Optimal ballscrew diameter for lathe

[vre]

Iam retrofitting a lathe with 1900mm Z axis length (1900mm is ballscrew/ways length the length between centers is 1400mm).
The lathe will have 10m/min rapid linear speed on Z axis from a servo 1.8kw 3000rpm with 1:3 reduction (1000rpm).
Two important parameters is critical speed and column strength because the ballscrew will be 1900mm.
Iam between 32mm and 40mm for the ballscrew but iam not sure if 32mm diameter ballscrew has enough column strength at this length and if it would be stable
at 1000rpm. If i put 40mm ballscrew the inertia would be much more because 40mm has the double mass of 32mm ballscrew.
Commercial machines at this length what ballscrew are using ?
What is your opinion ? Iam open to suggestions..

Ball Screw Selection (http://www.nookindustries.com/LinearLibraryItem/Ball_Screw_Selection)
Nook Industries Engineering Tools (http://www.nookindustries.com/EngineeringTool/Index)

[m_c]

Do the calcs.
However you either want to have the fixed end at the headstock so you're mostly cutting with the screw under tension, or anchor both ends and have the screw under permanent tension.

[vre]

For type C end support and 3210 ballscrew (27.3mm root diameter / 1900mm length / mass 10.64kg)
Critical angle speed 1344 rpm
Max column load 29764 newton (if we make the assumption that force can be represented in kg is 29764/9.8 = 3037kg )

For type C end support and 4010 ballscrew (34.1mm root diameter / 1900mm length / mass 17.1kg)
Critical angle speed 1679 rpm
Max column load 72453 newton (72453/9.8 = 7393kg )

For type D end support and 3210 ballscrew (27.3mm root diameter / 1900mm length / mass 10.64kg)
Critical angle speed 2039 rpm
Max column load 59528 newton (59528/9.8 = 6074kg )

For type D end support and 4010 ballscrew (34.1mm root diameter / 1900mm length / mass 17.1kg)
Critical angle speed 2547 rpm
Max column load 144906 newton (144906/9.8 = 14786kg )

These are ideal calculations without safety factor in reality because the carriage of lathe has on the ballnut (shortens equivalent length) and the ballscrew is mounted in the side of lathe (side load is worse that centered load) maybe these calcs are wrong in good or the bad way.

In reality from calcs seems that 3210 fulfill the 1000rpm in all setups with a good safety factor
but i have doubt for max column load what is your opinion for side load is enough in case of 3210 ballscrew ?
Where is better to mount Z axis servo near the spindle or near the tailstock ?
Also where is better to mount X axis servo in the side of hand wheels or the opposite ?

[m_c]

Look at the haas site (haascnc.com) to get an idea of the forces required, as they list them for all their machines.
I just had a quick look, and the ST20 only has 22686N force on the X-axis.

[vre]

thank you!
I have not problem with X axis because is only 600mm with the Z axis i have problem because it is 1900mm
In Haas catalog the thrust force is the max column load of ballscrew or the force that servos can give ?
If it is the max column load of ballscrew then i will go with 3210 ballscrew..

[m_c]

The force should be the maximum force the servo can apply before stalling/faulting.
I'd guess there will be quite a good safety margin in terms of the maximum force the ballscrew can handle.

[vre]

What is a good safety margin between force servo can supply and force ballscrew can handle ? x2 / x3 / x4 / x5 ?

A commercial lathe with this length on Z axis (1900mm) that driving mechanism has ? rotating ballscrew with fixed ballnut , rotating nut with fixed ballscrew, rack/pinion ?
If has ballscrew what size is this ballscrew ?