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break this down into steps first. Working on Metric system.

#1 Need Shaft Revs per Unit. So need tooth pitch(TP) and number of teeth on Pinion(PT). Shaft Revs per unti = 1 / (TP * PT)
So example...

Have you build anything before? I don think so or it was not that big

So let me help you a bit:

-You miss some basic understanding that Box section is stronger than U profile. Eliminate from...

Well it looks good but there are a few things I would comment on.

3500mm is a mighty wide gantry, it would be better from a rigidity standpoint if you have could have the axis running the other...

Sorry but your wrong R&P is the perfect choice in this application. Just about every industrial Stone cutting machine uses Helical R&P.
Your also Wrong about the Resolution and Micro steps because...

Maybe, try a few out. It depends on your steppers, drivers and how well they work together, there is probably a sweet spot. I would stay clear of the really high ones though, mircosteps aren't always...

The distance traveled per revolution with rack and pinion is the pitch circle of your pinion gear diameter * pi, for example 1inch 25.4mm pitch circle diameter pinion gear, 25.4*3.145 = 79.883mm...

You will not do much good with the type of bolt together frame that you are showing.
You do NOT need higher speeds, but you do need a RIGID machine and plenty of water, rough out leaving 4 to 6 mm...

The problem is at 3m long your going to need quite large screws so that they aren't flopping & wipping around. Large screws generally have a large thread pitch, plus you'd want to use a large thread...

Yasser first welcome to the forum. Are you sure about the 400mm/sec as that is 24mtr/min and is very fast. you need to give the specs of the controller and drives also the voltage of the output...

Is this machine to be used only for marble? I would have thought the only way to machine marble would be very slowly. In which case the maximum speed of the machine would be of little importance. So...

I suspect before anyone can help you, you need to provide more details. Your question is a bit like 'how do I solve world peace'?

Pics, specs? What speeds can you do, what are the issues etc ...

A Tutorial on motor torque calculations

A question oft asked on MYCNCUK is "how big a motor do I need?". There is no simple answer to this, and the options are usually:
a) follow someone elses...