Sizing lead screw and stepper motor

[Laytonrouter]

I am building an 4' x 4' cnc router table for wood plastics and possibly aluminum (aluminum not a must). After all the reading I have done I come up with a lead screw of 16mm diameter (sfu1605) for x and y axis and nema 23 425 oz/inch stepper motors. I really don't need to run this faster than 150 IPM.
My question is for anyone with experience with this. Do you think this is in the operable ball park or do you think I should jump to nema 34 600 oz/inch motors and SFU2005 lead screw.
As I said I have run the calculations but would like an experienced opinion if possible.

Thanks for any advice in advance.

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[servtech]

I am building an 4' x 4' cnc router table for wood plastics and possibly aluminum (aluminum not a must). After all the reading I have done I come up with a lead screw of 16mm diameter (sfu1605) for x and y axis and nema 23 425 oz/inch stepper motors. I really don't need to run this faster than 150 IPM.
My question is for anyone with experience with this. Do you think this is in the operable ball park or do you think I should jump to nema 34 600 oz/inch motors and SFU2005 lead screw.
As I said I have run the calculations but would like an experienced opinion if possible.

Thanks for any advice in advance.

Personally, I think ballscrew diameter is less important than its pitch. The longer the pitch, the more the motor starting load.

[joeavaerage]

Hi,
my first mini-mill had 20mm x 5mm (pitch) ballscrews and was very adequate.

Personally, I think ballscrew diameter is less important than its pitch.

I'm not sure I agree with that sentiment. The moment of inertia of a ballscrew is proportional to the 4th power of diameter. The acceleration equation is highly dependent
on the ballscrew inertia, so care must be excerized. Ballscrews of too greater diameter will cause the acceleration to suffer. Conversely a ballscrew of too small a diameter may whip at speed
or even buckle under load. Depending on the length I would guess the 16mm or 20mm ballscrews are right.

The finer the pitch the better the acceleration and thrust, both of which are desirable for tool path following and countering cutting forces. Coarser pitch, say 10mm or more is great for
speed but reduces acceleration. I personally favor acceleration over speed.

Your acceptable max speed is 150ipm? That corresponds to 3810mm/min or a rotational speed of 762 rpm assuming a 5mm pitch of the stepper. That's quite fast for a stepper. If it the stepper has high
or even moderate inductance the chances are that it will stall before reaching that speed. The classic method to overcome inductance is to use the highest voltage driver and supply you can.

Can you post the inductance of your steppers and the drivers/power supply that you intend to use?

Craig

[peteeng]

Hi Layton - 16mm is a good size for a 4x4 machine. 5mm pitch is good for the Z axis as it needs lots of force for plunging and the Z moves slowly. Using 5mm for the X&Y is a waste of speed. I suggest you go 10mm. 10mm for X&Y will give you high forces and good speeds. Today you may want 150ipm (3750mm/min 3750/5=750rpm which is top speed for a stepper usually) but once you get used to 150ipm you will ant 300ipm. A job can be done much faster at 300... 300ipm is 7500mm/min 7500/10=750rpm so is a good fit. I have 10mm pitch on my 4x4 machine and would use higher next time around.. Ballscrew diameter is important for buckling loads and vibration.... for a 4x4 machine 16mm or 20mm is a good size. 12mm would buckle and whirl or whip.... things you don't want to happen. If ypou use 24000rpm spind;les with 6mm cutters you will need higher feed speeds then 3000mm/min toi take full advantage of high speed machining techniques using the correct chip load for the cutters so a bit more speed is useful... Peter

[mactec54]

I am building an 4' x 4' cnc router table for wood plastics and possibly aluminum (aluminum not a must). After all the reading I have done I come up with a lead screw of 16mm diameter (sfu1605) for x and y axis and nema 23 425 oz/inch stepper motors. I really don't need to run this faster than 150 IPM.
My question is for anyone with experience with this. Do you think this is in the operable ball park or do you think I should jump to nema 34 600 oz/inch motors and SFU2005 lead screw.
As I said I have run the calculations but would like an experienced opinion if possible.

Thanks for any advice in advance.

For a 4' plus Ballscrew you want a minimum diameter of 20mm and a pitch of 10mm, 5mm pitch is not much fun for a long travel distance, 16mm Ballscrew over that distance is very wimpy, you have to look at the core diameter of the Ballscrew this will be somewhere around 12mm, for the 16mm Ballscrew, 16mm diameter is fine for the Z axis, around 24" is the max length for a 16mm Ballscrew without experiencing screw whip

[Laytonrouter]

Thank you all for your input, very valuable. I don't have the motors yet as I am taking it a step at a time. I previously built a 4' x 8' table using 20 mm lead screws on x and y. Y limited me to about 100 ipm due to whip. I'm not a production shop as I do more specialized work and am not as concerned with how long it takes as long as it's reasonable (whatever that is). These comments are very accurate and put me right in the middle of ; should I use 2005 or 16005 (or 2010 or 1610) lead screw. I was planning on using nema23 425 oz/in motors. I used nema 34 960 oz. on the 4 x 8 build so I am not comfortable at all with nema 23 even though many say it's plenty of power. My x axis only weighs about 50 lbs. with the spindle assembly.
Using 20mm diameter leadscrew and nema 34 motors is a big jump in price but I don't want something that is going to stall or skip steps under normal use. They do make 5xx oz nema23 motors. Also looking for motors with inductance less than around 3uH. Again this change to nema 34 would make me jump from 5.6A controllers to possible 7.2 amp.

Thanks again, valuable input.

[Laytonrouter]

Mactec54, practically speaking I think you may be right about whip. I bought a 16mm lead for the z axis and from the looks of it I can't imagine it not hitting resonance at higher speeds on the x y axis.

[joeavaerage]

Hi,
low inductance steppers have fewer turns of a heavier wire and consequently have a high current relative to the torque output.

They do make 5xx oz nema23 motors. Also looking for motors with inductance less than around 3uH. Again this change to nema 34 would make me jump from 5.6A controllers to possible 7.2 amp.

I suspect yes they do make such steppers, however the inductance will be high, 3mH or more, and thats too much. The question is less about what torque the motors have, 425oz.in vs 5xxoz.in, but rather how
much torque they have left at 1000rpm.

A low inductance stepper, say 1.2mH and 425oz.in, will have about 40% of its torque remaining at 1000rpm, about 170oz.in.
A medium inductance stepper, say 3mH at 550oz.in will have about 15% of its torque remaining at 1000rpm, about 85oz.in.

You might be tempted to believe that the 550oz.in motor is the best, but that is deceiving, the low inductance motor is better over-all.

Typically 34 size motors have a lot more torque, which is good, but they also have much higher inductance which is bad. They will often have less torque
at speed than a 23/'24 size motor of low inductance.

The only way to be sure about the torque at speed is to search for the torque/speed diagram published by the better manufacturers. If a manufacturer does not publish this data
then it's questionable whether you should buy.

Craig

[Laytonrouter]

I follow your reasoning on inductance. I think I'll look for a nema 23,24 motor with low inductance and use it to drive a sfu2005 ball screw on the x y axis .

Many thanks

[joeavaerage]

Hi,
I have attached the speed/torque curves for some Leadshine steppers.

I have highlighted three, a low inductance (1.18mH) 3.1Nm 23 size, a medium inductance (2mH) 3Nm 24 size and one 43 size of 2.95mH and 4.5Nm.

The low inductance 23 has 1.6Nm at 1000 rpm and the med inductance 24 has 1.2Nm. The medium(ish) inductance 34 has 1.5Nm, and that is by virtue of the higher drive voltage (72V cf 48V of 23 and 24 sizes).
So despite the 34 having greater initial torque it is at best only as good as the smaller motors at speed. If you were to run either the 23 or 24 at 72V I would expect even better performance and really leave the
34 in the shade.

Craig

[Laytonrouter]

Thanks a lot for this information. Looks like you are right in the sweet spot for my application. Could you resend the page for the nema 23 and 24. I can't make out the model numbers. Need to get a price and point of purchase.

Thanks again,

[joeavaerage]

Hi,
I got the data off the Leadshine website, the catalogue pages are a PDF:

https://www.leadshine.com/products/s...per-motor.html

Craig

[joeavaerage]

Hi,
the end result is that a low or medium inductance 23 or 24 size stepper with a 70V driver will have at least 1Nm of torque in the range of 750rpm-1000rpm,
with a modest safety factor. You should calculate the acceleration and thrust with the two different pitch screws. It seems the common preferred size is 20mm diameter,
mainly to do with whipping.

The acceleration of a ballscrew and attcached gantry is:

dw²/dt²= torque /J_total where
J_total=J_screw + J_motor + J_load

The fist moment of inertia (J) of 24/24 size motors is about 0.7 x10^-4kg.m² (from manufacturers data)

The first moment of inertia of a ballscrew 1.4m in length and 20mm in diameter is
J_screw =0.5 x m x r² where m is the mass of the screw, = pi x r² x l x rho (density of steel)
= 0.5 x (0.01)² x pi x (0.01)² x 1.4 x 8000
= 1.76 x 10^-4kg.m²

The equivalent of the first moment of inertia of the load, which is the linear axis and its mass is:
J_load= m x p²/(4.pi) where m is the mass of the gantry, assumed 25kg and p is the pitch of the screw in meters, assumed 5mm
= 25 x (0.005)²/ 4 x 3.141
=0.16 x 10^-4kg.m²

For a 10mm pitch screw:

J_screw=25 x 90.01)² / 4 x 3.141
=0.625 x 10^-4kg.m²

The angular acceleration of the screw is:
dw²/dt²= 1 / (1.76 +0.7 +0.16)x 10^-4
=3817 rad/s² for a linear acceleration of 3.03m/s² Note this is for a 5mm pitch screw.

The angular acceleration of the screw is
dw²/dt²= 1 / (1.76 = 0.7 = 0.625) x 10^-4
= 3241 rad/s² for a linear acceleration of 5.2 m/s² Note this is for a 10mm pitch screw.

In both cases (5mm pitch and 10mm pitch) the linear accelerations are very VERY good for a hobby machine, namely 0.3g and 0.5g. Therefore either 5mm or 10mm
pitch would be suitable.

The mechanical advantage of a 5mm pitch screw of 20mm diameter is:
Advantage= 20 x pi /5
=12.6
Whereas the advatage of a 10mm pitch screw of 20mm diameter is:
Advantage= 20 x pi / 10
=6.3

So the thrust with 1Nm applied in each case is 1000/10 x 12.6= 1256N and 1000/10 x 6.3 =630N

Naturally the finer pitch screw results in more thrust for a given 1Nm of applied torque than the 10mm pitch screw, but either figure (1256 vs 630) are both very adequate
for your machine.

The choice is 5mm, double the thrust with slightly less acceleration (0.3g) or 10mm with less thrust but 0.5g acceleration....either would be fine from the point of view of acceleration
and thrust. Clearly the 10mm pitch screw will result in better rapid traverses and is probably perferred.

Craig

[Laytonrouter]

Once again, thank you for your mathematical analysis, very telling and convincing. It looks like a nema 23 or 25 with with less than 2mH inductance that could maintain at least 150oz/in at high speed (600 to 800 rpm) would work. Clearly the inertial radial forces of the lead screw with a 50lb load are minimal, however this does not include the additional axial forces for the router bit pushing against the material it is cutting. I can't imagine more that 10 to 20 lbs of force if that. I think as you say, the key is to have low inductance as you can sacrifice a little torque at low speed for sufficient torque at higher speeds. Again, I'm looking more for higher accuracy than high speed so I might be inclined to go with 5mm on the x and y axis as well. If I am correct anything over 450oz/in motor torque should get me there.

Thanks again.

[joeavaerage]

Hi,

I think as you say, the key is to have low inductance as you can sacrifice a little torque at low speed for sufficient torque at higher speeds.

Yes, that is the important conclusion.....it's less about torque at low speed, steppers are very torque dense at low speed, but rather making the right choice to retain as much torque
as possible at high speed.

Again, I'm looking more for higher accuracy than high speed so I might be inclined to go with 5mm on the x and y axis as well.

Thrust verses speed.....speed verses thrust??? Its very much a matter of choice and the style of machine you want. Woodworking machines tend to be very fast and the reduced thrust is not an
issue whereas metal cutting machines, especially steel, favor lower speeds and require the extra thrust to retain cutting authority.

Craig

[peteeng]

Hi Layton - a 24" long 16mm ballscrew will critically vibrate around 6473rpm well above your service speeds. Hiwin use an allowable factor of x0.8 so the "safe allowable" speed will be around 5000rpm again well above usual service speeds. A 48" (1220mm) long Dia16mm ballscrew will have an allowable speed of 1295rpm which is above most system designs as steppers run out of puff before then. Steppers can go faster but say its a 10mm pitch then 1000rpm a velocity of 10m/min and it does not sound like you need that. A 48" long 20mm ballscrew has an allowable speed of 1706rpm FYI according to Hiwin. IMHO 5mm pitch for X&Y is too fine and you will not be able to achieve correct chip loads for your tools, you will be rubbing vs cutting. What tool diameters, edge count and spindle speeds do you typically use? . Cheers Peter

re accuracy - a C7 ballscrew will be the same accuracy if its 5mm or 10mm pitch. The accuracy is set by the screws manufacturing process, the motor specification (usually +/-5% by angle and 200 steps per rev and the quality of the microstepping functions/electronics. Theoretical accuracies are usually extremely high then you add backlash and machine compliance and you get down to the real achievable accuracy. Also don't confuse accuracy, repeatability and tolerances... they are all different metrics.

[peteeng]

Hello Layton - I think you are underestimating the possible forces involved with these ballscrews. A 425ozin motor (3Nm) with a 5mm pitch screw will have a starting force of 346kgf or 764lbf on the axis with 2 motors this is doubled!! At half speed say 500rpm this is about 764/2=382lbf. A 10mm pitch ball screw with 3Nm could have 173kgf or 382lbf at slow speed and 173/2= 87lbf at 500rpm... Peter

[Laytonrouter]

Thank you Peteeng for your response. Hiwin's calculations are impressive however I previously built a 4' x 8' table with a 20mm lead screw with a 10 pitch on the Y axis. Very heavy gantry but at speeds in excess of 150 ipm it would vibrate terribly. I guess that's why I have been so concerned about dropping down to 16mm lead and nema 23 motors. After reviewing yours and joeavereange's math I think I am comfortable trying a 16mm lead screw and steppers of no less than 425 oz/in torque.
I generally run a 1/2" ball mill for roughing in 3D reliefs then transition down to 1/8" ball diameter on wood. Usually run at 20,000 rpm.
3Nm might be difficult to maintain at high rpm however based on your calculations there is a lot of wiggle room from 87lbs/ft at 500 rpm with a 10 pitch. Not concerned with a few extra seconds with rapid movements. Careful programming can mill in both directions. If I can run between 75 and 150 ipm I'm perfectly satisfied which I think this combination will more than do.

Again, thanks to everyone for your input.
Forums rock!

Glad to report my findings when I complete this if anyone is interested.

[peteeng]

Hi Layton,- what vibrated? Just the screw or the machine? In regard to chip load I have found this table useful. It recommends a chip load of 0.5mm/tooth for the 1/2" tool in timber. At 20,000rpm this means the feed should be 787in/min. At 150in/min the tool is rubbing most of the time. This is why you need more feed speed. The 1/8" tool is spot on 157in/min at 20k... Or use a smaller tool for roughing or use a 1F tool at 10k and 200in/min to get the CL right. Your tools will cut better and last longer with the correct CL.

If you used the 1/2" tool at 10k then you need 400in/min or 10m/min which is the 10mm pitch screw at 1000rpm. I'd be inclined to go to 1616 to give you some headroom in the feed. I'm going there for my next machine....

cheers Peter

[Laytonrouter]

Hi Layton,- what vibrated? Just the screw or the machine? In regard to chip load I have found this table useful. It recommends a chip load of 0.5mm/tooth for the 1/2" tool in timber. At 20,000rpm this means the feed should be 787in/min. At 150in/min the tool is rubbing most of the time. This is why you need more feed speed. The 1/8" tool is spot on 157in/min at 20k... Or use a smaller tool for roughing or use a 1F tool at 10k and 200in/min to get the CL right. Your tools will cut better and last longer with the correct CL.

If you used the 1/2" tool at 10k then you need 400in/min or 10m/min which is the 10mm pitch screw at 1000rpm. I'd be inclined to go to 1616 to give you some headroom in the feed. I'm going there for my next machine....

cheers Peter

Thanks Peter,
Very useful numbers to think about. Can't imagine running at 200 ipm but this might be able to do it. To answer your question, the 8' lead screw was vibrating. I know the shorter screw will make a big difference.

Many thanks,