Now we come to the third (and most problematic) part of working on the horn/mouthpiece buzzing/free buzzing triumvirate,free buzzing (buzzing without the mouthpiece).
Free buzzing can be VERY destructive if done incorrectly, and equally constructive if done correctly. It should be approached with the utmost caution because a wrong approach or initial overuse can really screw up an embouchure.
I speak from direct experience here. Free buzzing always seemed like such an elegant IDEA to me that I kept on trying to use it for over 15 years, but every time I'd start I'd have to stop after a couple of days because my playing would begin to radically suffer. Eventually I believe I began to get the concept sorted out, and now I use it regularly to great advantage.
Here are some questions and answers regarding this topic:
Regarding free buzzing, some people have recommended buzzing my lips without a mouthpiece as a way of warming up, making my pitch more centered, etc., but others have claimed this will make my lips "too loose." The latter advice came after about a year of practicing and becoming rather accurate in buzzing pitches in tune and in a wider range, so I would question it.
You'd do well to question it.
If it works, USE IT.
If you ALWAYS relate your buzz to your mouthpiece and/or rim in increments of only a few seconds, you will neither stiffen nor loosen your lips any more than they NEED to be stiffened or loosened. Buzz off the mouthpiece (which can either be in or out of the horn, I use both), then, while continuing the buzz, place the mouthpiece on your embouchure. Next, with out taking the mouthpiece off your lips, do the opposite: buzz a note ON the mouthpiece (and/or on the horn) and then, while continuing the note, take the mouthpiece off your lips. You can then progress to simple exercises or etudes using the same approach, and ultimately to studies that travel through all the technical demands of making music.
These exercises will be much more difficult in some ranges than in others, and free buzzing in some registers (different ones for different people) will often result in extremely unfamiliar and seemingly "wrong" lip settings.
These "wrong" settings are in fact a direction toward which your "normal" setting could probably profitably travel, and the ultimate playing settings that will result from continued pursuit of these techniques will be compromises between the way(s) your lips most naturally play different registers without the mouthpiece and the demands put upon you by the mouthpiece, the horn, and real performance.
There are myriad ways to buzz your lips. Many are radically different from anything you'd want to do to play a brass instrument, so your first task is to be sure that what you're doing functions with the mouthpiece and with the horn.
Regarding free buzzing, you can most simply envision the rim as a fence, beyond which the aperture should not extend. If you buzz a note with an aperture of 3/4", but your rim is only 1/2" wide, that embouchure, no matter HOW strong the buzz, won't function when placed in that mouthpiece. The rim will stop the vibration, just like a finger will stop a vibrating string.
Another thing to think about is that at the upper and lower extremes of range, volume, and endurance, the embouchure, no matter HOW strong, NEEDS the rim as a surrogate ring of muscle for definition and restraint. You can EXTEND the upper and lower limits of where that need will begin to occur, but inevitably, at any and all extremes of playing, it will appear.
You can very profitably discover new approaches to playing, and develop muscles that you never would have known existed, by buzzing without the mouthpiece, but you can also destabilize your embouchure to the point where you can create serious playing problems as well.
Only do this buzzing outside the rim or mouthpiece for a few minutes a day at first, constantly checking back to see if your buzz will function in the mouthpiece, and if over a few days or weeks you begin to see detrimental results in your playing, STOP, at least until you've regained your normal balance.