[joeavaerage]

Hi,
the important takeaway from the calculation is:

The rotational inertia is dominated by the ballscrew and it varies as the 4^th power of the ballscrew diameter.

For instance if you reduced the ballscrew to 25mm then you would achieve a (25/32)⁴ =0.37, and a consequent BIG increase in acceleration with the same size servo.
In general small diameter ballscrews are favoured for high accelerations....and have to be balanced against ballscrew whip and stiffness which indicates larger diameter screws.

The linear inertia varies as the square of the pitch.

If you increase the pitch of the ballscrew to 10mm from 5mm then (10/5)²=4, a major increase in linear momentum relative to rotational.
In general small pitch ballscrews are favoured for high accelerations.....and has to be balanced against axis speed where higher pitches are indicated.

Unlike peteeng I argue that acceleration is the hands down most important consideration because the highest acceleration results in the best toolpath following.

Craig

[MikeGM]

Hi,

Thanks for the suggestions and calculations (very helpful).

I should clarify that I am certainly not looking to achieve 1g accelerations now. This was simply where I happened to start when looking at online calculators - I had been looking at relatively low horsepower commercial machines, as this seemed closer to what I am trying to achieve, which led me to machines like the brother Speedio line (which I now know are some of the most dynamic machines) - I saw that they advertised 2.2g accelerations and aimed lower. I have since seen that even very high quality machines utilize much lower accelerations e.g. 0.5g. I am not necessarily targeting this, but it illustrates that 1g was a far higher target than would have been sensible for my application. I welcome your insights into a suitable target for accelerations, as this sort of information is rarely published, and I don't have experience with it myself.

I was under the impression that I could rely on the maximum/temporary torque figures as opposed to rated torque, for acceleration - I note that you have calculated on the basis of rated torque. Was this just for illustration or is this how the motor needs to be spec'd? I wonder whether the acceleration figures published by the manufacturers I mentioned are based on continuous ability, as I know the Hermle c400 is advertised as having a 20kw spindle, but this is only at a 20% duty cycle (the 100% duty cycle is only 10kw).

I had considered something like the 1.8kw DMM with the following spec which has lots of torque (I note the rotor inertia is much higher than the 750w model):

Servo Motor Model 120-DST-A6 _ _ 1
Rated Output 1.8kW
Rated Voltage 200V
Applicable Servo Drive DYN4-T01
Rated Torque 11.5Nm
Instantaneous Max. Torque 28.7Nm
Rated Current 16.7A
Max. Current 36.3A
Rated Speed 1500rpm
Max. Speed 3000rpm
Rotor Inertia 23.8kg-cm^2
Torque Coefficient 0.74N?m/A
Encoder 16-bit Absolute [ ABS-16-01 ]

I haven't been able to download any specs for the delta servo's or see prices on their website.

It looks like a rotating ball-nut design could be useful for maximizing accelerations from a given motor, but I only seem to see this design on gantries with long travel to avoid whip. I imagine this could be more difficult to incorporate.

I will have to do some investigating to see what diameter and pitch ballscrews to use, and will certainly value any suggestions. I have seen some excellent builds with max travel speed of about 15m/min but the travel lengths were much lower than mine. I certainly take your point about acceleration and toolpath following.

Thanks for the help guys.

Mike

[peteeng]

Hi Mike - Do not design using peak torques. This is only available for a second maybe milliseconds and then the motor cooks. You can ask the manufacturer for the thermal characteristics of the motor if you want to delve into this aspect. The motor generates heat and this has to get out of the motor. It's easy to heat a motor, harder to cool it. The continuous rating means that the heat generated has time to get out and will achieve a safe equilibrium at that torque output. Servos can be "overdriven" whereas steppers can't. Steppers have a dropping torque curve so as they speed up or load up the available torque drops and they will stall before they thermally overload. Servos are the opposite, they can provide very high peak torques in reaction to loads say a deep cut which allows it to carry on (vs stalling) but this overdrive has to be given time to allow the heat to get out. Designing at this end of the motor is a fine line between operating motors and cooked motors....Peter

Hi Craig - in constant velocity mode while cutting, path accelerations are minimal so therefore acceleration potential is not important. Rapids do require high accels if you are trying to minimise air time on production machines. HSM techniques do have some air time so in this respect high accels maybe needed, is this what you mean? Peter

[joeavaerage]

Hi,
yes, accelerations of 1g and axis speeds of 30/40/50m/min are the realm of high throughput production machines, certainly possible to build but eyewateringly expensive.
I would recommend accelerations of 0.2 to 0.4g and axis speeds of 20-30m/min would be a more realistic target for your machine. I promise you will find
those speeds/accelerations entirely scary enough so much so that I run my machine at 0.15g and 12.5m/min, approx half of what it is capable of...just to soothe
my heartrate.

I would suggest that you design to the rated torque. The extra or overload torque is nice to have but you should not in general be calling on it. Let's say you design using
rated torque and find that you can achieve 0.3g. All well and good, but my calculation made no attempt to allow any torque to counteract cutting forces. The 0.3g that you
were expecting to be able to call on at a toolpath direction change is not all there because 25% of the torque of the servo is be called on for cutting. This is where the overload
saves you, for the brief few milliseconds that the toolpath demands that the acceleration be 0.3g that extra is available. After the brief period of overload, the acceleration demanded
of the machine drops back to 5% or less.

My experience is that my servos are 750W or 1 hp but they seem to perform as if they were 2 or even 3 hp. I did not design nor routinely call on the servos for that level of
performance but they certainly deliver in a tight spot.

Clearpath are in the business of selling servos to first time servo buyers and make extensive use of the peak or overload torque spec of their devices to encourage sales....
don't believe the hype, find and use the rated torque and rated power for design purposes or even comparison purposes.

Spindles are a different kettle of fish. Unlike a servos they often have to operate at high even rated power for very extended periods. The thermal characteristics of a device for
spindle operations are very closely studied whereas axis servos rather less so.

I've always bought my Delta gear from this company, and they have always been very responsive with sharp prices, not often the lowest price but sharp. They are in
Schenzen (spelling?) and have been forced to close down a bit with Covid, and it seems the prices are on the up too.... but I still have confidence in them.

https://www.fasttobuy.com/

The specs of the 1.8kW DMM servo are typical of servos of that size. Note that while the rated speed of my 750W servos is 3000, the rated speed of the 1.8kW device is 1500.
With a direct coupled 5mm pitch ballscrew the 1.8kW device would have a rated axis speed of 7.5m/min....a little slow. Note also that the rated speed is 1500
but the maximum speed is 3000....what gives? The is a technique called 'field weakening' which can be applied to Field Oriented Control motors such as AC servos
that will allow you to somewhat reduce the back EMF of the motor by temporarily applying a reverse magnetic field to the armature. Thus the 1.8 kW servo will have
rated torque, 11.5Nm up to rated speed, 1500rpm, but at somewhat reduced torque can carry on right up to 3000rpm. The torque will have reduced to
approx 11.5 x 1500/3000 =5.75Nm.

The only time you are likely to call on maximum speed is when you are doing g0 rapids and the reduction in torque is probably quite acceptable. This is why you will see machines
advertised with g0's of 35m/min but max full thrust g1 cutting speeds of 20m/min. The full thrust (20m/min g1) is using the servos rated speed and torque while the 35m/min g0
is when the servo is operating in field weakened mode.

This is a 2kW Delta B2 servo from Fast-to-Buy:

https://www.fasttobuy.com/delta-220v...le_p28105.html

Note that despite being even slightly more powerful than the 1.8kW DMM it has only half the rated torque, but can spin at 3000rpm rated and 5000rpm in field weakening mode,
with corresponding axis speeds, assuming a 5mm pitch screw, of 15m/min g1 and 25m/min g0. This servo would be a good match for a 5mm pitch screw whereas the 1.8kW DMM
would be better matched to a 10mm pitch screw. As you might expect given the near identical power output the performance (speed and acceleration) of the two combinations
is likewise near identical if matched to the right ballscrew.

(I note the rotor inertia is much higher than the 750w model):

In fact no......bloody manufacturers are all over the place with their units. In this case DMM have specified the first moment of inertia as:
23.8 kg.cm².

Who ever heard of a unit system that mixes kilograms and centimeters? That's BS......if I ever catch a DMM engineer I'm going to thrash him soundly.

The two world supported metric unit systems are CGS (uncommon these days), that is centimeters, grams, seconds OR MKS, meters, kilograms, seconds.
You are asking for trouble and confusion if you deviate from one or the other or as in this case mix the units. The DMM spec, if they troubled themselves to use
standard units is:
2.38 x 10^-4 .kg.m².

Further note that I made a ballpark guess of armature inertia in my calculation of 2 x 10^-4 kg.m², and is a pretty fair approximation
to the measured and specified figure published by DMM. I note though the Delta servo to which I linked is 100mm size and has an inertia of 4.45 x10^-4.kg.m².
If you were considering the Delta device then you would want to recalculate with the accurate spec.

Do yourself a favour....always ALWAYS convert any specs to MKS and stick with MKS religiously otherwise your calculations WILL go awry, and you'll confuse the hell
out of everyone, most importantly yourself.

Craig

[joeavaerage]

Hi,

Hi Craig - in constant velocity mode while cutting, path accelerations are minimal so therefore acceleration potential is not important.

BS, if your machine approaches a 90 degree corner the X axis must decelerate to zero while the Y axis accelerates to its g1 speed. Acceleration is the ONLY determinate of
how fast that can happen. Acceleration is the GOLD standard for toolpath following....any suggestion otherwise is pure confusion.

Craig

[peteeng]

Hi Craig - So approaching a corner is a special case & sure there is geometry where the tool has to slow down and speed up.... But generally the toolpath will be made trying to keep it at the same chipload ie so the same velocity. In HSM the tool is travelling in loops at near constant speed. I'm not saying that accelerations are not important I'm just saying that they may not be top of the list important for a prototyping machine... Peter

[joeavaerage]

Hi,
I suppose yes a corner is a special situation but wherever an axis changes direction, even if not speed, there is a change in momentum and the
MUST therefore be some accelerating force or thrust to have accomplished this.

Lets start with exact stop mode. An axis will decelerate to a stop before the next axis starts to move. Clearly the higher the acceleration the quicker the transition
from one direction to another.

Now consider constant velocity mode. In this case the moving axis decelerates but before it actually stops the new axis starts to move. This means that the actual toolpath
differs from the programmed toolpath. Usually to divergence of the two paths is limited to some extent so it does not degrade the accuracy of the part, but the advantage is that
the time take to transition from one direction to another is minimized for a given toolpath divergence. Clearly the higher the acceleration potential of the axes the faster the transition
can be made. Another way of describing it is that the higher the accelerations the smaller the toolpath divergence need be for the transition to occur in a given time.

In both descriptions the higher the acceleration the better the toolpath following.

Consider this thought experiment, a toolpath advances towards a point whereon the machine goes off in another direction. Lets also say that the machine moves at 100mm/sec
when approaching the change point and after the change point it again accelerates to the same speed. So between to entry and exit the momentum does not change
..except in direction. Let us also define a zone within some small diameter of the change point , say 1mm in diameter. The speed at the input to that zone occurs at t=0 and it exits
the zone at t=20ms at it's correct speed and new direction.

Irrespective of what happens inside that 1mm diameter zone at the entry the momentum is nnnn at direction mmm and when it exits the zone 20ms later it has momentum
nnnn but at direction ppp. Classical physics tells us the force equals the time rate of change of momentum. We have had a change in momentum over a brief interval
thus a force MUST HAVE BEEN APPLIED. This has remained true since Newton first described it and subsequent descriptions including relativistic or quantum effects change not one
jot the classical description concerning motion of objects at non-relativistic speeds or quantum mass levels.

Within the 1mm zone, it does not really matter whether the move is at constant velocity, or exact stop, or 'S' curve or even some Alice in Wonderland zone where magic happens,
when the toolpath leaves the zone back into Newtonian space that the rest of us live in that a force must have been applied otherwise the momentum cannot have changed....
end of story.

I contend that the higher the acceleration the better the toolpath following.

That is a different thing to cycle times. In many jobs, say woodworking, there are many straight moves and to minimize cycle time you would have the linear moves be as fast
as possible. For many 3D toolpaths or any HSM type toolpaths high axis speeds are moot, the machine is always changing direction and accelerating off in a new direction.
Under these circumstances high acceleration result in significant cycle time savings.

Craig

[peteeng]

Hi all - Since we are discussing motion control I thought I'd mention this is the best motion controller available to the Maker level & probably professional that I can find. Unfortunately its interfacing is a bit clunky but having researched and studied motion control over the decades this is the bees knees. I'd like to use it in a future machine.. It would need to be hacked a little to get it to work in servos but the math is available (open source) and has been implemented in Linuxcnc by someone....very impressive motion. Peter

https://synthetos.myshopify.com/products/tinyg

[MikeGM]

Thank you very much for the detailed responses.

I think I will take your advice regarding the targeted accelerations and axis speeds, as well as designing using the rated torque. I will also take a look at the TinyG, thanks for the tip.
I have been looking into the rotor inertia figures of various motors that appear to be suitable for my application and the figures vary wildly. I have, for example, downloaded a catalogue for leadshine ac servos (no idea of prices) which publishes the inertia figures of the motors in the "[kgm2*10-4]" units. here is a screenshot of some of the figures:



I note the 1.8kw model reports 30.15 kgm2*10-4. Figures for a 750w model from the same manufacturer indicated only 1.56 kgm2*10-4.

On the DMM site the 1.8kw model is advertised as "23.8kg-cm^2" and the 750w model is advertised as "2.45kg-cm^2" almost a factor of 10 difference. I think you may have placed the decimal point in the wrong place in your conversion; should it not have been 23.8 x 10^-4 kgm^2? I have 1cm^2 as equal to 0.0001m^2 - and scientific notation as 1 x 10^-4 m^2, unless I have missed something.

If I input the figures for the aforementioned 1.8kw leadshine or the DMM into the calculation you did for me earlier in the thread, would the motor inertia not then become by far the largest component of inertia in the system?

Am I missing something?

Kind regards,

Mike

[peteeng]

Hi Mike - Your conversion is correct and if the motor inertia is the biggest rotational inertia then yes it is. Peter

[joeavaerage]

Hi,
yes, you are 100% correct, I shifted the decimal place three places rather than 4. My apologies. That is the issue when manufacturers use non-ISO units, confusion and
mistakes ensue.

The first moment of inertia of a cylindrical object is:
J=1/2 x m x r²
where:
m= mass
r=radius

But the mass of an iron armature is approx:
m= PI x r² x l x 8000
where:
l=length and 8000 is the density of steel/iron

Combining:
J=1/2 x l x r⁴ x 8000

Note the dependence of J on radius to the fourth power

Note also that 750W servos tend to be 34size or 86mm (across the flats) with an armature of about 50mm diameter.
The servos you linked to are 130mm across the flats with about a 100mm diameter armature. Given the sensitivity of J to radius the wide variance can well be expected.
Note also that the 2kW Delta servo I linked to is 100mm across the flats with about a 75mm armature and hence its intermediate J spec.

Lets redo the calculation but with these two servos in mind:
1.8kW servo, 11.5Nm @1500 rpm J=30 x 10^-4.kgm²
32mm diameter ballscrew, 10mm pitch, 1m long

J_screw=8.23 x 10^-4kgm²
J_axis= 1000 x (0.010)²/ (2.PI)²
=25.3 x 10^-4.kgm²

J_total= (8.23 + 30 + 25.3) x 10^-4 kgm²

Note that the rotational inertia of the armature now dominates followed closely by the linear axis by virtue of the 10mm pitch.
d²/dt²= 11.5 /63.53 x10^-4
=1810 rad/s²
or 2.88m/s² or 0.288g

Now the Delta servo:
2kW, 6.37Nm@ 3000 rpm J=4.45 x10^-4 kg.m²
ballscrew 32mm diameter, 5mm pitch, 1 m long

J_screw=8.23 x10^-4 kgm²
J_axis=1000 x (0.005)²/(2 .PI)²
=6.41 x10^-4kgm²

J_total=(8.23 + 4.45 +6.41) x 10^-4kgm²

Note that the ballscrew dominates weakly, but the rotational components combined dominate the linear momentum by virtue of the 5mm pitch.
d²w/dt²= 6.37/19.09 x 10^-4
=3336.8rad/s
or 2.65m/s² or 0.265g

So despite the quite wide variation in spec (J and rated torque) between the two servos (excepting power output), they when matched to the right ballscrew result in very similar accelerations.
Price and availability of either servo might swing your choice, but more likely its the price and availability of the ballscrew that will determine your choice.

I would suggest that you need to source ballscrews for your project, the price and availability of these components will have a distinct influence on what servo you want.
I would suggest that ballscrews of 25mm diameter would be adequate, and given the slightly smaller diameter may result in very favourable acceleration calculations.
32 mm ballscrews are also a viable choice, but larger 36mm or 40mm are likely just to big and will degrade your accelerations unless you use outsize servos at huge cost.

Craig

[joeavaerage]

Hi,
just as a comparison, if you reduced the diameter to 25mm, with the Delta servo

J_screw =8.32 x (25/32)⁴ x 10^-4kgm²
=3.07 x 10^-4 .kgm²

Therefore
J_total =(3.07 + 4.45 + 6.41) x 10^-4kgm²

For an acceleration of:
d²w/dt²=6.37/13.93 x 10^-4
=4572.9 rad/s²
or 3.64m/s² or 0.364g

Quite a large improvement in acceleration by reducing the ballscrew to 25mm. ( 0.364g verses 0.265g)

If you did the same with the 1.8kW DMM servo the improvement would be very small by virtue of the armature inertia and the axis inertia dominating the
acceleration, that is to say you'd get no noticeable improvement by reducing the ballscrew diameter.

Craig

[MikeGM]

Thank you again. These calculations and tips are very helpful.

It looks like I have a number of suitable options to achieve targeted speeds and accelerations, within rated torque specs. I think you are right that I should look to source ball screws and then select motors based on this; I will therefore start looking for suitable ballscrews.

Kind regards,

Mike

[joeavaerage]

Hi,
what length screws, particularly the travel length?

Craig

[MikeGM]

Hi Craig,

I've just revisited the CAD Model; the maximum travel lengths I can achieve (and would therefore target) are approx: 1100mm (table axis); 1600mm (cross-bridge axis) and 700mm (z axis). The constraints on overall length that I have are based on the length of frame components. The base is approx 1924mm long and the bridge is the same wide. The saddle will be approx 1200mm tall.

Mike

[joeavaerage]

Hi,
I found and bought the ballscrews that I wanted/could find/at the right price before I designed the machine. So I designed around the ballscrews rather than the other way around. Trying to find
C5 or C3 ballscrews to match your design is a long shot.......matching your design to what you can actually get is much easier.

700mm travel, 25mm diameter, 5mm pitch, 930 overall, C5 grade, includes support bearings

https://www.ebay.com/itm/20392020885...sAAOSwavFiYQkc

1300mm travel, 32mm diameter, 5mm pitch, 1530 mm overall, no support bearings, C5 grade, two available

https://www.ebay.com/itm/19451328255...YAAOSwao9hl7Ky

Craig

[MikeGM]

Thanks Craig,

I'll take a look.

Mike

[rajhlinux]

Holy cow, MikeGM won the world's award for making the largest DIY CNC mass base and gantry. Seriously wants high tolerance.

I wonder what tolerances he would get in real life...

[jackjr-123]

Mike,

This is a colossal build!

How did you heat the molds?

[MikeGM]

Hi Jack, and Raj. Thanks for your interest.
I employed the concrete's own 'heat of hydration' to thermally cure the frame elements. Essentially, as the cementitious materials reactions are exothermic, the heat given off can be trapped with insulation to cool much more slowly. This gives two advantages, firstly, and of principal concern for my application is the thermal curing capability (I posted a paper which examined this in more detail on the first page of the thread) and secondly; it helps to mitigate the risk of cracking due to any thermal gradients. I would note that this would be less effective with much smaller elements, as the surface area to volume ratio would be less desirable and the UHPC wouldn't reach such high temperatures or maintain them as long.
Mike