Assuming your old wiring isn't arcing and about to burn down the house (knock on wood), the problem sounds like a motor mounting problem or just an old, unbalanced motor. Any 'fixes' would be intrusive and unwelcome to the downstairs resident, so when it's annoying, it may be a better idea to raise the ambient noise level in your apartment. You can get a cheap (but high-quality) white noise machine for about 50 bucks.