How much HP to spin this ring?

[prodriverex]

OK I'm super frustrated.. I spent 50min typing the whole text here earlier and click preview only to be told I was logged out. Click back and and all was gone. Damn..

Ok here's the question, AGAIN.

Weight: 1kg
Type: Flywheel, OD is 80mm, ID is 40mm if that matters.
So that's a typical Ring calculation?

Torque, T = Moment of Inertial, I * Angular Acceleration, α
HP = N * T/5252

MOI, I, depends on Ring or Solid
Solid cylinder = (1/2)*m*R²
Hollow cylinder = m*R²

So if this is ring, then I = 1kg * 0.08 * 0.08 = 0.0064


Angular Acceleration, α (rad/s²): dω / dt = α_T/ r.

ω is the angular velocity
α_T is the linear tangential acceleration.
r is the radius

Simpler term, one radian (rad) is one revolution, i.e 2∏

So if the unit is rad/s² is essentially how many rad in a squared-second?

If it is true, t being 8000rpm or 133.333 rev/sec. In square sec, divide further by 60.

Therefore, 133.333/60 = 2.222 rad/s²

Torque, T = 0.0064 * 2.222 = 0.0142 (Nm?)

So HP = 8000 * 0.0142 / 5252 = 0.02166 hp? Doesn't look right!

Appreciate any enlightenment please. Thank you..

 

[tiny-tim]

welcome to pf!

hi prodriverex! welcome to pf!

Flywheel, OD is 80mm, ID is 40mm
…
MOI, I, depends on Ring or Solid
Solid cylinder = (1/2)*m*R²
Hollow cylinder = m*R²

So if this is ring, then I = 1kg * 0.08 * 0.08 = 0.0064

no, it's not a ring, it has an OD and an ID, so it's a solid cylinder with a cylindrical hole …

you'll need to find the moment of inertia of the "whole" cylinder, and subtract the moment of inertia of the "hole" cylinder

(i haven't checked the rest of what you've done, since I'm not sure what the question is asking for … the HP needed to achieve what acceleration? )

 

[prodriverex]

Thanks Tim!
So the simplest formula is I = M*R²
And OD is easy as what was quoted at 0.0064 taking 0.08 as R. This is the whole

As for the hole, say the bearing and spokes weigh 80gm, that will be I = 0.08kg * 0.04² = 0.000128.

Nett I is thus 0.006272!?

But if I put a weight to the hole, then it should be also sum into the equation, not subtract. If I don't put a weight, then anything * zero is meaningless?

 

[the_emi_guy]

prodriverex,
There are a couple issues here:
1 - In your formula for horsepower, torque should be in lb-ft not Newton-meters.
2 - One radian is not one revolution. There are 2π radians in one revolution.
3- We do not get from velocity (rad/s) to acceleration (rad/s^2) by dividing by 60.

 

[tiny-tim]

So the simplest formula is I = M*R²

no, the moment of inertia of a solid cylinder is 1/2 MR² (with R = OD)

from that, you need to subtract the moment of inertia of a solid cylinder with R = ID

 

[CWatters]

Prodriverex: It doesn't take any power to keep it spinning at a constant rpm. It only takes power to accelerate it upto that rpm. That's why the units are per second²

 

[the_emi_guy]

He is actually trying to use the formula for engine horsepower given constant RPM and constant torque (braking device in dynamometer loading engine). But he is calculating torque using unloaded kinematic equations from acceleration. But he is getting acceleration by dividing angular velocity by 60.

 

[CWatters]

There is a brake?

Prodriverex: I think we need more info on what the exact set up is.

 

[prodriverex]

no, the moment of inertia of a solid cylinder is 1/2 MR² (with R = OD)

from that, you need to subtract the moment of inertia of a solid cylinder with R = ID

Oh my bad..
I_whole = 0.5 * 1 * 0.08 * 0.08 = 0.0032

And what to do with the hole? Subtract by 0.000128?

There are a couple issues here:
1 - In your formula for horsepower, torque should be in lb-ft not Newton-meters.
2 - One radian is not one revolution. There are 2π radians in one revolution.
3- We do not get from velocity (rad/s) to acceleration (rad/s^2) by dividing by 60.

He is actually trying to use the formula for engine horsepower given constant RPM and constant torque (braking device in dynamometer loading engine). But he is calculating torque using unloaded kinematic equations from acceleration. But he is getting acceleration by dividing angular velocity by 60.

Ha I was taking ref from https://www.physicsforums.com/showthread.php?t=201254 and got, probably, confused too.

So as in one rev = 2.∏ rad.
Rad defined as the arc length = radius

Much as i want to get the result, i am also interested to know the process and learn.
So if i have a radius of 0.08m, one radian = 0.08m.
One rev = the circumference = 2∏R = 0.50265544m
∴one rev = 0.50265544/0.08 = 6.283193 rad?

Ok now, how do i get to Angular Acceleration, α, from here?

Appreciate all your help.

There is a brake?

Prodriverex: I think we need more info on what the exact set up is.

No brake. spool up and braking relies on the engine's torque.
I had design a generator that shapes like a fly wheel which is the easiest to imagine. But I was afraid that the weight is too heavy on that puny 3W 2 stroke engine. So I like to get a feel of how breathless the engine will go spinning that generator. If it is ok, then what if I add in another pair of plate to churn out double the kW output at double the weight at 2kg, can it cope? I do not want the fuel consumption of the engine to suffer.

 

[the_emi_guy]

prodriverex,
Are you trying to analyze a motor that is running at final rpm, or are you trying to analyze the spinup of the motor.

By the way arc length is not the same as radius.

 

[AlephZero]

No brake.
...
I had design a generator that shapes like a fly wheel which is the easiest to imagine.

So there IS a "brake". It's the electrical power your generator is producing.

Apart from the time it takes to run up to speed, you can forget everything you have done so far. Just compare the electrical power output with the HP of the engine (1 HP = 746 watts) and add say another 20% to the engine power because the system isn't 100% efficient.

 

[prodriverex]

prodriverex,
Are you trying to analyze a motor that is running at final rpm, or are you trying to analyze the spinup of the motor.

By the way arc length is not the same as radius.

I think both. Spin up will determine how long it takes to get up to speed to reach desire power.

Running at final rpm will determine the burn rate of the engine.

Arc length is different as radius I know. But 1 rad is the ratio of arc length to radius.. no?

 

[prodriverex]

So there IS a "brake". It's the electrical power your generator is producing.

Apart from the time it takes to run up to speed, you can forget everything you have done so far. Just compare the electrical power output with the HP of the engine (1 HP = 746 watts) and add say another 20% to the enugine power because the system isn't 100% efficient.

Not to sure if you are referring to cogging effect or final motor efficiency. Yes I am concern about final motor efficiency as it will determine how useful this gen is. That is why the final product must go for further diet..

3hp engine say 80% efficient, the gen must produce more than 2700W to be classified as a good gen, that's what you mean?

 

[tiny-tim]

hi prodriverex!

(just got up :zzz:)

Oh my bad..
I_whole = 0.5 * 1 * 0.08 * 0.08 = 0.0032

And what to do with the hole? Subtract by 0.000128?

no, you add the moment of inertia of the hole, which is minus 0.5 * 1 * 0.04 * 0.04 = -0.0008

(because the hole is made of the same material as the solid cylinder, except that its mass is negative! )

 

[prodriverex]

hi prodriverex!

(just got up :zzz:)no, you add the moment of inertia of the hole, which is minus 0.5 * 1 * 0.04 * 0.04 = -0.0008

(because the hole is made of the same material as the solid cylinder, except that its mass is negative! )

Good morning. I'm from another side of the earth. Ha..
Ok that make sense to me now.

I is then, 0.0032 - 0.0008 = 0.0024

Let me try again on Angular Acceleration (rad/s²) again.

Radian is the ratio between the length of an arc and its radius.

That's what I meant. My radius is 0.04m (not 0.08 as in previous cal).
So 1 rad is ratio of arc length, 0.04m / radius 0.04m
Ok this has not much meaning.

Circular Motion & Acceleration
Uniform circular motion is an example of a body experiencing acceleration resulting in velocity of a constant magnitude but change of direction. In this case, because the direction of the object's motion is constantly changing, being tangential to the circle, the object's velocity also changes, but its speed does not. This acceleration is directed toward the centre of the circle and takes the value:

where v is the object's speed

In a linear speed, we measure in m/s. In circular speed, we measure in rad/s.
So if we are talking about 8000rpm, the circumference being 0.2513m, in equivalent circular speed it will be 133.333rev/s * 0.2513 = 33.51 m/s.
And we need to convert it to rad/s.
Since one rev is 0.2513m/0.04m = 6.2825 rad,
The velocity is 133.333 * 6.2825 rad = 837.665 rad/s?

Ok still wrong..

 

[tiny-tim]

In a linear speed, we measure in m/s. In circular speed, we measure in rad/s.

yes (and rpm is also a circular speed)

So if we are talking about 8000rpm, the circumference being 0.2513m, in equivalent circular speed it will be 133.333rev/s * 0.2513 = 33.51 m/s.
And we need to convert it to rad/s.
Since one rev is 0.2513m/0.04m = 6.2825 rad,
The velocity is 133.333 * 6.2825 rad = 837.665 rad/s?

it's a lot easier to convert the "r" in "rpm"

r = revolution = 2π radians,

so 1 rpm = 2π rad/minute

 

[prodriverex]

yes (and rpm is also a circular speed)it's a lot easier to convert the "r" in "rpm"

r = revolution = 2π radians,

so 1 rpm = 2π rad/minute

8000rpm = 8000 * 2∏ = 50,265.48 rad/min

or 837.758 rad/s - and this is angular velocity.

So now to calculate the Angular Acceleration, , I can use v² / r?
And r is not radius but radian as in 2∏?
= 111,701 rad/s²?

Then T = I * a: 0.0024 * 111,701 = 268 lb-ft²?

 

[tiny-tim]

So now to calculate the Angular Acceleration, , I can use v² / r?

no!

v²/r isn't angular acceleration

-v²/r is the radial component of linear acceleration, and is in m/s²

angular acceleration is simply d/dt of angular speed (in rad/s²)

to calculate angular acceleration (if it's constant), use the usual constant acceleration equations


(your original post was correct …)

Angular Acceleration, α (rad/s²): dω / dt = α_T/ r.

ω is the angular velocity
α_T is the linear tangential acceleration.
r is the radius

 

[prodriverex]

α: dω / dt = 837.758 / dt

And what is dt now? I know it must be a timing of t or something, timing per rev in rad, 2∏? Argh..
My apology for being slow. TIA!

 

[tiny-tim]

well, now we come back to my original question …

(i haven't checked the rest of what you've done, since I'm not sure what the question is asking for … the HP needed to achieve what acceleration? )

… what exactly is the question asking for? accelerating from what speed to what speed in what time?

 

[prodriverex]

Cool. You are a great tutor! Thanks!

As for the detail, I have no prior experience honestly.

All I know is I have to design a 2.5kW nett peak output generator and 1.5kW nominal between 4000 and 5500 rpm and 8000rpm for accidental buffer.
The fundamental of my electrical design has been conceptualized. Now I have to get it down to 800gm instead of 1kg. 600gm to be competitive but we will see.

The other equation is the engine which is not my responsibility but its good to know if the engine can even spool my gen during startup to peak for first 2.5min for eg. How long will it take to hit 5500rpm, i need to know. from 4000 to 5500rpm, how much effort i need to discover.

After reading this, maybe someone will tell me here dude, don't worry, the power of the engine is more than enuff to spool even 1.5kg, just need longer time.. How long is long? Then maybe we need to look at the engine specs?? If that's the case, then no more work for me :)

See, what's more important is that the engine must keep within the BSFC under certain load its design for. If I can't get to the light weight, I need to know the number to advise the engine tuner to see how bad it will go for them. Of course, this is an experiment for me. We have already in mind a commercial gen that is proven and lighter, which will be used. But I am trying to break their power output/kg design and mine is a back up design :)

So, how fast to attain 8000rpm you may ask again. 10sec reasonable for a 3hp engine? Do we need the torque figure?