Oh...so this is what math is for

[skubajon]

So like most teens in highschool..I hated math. I was ok at it but never thought u would need it. Well then someone created this site and behold....I needed it haha

So here's my setup. Building a gantry and I have profile rails. The x has 2 rails per side...y has 2..z has 2. I got a good connection for rails and extrusion. These are 15mm hiwin rails

The extrusion is a proprietary design that is used for supporting up to 2500 lbs with spans of 30 feet. It's beefy stuff

We want to do hsm machining in aluminum and push some decent speed. So that is where math is used for all students interested in not flipping burgers!

I can't seem to figure out how big of motor to use. Now profile rail has .01 friction coefficient and ball screws are 85 to 95 percent efficient.

Can someone walk me through the math please on motor size

Let's say I have 100lb static load and 100lb of cutting force. What would I need to do to calculate motor for that. For equation purpose let's say I'm using 20mm ballscrew 1000mm long at 10mm lead. I get lost on the rotational friction etc. How much to turn a ballscrew to the the load moving. How much to move the load with another force against that load

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[tinmancarving]

Take a look at the last post on this thread. There is a spreadsheet attached that should help you with some of these calculations.

http://www.cnczone.com/forums/linear...culations.html

I hope this helps.

Rob

[hanermo]

Your motor is irrelevant .. with 99% probability.

Whats your rigidity ?
IMO, ime, you will have less than 1% of the rigidity needed to actually do HSM in alu efficiently.
This, because you propose to use small, tiny, rails that are not suited for HSM milling, efficiently.

Anyway, the needed data, you have not provided, is
1. open span
2. rigidity in N/kgf
3. spindle power available or desired
( design type)

The carrying capacity of the extrusion is irrelevant.
The rigidity is the limiting factor, and usually will be 1000x lower than carrying capacity.

Some notes;
All good mills that have real ability to do HSM in alu, efficiently that I know of, (e.g. Brother, Robodrill, Haas DT1) use 45 mm linear rails, on a == 1-1.5 m open span, in a c-frame design.

A Haas DT1 could carry (failue) about 32.000 kg, == 80.000 lbs, over 1 m (Using typical 45 mm profile rails) (rated to 2400 kg or so, iirc, about 1/12 of real "capacity").
Its suited to do high speed milling at up to the limit of the spindle power (25 kW /40 Hp VFD inside, electrically limited to 15 Hp iirc).

Neither the ballscrew size, friction, stiction or anythign else is relevant, unless the frame is sufficiently rigid.
Strong => carrying capacity, is irrelevant, unless the rigidity, that prevents vibration, is there.

Example;
My VMC frame is made of steel, 20 mm thick, in a box frame.
On edge.
Yes, the main steel members are 200 mm tall and 2200 mm long.
Bridge is thus == 200 mm thick honeycomb.

The vertical bridge is == 700 kg in mass.
It has a carrying (load bearing) capacity (failure load) of == 100 metric tons.
(External main load bearing members are 2200 x 200 x 20 mm tool steel, "F1 calibrado". == 100 kg each, 2 of ).

It is by no means sufficiently rigid to do good HSM milling (say 400-600 ipm) !
I use 32 mm ballscrews, and 35 mm linear rails, with 8000 kg carrying capacity on each block (4 of).
The open span is 1600 mm.
Design is a bridge mill, with moving table, the most rigid format there is.
Approx 10x more rigid than a c frame of the same workpiece size.

.. See what I mean .. ?

I use this to mill steel, and am now fitting an ISO-BT30 spindle.
I expect to be able to use about 2-3 kW of power, properly.
Brushless servos on all axis, servo index spindle (eventually, soon).


And yes, you *can do* HSM .. but it will not be "efficient".

Machine tool designs call for about 20-70 N to deflect the frame by one micron.
All machine tools have this rigidity, if they are to work at all properly.

Go put a DTI on the spindle, measure deflection to get rigidity, and then get back to me.

Example;
I stand on the spindle, 80 kgf force = 800 Newtons (vertically).
Measured deflection is 0.05 mm (with simple single-point support.
= 50 microns.
800 / 50 = 16 N/uM rigidity.
This is actually pretty good, borderline ok for a *new, modern, VMC* !

New linear blocks on vertical rails (35 mm profile, 2 blocks each rail) will make this approx 4x more rigid).

I hope to get to == 0.02 mm deflection, with the new blocks, and 4 new vertical tool steel members.
The new vertical posts are 250x10x1500 mm steel, 4 of.

The above is an explanation of what you need, why, and how to calculate it.

Fwiw..
My axis motors are servos, 3000 rpm, geared down 1:3.75, with a 4 mm rise.
400W each, 1.3 Nm continuous.
Approx 10 more rigid than yours, and my screws at 32 are about 10x more rigid than a 20/10 mm screw.

At this gearing, 10x "slower" than yours, they still provide way more speed than I need, with a big work envelope of 1600 x 800 mm.
Rigidity and resolution are everything, in this order.
Top speed is the last thing to be interested in, UNTIL you get to the 30 N/um rigidity levels.

Testing any working mill from the last 50 years will provide similar numbers.

PS.
The 20-70 N/um numbers come from Machine Tool design handbooks in university courses.
"Principles of rapid machine design", "machine design fundamental principles", etc.

[skubajon]

Ok definitely not HSM 600 to 800ipm on this one. I guess I was more going for the HSM tool paths. I suspect rigidity will be close to that of a datron type system minus the steel beam for gantry though that may change because I'm still not convinced on the strength of them. I have seen a lot of videos of machines in this size that are doing quite amazing things with aluminum and are no where near as rigid as this machine will be .

The 15mm rails are a little small but hey, I can pick up a brand new HIWIN rail for 25 dollars and each bearing block for 20 dollars. I will be using 4 15mm rails for the x axis with a total of 8 blocks. These will be mounted to some solid extrusions that are then bolted down securely to a fully welded frame. (I build late model racecar frames) so I will be building a similar type structure. I estimate in all aspects being in the 1500 lb range with everything mounted. My machine should have about 2-2.5 x 3ft cutting table with z axis about 6 to 7 in travel. Everything will be boxed out very nicely. I don't expect to cut like a HAAS or anything like this. This whole build is because of new federal laws that hinder my ability to prototype. I am a NFA firearms manufacture as my side biz. So I needed a quick small way of prototyping new items in aluminum that I can then send out to my machine shop. New federal laws state that a machine shop or any company doing anything with firearms MUST HAVE a type 7 manufactures license which took place in like feb of this year.

So rapid prototyping is really what this machine will be. Doesn't have to hold .0005 of an inch or anything like that. Solid enough to machine some aluminum as well as make some larger parts that I sell. I also will be doing all my serial numbers on this machine. I have been planning on using 20mm screws for the x and y and haven't really decided on z yet. Been looking at 3 to 5 hp spindles but reason I'm leaning to 3hp is because I can get one that has 60k rpm which will cut the force down tremendously compared to a standard milling type machine. So as far as screw speeds etc I don't want to blow the money on lets say 1850 nema 32's if I don't need them. Yes I will run slave X axis with this setup. I probably will be happy taking an ok depth of cut at say 40 to 60 ipm with this machine. So that's why Im looking for a little help on the math for this thing is because its a matter of spending 5k to buy big, or maybe 3k to buy smart

[hanermo]

Multiple blocks are better .. due to geometrical averaging.
Getting accuracy is very easy.
Getting rigidty is quite hard.

2x3 ft .. on what type of structure ?
A moving bed will be 2-6x more rigid than a c-frame.

Dont use direct coupled steppers, if you expect rigidty or accuracy !

In fact, I would never use steppers for anything, any more.
I use small servos ..
that are about 5x more accurate,
accelerate 10x faster (not really needed)
and 5x faster (not needed at all).

I also use belt drives, even with the older stepper machines.
Direct coupled steppers are a horrible idea - the cripple your accuracy, and your acceleration.

I have never needed high speeds, on the mill or the lathe.
Lathe is usually limited to 20% of max speed.

Something to think about:
I suspect you wont be able to use even 1.5 hp of spindle power.
Note that a bridgeport at 1000 kg in cast iron can only use about 2 hp.

Comparison:
Will your machine be more or less rigid than a bridgeport ?

For comparison purposes, my machine is about 3-6x more rigid than a Bridgeport.
(2000 kg (==2x rigidity), and moving-bed (==3x rigidity).

Adding extra steel or cast iron to the frame will only improve the machine.
Its also cheap.
Consider planning to add about 400 kg of CI or steel frame to it.
It will HUGELY improve the machine.

Re: extrusions.
It is not possible to make an accurate machine if you also use aluminium in it.
Thermal effects make this impossible.

As you are in the us, you can very cheaply and easily get the mounting surfaces milled flat, and rail bolt downs drilled & tapped.
This will make it very easy, and very much less work, to make the machine accurate, planar, and square.

Fwiw..
My and lathe have better than 1 micron real-world resolution.
Ie it will move in 1 micron increments at all times.
(Step size 0.2 microns).
Resolution is not accuracy.

I would urge you to use servos .. because they will make the machine very much more accurate.
400W ac brushless servos are about 290€ / per axis.
Larger steppers (34 frame size, 80v or 220 v drivers) cost about the same, but you get 5x better results from the servos.
Large steppers will only run about 500 rpm - servos run at 3000 rpm.
You can only run the screw at around 1000 rpm, so using a belt drive
1. improves resolution by 3x,
2. imroves accuracy by about 3x,
3. improves acceleration 3x
1000 rpm with a 4 mm rise screw, = 66 mm / sec, 2.6 "/sec.
So crossing the table at 3 feet = 13 secs.

If you do direct-couple the servos, use 1-2 sizes larger couplers. They are very much more rigid.

Rigidity is everything.
2 hp in spindle power needs about 100 kg of push force at tooltip.
Consider standing at the tooltip, with the machine tilted sideways.

Now think of standing on the spindle tooltip.
Will the machine bend, and how much ?
Over 0.1 mm, and carbide tools will snap.

The original Q re: maths is not needed - because if you use steppers, the acceleration and top speed will be limited by the steppers.
If you use servos,even the tiny 400W servos are so much more powerful than needed, that they work at 100% speed at all times.

Example:
The big steppers, direct coupled, accelerate to 500 rpm in about 1 sec (heavy table).
The servos, 0.1 - 0.2 secs.
0.1 secs works perfectly, but is very violent on the machine. I prefer to use a lower acc, still 5x faster than the steppers.

I would never use a screw with a high rise, like a 10 mm-20mm / turn.
It will cripple your acceleration (unless you use servos), and even worse
* it will cripple your rigidity*.
It will also kill your repeatability and accuracy.

Haas gets away with this by using very high end ground screws, and very high end linear guides, on the SS machines.
These cost about 6000$ more, per machine (extra cost for the better screws and linears).
The SS is still less accurate than the standard VF series.
You also need a much bigger screw to have any repeatability/rigidity at all.

Look at rigidity = stiffnes of screws, in N/um.

A 32 mm screw (SFU3204) is about 56 kg of force / micron.
So, for me, I get about 56 kg, and I can use about 3 kw spindle power.

Ex: SFU1605 is 22 kg/um. SFU 1610 = 16 kg/um.
So you are getting 1/3 less machine (=rigidity) for your money, when using a 10 mm rise screw vs a 5 mm rise screw.
A 2020 screw is only 19 kgf vs 39 kgf for 2005, less than half.

2504 screws are 48 kgf.
2005 screws are 39 kgf.

Everything ! hinges on rigidity.

Fwiw .. I import servos, steppers, drives, screws and linear rail components.
All data is from the manufacturers, and works on my machines as promised.

[AORD]

There is a stepper motor calculator speed sheet (MotorCalcs.zip) here:
What size stepper motor do I-need.

[hanermo]

The calc is useless .. as it also talks of apples and oranges, mixing power with speed and acceleration, that have no relationship whatsoever.
Mentioning 12 Nm nema 34 motors (yuk) that are very slow, and usually very inaccurate, as related to servos.

The basic numbers are correct, but again, useles, as the limiting factors will be the steppers themselves, and not the required motion-control paths.

Example:
My table is 240 kg in steel, and workpieces + vices easily 40-100 kg more.
It works fine with a small nema 23 stepper, 3 Nm, 48V, 2M542 stepper driver (replacing old gecko 251) at 1:3.

No calcs are needed, as the limiting factors are stepper acceleration/top speed, like always.
Because of no s-curve acceleration, actual usable torque from 3 nm motor is about .9 Nm, around 600 rpm.

At 0.9 Nm, you get == 150 kgf push force.
It was about 1 sec to top speed (with margin), or 200 rpm at screw.

Steppers:
You only need to see torque curve / volts.
Then pick about 1/3 the torque, and thats your max speed.

Then increase acceleration till you just fail to reach that speed, go down to 70% of that value.
Done.

Better:
Use small servos.
Put all numbers at max. Done.

If the accelerations are too sharp (usually are) back down to about 1/2 in acceleration, or less.
5x more accurate, 5x more acceleration, 3-5x more speed.

Same cost as bigger steppers (with 100-220V drivers at 130-150€ each), but 5x the results.

There is a stepper motor calculator speed sheet (MotorCalcs.zip) here:
What size stepper motor do I-need.

[wizard]

Hanermo;

I see you are a big advocate of servos these days. I suspect that much of that is due to the costs dropping like a rock over the last few years. The question I have is what is your preferred Interface method, step and direction analog or something else. I ask because even though the amps and motors are much cheaper these days, traditional CNC electronics is still relatively expensive compared to step and direction interfaces.

I guess the real question is what do you implement for a CNC controller?

[hanermo]

I have used step and dir, so far.
My servos, both smaller and bigger, support both analog +/-, and step/dir.

I use 2 different manufacturers servos, 200/400 W, 60V, and 750 W to 10 kW, 220 V.
Both function about the same, with similar wiring.
Both support differential signals, but will work fine wired single ended.

Cheaper one with 5000 count encoder, bigger ones with 10.000 counts.

Both work with pokeys and csmio-ips controllers, the 2 best controllers I know of.
Csmio also has an analog version.
One of the most knowledgeable people I know of, hood, is very happy with the analog versions.

I dont see any real benefit to anything other than step/dir - apart from, possibly, being able to track the error via the analog drives.

Re: controllers.
Pokeys supports only 4 axis and 125 kHz, is very cheap, and has excellent plugin sw.
CSMIO is by far the best, but is quite expensive as a full-on solution for lathe (with ENC, and MPG modules).

CSMIO runs at 4 Mhz, and is good enough for 50.000€ plus machines.
Its perfectly equivalent to a modern VMC controller, like I scratch-built.
Some sw issues remain, as we are transitioning to M4.

Note that for me, a full controller has about 100-120 IO points.
4-6 axis, 2 overrides for FRO and Spindle O, 12+ limits, 4-6 homes, 4-6 digital ios plus interlocks (4-20), pendant, and so on.

It needs about 100 din rail blocks for connecting wiring, 2 DC PSUs at 24 V, proper ssr relays (zero cross 24 V), etc.
The costs for wiring a real machine are about 1000 € in bits and pieces, 1000 boot-lace ferrules, 5 spools of wire (colours), 50+ hours, multiple MPGS etc.

At the moment, I am refitting some bits onto the VMC, to have it be a production machine.
Its also getting a new ISO-30 spindle with auto toolchanger.
ATM, with pokeys+cncaddon for controller.
Basic 3-axis VMC, plus spindle as 4th.

The lathe with CSMIO is much more complex.
My main focus is on lathe stuff, with a goal of doing perfect threads, with 0-1 micron errors via glass scale feedback, live tooling, multiple toolchangers (2 of), and soon, dual spindle.
Lathe spindle is a 2.5 kW AC brushless servo, step/dir, 220V AC.

I need to refinish the VMC, to make the next 15+ servo motor mounts efficiently, its tool labor intensive/slow by hand.

With any luck, in 4-5 work-days, the VMC is (re)finished.
I have all the bits, apart from a mount plate for the new spindle.

Basically, bore 120 mm hole in 200x500x50 mm tool steel, mark bolts, drill and tap for spindle.

[skubajon]

Well I'd love to jump into servos but that's when things push beyond my budget. I've been looking into servos but there is absolutely no way I can budget for them so I'm going to have to probably use steppers. That's where I'm getting a little lost. I don't want to have to use the 12nm motors if not needed. I wouldn't mind running nema 23 motors if they could work efficiently. So far the gantry sits in at about 120 to 130 lbs and I'm guessing will be around 150 all said and done.

My goal is high speed spindle and ok ipm for a hobby setup. Effectively machine aluminum for prototyping before I finalize a product to have the machine shop run production. The company I work with doesn't do 1 off parts.

As far as rigidity.. the whole machine is going to be sitting on a steel structure welded up. For my cutting table I will be using epoxy granite 2 inches thick then supported by a steel structure below that.

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[skubajon]

So if I was looking at 1200oz motors with 5mh inductance and supplying 80v to them would that be sufficient on 5mm lead ballscrews?

What would be a servo alternative to move that amount of weight at a good speed? I'm wanting 30+ inch per minute using hsm type tool paths. Again it's for prototype where most stuff can be plus or minus .003.

This machine also will handle all my engravings of tools I sell which are built in 4130 steel.

Reason I was thinking 3kw was because price. Not much difference in price for the motor and they both spin same rpm. Plus I like the square look better than the round look as well as the way it all bolts together

Am I way over thinking even at 1200oz motors?



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[ger21]

150lbs at 30ipm is nothing. Guys here run routers with 100lb gantries and Nema 23's at 500+ ipm.

I'd say that 1200oz motors and 5mm ballscrews would be a terrible match.
With those screws, if you want the most power and speed, look for Nema 34 motors in the 400oz range, rated at 6-7 amps, with an inductance under 2.

[skubajon]

Ok perfect. See I'm also trying to think of cutting forces of softer metals like alum. I won't be doing wood on this unless kid wants some butterfly or something lol.

So maybe if I go with a little bigger than that and run 10mm lead is that ok or is that bad as well?

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[skubajon]

Ok now I'm catching on a bit. See math sucks.

So at 5mm lead on 400 oz motors with ballscrews I can put about 750 lbs of force on what I'm moving. Is that correct? If so since I'm running slave x axis I would be putting in theory 1500 lbs of force which is enough to machine aluminum.

I guess what I need help now determining is what my acceleration torque etc is to get the load up to full velocity. Where is a point where I'm going to stall out.

Now if I say I overkill it by getting some motors in the 800 to 900 oz range on a 5mm lead and keep inductance low (I'm seeing about 3mh) will that be ok?

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[ger21]

So at 5mm lead on 400 oz motors with ballscrews I can put about 750 lbs of force on what I'm moving. Is that correct?

No, not really. Steppers are rated for holding torque, when they're not spinning. As soon as they start spinning, the torque starts to drop, and drops more the faster they spin.
This can make sizing stepper motors tricky. You need to determine the amount of torque you'll need at the maximum rpm you'll be running at, and find a motor that fits the bill. You'll usually need to look at a torque curve for the motor to find out this info.

Now if I say I overkill it by getting some motors in the 800 to 900 oz range on a 5mm lead and keep inductance low (I'm seeing about 3mh) will that be ok?

What's important is your maximum velocity, and how much torque you need to accelerate. You're motor needs enough torque to accelerate at your target rate, at the maximum rpm you'll be accelerating too. Another 25% for headroom is a good idea, too.

[skubajon]

I used the spreadsheet and hope I have right parameters entered in. I calculated at about 200 lbs but I'll wait to do again once I get my cad all done.

It was saying at 50ipm I would need 800 to be in the safe zone

Now this is kind of making sense as the force calculator was saying about 50lb of force at the rpm of my spindle.

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[skubajon]

50lb of force cutting alum that is

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[skubajon]

What do you guys think of the closed loop steppers? Those systems are much more affordable for around 200 an axis or so.

Any recommendations on a place to get servos and drives I can look into? Someone affordable with good hobby grade products?

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[wizard]

What do you guys think of the closed loop steppers? Those systems are much more affordable for around 200 an axis or so.

If you are going to that much trouble why not go all the way to conventional servo technology? I just don't see where the big benefit here is.

Any recommendations on a place to get servos and drives I can look into? Someone affordable with good hobby grade products?

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Never did business with these guys: https://www.sinjoe.com/index.php?rou...&path=87_61_66, but they are probably one of thousands of vendors in China if you are looking for the absolute lowest prices. Not everything needs to be made in China though and frankly there are advantages to buying hardware with good support locally.

[ger21]

I also don't see the benefit of the closed loop servos. I don't think I've really seen anyone using them.

I plan on using these on my router project:

Leadshine AC Servo Motor & Drive Sets (220/230 VAC Input)

You might also want to look at these.
Brushless DC Servo Motors with Integrated Drive & Controller by Teknic