Device for machining workpieces or objects, comprising - a tool by means of which the workpiece or the object can be machined, - a pressing device by means of which the tool can be pressed against the workpiece or the object, - a vibration generating device with a vibrator for generating vibrations on a working surface of the vibrator , in particular ultrasonic vibrations, and - a pulse transmission element with an excitation surface and a pulse transmission surface opposite the excitation surface , wherein the excitation surface can be brought into contact with the working surface of the vibrator , and wherein in particular the working surface of the vibrator is concave and the excitation surface of the pulse transmission element is convex or the working surface of the vibrator is convex and the excitation surface of the pulse transmission element is concave, and wherein the pulse transmission surface can be brought into contact with the tool , the workpiece or an intermediate piece , so that vibrations can be transmitted from the vibration generating device to the workpiece or tool by means of the pulse transmission element , characterized in that a centering arrangement is provided between the vibrator and the pulse transmission element , wherein the pulse transmission element has a greater mass in an end section of a certain length (l1) adjacent to the excitation surface and/or in an end section of the same length (l3) adjacent to the pulse transmission surface than in a central section of the same length (l2) between the end sections . - a tool by means of which the workpiece or the object can be machined, - a pressing device by means of which the tool can be pressed against the workpiece or the object, - a vibration generating device with a vibrator for generating vibrations on a working surface of the vibrator , in particular ultrasonic vibrations, and - a pulse transmission element with an excitation surface and a pulse transmission surface opposite the excitation surface , wherein the excitation surface can be brought into contact with the working surface of the vibrator , and wherein in particular the working surface of the vibrator is concave and the excitation surface of the pulse transmission element is convex or the working surface of the vibrator is convex and the excitation surface of the pulse transmission element is concave, and wherein the pulse transmission surface can be brought into contact with the tool , the workpiece or an intermediate piece , so that vibrations can be transmitted from the vibration generating device to the workpiece or tool by means of the pulse transmission element , characterized in that a centering arrangement is provided between the vibrator and the pulse transmission element , wherein the pulse transmission element has a greater mass in an end section of a certain length (l1) adjacent to the excitation surface and/or in an end section of the same length (l3) adjacent to the pulse transmission surface than in a central section of the same length (l2) between the end sections . wherein the pulse transmission surface can be brought into contact with the tool , the workpiece or an intermediate piece , so that vibrations can be transmitted from the vibration generating device to the workpiece or tool by means of the pulse transmission element , characterized in that a centering arrangement is provided between the vibrator and the pulse transmission element , wherein the pulse transmission element has a greater mass in an end section of a certain length (l1) adjacent to the excitation surface and/or in an end section of the same length (l3) adjacent to the pulse transmission surface than in a central section of the same length (l2) between the end sections . <EOS>