Is it normal to bite during sex

ok so i am with my partner for over 3 years now and our sex life is great but the problem is:
during sex i have developed the habbit of biting my partner.
i never really noticed it at the start but it has now got to the point of when during sex my partner will scream with pain and it is then and only then that i realise that i have been biting her !!

i have to say for myself that i enjoy doing it, i dont know why but i do.
i suppose what worries me is that when i do it i feel i would love to bite right through the skin (this i would never do(i hope))

it is her nipples i feel sorry for the most lol, she really seems to feel it when i chomp down hard on them.

so is this normal ??