I have a CNC6040 machine.

Yesterday we cut a few small (3x4 inches) rectangular pieces from 1/2 inch aluminum plate. (profile cut... so one site of the cut is climb and one side is conventional)

The machine long axis is X and short axis it Y. Zero of each axis of the machine is at closest point to motor mount.

Cutting was done with 1/4 inch 4 flute carbide bit VERY slowly (1/5 mm depth of cut per pass, feed rate was tried from 200-600 mm/min) RPM was varied from 6000-14000 to get largest possible chips.
The groove of the cut was constantly flooded with WD-40.

On 3 of the 4 sides of the cut we got zero chatter and the cutting was very quite. On the 4th side we got quite a bit of noise and chatter marks on that side of the part.

The direction of that chattery cut was on the short axis (Y) of the machine while the cutter was moving towards the motor.

Later I put a micrometer block and pushed on the motor spindle as hard as I could and there is total of 1~2/1000 deflection BUT it is the same in both directions.
I moved the head several times 50 mm back and forth and the machine has virtually zero backlash.

Also re checked that all the bolts are tight.

What should I do next to figure this out ?

-D