Abstract: A burnishing attachment includes a carriage mounted for traversing movement in a path that extends along the workpiece. A non-rotary burnishing tool is mounted on said carriage for movement perpendicular to the carriage path. The tool is urged toward the rotating workpiece with a force that is a preset function of the position of the tool along the workpiece whereby the burnishing force adjusts to the appropriate amount. The tool is pivoted so that its surface maintains a normal relationship to the workpiece notwithstanding a change in angularity of the workpiece surface and the tool mounting.