RE: [CAD_CAM_EDM_DRO] treadmil motor speed reduction analysis

Hi Ron

Inertia is less of a concern with expensive commercial servos.
With a treadmill motor it is of great concern. But we need to actually
measure it.

The torque to inertia ratio of a motor is basically an indicator of how fast
it can accelerate.
This affects how fast a cnc machine can accelerate.

Why does this matter? When you are going around a corner at speed
acceleration is required.
It turns out that the MINIMUM radius that you can go around a corner at
speed V is
equal to V^2/acceleration. So if the acceleration is low the machine can't
do tight radii at speed.

Let's put some numbers on this.

My example was .25g. That is 96 inches/sec^2.
At the design goal of 4 inches /sec, that means the minimum corner raduis it
can
do is 4^2/96= 0.16 inch. If you want to do better you have to slow down at
the corner.
But slowing down has consequences.... chip load drops, and burning and tool
wear
can happen. So we want to have reasonable acceleration to prevent this. The
Numbers I chose were for a light industrial quality machine.

As far as your questions for a bridgeport...the analysis was for a router
only.
The numbers would not be right for a BP type machine. That could be analyzed
though.

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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-----Original Message-----
From: CAD_CAM_EDM_DRO@yahoogroups.com
[mailto:CAD_CAM_EDM_DRO@yahoogroups.com]On Behalf Of R Rogers
Sent: Tuesday, May 17, 2005 7:45 PM
To: CAD_CAM_EDM_DRO@yahoogroups.com
Subject: Re: [CAD_CAM_EDM_DRO] treadmil motor speed reduction analysis


Having a bit of trouble understanding why so much emphasis is being placed
on rotor inertia. That only effects acceleration and deceleration, correct?
The treadmill motor and a Nema 42 servo having basically the same armature
dimensions, how much difference could there be? Would it even be worth
considering since these motors are at top speed under load in less than a
second if geared properly? A 1-2 horsepower DC motor basically disregards
armature weight when the voltage and current is applied. If I'm missing
something, please explain.

A note on ratios in relation to machine load. Driving the knee on a
Bridgeport which is similar in task to accelerating a large gantry, I gear
them at 25 revs of the servo to traverse 1 inch of the Z axis. The X and Y
are 12.5 revs to traverse 1 inch. Every rev of Dave's proposed pinion gear
will represent 4 inches of traverse. So to arrive at the same cutting forces
and speed one would have to mutiply the 25:1 by 4. Making it 100:1 ratio
from the servo to the pinion gear. Obviously a gantry machine wont require
the cutting forces that a Bridgeport encounters so the ratio could be
reduced by whatever force and speed is desired. 10:1 would not make the
servo very happy. Maybe I'm way off on this??

Ron



Leslie Watts <leswatts@...> wrote:
Hello all,

As promised I did an analysis of a hypothetical cnc router
with belt or rack drive using treadmill motors.

I had to do some eductated guesses...because there are few
specs on them. These are the cheap 1-2 hp 100vdc units
at surplus center and others.

First, I am going to seriously derate these things because they are
"treadmill" duty. I don't believe the HP ratings anyway. Let's derate
them 50%.

Second I have to get some idea of the rotor moment of inertia. None have
such specs, but I know a 3/4 hp square frame typical PMDC motor comes
out at about 0.4 oz*in*sec^2. I will use that figure. This is a very
high inertia compared to a typical industrial servo and will be one of the
biggest factors limiting performance.

Here is the router specs:

100 kG moving mass
125N (25 lb) cutting force
50 N (10 lb) friction force
100 mm/sec (4 inches/sec) max speed
.25g (2.45 M/sec^2) max acceleration
50mm (2 in) rack pinion/timing pulley diameter

Ok.
First the moment of inertia at the pulley/pinion.
That is simply Mr^2= 100*(.025M^2)= 8.8 oz*in*sec^2

A 1:1 load to motor inertia match occurs with SQRT( 8.8/.4)=
4.69 gear reduction ratio. Lets make it an even 5:1.

Starting with that I went to motioneering and
checked it with real motors.

I needed 600 in oz peak at only 171 rpm.
Peak input power was only 90 watts.
But....this is a no go because I have derated the motor.
I don't think they can put out much more than 400 in oz peak
and much less continuous.

Let's go with 10:1 gear ratio.
Peak input power was 170 watts.
but required inertia for 1:1 was .12 oz*in*se^2
...4 times lower than our motor.
But inertia match does not have to be exact
... 0.25 to 4 is generally ok.
At .25 we have about 375 oz*in required.
Looks close!

Now 20:1
270 Peak input power
Still about 375 in* oz
But even at an inertia ratio of .25 we need
about 0.1 in*oz*sec^2. So there is no solution.
The treadmill's high inertia has killed it.


OK...done I think! With the derated motor we just
get by with a 10:1 gear reduction. anything much higher
or lower gets worse.

Max rpm is 382 so we can go much much faster than design
top speed if we want.

We are right at the comfortable motor current limit.

The motor will only need about 20V for design speed but
LOTS of current. This depends on the torque constant
but might be in the 10 amp range.

If the Pinion was one inch diameter rather than two,
5:1 would be optimum and so on.

Understand the results might be VERY different for
industrial servos and steppers...this is only for the
treadmill motors.

As a last bit...if any one has some of these motors
and a reasonable power supply I can show you how to
measure moment of inertia etc so we won't be doing
educated guesses.
I would like to know!

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






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you have trouble.
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sister site to the CCED group, as many of the same members are there, for OT
subjects, that are not allowed on the CCED list.

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