Modals to express willingness / unwillingness: WILL, WOULD

Present

Will can express willingness in the present:

I will take you to the airport. I have nothing to do tomorrow.
If you will wait for a moment, I'll see if Mr Hawking is available.

Won't can express unwillingness or refusal:

My bank won't allow me to make international transactions.
Greg just won't answer the phone.
The door won't open.

Wouldn't can express unwillingness or refusal in the past:

I took the phone back to the shop, but they wouldn't give me a replacement.
Try as I might, the door wouldn't open.