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

> 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

> bit less
> silly.
>
> I am going to pick a motor. I will use the SEM servos I used to

> I have the specs handy and they are in the torque/rpm range of many

> 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

> don't buckle.
>
> Now let's see how well this machine can accelerate. There is a

> in the motor specs called max angular acceleration. It indicates
> how fast the motor can wind up to speed with nothing hooked to it

> power is applied.
>
> That number is 7100 radians/sec^2. let's convert that to

> 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

> supposed to be run that fast...but if we only go to 4000 it will

> less than 0.1 seconds! Cool. The actual numbers (with real servo

> 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

> 200 ipm in the same time. 200 ipm is 3.33 in/sec so our accel is

> 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

> What nice round numbers. But a one inch circle is the best I can do

> ipm
> with all that power and torque? After all I am using the motor to

> ----------------------------------------------------------------
>
> 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

> and hook it up to the ballscrew DIRECT DRIVE. Gosh it will only

> get up to 400 rpm so we will only use a tenth of it's power

> 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

> to get to 4000 rpm. But..we only will be going to 400 rpm...so it

> take .015 seconds.
>
> So now our ballscrew driven load gets to 200 ipm in a tenth the

> 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

> this way...we specify a REASONABLE inertia ratio between motor and

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

> 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

> typical.
> So the inertia ratio for the first case was 400. For the second it

> We try to keep it no more than about 5.
>
> I hope this example helps to show that inertia is an important

> I might have even made an arithmetic error somewhere....but it

> illustrate the concept. Some drives need large transmission

> don't.
>
> Much free software like the Kollmorgen stuff can calculate

> 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
>
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