To automatically and stably grind reverse side beads, and enhance grinding properties.

A grinding wheel 31 is disposed while being perpendicularly intersected with reverse beads 33, there causes no change in grinding resistance at the time of up-cutting/down-cutting, grinding is carried out stably, a device 34 at the side of the grinding wheel is clamped by the straight pipe part 32a of a pipeline 32, any non-conformity such as the slipping of a grinding device due to grinding resistance at the time of grinding is eliminated, pressing force caused by the revolutions of the grinding wheel is accurately estimated, grinding properties are thereby enhanced, accurate grinding at the high speed is made possible, a motor 46 for pressing the grinding wheel is controlled based on detected information from a tachogenerator 51 and a pipeline inner surface shape measurement sensor 48 so as to allow the grinding wheel to be controlled in feeding rate, and reverse side beads 33 are thereby automatically ground as far as the surface of parent material 58.