Abstract: An arrangement and method for precision machining of rotationally symmetrical, disk or ring-shaped components. The arrangement includes a container which is open at the top and mounted such that it is able to vibrate. An unbalanced rotor causes the container to vibrate in a rotation-induced manner and has a drive. The container is filled with an abrasive substance including a multitude of abrasive bodies and a liquid. A device for fixing the component is also arranged in the container which has a rotationally symmetrical shape and is arranged in line with a vertical axis. The container also includes a rigid fixing device for horizontally positioning the component.