# Can a flywheel add torque?

## Main Question or Discussion Point

Hello guys,
I am working on designing a flywheel to couple to a generator however i have a small problem and i have low knowledge in flywheels

I have a pinion rotating at w = 14.13 rad/sec and torque Tpinion = F*Rpinion = Mass of inertia *alpha pinion
All is known I can find Tpinion euqal around 0.0006 N.m (Rp = 2cm , alpha pinion = 88 rad/s^2 , m = 700g) Now the question :
After the pinion there is a gearbox of 1/20 coupled to a flywheel coupled to a generator

My generator gives 10 w with minimum RPM of 2500
My system gives me around 2700 RPM
So i need a certain amount of Torque = 0.035 N.m to get this power output.
Does the free wheel add torque ? and what the equation coupled with the gearbox be?

thank you for your time and I appreciate every help
Edit: I was considering the angular acceleration for the Flywheel to be alpha pinion *20 due to gearbox is it correct as well?

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This sounds like a small wind turbine connected to a 10W generator. The flywheel on the generator shaft is a good idea and will serve to smooth out speed variations. The flywheel adds no torque at constant speed. Yes, the angular acceleration of the flywheel would be 20 times that of the pinion.

• russ_watters
Second of all i need 0.035 N.m torque to get this 10 w however i only have 0.0006 N.m due to my small size and weight of the pinion. Can i increase this torque by adding a flywheel?
( the pinion size and weight cannot be changed )

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russ_watters
Mentor
As insightful said, the flywheel does not add torque. You need more input power to generate the output power you want.

Second of all i need 0.035 N.m torque to get this 10 w however i only have 0.0006 N.m due to my small size and weight of the pinion.
Now I'm confused about your setup. Could you provide a sketch? Your 0.035 N.m at 2700 rpm does give 10W at the generator, but would require 20 times that torque at 14.13 rad/s at the pinion input to the gearbox.

Sorry for the confusion. This is a sketch.
I am a bit as well confused due to many things.
So as seen in the picture I have the pinion with the force F2 then gearbox with 1/20 then the flywheel then a generator.
I derived two equations please correct me as I am not sure yet which one is correct.

If I use equation 1 :

F2.Rpinion = Jsystem * omega pinion

with Jsystem = Jpinion + (smthing)*Jflywheel this means that the mass and radius of the flywheel can increase the torque.

So can i increase my torque using this formula?
Or equation 2
Torque gearbox + Torque flywheel = 0.035 N.m (Power out = 10 W , RPM = 2700 so i need to supply to generator this torque of 0.035 N.m)
Having Torque pinion = 0.5* mpinion * r^2 * alpha with m = 700 g and r = 2 cm and alpha =88.5 rad/s^2
I can find the Torque done by the pinion which is this 0.012 N.m
After gearbox , T = 0.012/20 = 0.0006 N.m
I need 0.035 N.m so Torque flywheel = 0.034 N.m
I know energy is conserved and i cannot add torque but the fact that moment of inertia can add torque i got a bit confused

Sorry for the long post and thank you for your effort and time

#### Attachments

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Having Torque pinion = 0.5* mpinion * r^2 * alpha with m = 700 g and r = 2 cm and alpha =88.5 rad/s^2
I can find the Torque done by the pinion which is this 0.012 N.m
After gearbox , T = 0.012/20 = 0.0006 N.m
OK, this is the torque needed to accelerate your 700g, 2cm radius pinion disc at 88.5 rad/s2.
I do not see how this is relevant at all to your operating a generator at a steady-state 2700 rpm.
I need 0.035 N.m so Torque flywheel = 0.034 N.m
You need 20*0.035 = 0.70 N.m torque at the pinion at 2700/20 = 135 rpm.
If you cannot provide this torque, your project (as I understand it) will not work.

Mmm ok that i understand well bas the trick is if i need to writr the equation of motion to my system it will not be like equation 1 ?
Equ 1 :
F2*Rp = Moment of inertia system*alpha
With MOI system = inertia of pinion +(smthing) inertia of flywheel
Doesnt this mean if i add the flywheel it will help increase my torque?

Mmm ok that i understand well bas the trick is if i need to writr the equation of motion to my system it will not be like equation 1 ?
Equ 1 :
F2*Rp = Moment of inertia system*alpha
With MOI system = inertia of pinion +(smthing) inertia of flywheel
Doesnt this mean if i add the flywheel it will help increase my torque?
No. Adding the flywheel just adds to the moment of inertia of the system and so reduces alpha.

• Oh i see now

I have one last question
I understand i need now 0.7 N.m of torque
However if equ of motion on pinion without flywheel is F*r = Jpinion* alpha
If my torque should be 0.7 then using Jpinion= 0.5× mass pinion* r^2 i can find m = 40 kg. ( r = 0.02 m and alpha 88.5 rad/s^2)
However my max pinion mass is 700 g so does adding a flywheel help me distribute this weight to get my desired torque?
Because ill have F*r =0.7= Jsystem*alpha
Where Jsys = Jpinion+ n^2 *Jflywheel ?

Why are you concerned with accelerating the pinion at 88.5 rad/s2?

Suppose my design is giving me those values
Can I get my torque to be 0.7 like i said in my previous post? (by adding a flywheel to distribute the weight)

russ_watters
Mentor
s1h1ad2ow, what you are asking (or rather, how you are trying to go about it) does not make much sense. You should not be looking at a situation where the system is accelerating because your goal is to generate power under steady state conditions (not accelerating). Your approach is not helping you get where you want to go.

• insightful
Suppose my design is giving me those values
That doesn't mean those values are relevant to your design.
Can I get my torque to be 0.7 like i said in my previous post? (by adding a flywheel to distribute the weight)
No. Your force on the pinion must be 0.7N.m/0.02m = 35N.

I understand know I was using a wrong approach for this issue