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[DPRG] Motor Calculations

Subject: [DPRG] Motor Calculations
From: Chuck McManis cmcmanis at mcmanis.com
Date: Wed Aug 29 00:44:20 CDT 2007

Hi Rick,

More questions than answers but if you get a bit more data the answer 
would fall out of the calculations so to speak.

>1. Will need to rotate a weight of about 600 lbs. evenly distributed 
>with a  maximum distance from center of 2 feet.

So 600 lbs is roughly 272 Kg of mass,

    First you need to know what sort of bearing this weight is on,
    it will contribute potentially significant friction into the
    equation.

    Next you will need to know at what speed you will be rotating
    this mass. Given its 272 Kg it is going to be carrying a *lot*
    of angular momentum.

    Finally you will want to know what other loads (besides bearing
    friction and wind resistance) are going to be applied to the
    load.

The reason these other bits of information are important is that if 
the bearing is very low friction then you can start the thing 
spinning with a pager motor, if its on an axle with a steel on steel 
oiled bearing you may find you need a bit more starting torque.

>2. The motor will need to rotate a weight of about 800 lbs. evenly 
>distributed with a maximum distance from center of 4 feet.

Same questions.

>The motors should be strong enough to get up to a maximum speed of 2 
>rpm within 1 second.


Ok, this gives us almost enough information (actually it is if we 
assume a frictionless bearing and no other resistances). The formula 
for angular momentum is Iw (Moment of Inertia * angular velocity), if 
you calculate the angular momentum of your 600lb disk, its 
approximately 1/2MR^2 (M = Mass, R = Radius) so keeping everything in 
SI units for your first disk, 272 Kg * your angular velocity is 720 
degrees / minute or 12 degrees/sec and your radius is .61 meters.
So about 608 degree*Kg*m^2/sec. That's about 608 joules or 608 
watt-seconds. Since a 1 hp motor is about 750 watts, that means for 
your 600lb disk you can use a 1HP motor to get it spinning at 2RPM 
(ignoring bearing friction and other factors), you'll probably want 
something better than that.

For your 800lb disk with the 4' radius your looking at more than 3200 
wattseconds so something bigger than a 4.4HP motor.

So in the first case I'd start with a 1.5HP motor (unless you know 
the bearing is high friction) and in the second case a 5HP motor.

--Chuck


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