thank you!
I have checked the rotating nut mechanism it can give better column strength and better critical speed with the
caveat that the Z axis servomotor must be fixed to carriage and move together with carriage.
(I also found that some high end machines use hollow shaft servos for direct driving the ballnut )
My Z axis servo is 8kg so it is too much to move x & z axes motors with carriage.
So I have 2 solutions remaing
1) Bigger diameter Z axis ballscrew (40mm) to overcome column strength and critical speed.
I have a dilemma if i would use 32mm or 40mm diameter ballscrew because both ballscrews fulfill the critical speed but the 32mm has about 2900kg column strength and my servo can give force about 3500kg the 40mm fulfills both critical speed and column strength force but has about triple inertia of 32mm ballscrew and this will degrade much the performance.
2) Do not use a ballscrew but the rack pinion mechanism that lathe has for semi-auto feeds.
This would be inaccurate and will have a lot of backlash but it will not have the the problems of critical speed & column strength
From that i can see this lathe which is very long uses this method
http://www.youtube.com/watch?v=E-F5vgQnKVg(or uses a ballscrew ? i can't see clearly)
Your Z axis ballscrew is 900mm and 10mm pitch but what diameter ? 20mm 25mm or 32mm ?