Abstract: A method for machining an annular layer or coating of grinding discs of boron nitride or diamonds at the circumference and/or the end face of a disc by means of a tool grinding disc which is especially coated with a silicon carbide layer. The workpiece disc is fed with a first predetermined rate of feed towards the workpiece disc. After the contact of the tool disc with the workpiece disc the tool disc is fed with a reduced rate of feed until a cylindrical or plane surface of the grinding coating of the workpiece disc is achieved. One or a plurality of ultrasonic sensors measure the sound or the vibration generated by the spindle of the workpiece disc. The sound or vibration analyzed in order to automatically reduce the rate of speed if at least one ultrasonic sensor detects contact between the tool disc and the workpiece disc. The grinding process is stopped if at least one of the sensors detects that the workpiece disc is cylindrical or plane, respectively, at least during one revolution term.