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Horsepower, torque and acceleration of mass

HuFlungDung

Diamond
Joined
Jan 19, 2005
Location
Canada
I'm trying to find an accurate estimation of what size of an electric motor is required to accelerate a multi-spindle drilling machine.

There are 30 gear driven spindles, each one has a tentative rotating mass of about 1.75 pounds. When the machine runs, it will have an idle speed of about 1000 rpm, then accelerate as quickly as possible to 3000 rpm, drill for a duration of about 2 seconds, decelerate to 1000 rpm for about 4 seconds, and repeat this same cycle continuously for many hours.

Suppose I wanted to accelerate these at a rate of 2000 rpm/sec^2, how large of a motor would be required to provide sufficient torque? In this situation, the actual torque required to do the drilling is small, I would think less than the acceleration torque requirement.

Of course, a VFD will be involved in the speed change. The ratio between the main motor and the spindles will be 1:1

I hate to just guess at it, and end up having to change out some expensive components, plus potentially have to redesign due to physical size requirements.

At this stage, I might also be able to figure out ways to lighten the spindle assemblies to shave off ounces here and there.

Thanks for any assistance.
 
Hu,
The main determining factor in acceleration will be the polar moment of inertia of the rotating spindles and gears. Polar moment calculations are covered decently in Machinery's Handbook.

Each assembly will act like a flywheel, where the energy required to accelerate it is going to be heavily dependent on the radius of the mass as measured from the centerline it's rotating about. Depending on the diameter of your gears, they could actually weigh less and still have a larger polar moment than the drill chuck, depending on the gear's diameter vs the diameter of the chuck.

Once you make the approximations of the radius of the masses and the polar moment calculations for one typical assembly, the numbers should be additive for the other 29 assuming they're basically identical.

Once you get into the polar moment calcs a bit, you'll begin to see where lightening might be worthwhile, and where it would be wasted effort. For example, if you are using solid constant thickness spur gears, you can gain quite a bit by thinning the cross section or drilling large holes to lighten the gears. OTOH, you might have a 1" diameter shaft where you could drill thru with a 1/2" hole, and even though it would remove more weight than modifying the gear would, the effect of lightening the gear would have much more effect on polar moment since you're removing weight that's at a significant distance from the center of rotation.
 
Is it really worth the effort to speed this machine up and then slow it down when the RPM difference is so slight and duration between fast and slow is so short?

I have no idea what the process is but it would seem to me it would be easier on the involved gear train to merely run it up to speed and leave it there...but what the hell do I know!:):)

Stuart
 
Hu...

Is distributed hydraulics or pneumatics definitely out for this? Kick me to the curb if it's a no-go, but it seems like the responsiveness would be easier to manage.

Chip
 
Muncher has set you in the right direction . . .

Calculate Wk^2 in units of lb-ft^2

Torque (ft-lbs) = (Delta RPM) x Wk^2 / (308 x t (sec))

I can't tell you how many thousands of times I have used this equation.
 
Murray,

It won't take that much horsepower to do what you need. However the duty cycle requirements and management will most likely be the major consideration in a system like you described. Running the spindles speeds up and down is all fine a dandy but you know from experience how how much heat your Haas puts out running all day long. All that power coming from your wall plug turns into heat, enough to evaporate gallons of coolant or fry undersized drives and motors. Try putting your hand on the spindle motor of your mill after a good run of several hours.

Your electronics and motor need to be sized for the managing the duty cycle requirement if your device will run as you described. There are many places on a thirty spindle drive setup to suck off power. You need to understand the system mass, that is spindles, belts, pulleys shafts, idlers etc. I always start out looking at similar successful systems just to calibrate my expectations.

The typical way these get designed is to make your best guess at everything, calculate it out, arrive at some number with a generous safety factor say 1.6 HP, then go out and install a 5 hp drive and get some sleep.

.02 entered.

Tom Lipton
 
This machine drills holes with slight negative clearance on the drills. Crazy but true :D

So extra heat is generated whenever the drills are engaged in the soft workpiece. The notion of slowing them down on retraction (to lessen heat buildup) may not work wonderfully well, but I feel that we have to try it. In previous versions of this machine, we've run the spindles constant speed, and we're now looking for small improvements that will add up to increased output over many hours of operation. For example, running the spindles faster while drilling, feeding faster, but trying not to increase the heat rise of the drills per cycle.

A hydraulic drive motor is an option to consider and may give us better power reserve for fast acceleration.

Thanks to all for the equations and references, I will set to work.
 
Just to be clear I wasn't talking about the heat generated by the drills. The power input just from running the spindle speed up and down is the major consideration.

Tom
 








 
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