Blower motor makes a vibrating sound when the fan is set on high

Today, I replaced my uncle's blower motor for the second time. The fan had broken to bits, probably got cracked trying to wedge that sucker in there! That's a tight fit. The problem I need advice about isn't the broken fan, but the fact that the blower motor makes a vibrating sound when the fan is set on high. It kind of sounds like the fan may be touching something, but I don't think that's the case, because it would make the noise on any speed setting, right? It happened with the previous new motor, and I think it's unlikely that both motors were defective. The voltage on it is 12 volts. I'm wondering if the car, being as old as it is, may need a higher voltage. I don't know what the original motor's voltage was, I didn't think to check. Now I wish I had. So, if anyone can clear this up, I'd be very grateful.