Which thickness CY cable do I need for 1.5kW spindle?

[A_Camera]

Do you have a hair dryer at hand? Check the cable and power. Mine has 1700W and a 2x0.75mm2 cable. And is german made.

Fine. Now, run that hair dryer for 8 hours non-stop and see what happens...

Hair dryers are NOT high frequency controlled equipment, they have a tiny motor and they are not designed to be run for more than a few minutes a time so you can't really take that as a good example. My drilling machines have 1.5mm2 cables, they are also German made, and none of them are over 1kW. Why? Because they are designed for sudden current rushes and for long usage time.

Now regarding the question in this thread, I would never use a 0.75mm2 "normal" stranded cable in a CNC machine. Since all the cross-sections are composed of thin wires with the same diameter, a larger cable will last longer. If/when half the wires of the 0.75mm2 conductor (only 10-12 of them) will be broken, probably the rest will blow. For a 1.5mm2 cable, three times the number of wires needs to be broken to come to the same situation.

That is yet another good argument for a stronger cable. On the other hand, if you handle the cable as you supposed to handle and don't bend it more than it is specified for *AND* use the cable type which is designed for the application (i.e. flexible cable chain use) than you should not have any broken wires during the life time of your machine. Remember that I am talking about quality cables, not the one used in the hair dryer.

Using special flexible fine stranded cables, even 3x0.5mm2 will be enough for a 3 phase 1.5kw spindle on a short distance

Yes, of course. I have never claimed otherwise. Just that I can't really see any *GOOD* reason for not using something stronger than 0.75mm2. Never the less, there is a group of people who prefer the easiest approach, which is using the thinnest possible cables. Beats me why, I don't understand that philosophy and prefer to have margins if I can. On the other hand... so far I have not had any electrical issues, and I don't expect to have any later on.