Re: Servo drives- exploding head prevention

> Good post, thanks for all the time it took to write it up. This is

> keeper.
>
> Wally
>
>
>
> --- In CAD_CAM_EDM_DRO@yahoogroups.com, "Leslie Watts"
> <leswatts@a...> wrote:
> > Dave , I thought about this a bit. I want to talk a little
> > about the effects of inertia matching, but without exploding

> > 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

> > 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

> >
> > 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

> of the
> > treadmill motors, although they have less cogging and other

> >
> > 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

> > 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

> > 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

> > current to the motor at a standstill (don't do this!) in 0.1

> > it will be already wound up to 113 rev/sec or 6700 rpm. Oops it

> 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

> > 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

> 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

> > 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

> > 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

> > = 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

> load.
> > Without details I can say that the moment of inertia for the

> case was
> > over
> > 20 oz*in*sec^2 at the transmission output. In the second case it

> > 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

> 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
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> > http://www.lmwatts.com/forsale.html
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