A machine for machining a work piece with at least one revolving or rotating tool, having a ball screw, which is pivoted by a fix and a floating bearing whereas the machine has a device for measuring the length of the extension of the ball screw. Furthermore, a method is provided for measuring and compensation a thermal displacement comprising the steps of: detecting the length U of the axis of the ball screw, detecting the length I2 of the axis of the ball screw, calculating the difference Δl of the length I1 extended axis and the reference length I2 of the axis and compensating the difference value to the correct value.