Abstract: An orbiting head is rotatably mounted in the housing. The orbiting head has an axial end with a grinding surface for contact with the workpiece having its surface finished. The orbiting head defines a fluid passage with one end having an opening at the grinding surface. A spindle arbor is connected to the orbiting head and rotates with the orbiting head. The spindle arbor also defines a passage having one end connected to the passage of the orbiting head, and having another end connected to a fluid source. A drive is connected to the spindle arbor for driving the spindle arbor and the orbiting head in rotation. The orbiting head is rotated, and the grinding surface is placed into contact with the surface of the workpiece, and in relative rotation to the surface of the workpiece. Fluid is then moved through the passages from the fluid source to the opening in the grinding surface, and from the opening to an area between the grinding surface and the workpiece.