Abstract: A method for reducing vibrations originating in a mechanical processing for removal of swarf comprising monitoring the vibration resulting from contact between the tool and workpiece, detecting the occurrence of a regenerative vibratory phenomenon, calculating the frequency of the phenomenon, estimating a value representing a resonance frequency of the machine as a function of the frequency of the phenomenon and determining a threshold value on the basis of the value. Also, comparing the operating speed of the mandrel with the threshold value and reducing the intensity of the phenomenon by a first reduction strategy based on correction of the operating speed of the mandrel being greater than the threshold value or by a second reduction strategy based on a continuous modulation which imparts an oscillation to the speed around the value of the operating speed, when the operating speed of the mandrel is less than the threshold value.