i am currently trying to improve my tone. i can get a good tone but i must play for about 10 to 15 minutes to get my throat opened enough to flow enough air to support a good tone. any help on how to push more air or improve my tone would be greatly appreciated

As brass players it is extremely important that we warm-up before we play. Why? well you proved it yourself. it takes 10-15 minutes before you can make good tone. You have to get your mind and body warm before you play. remember to take warm-up slow.

tone in almost any instrument is based on 2 things vibration medium and resonance chamber. Take a guitar put a low gage string on it and you get a brighter sound. Get i higher gague and now you have a darker sound. your lips are the same as the guitar strings. A smaller mouthpiece eg less lips provides a brighter tone where as a big mouthpiece like a bach 5 or 4 1/2 alows more lips and a darker sound.
Resonance chamber...Again like the guitar the size and shape of the resonance chamber greatly affects the sound of the instrument. For us that is not the bell like some of you are thinking it is our mouth and throat. try inhaleing using the p-oh sylable it will open you up and change your sound. Focus on opening up durring your warm up (which should be 15-20 minits) and your tone will improve much faster.
I guess lastly this needs to be addressed if your horn is made of diferent materials it will aslo affect tone quality so next time you are looking for a horn look for somthing that has the charistic tone you want go with a heavy german bell for dark sound or with a light (yamaha) bell for a brighter sound.

Good luck.

Three rules:

1. Air

2. Air

3. AIR

Always use more air. Practice long tones in a long warm up routine, using more air than you are used to. Use as much air as you possibly can, but don`t concentrate on playing loud, concentrate on playing phat.

would getting a mouthpiece with a bigger cup help?

have top plate [3 front teeth ]since accident
tone in middle -lower registers ok
higher register too tight /inclined
to go sharp.any good suggestions ?

Yeah. Open up, don`t tighten up in the upper register. Also, more air might be required. In order to play high don`t think tighten up and scream, think that you are playing for someone 15 or 20 yards furthur, which forces you to think projection and sound instead of just squeking out a high note.

But again, the main thing is air support.

Id recomend lipslurs with tuner. Start in seventh position one overtone higher than a pedal tone and lip slur up 2 octives then back down making sure each note is in tune. then go to 6th position and do the same then 5 4 3 2 1. It will help a bunch. If yo ucant hit the 2octive then only go up to what you can hit.