The thing I perhaps should have made a bit clearer was that the squeaking doesn't happen when the chisel is plunged rather just when the auger is spinning freely. I wonder if the chisel and the bit aren't quite in exactly the same plane. Has anyone else had this problem?
Personally I wouldn't worry about a squeaking chisel and auger . There could be several factors contributing to this . As long as the auger isn't causing the chisel to over heat , change colour and crack then its not really worth worrying about
I certainly wouldn't put a heavy oil or a silicon spray on the chisel . Glue and grease don't mix .
