This document discloses a system and method for polishing a metal surface, using a grinding machine and a burnishing machine. The grinding machine comprises an arm coupled with a grinding wheel for grinding the internal surface of a workpiece, an arm rotation drive block configured to drive rotation of the arm around its longitudinal axis, an arm movement drive block configured to move the arm longitudinally and vertically, and rollers for rotating the workpiece around its cylindrical axis via friction with an external surface of the workpiece. The arm comprises a fixed main shaft, a universal joint shaft and a head section coupled with the grinding wheel, wherein the head section is configured to oscillate vertically, allowing the grinding wheel to follow up-and-down fluctuations of the workpiece. The burnishing machine is configured to tumble the workpiece including a tumbling detergent and tumbling beads therein.