Designing a flywheel is serious business because a flywheel operating beyond its design stress can explode, sending shards of sharp metal debris flying in unpredictable directions. Safety is the key guide to flywheel sizing.
As a measure of reference, only atomic (i.e. nuclear chain reactions) and chemical sources (ie exploding C4, TNT etc) have higher energy release potential than flywheels.
Safety is number 1 with flywheels because of their potential for damage. If you cannot explicitly overcome a safety issue, you just can't go further with the design - the design is flawed and potentially dangerous. Before you can design a flywheel, you have to already pass the following safety audit:
a) How sure can you be about the absence of air bubbles or other structural problems within the material ? There are ways to look inside using powerful electromagnetic rays. If you don't or can't do that, what can you do to take into account a bubble that is located within the thinnest parts of the central area of the wheel? Such a bubble could fatally undermine the correctness of your calculations. Therefore, you have to explicitly include a large safety factor. For the novice, I recommend a minimum safety factor of 4.4 - which means you design your wheel such that it's experiences no more stress than 1/20 of Yield Strength of the material.
b) What is the maximum velocity at which the wheel will be spinning? Suppose you want to operate your wheels at 5000 rpm. The maximum is not 5000 rpm – rather there is a working range around it, say 46,00-5400 where your motor is likely to jog, depending on the relative size and type of electronics of your motor. Also, make sure you check your electrical supply for the motor has a max. cut off current or voltage that is variable. This way you can set it deliberately to trip in case of an electrical surge. If that is not something you want to do, then you have to answer the problem of how you intend to personally monitor the velocity of the flywheel while it is spinning. How you intend to prevent others, for example children from being able to power up the flywheel inadvertently in a way that makes it keep speeding up.
c) What is the material you are going to use to make the flywheel? A closely related question is: What is the radius of your flywheel? Answering these questions is impossible without knowing what kind of lift your vehicle will produce (or at least guesstimating it, using sound calculations) and how much motion you want to produce. At this point, only you can answer these questions, but you have some tools to do the job right.
I am listing one of the two formulae that I have found to be good.
I recommend using both of them to calculate the stress on the flywheel and compare the two. So if you want to seriously do this, contact me and I will look the other one up too. The two dont agree with each other exactly, but they are close to each other and serve as a cross check for the designer.
Any good mechanics book will tell you that a flywheel undergoes two kinds of stress:
i) Tensile Stress
ii) Bending Stress
The following are both formula and a composite formula for combining the two, to help determine the total stress on the flywheel.
Source: Machine Design Handbook, Lingaiah, Bangalore University, Call Number TJ 230.L65
Tensile Stress
σt = 0.01095*ρ*r2*n2/g MPa (psi)
where
ρ is in N/m3 (lbf/in3)
g is 9.8 m/s2
r is the mean radius in m (in)
n = mean speed (rpm)
Bending Stress
σb = 0.2146*ρ*r3*n2/(g*h*i2) MPa (psi)
h = depth of rim in m (in)
i = number of arms
Total Rim Stress (Tensile) = 0.75*σt + 0.25*σb
This total rim stress MUST be less than the Yield Strength by 20 times, in order to account safely for common flaws probably present in your wheel (it its made to the good standards - if its inferior material, it might have to be 30 or 40 times or more). 20 times would give you a safety factor of roughly 4.4.
d) What about balancing the flywheel? Dynamic balancing of flywheels is another important safety feature we just cannot skip if there is even a suspicion of imbalance in the mass distribution of the flywheel. It will also save you a lot of grief later on, if you have the wheel balanced BEFORE you install it because otherwise you will be disassembling a lot of parts to correct this mistake.
Click here to see one of the flywheels machined from these calculations.
Click here to read how flywheels maybe the key to a new kind of flying machine.
Click here to read the latest on my research and see videos of the experiments I am currently conducting to make such a flying machine.
Thanks
Ravi
