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
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>
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