A grinding arrangement is described to remove sharp edges on a pipe coupling (51) of a drill string (50), as a consequence of marks from the jaws of pliers and machines used to connect the pipe couplings (51) on a drill deck. A receiving unit (30) is arranged to receive a grinding unit (36) which is equipped with at least one grinding element (38), as the grinding unit (36) is arranged to be driven into the receiving unit (30) with the help of the drill string (50) or a suitable running tool and to be locked securely into the receiving unit (30). Furthermore, the receiving unit is arranged in a riser, landing string or in other connections between the drill deck and a wellhead and over a sealing arrangement for dynamic sealing around the drill string (50) during pressure controlled drilling.