RE: [CAD_CAM_EDM_DRO] Re: Servo drives- exploding head

Dave , I thought about this a bit. I want to talk a little
about the effects of inertia matching, but without exploding heads.
I think I have a way to do this....let's see how it goes.

Moment of inertia can be confusing. The second moment of area
( often called moment of inertia) of a circle of radius r
is 1/2* PI* r^4. The mass moment of inertia of a thin disk
of radius r and mass M is 1/2*M*r^2. For units you see things
like oz*in*sec^2. You also see kg* m^2. or N * m * s^2. The last two
are actually the same.

OK, the cranial pressure is building! So....lets not talk about moments
of inertia for a while. Let's use something else that is equivalent.

Let's do two designs. The first will be a silly one. The second will be a
bit less
silly.

I am going to pick a motor. I will use the SEM servos I used to sell because
I have the specs handy and they are in the torque/rpm range of many of the
treadmill motors, although they have less cogging and other things.

I want a machine that can do 200 in/min.

I have some nice 2 turns per inch ballscrews.

I had to write a big check to that Les guy for these motors and I
want to use all the power they can produce. Since the torque is the
same at any rpm and power=torque*rpm I will run them at 4000 rpm,
the max cont rated speed.
------------------------------------------------------

Ok. 200 in per minute should have the motor going at 4000 rpm. The
ballscrew will need to turn at 400 rpm because it needs to turn two
revolutions per inch of travel.

4000 rpm...400 rpm...ok, I need a 10:1 gear reduction. Gee these
numbers are turning out to be convenient. ;)
10:1....wow...that should be some serious torque! Hope the ballscrews
don't buckle.

Now let's see how well this machine can accelerate. There is a number
in the motor specs called max angular acceleration. It indicates
how fast the motor can wind up to speed with nothing hooked to it when
power is applied.

That number is 7100 radians/sec^2. let's convert that to revolutions by
dividing by 2PI. So that's 1130 revolutions/sec^2. If we apply rated
current to the motor at a standstill (don't do this!) in 0.1 second
it will be already wound up to 113 rev/sec or 6700 rpm. Oops it is not
supposed to be run that fast...but if we only go to 4000 it will take
less than 0.1 seconds! Cool. The actual numbers (with real servo amps)
will be only about half as good, but that is still fast. let's use
0.15 sec to get up to speed.

Well the ballscrew driven load (we'll assume very light) will get up to
200 ipm in the same time. 200 ipm is 3.33 in/sec so our accel is 3.33/.15
or 22 in/sec^2. One g is 386 in/sec^2 so we can do about 0.0575 g.

Hm...with multiple identical axes the acceleration is related to the
smallest
corner radius we can do at speed.

Min radius = v^2/a so that's 3.33^2/22 or almost exactly half an inch.
What nice round numbers. But a one inch circle is the best I can do at 200
ipm
with all that power and torque? After all I am using the motor to the max!
----------------------------------------------------------------

Now let's do another design with the same components and specs.
This time we are just going to waste the power capability of that nice motor
and hook it up to the ballscrew DIRECT DRIVE. Gosh it will only need to
get up to 400 rpm so we will only use a tenth of it's power capability.
What a waste.

Now lets look at the acceleration. It will probably be crummy due to
that low power. The ballscrew is light, so we will use the same 0.15 sec
to get to 4000 rpm. But..we only will be going to 400 rpm...so it will only
take .015 seconds.

So now our ballscrew driven load gets to 200 ipm in a tenth the time.
The acceleration is 220 in/sec^2 or 0.57g!

The minimum radius v^2/a is now 3.33^2/220 or 0.05 inches. TEN times
better!!

As a last bit let's check on how much force the system can make.
The motor can put out 1200 oz*in torque, so the force is 1200*2PI*2
= 15702 oz=942 lb. That's plenty!
---------------------------------------------------------

Ok. I did this to show what inertia does. We engineers do not calculate it
this way...we specify a REASONABLE inertia ratio between motor and load.
Without details I can say that the moment of inertia for the first case was
over
20 oz*in*sec^2 at the transmission output. In the second case it was
0.2 oz*in*sec^2. I said the load was light... 0.05 oz*in*sec^2 might be
typical.
So the inertia ratio for the first case was 400. For the second it was 4.
We try to keep it no more than about 5.

I hope this example helps to show that inertia is an important design issue.
I might have even made an arithmetic error somewhere....but it still should
illustrate the concept. Some drives need large transmission ratios...some
don't.

Much free software like the Kollmorgen stuff can calculate this....or we on
the
list can help.

But DO consider inertia...it's important.

No blown up heads?


Les


Leslie M.Watts
L M Watts Furniture
Tiger Georgia
(706) 212-0242

Main page:
http://www.lmwatts.com
Engineering:
http://www.lmwatts.com/shop.html
Cnc surplus for sale:
http://www.lmwatts.com/forsale.html
Carved signs:
http://www.lmwatts.com/signwp.html