Looking at a few websites, the Rhine switch obviously sends a different voltage to the fan at each speed setting (I was about to ask about the wiring between the switch and the fan). I think you need a VOM to determine if the switch really isn't doing the right thing at the higher settings or if the fan isn't responding well to the higher voltage output.

I'm guessing that is a burnt resistor and I'm making the assumption this is the same problem with the other switch. I can't tell the color bands on it, but it looks like a fairly easy solder job if I can figure out what it is supposed to be.

I'll be honest I don't understand how these things work, I can just identify what is there. It looks like there are only resistors and capacitors and this somehow controls the fan speed.

Which still doesn't answer my question.
Are these standard resistances/capacitances for all industrial fan switches?

Can I replace this with any 4 speed switch?

Do you have an electrical supply store in your area? If so, take that in to them and see if anyone there knows what that may be, and a solution to fixing it. I've done that in the past, and all the electricians in the store shopping helped me out and answered my question. It was like a challenge for them, and they all seemed willing to help! Plus if you need a new one, chances are good they will have what you need. Good Luck!

It may work like the blower motor resistor in a car. On high speed you get full voltage, and the other speeds are set by switching in various resistor values. Since many folks use mostly the lower speeds it often burns up the resistors for those speeds.

The big difference I see (from what is in a car) is that the resistors in a car are mounted so the moving air flows over them. This keeps them cooler and they last longer.

Bruce