What is the purpose of a vocal warming up? If you ask singers and conductors this question they will give you more than one reason. There is more to it than only a warming up of the muscles. What you want to achieve with the warming up determines what exercises you do.
For example, a singer would like to prepare his/her instrument for singing and will use a vocal warming up to bring the voice into ‘singing gear’. There are huge differences between the techniques used in speaking and in singing. So a singer might need to make some adjustments to his/her instrument.
For example, you want your soft palate to rise more than when you speak, or you want to sing with a tilted larynx (the classical sound). Most people do not speak with a tilted larynx!
Another very important thing is that while singing your breath support needs to be much more active than while speaking. So breathing exercises are important to allow the muscles to feel/remember what it is like to sing with proper breath support. The liptrill is often used in warming ups.
There is no warming up routine that serves every singer. It depends on your vocal abilities, your voice type, your physical skills, your repertoire, etc. So the best thing you can do is to make your own recipe of favourite exercises that will help you find ‘singing gear’. The exercises on this website all can be very helpfull in your warming up.
In this video Luciano Pavarotti talks about vocalizing; the daily routine to keep the singing voice in shape.