"What time are you expected to be?" doesn't really make sense because it's unclear. Depending on context, you could use the following:
"What time are you expected to be here tomorrow?" This one works if it's not your friend's choice, but someone or something else that decides when he/she arrives (for example, he/she is flying in and his/her flight is landing at a certain time).
"What time can you be here by?" This one works if you'd like him/her to arrive on or before a certain time.
"What time do you want to come?" This one works if you're allowing him/her to make the choice of time.
"What time can I expect you?" This one works if you want him/her to set an exact time immediately.
I hope this helps you.