Hi Baron, I'm not sure what you're getting at about the flow of heat. If the tool tip is producing the heat, which it should be unless the sides are rubbing for some reason, then the heat will be 'entering' the workpiece at the point it is being cut. As we cut, this point becomes the thinnest diameter of the piece (assuming we start with a cylinder just for ease, it doesn't really matter). So the thinnest diameter is the hottest point and the heat flows into the rest of the part, not necessarily uniformly but again it doesn't make a difference. If we now had a FLIR (which I love playing with but don't have my own) and we scanned the linear length of the part, the highest temperature would be our groove and thus it would have the highest linear expansion making our groove wider than it was.

Making up some figures for ease, let's say *α *is 0.0001 and our groove is 2mm wide and has heated up by 100 degrees over ambient. Let's also say the part each side of our groove has heated to 98 degrees over ambient. So our 2mm groove is now 2+ (2*0.0001*100) = 2.002mm wide. Now even without doing the math, as the material each side has not increased in temp as much, it cannot have expanded as much as our groove. Even if the heat flow was perfect, it could not be hotter than our grooved area so, at worst, it would have expanded at the same rate and our part is just 'scaled up' uniformly.

The diameter of the part would be increasing by a larger amount in other areas, simply because there is more material to expand in that direction, but this diameter increase makes no difference to our groove clearance.

Finally (phew) I can see that of one end of our workpiece is constrained by the lathe jaws and thus cannot move, then all the linear expansion that occurs between the jaws and the cut would be to the right (assuming normal lathe orientation) so our groove would be displacing to the right as the piece expands. In this case, I can see the left side of the parting tool rubbing on the side of the cut. Realistically though, as we part reasonably close to the chuck, coefficients of expansions are small, and the chuck is a heat sink, I can't see this having much effect. (I just did a quick calculation, for aluminium being parted 20mm from the chuck and increasing in temp by 100 degrees C, our cut would shift 0.044mm to the right in the above scenario, using the actual figures).

That's what I'm thinking, but if I've missed something I'm happy to be corrected.