Warm-up exercises are meant to loosen up the muscles used in singing. It's best to start on a light voice. No demands, no expectations. Just let your voice wake up before you put it to work.
A lot of singers don't realise that a lot of their voice strain while singing their repertoire comes from simply not warming the voice up before they make it work.
I've had singers come to me and refuse to do any warm-up exercises because they don't see the benefit of them. And then they want to work on some song like "I Will Always Love You" and want me to help them fix the problem of their voice breaking down half-way through the song. Well...
I had a singer come to me once and I said, "Ok, first, let's warm up your voice a bit."
She said, "oh, I don't do warm-up. I just sing. That's what I do." (Well...)
One singer said to me once,
"I don't want to do these warm-up exercises. My voice feels terrible while I do them so I don't see what I'm supposed to get out of it."
Some singers are willing to do them but they start right out forcing their voice to "perform" at full volume and I have to stop them. I usually end up asking the singer how they feel first thing in the morning just after they wake up. Do they like to start their day with a simple routine? Do they like being ordered around and made to do things that they would happily do later once they've woken up a bit, but NOT NOW...?
The reason warm-up exercises don't feel too good is because they are the first thing your singing voice is having to do in it's day. You need to get this out of the way so that you don't experience it during performance. This is just plain logical.
Give it something easy that it knows well and DON'T WORRY if it doesn't feel so good. The main thing is to keep it stress-free. Don't harbour any expectations; it's too soon in your voice's day. And stop whenever you feel any strain setting it, usually around your peripheral range. Your voice will reward you later by performing much better.
Always make your first warm-up a short one. I always stop after a few minutes because I can feel where the current limits are. I could get depressed about it, but I know the next time, say, half-hour later will be easier. On a performance day, I would give my voice many short warm-up sessions (a few minutes) throughout the day. I might have a rehearsal that day, or there's a song I to run through a few times which means a lot more than a few minutes of singing, but this is all easier if my voice is awake and ready.
Everyone has their favourite warm-up exercises. It's a personal thing, but they are basically the same for all of us.