Estimating the amount of time it'll take a tool to decelerate

[MechanicalChef]

The machine is a filament winder, with the tool installed horizontally, like a rotisserie. What I'm trying to estimate is how long the mandrel spin before the E-brake stops it. My issue is units, as they're just not falling out properly.

Based on initial estimates, the tool's centroid will be located about 3.5' from the axis of rotation. The mass at this distance we've estimated to be about 4800 pounds. When the E-stop circuit is tripped, the motors disengage and a caliper-type E-brake engages. It's a Kobelt 5024, and using this information, it's capable of 11261 ft*lbs of static holding torque.

The machine has an upper limit of 6.8 rpm, or 0.712 rad/s

Using the other data they list, I went back to my old Machine Component design text and estimated the dynamic retarding torque would be approximately 2250 ft*lbs.

Here's where things start getting screwing. I'm using the equation: Torque = I*(alpha), whereas alpha is angular acceleration.

T = I*(alpha)
T = (M*r^2)*(alpha)
T = (M*r^2)*(0.712 rad/s)/time
2250 ft*lbs = (4800 lbs*(3.5 ft)^2)*(0.712 rad/s)/time

Time = 18.6 ft/s Obviously, this is inconsistent units. What am I doing wrong here? Thanks.

 

[hydtools]

You need to divide 4800 lbs weight by g, 32.2 ft/sec^2, to get mass, M. Then units work out.

Ted

 

[MechanicalChef]

Ah, thanks. Pound mass versus pound force. 'Preciate it.

 

[hydtools]

Actually slugs, but the mass units are lb-sec^2/ft.

Ted