English Modals

What part of speech represents the phrase "It is time... " and where can I find it for a more introspective study

[tony1_hk]

This is the reply from my tutor:

The question basically says that although all three can be used to give
ADVICE, is there any difference (however slight) among the three? Have a look at what the grammar books or websites have to say.

So, any other suggestions?

[rewboss]

should = it would be a good idea to do this

ought to = if you want to show that you are a virtuous person, you will do this

had better = if you don't do this, something unpleasant will happen to you