Correct Ballscrews pitch

justingro

Justingro
Building a router for home and am trying to find out what pitch Ballscrews to go for to get a reasonable speed machine and trying to keep repeatability will be looking at closed loop steppers NEMA 34 8nm direct drive or gear down I really don't know advice would be appreciated

Justin
 

zombieengineer

ZombieEngineer
If you can afford an 8 N.m stepper motor then you should be looking at direct drive (no annoying backlash :)).

What is the phase current of the stepper motor and what voltage are you intending to run the stepper motor driver from?
Supply voltage x Phase current give the nominal power of the stepper motor in Watts.
The speed could be limited by the stepper motor power (Velocity (m/s) x Force (N) = Power (W))

What is your spindle power and maximum spindle speed?
This should give us an idea of the maximum force required (to drive the cutting bit through the wood).

What is the expected weight of the gantry in kg?
The maximum force should be the cutting bit but moving the gantry could be the limiting factor.

What sort of accuracy are you looking for?
Recommend aiming for 0.01 mm/step, any smaller can limit the maximum speed (try and keep it below 50,000 steps/second)
 

zombieengineer

ZombieEngineer
The gantry weight might be a bit of a "red herring" - so ignore that question (modern linear rails have a friction co-efficient so small that it isn't significant).

Converting spindle power to force:
Did a quick bit of research and the average surface cutting speed for carbide in hardwood/plywood is about 5 m/s (this is the speed that the cutting tip scrapes the wood). Using a 2kW spindle the maximum force would be => Force = Power / Velocity = 2000 / 5 = 400 Newtons (equivalent to force required to lift 40 kg).

Converting Torque to Force:
This can be done by 0.9 x Torque (N.m) x 2 x Pi = Force (N) x Lead (metres / revolution)
The 0.9 is an efficiency factor that should be used for ball screws.

Since we have a torque (8 N.m) and a force (400 N) the only unknown is the "lead":
Lead (m/rev) = (0.9 x Torque (N.m) x 2 x Pi) / Force (N) = (0.9 x 8 x 2 x 3.14159) / 400 = 0.113 m/rev (or 113 mm/rev)
Any ball screw with a lead smaller than 113 mm/rev will generate sufficient force - no gear box required!

NOTE: I have used "lead" rather than "pitch" as some ball screws have "multiple starts".

With a direct drive ball screw with an 8 N.m motor you should be able to use any available lead/pitch. It is then a matter of choosing an appropriate steps/revolution to get the desired accuracy (10 mm lead => 1000 steps/rev to achieve 0.01mm accuracy). The upper limit for stepper motor speed (for useful work) is about 1000 RPM, for a ball screw with a 10 mm lead this works out to be 10,000 mm/min.
 

jaber

New member
The gantry weight might be a bit of a "red herring" - so ignore that question (modern linear rails have a friction co-efficient so small that it isn't significant).

Converting spindle power to force:
Did a quick bit of research and the average surface cutting speed for carbide in hardwood/plywood is about 5 m/s (this is the speed that the cutting tip scrapes the wood). Using a 2kW spindle the maximum force would be => Force = Power / Velocity = 2000 / 5 = 400 Newtons (equivalent to force required to lift 40 kg).

Converting Torque to Force:
This can be done by 0.9 x Torque (N.m) x 2 x Pi = Force (N) x Lead (metres / revolution)
The 0.9 is an efficiency factor that should be used for ball screws.

Since we have a torque (8 N.m) and a force (400 N) the only unknown is the "lead":
Lead (m/rev) = (0.9 x Torque (N.m) x 2 x Pi) / Force (N) = (0.9 x 8 x 2 x 3.14159) / 400 = 0.113 m/rev (or 113 mm/rev)
Any ball screw with a lead smaller than 113 mm/rev will generate sufficient force - no gear box required!

NOTE: I have used "lead" rather than "pitch" as some ball screws have "multiple starts".

With a direct drive ball screw with an 8 N.m motor you should be able to use any available lead/pitch. It is then a matter of choosing an appropriate steps/revolution to get the desired accuracy (10 mm lead => 1000 steps/rev to achieve 0.01mm accuracy). The upper limit for stepper motor speed (for useful work) is about 1000 RPM, for a ball screw with a 10 mm lead this works out to be 10,000 mm/min.
Really impressive... made me think to switch my 8mm Acme Lead screw with ballscrew. I just got a ClearPath Servo motors (did not install yet) and I dont know how good my Acme lead 8mm will do !!!?? Not that good I assume. I have Hiwin Lead screw on all axis. What should I get for Ballscrews (type and Brand to match my setup - Servo and masso- Please advise.... Thank you - and I am new to CNC..lol
 

jcoldon

jcoldon
ball screws are geared down like a 1605 that does 5 turns to move 1 inch Dmm servo has a xl program that figures out ball screw and rack pinion
but this site will not let me post it
 

zombieengineer

ZombieEngineer
@jaber

ACME style threads are far less efficient in converting torque to linear force due to the need to overcome the sliding friction between the ACME thread and nut. The efficiency can vary between 20% to 80% depending on the lead of the lead screw (finer pitch = less efficient).

See the following link for details on ACME thread efficiency:
https://www.pbclinear.com/Blog/2018/February/What-is-Lead-Screw-Efficiency-in-Linear-Motion

In my previous calculations I had used the nameplate stepper motor torque. The nameplate torque for a stepper motor is the holding torque, for actual movement I should have used 80% of the nameplate value as part of the holding torque comes from the "detent resistance" (the cogging you feel when you turn a shaft of an unpowered stepper motor).

@jcoldon

To upload "unsupported file types" first ZIP the file then upload.

BTW - Ball screws only come in metric leads so 5 turns of a 1605 will move 25mm / 0.984" and not a full inch.
 
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