PURPOSE:To prevent the springing of a polished article by installing a constant flow rate device which generates a certain angular speed by the suction and discharge of liquid at the limited flow rate onto a swing arm, in a work painted- film polishing machine for the car body, etc. CONSTITUTION:A rotary polishing member 1 is revolved by a motor, through a V-belt 2, and pushed onto a work 9 by the swing of a swing arm 3 by an air cylinder 7. Though the swing arm 3 swings in the approaching direction to the work 9 in this case, the movable vane 21 of a constant liquid flow rate device 20 turns counterclockwise, and liquid flows from the second liquid chamber 24 and flows into a variable throttle valve 28, and flows into the first liquid chamber 23 from a check valve 27a, and applies brake to the swing of the swing arm 3 and provides the damping effect. Therefore, formation of uneven parts at the polishing starting position is prevented, and the flat and uniform polished surface can be obtained.