Ask Me Help Desk - Need help for torque calculations

I have buildup the wheel that weight about 200Kg and hookup to the motor in vertical direction. It is operated at variation speeds ranges 500-1000 rpm. Now I am looking for brake just in case of emergency stop so I would like to know how many torque force (N-m or Ft-lbs) to buy the right kind of brake. Your helps on this matter are very-very appreciated.
HN

How quickly do you want this brake to be able to stop the wheel?

Quote:

Originally Posted by ebaines

How quickly do you want this brake to be able to stop the wheel?

It doesn't need to be stopped instantly but slowly in about 1min max.
I use this for VAWT. This emergency stop is just for repair only.
Thanks for helps.
HN

What's the diameter of the wheel in meters?

The torque that you will need to slow the wheel is:

$ T = I \alpha $

where I = moment of intertia, which for a wheel of uniform cross-section, radius R, and mass m is:

$ I = \frac 1 2 mR^2\ = \ \frac 1 2 (200Kg) R^2 $

and the acceleration of the wheel in radians per second squared is:

$ \alpha = \frac {\Delta \omega} {\Delta t} $

You're starting with

$ \omega = 1000 \frac {Rev} {Min} \times 2 \pi \frac {rad} {Rev} \times \frac {1 min} {60 sec} = 105 \frac {rad} {s}. $

To slow this over a period of 60 seconds requiresa deceleration of :

$ \alpha = \frac {\Delta \omega} {\Delta t} \ = \ \frac {105 Rad/s} {60 sec}\ =\ 1.75 \frac {Rad} {s^2} $

So the total torque needed is:

$ T = I \alpha = \frac 1 2 (200Kg) R^2 \ \times \ 1.75 \frac 1 {s^2} $

This result is in N-m. Be sure to specify R in terms of meters. And please verify that the wheel has uniform cross-section.

Dear Ebaines,
It is wonderful answer.
Thanks a lot for your helps . Now I can figure out how many torques that applied for the Electromagnetic Brake that I am looking for.
Best regards.
Huy Nguyễn