Did you put the bobbin in correctly for your 15? Some of them rotate clockwise, some counter clockwise as the thread is pulled off. It do make a difference.
You would not believe how many bobbin designs there is.
I don't know of any chart, but right now I have machines that use:
Class 66 - metal and plastic
Class 15 - metal
FW type - ( fits= 9W-7, 221, 222, 301 and can be used in Kenmore 120-491 types.)
White / Kenmore style
A different Kenmore style ( 120-491 )
319 style
Singer T&S white stripe type
Bernina (a really nicely made fancy Class 15 with knurling on the inner hub)
Then there is Janome, Elna, other Singers, and the industrials.
Class 15 L - plastic
Class 15 - plastic
And that don't cover the long bobbins.
The only suggestion I could make would be to go to some of these big wholesale places such as Brewer and steal the pics they have of all the bobbins they sell. Then make your own chart.
Sew-Classic has quite a few bobbins with pictures and listings of what models they fit too. That might help.
Joe