Ballscrew accuracy and considerations

As with all components there is an accuracy value involved. Ball screws have accuracy issues with the pitch of the screw and the variance of accuracy of the central point of the channel over a length as a result of this, ball screws are rolled or ground to a specification set out my the international standards organization.



https://tech.thk.com/en/products/pdf/en_a15_011.pdf


Here is a table stating those tolerances, its probable this machine will use a 1600mm screw in both X and Y direction due to the cutting area required. This results in an error of 16 micron over the total length in regards to screw pitch. With a total travel error with a maximum of 35 micron over the full length. However it is likely that this will be less.

C3 Ball screws will be chosen from a company called true systems. In 20mm diameter and 5mm pitch these screws can withstand a force of 1130kgf. This will be more than suitable for the application of this machine. Being 20mm and hardened to the core wear characteristics will allow the life of the ball screw and nut to outlive the life of the machine.

http://www.trusystems.co.uk/wp-content/uploads/2011/03/Tru-Systems-12pp-A4-Ball-Screw-Brochure-lr.pdf

With a 2400 line rotary encoder on the servo motors should allow for a 2.01 micron resolution on a 5mm pitch screw.

Ball screw whip

The required speed on a 5mm pitch screw = 2000

Ballscrews will "whip" when at or above a certain speed, this speed can be calculated with the formula


http://www2.steinmeyer.com/content/cnt_cnt/docid_961/iso_en

n_k  Critical speed [rpm]
d_N  Nominal diameter [mm]
l_s   Unsupported length [mm]
k   Support bearing factor

Support type

Fixed = contained in place (A motor could be a fixed support, or a support that allows no rotary movement)
Supported = supported on a bearing or similar
Free = no support

fixed - fixed: 25,5
fixed - supported: 17,7
supported - supported: 11,5
fixed - free: 3,9

d_N  Nominal diameter [mm] = 16.5 (http://www.mooreinternational.co.uk/carry-ball-screw/screw20x5.html)
l_s   Unsupported length [mm] =1550 (25mm each end for support)
fixed - supported arrangement (motor one end bearing on the other)



=17.7*16.5*(1/1550^2)*10^7
=1215(3SF) RPM (Not suitable for application)

A rotating nut as opposed to a rotating ball screw would enable a fixed-fixed arrangement

=1751=137 (4SF) RPM (Not suitable)

Increasing the diameter to a 25mm screw will raise the critical speed

http://www.mooreinternational.co.uk/carry-ball-screw/screw25x5.html

d<sub>N=21.5mm

nk=2282 RPM (4.S.F) This is suitable and will allow for a maximum travel speed on a 5mm pitch screw of 11.41 meters/minute without the screw whipping.</sub>