Machining system comprising a tool holder, a machining bar and a clamping nut, in which: - the tool holder has a bore extending in a longitudinal direction and within which the machining bar is intended to be placed, - the machining bar comprises a cutting area provided with a cutting edge for machining a workpiece by being subjected to a cutting force F3 defining a cutting direction perpendicular to the longitudinal direction, and a holding area designed to be arranged inside the tool holder, said holding area having at its two ends a first support area on the side opposite the cutting edge and a second support area on the cutting edge side, - the clamping nut is provided with an opening allowing the cutting edge of the bar to pass through and is arranged so that it can be tightened on the end of the tool holder including the bore and to cooperate with the machining bar in the second support area, the machining system being arranged in such a way that tightening the nut on the tool holder generates bearing forces F1, F2 respectively on the first and second bearing areas of the bar which position and hold the machining bar with reference to the tool holder and at the first bearing area, in the longitudinal direction and the cutting direction, characterized in that the wall of the opening of the clamping nut has at least one rotational surface (28, 29) coaxial with the thread of the nut, the rotational surface having an increasing radius so that the opening widens towards the inside of the nut and the tool holder and in that the second support area is formed by a second conical portion of the machining bar, arranged at the second end of the holding zone in such a way that the bearing force F2 of the nut on the bar at the second support area comprises a component parallel to the cutting direction for positioning and holding the bar with reference to the tool holder and at the second support area, according to the cutting direction. - the tool holder has a bore extending in a longitudinal direction and within which the machining bar is intended to be placed, - the machining bar comprises a cutting area provided with a cutting edge for machining a workpiece by being subjected to a cutting force F3 defining a cutting direction perpendicular to the longitudinal direction, and a holding area designed to be arranged inside the tool holder, said holding area having at its two ends a first support area on the side opposite the cutting edge and a second support area on the cutting edge side, - the clamping nut is provided with an opening allowing the cutting edge of the bar to pass through and is arranged so that it can be tightened on the end of the tool holder including the bore and to cooperate with the machining bar in the second support area, the machining system being arranged in such a way that tightening the nut on the tool holder generates bearing forces F1, F2 respectively on the first and second bearing areas of the bar which position and hold the machining bar with reference to the tool holder and at the first bearing area, in the longitudinal direction and the cutting direction, characterized in that the wall of the opening of the clamping nut has at least one rotational surface (28, 29) coaxial with the thread of the nut, the rotational surface having an increasing radius so that the opening widens towards the inside of the nut and the tool holder and in that the second support area is formed by a second conical portion of the machining bar, arranged at the second end of the holding zone in such a way that the bearing force F2 of the nut on the bar at the second support area comprises a component parallel to the cutting direction for positioning and holding the bar with reference to the tool holder and at the second support area, according to the cutting direction.