A method for reducing vibrations originating from a mechanical processing for removing swarf, the mechanical processing being carried out by a machine tool having a mandrel rotating at a relative operating speed (ω L ) on which it is mounted a predetermined tool equipped with one or more cutting edges defining a plurality of characteristic frequencies of the machine, the method comprising the following steps: - monitoring the vibration which arises from the contact between the tool and a workpiece (WP); - measuring the occurrence of a regenerative vibratory phenomenon when the vibration exceeds a pre-set limit value (V TR ) or has a frequency content which is not related to the characteristic frequencies; - calculating the frequency of the vibratory phenomenon (fc); - estimating a value representing a resonance frequency (f R ) of the machine as a function of the frequency of the vibratory phenomenon (fc); - determining at least one operating speed threshold value (ω TR ) on the basis of the value representing a resonance frequency (f R ); - comparing between a real-time value of the operating speed (ω L ) of the mandrel and the operating speed threshold value (ω TR ); - reducing the intensity of the vibratory phenomenon by the execution of: a first reduction strategy (SST) based on a correction of the operating speed (ω L ) when the real-time value of the operating speed (ω L ) of the mandrel is greater than the operating speed threshold value (WTR); a second reduction strategy (SSV) based on a continuous modulation which imparts an oscillation to the value of the operating speed about the real-time value, when the real-time value of the operating speedω ( L ) of the mandrel is less than the operating speed threshold value (ω TR ). - monitoring the vibration which arises from the contact between the tool and a workpiece (WP); - measuring the occurrence of a regenerative vibratory phenomenon when the vibration exceeds a pre-set limit value (V TR ) or has a frequency content which is not related to the characteristic frequencies; - calculating the frequency of the vibratory phenomenon (fc); - estimating a value representing a resonance frequency (f R ) of the machine as a function of the frequency of the vibratory phenomenon (fc); - determining at least one operating speed threshold value (ω TR ) on the basis of the value representing a resonance frequency (f R ); - comparing between a real-time value of the operating speed (ω L ) of the mandrel and the operating speed threshold value (ω TR ); - reducing the intensity of the vibratory phenomenon by the execution of: a first reduction strategy (SST) based on a correction of the operating speed (ω L ) when the real-time value of the operating speed (ω L ) of the mandrel is greater than the operating speed threshold value (WTR); a second reduction strategy (SSV) based on a continuous modulation which imparts an oscillation to the value of the operating speed about the real-time value, when the real-time value of the operating speedω ( L ) of the mandrel is less than the operating speed threshold value (ω TR ). a first reduction strategy (SST) based on a correction of the operating speed (ω L ) when the real-time value of the operating speed (ω L ) of the mandrel is greater than the operating speed threshold value (WTR); a second reduction strategy (SSV) based on a continuous modulation which imparts an oscillation to the value of the operating speed about the real-time value, when the real-time value of the operating speedω ( L ) of the mandrel is less than the operating speed threshold value (ω TR ). <EOS>