1947 D4 7u with loose fan pulley

About a year ago I bought a 1947 D4 7U (serial number 7U469). I ran it some but I had to tighten the castle nut on the end of the fan pulley several times when the pulley would loosen. After several adjustments with no luck, I took the water pump off to see what the issue is. What I discovered is that the water pump has a 7/8" straight shaft while the pulley has a coned shaft receptor. Someone has obvious replaced one of the items (shaft or pulley) with a non-standard item.From what I read, it seems to me that the shaft is correct, but I could be wrong. Has anyone seen this issue. Does anyone have a solution for me (e.g., proper part I can buy).  Thanks.

I out of my confort zone trying to help you. Never had a machine like yours. On utube scratch rebuilds a water pump on a d2.  Similar to yours maybe. Why not look at this and see if it tells you what you need?  I feel like it might.  Good luck Mike Hudson 

Like Mike I never had a water pump from a 315 apart. But many from a Cat 318 (same vintage, so probably the same design). There is a woodruff key so I don't think it is tapered. But Cat used a lot of tapered shafts so it well could be. The only thing is start looking for new parts if one is tapered and the other part not. Cat still had all the parts for a 318 engine water pump last I needed any. But time flies so could be over 10 years ago.