Tangential grinding machine

A tangential grinding machine provided with at least one grinding device (7) comprising a rotary member (20), a plurality of abrasive sectors (40) mounted on supports (30.33) radially mobile on said rotary member (20), and members (23,27) for radially shifting said supports (30,33) in order to cause said abrasive sectors (40) to move outwards by an amount suitable for compensating their wear characterised by comprising a plurality of sensors (50) which are activated when a predetermined degree of wear of the abrasive sectors (40) is reached and which act on the radially shifting members (23,27) and further comprising an electronic apparatus (52) which processes the signals originating from the sensors (50) and controls members (46) for radially shifting the supports (30,33) for the abrasive sectors (40).