Fish mouth fitting or “coping” tube for motorcycle frames is pretty easy with a low cost tube-cutting jig. Below is a picture of an import version of this type tube cutter. The base angle was missing so a cheap vise is used to fasten the jig to the drill press table. You can use these jigs without a drill press and use a drill to power the saw. Using the drill press makes the jig and saws last longer. Hole saws are used to make the actual cut. The tube is held in a clamp in the jig and the clamp can be set to various angles for angle cuts.
Here is a shot of the saw part way through the tube showing progress of the cut.
After you cut through the tube the end of the tube looks like the picture below. The tube is pretty worthless for welding at this point. Note the rough and sharp thin edges.
Next, the tube is sanded (disc or belt sander) or filed (half round file) so the sharp edges are squared off back to the tube wall thickness. Then the tube is beveled to allow the weld to fully penetrate. The bevel allow the weld to start at the inside diameter of the tube to the outside of the tube. The joint is very tight so there are no gaps around the inside of the tube where it meets the other tube. A tight fit protects the root of the weld from air contamination that leads to oxidation, bubbles or inclusions in the weld.
Tubes are fitted together and tacked in several locations around the tube. Short welds are done to prevent distorting the frame. Also, this is probably one of the hardest welds to do since there are no straight lines and position changes constantly throughout the weld. After you do several sample welds and can make the weld look good on the outside, it is time to cut some apart and really find out how good they are. In the picture below, a “Tee” sample was cut though the centerline of the tubes. You can see the outside of the weld fillet where the two tubes were welded from the outside. There is no gap at the inside of the tube and the weld has completely fused the two tubes together. If the sample was polished, you would be able to see the actual weld which is a bullet shape starting from the outside fillet to the inside diameter of both tubes without burning through either tubes.
Weld that burns through the tube at the cut end or sidewall will be exposed to air and can cause issues with the weld strength. Ideally, the weld will just barely penetrate the tube and not be allowed to pick up oxygen. The welding process shield protects the outside of the weld. A sample cut like the picture above lets you see the inside of the tube, weld fillet, weld penetration, weld porosity or inclusions and wall thickness of the tube. Be sure the weld has not consumed part of the tube wall thickness or strength will be lost. The tube wall thickness should not be thinned near the weld (also called undercutting).