anorlunda said:
As
@CWatters said, you also need to know the friction in the motor, flywheel and bearings. In other words, how much power does it need to keep running after reaching full speed?
This purports to be the curves for your motor.
https://www.grainger.com/ec/pdf/6K778_16.pdf
purple line M is torque. I extended it on down to zero speed with Paint.
Observe torque starts out low at standstill , builds to a peak 20X greater, then drops off quickly as RPM moves into operating range.. That's how induction motors work.
Would another old-timer kindly check my physics? Been having senior moments of late.
Just like F = MA,
Torque =
M(oment of Inertia) X
A(cceleration in radians per second
2)
Your desired final speed is almost 1800 RPM which is 1800 X 2π radians per second
to reach that in 10 seconds requires
average acceleration of 180π rad/sec/sec.
Acceleration can start out somewhat slower and finish somewhat faster
but you need to pick a flywheel with a moment of inertia that your motor can accelerate into its higher torque range within just a few seconds . Else you'll waste all your 10 second start time with motor laboring at low speed.
Let us just pick a MOI to give half the requisite average acceleration at zero RPM.
Torque at zero speed = 1.5 ft⋅lbs
1.5 ft⋅lbs = MOI X ½ 180π rad/sec
2
MOI = 1.5/90π = 5.305 X10
-3 ft⋅lbs/sec
2 , radians having no units
NOTE lbs is pounds force not mass
now to calculate MOI
i'll guess your flywheel will be a thin disc like a grinding wheel
http://hyperphysics.phy-astr.gsu.edu/hbase/tdisc.html
I = ½MR
2
Hmm you get to trade off diameter for mass.
Let's just pick a six inch diameter, half a foot, radius ¼ foot
0.005305 = ½MR
2
0.005305 = ½M X ¼
2
M = 0.005305 / (½ X ¼
2) = 0.1698
NOTE : Since we expressed force in pounds , mass is in slugs
0.1698slugs X 32.174 lbf/slug (at 1g) = 5.46 pounds
so a small diameter flywheel can be pretty heavy. A bigger diameter will have to be lighter.
Look at the MOI formula -
I = ½MR
2
If you keep same mass by doubling the diameter and reducing the thickness , you quardruple the MOI.
(Geometry pop quiz- by how much would you have to reduce thickness? hint- not half)
I really suggest that you repeat my arithmetic using Newton-Meters and kilograms to make sure i haven't inverted something.
When you try this thing out, listen carefully to the motor.
You'll hear its rate of acceleration increase with speed as it walks up its speed-torque curve. It almost snaps over the peak.
Once you recognize that sound and relate it in your mind's eye to that curve, it helps you "feel" induction motor behavior.
Torque falls off as square of applied voltage. That's why long extension cords that drop voltage are so deadly to induction motors - they never make it to torque peak so current stays high , see the blue "I" curve up above. They'll burn up.
Okay that's induction motors in a nutshell.
I hope you get interested enough to do some predictive iterative calculations.
Calculate acceleration from standstill, new speed after one second,
insert new torque from curve for that speed, calculate new acceleration, new speed at end of that additional second,
insert that greater torque,
etc
If you curve fit that torque curve you could simulate startup with say 1/10 second intervals in a spreadsheet and play with flywheel weights and diameters. I loved to do that sort of thing in BASIC before Miscroshaft forced everybody from QBASIC into spreadsheets. I never went along.
Of course all this neglects air friction on flywheel, another reason to keep it small diameter so edge velocity is slow.
last but not least - SAFETY
DO NOT MAKE SOMETHING THAT'S FLIMSY AND CAN FLY APART !
It
WILL embed pieces of itself in the floor, walls and spectators. I've done that with a brass fan blade.
EDIT that motor is set up for belt drive. I'd suggest you
not mount a heavy flywheel on that shaft, it's only intended for a light pulley..
Go to the hardware store , buy a quality grinding wheel rated for 3600 RPM because you'll run it at half that speed. Get a proper mounting attachment too.
(oops)
Beware junkshop wheels because you never know if they got dropped and have a crack.
______________________________________
end digression.
That's how you can calculate what you asked about.
