# Calculating force during motor stoppage

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1. Dec 12, 2015

### andrey-g

When a motor with a flywheel spins up and then stops, what is the force translated on the surface onto which the motor is connected? I'm assuming the value of this force equals to the centripetal force in the flywheel, but I'm not sure.

The setup: http://imgur.com/IiOrRoQ

How does the force change if flywheel's weight isn't distributed uniformly across the volume?

How does the energy dissipated inside the motor come into the calculation?

2. Dec 12, 2015

### billy_joule

The force depends on the motor geometry and the torque the motor applies to it's load.
Centripetal force is not relevant.
Can you draw a free body diagram? Do you know Newtons third law? Are you familiar with the term 'static equilibrium'?

No, not unless you are finding the torque out from electrical power in.

3. Dec 14, 2015

### andrey-g

I made the FBD, but I'm not sure what information I could get out of it, since I need to find F_motor as a function of flywheel mass and speed.

4. Dec 14, 2015

### billy_joule

Torque is defined as T=Fr. The motor casing is not accelerating so all torques and forces must sum to zero.
if we call the horizontal distance between the shaft axis and a mounting bolt 'r' then we have:
(letting anticlockwise be positive)
ΣT = 0 = Fbaser + Fscrewr - Tmotor

So as r gets larger, the force on the screw gets smaller.

Nice diagram.
The speed of the flywheel doesn't matter. What matters is the torque the motor applies to it's load.
If the motor is accelerating the flywheel then the torque can be found via:
T = Iα
Where I is the moment of inertia (found from the geometry and mass of the flywheel)
https://en.wikipedia.org/wiki/Moment_of_inertia
https://en.wikipedia.org/wiki/List_of_moments_of_inertia

and α is angular acceleration:
https://en.wikipedia.org/wiki/Angular_acceleration

If the motor is hoisting a weight or something at a constant velocity then the torque can be found via one of the other definitions:
T =Fr
T = P/ω
https://en.wikipedia.org/wiki/Torque

5. Dec 15, 2015

### andrey-g

Correct me if I'm wrong, but aren't equations above valid only when the motor is continuously running?
I'm interested in momentary forces occurring when the motor stops.

6. Dec 15, 2015

### billy_joule

They apply at all times, a motor must decelerate to stop. The torque during which can be found via T=Iα. The motor can apply torque without moving at all, in fact many (most?) motors apply their greatest torque at 0rpm; stall torque.

7. Dec 15, 2015

### andrey-g

So what you're saying is that the force created during the stoppage is a function of moment and inertia and α (in this case α is angular de-acceleration from ω to 0)?

This is confusing to me because in my mind, the higher the energy stored in a flywheel (W = I ω2 / 2), the higher the force acting on the block will be, because that energy has to go somewhere.

8. Dec 16, 2015

### billy_joule

That's right. But more directly,The force depends on the braking torque the motor applies to the flywheel.

No energy goes to the block, as no work is done on the block (as W=Fd will show). All the flywheels energy is transferred to the motor as it brakes. This (now electrical) energy is either dumped as heat (rheostatic braking) or may go back to the power supply (regenerative braking):
https://en.wikipedia.org/wiki/Dynamic_braking
If the motor applies constant power then the force value will not be constant, it'll go from some minimum up to max as ω approaches zero. The rate of deceleration will also vary (ie α will increase as ω decreases).
If α is constant then the force on the block will be constant but the braking power will go from some maximum down to zero as ω reaches zero.

Last edited: Dec 16, 2015
9. Dec 17, 2015

### andrey-g

My original idea was to stop the motor by power reversal as I've heard it leads to best stopping times. But if I've understood you correctly, all electrical stopping methods result in energy being converted into electrical energy?

That would explain why Cubli (link to paper in PDF), my original inspiration for the question, uses mechanical braking.

10. Dec 17, 2015

### billy_joule

The Cubli looks like a cool project, are you trying to make one?
Yes that's right. That energy can be dumped as heat in the motor windings as long as it's not so much or so often that the motor overheats. I am far from an expert though, I studied mechanical engineering not electrical.

To me, the paper implies they couldn't get sufficient braking torque from the motor alone so has to resort to a more primitive approach (ie slam the flywheel into a stop). Maybe you'll find a better approach. Have you looked for more recent work? It's been 4 years, maybe they found a more elegant solution for the final design?

11. Dec 17, 2015

### andrey-g

No, just trying to figure out how much force can be extracted from this kind of device to confine a potential area of application.

So... is it that electrical braking can only convert energy stored in the flywheel into electrical energy inside the windings or is it actually possible to convert it to a mechanical force (given large enough braking torque)?

12. Dec 17, 2015

### billy_joule

When the motor applies a braking torque to the flywheel the motor must apply force to its mount as in post #4.
I think your confusion stems from your understanding of force and energy - you can apply a large force without expending any energy (eg like a boulder sitting on the ground does, or a motor applying force to it's mount). No energy goes to the motor mount as no work is done on the mount*, the flywheels energy is going elsewhere.

This concept applies to pretty much all braking types eg traditional frictional braking - when you brake in your car, its kinetic energy is converted to heat and dissipated from the brake pads and discs, no energy is transferred to the brake mounts.
If you brake in a Prius or sim. its kinetic energy is converted to electricity and sent back to the battery pack. The result is identical in each case - the cars kinetic energy is transferred elsewhere so the car slows down. ( I think a Prius still uses traditional brakes during hard braking as the electric motor braking cannot provide enough torque - a lot like the Cubli)

*note that the Cubli is a little different as some work is done on the mount during braking when/if tipping occurs, in which case work is done to raise the Cubli's centre of mass and increases its kinetic energy.