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Help chatter while machining a shaft (CNC lathe).

weird thing that happens on the part the first 150mm (closer to the tailstock) when taking a reading at e.g 20mm and at 140mm with the micrometer I get exact readings (maybe about 0.002 to 0.005 mm difference) but then readings at eg 160mm and 560mm I have difference of 0.02mm (cutting exactly the size I want at 160mm and at the back closer to the chuck I sit with a -0.02mm difference) which luckily still falls into the required tolerance of 0/-0.03.
T’s got to do with the spindle bearing(s) closer to the nose. The work can wobble together with the chuck between the rear spindle bearing(s) and the tailstock center (bearing).