Hi
I thing we uncovered all potential problem for slow speed machine.
Here a will use more refined numbers and it looks more close to real
situation.
Minimum counts to controller about 30 pulses per second.
Or 1800 counts per minute.
One revolution is 8192 pulses.
So, per minute I will have 1800/8192 = 0.22 rpm.
0.22 rpm is equal to 80 degree of revolution per minute.
80 degree per minute is a min speed to AC servo motor to be stable.
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Machine moves 0.00025 per minute what is 0.45 degrees per minute. ( ball
screw 5 rev per 1 inch = 1800degree per 1 inch of travel)
So, motor can rotate 80 degree per minute but machine needs only  0.36
degree per minute.
So reducer must accommodate that, 80 /0.45 =177 ratio.
Closest ratio of standard harmonic reducer 160 and it is close.

AC servo motor can spin up to 7000 rpm.
So, min feed is 0.00025 per minute with 80 degrees of rev per minute,
And max feed will be 7.875 inch/minute per with 7000 x360 = 2160000
degrees of rev per minute.
I think it is reasonable range of feed to travel.
So, one stage of harmonic drive with ration of 160:1 will be enough to
satisfy grinding process.

aram







> John Kasunich wrote:
>> Kenneth Lerman wrote:
>>
>>>A simple solution is to use a dual drive.
>>>
>>>Use a course mechanism with long travel for course positioning and a
>>>fine mechanism with limited travel for fine positioning. The fine
>>>mechanism has a large mechanical advantage and can use a smaller motor
>>>and driver. Of course, some sort of clutch mechanism could be used to
>>>allow switching between the course and fine speeds.
>>
>>
>> You might be able to avoid the clutch as well.  One possibility would be
>> to stack a very high resolution slow stage on top of a fast coarse one.
>>
> With the right speed reducer, I think these extra complications
> are not needed.  The problem is that asking a motor to give
> smooth motion at a speed of a few degrees per MINUTE is just too
> slow.  But, a servo motor can also run at pretty high speed.
> So, a modest speed reduction between motor/encoder and leadscrew
> should satisfy both the slow and fast requirements.  The speed
> reducer must be stiff and backlash-free, which requires a higher
> class of unit.  Either a worm drive or planetary would work, as
> long as it was designed from the ground up for zero backlash.
> A problem with a worm drive is it has sliding friction, and will
> wear.  There is a new style of zero-backlash planetary drives
> that use slightly offset pins on the planetary carrier, causing
> it to spring-load the gears.  I'm guessing this is a patented
> technique, and so there's only one supplier for a few years.
>> You could also do things like having the fast motor turn the screw, and
>> the slow motor turn the nut with a worm gear to increase the resolution
>> and decrease the speed.  In this latter case, the stiffness of the fast
>> motor will be an issue, even though it isn't turning.
>>
>>
>>>You haven't answered the question of what type of mechanism you are
>>>planning to use to provide smooth linear and rotary motions at this slow
>>>speed.
>>
>>
>> I think Ken has hit the nail on the head here.  At very low speeds, it
>> is very hard to get smooth motion.  You are more likely get stick-slip
>> behavior, where the motor turns a little but the table doesn't move.
>> The screw and other parts deflect until they build up enough force to
>> overcome the static friction and start it moving.  As soon as it moves,
>> the dynamic friction is much lower than the static friction, and it
>> moves farther than you wanted it to, then stops.  And the whole cycle
>> repeats...   The individual movements are tiny, but at the extremely
>> slow speeds you are talking about, stick-slip is more likely to be the
>> limiting factor than your encoder resolution.
>>
> Yes, you need all rolling elements, leadscrew, slide, etc. to
> combat this.
>> Gearing down does not help - the issue is the flexibility and friction
>> of even the most "rigid" screw/nut/bearing combination.  At these
>> scales, you almost have to think of the metal parts as if they were hard
>> rubber.
>>
>> Sliding ways are usually the worst choice for stick-slip.  Rolling
>> element Linear bearings are better, but they are not very happy in a
>> grinding environment with abrasive dust.
>>
>> Depending on the loads, you might want to consider air bearings.  They
>> do not suffer from stick-slip, and to some degree are self-cleaning in a
>> dusty environment.  One of the regulars on IRC, who uses the name
>> "toastydeath", works (or worked) for a company that makes air bearings,
>> and may have some suggestions.
>>
> Air bearings are insanely easy to make, although getting just
> the right geometry to prevent oscillations is slightly tougher.
> Really, you can make surprisingly good air bearings with a drill
> press, a block of aluminum and a surface plate.  You drill a
> hole in the block, then make a slight relief in the center of
> the block, and lap the rest of the block flat with fine
> sandpaper and the surface plate.  Apply air pressure to the
> hole, and voila- an air bearing slider!
>
> Jon
>
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