Formula for optimizing a Flywheel Design

In summary: I recommend Designing an Engine from Scratch by Oldengnr for a more detailed discussion of the topic."In summary, flywheel design is more than just saying "x" pounds is best. The actual shape of the flywheel, width and thickness of the rim, and how close the mass is to the center of rotation matter too.
  • #1
MaterSammichM
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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.
 
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  • #2
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
OldEngr63 said:
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.

Will it not increase centrifugal stresses by increasing rim mass and reducing mass at center?
 
  • #4
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
wouldn't the amount of compression that the piston is fighting against also be a factor?
 
  • #6
MaterSammichM said:
wouldn't the amount of compression that the piston is fighting against also be a factor?
Yes. That comes under the energy Oldengnr speaks of in the first paragraph of his first post - energy required to reach TDC.
 
  • #7
thank you
 
  • #8
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.
 
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  • #9
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.
 

1. What is a flywheel and what is its purpose?

A flywheel is a mechanical device that stores rotational energy. It consists of a heavy rotating disc or wheel with a high moment of inertia, and is designed to maintain a constant speed or provide a smooth and consistent output of energy. It is commonly used in machines and engines to store energy and regulate the speed of rotation.

2. How does the flywheel design affect its performance?

The design of a flywheel has a significant impact on its overall performance. Factors such as size, shape, weight distribution, and material all play a role in determining the efficiency and effectiveness of a flywheel. A well-optimized flywheel design can improve energy storage capacity, reduce vibrations and noise, and increase the overall lifespan of the device.

3. What is the formula for calculating the moment of inertia of a flywheel?

The moment of inertia of a flywheel can be calculated using the formula I = 0.5 * m * r^2, where I is the moment of inertia, m is the mass of the flywheel, and r is the radius of the flywheel. This formula assumes that the flywheel has a uniform density and a circular shape.

4. How can the flywheel design be optimized for a specific application?

The optimization of a flywheel design depends on the specific application and its requirements. However, some general considerations include selecting the right material for the flywheel, balancing the weight distribution, and minimizing friction and energy losses. Advanced computer simulations and testing can also be used to fine-tune the design and achieve the desired performance.

5. What are some common challenges in optimizing a flywheel design?

One of the main challenges in optimizing a flywheel design is finding the right balance between weight and energy storage capacity. A lighter flywheel may have better acceleration and deceleration rates, but it may not store enough energy for the desired application. Another challenge is minimizing energy losses due to friction and other factors, which can significantly affect the efficiency of the flywheel. Finally, finding the right material and ensuring its durability and stability can also be a challenge in flywheel design optimization.

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