes. That comes under the energy Oldengnr speaks of in the first paragraph of his first post - energy required to reach TDC.

7. Apr 4, 2015

thank you

8. Apr 4, 2015

### Randy Beikmann

There are two factors here. One is that you need to have some idea what the moment of inertia needs to be to be "effective," which usually means reducing the pulsating twist in the driveline the engine is driving (or tension fluctuations in a belt drive, etc.).
Once you have a target value for the inertia, the way to obtain it with the least mass is to concentrate most of the mass at the largest radius possible - start at the largest radius you have room for and work inward, using the maximum thickness you can, until the inertia is large enough. You'll end up with a thin ring. Then add a thin disc between that and the center hub. Of course everything needs to be design to withstand stress.

9. Apr 5, 2015

### OldEngr63

I don't think that there exists a "formula for optimizing a flywheel, simply because the available space and other constraints are different for every case. That said, the process for any particular situation is pretty obvious as has be outlined above.