Okay, waiting on some stuff to cook, so....
Happy Mother's Day to the better halves....
To be honest, you don't tend to see a contribution to a ballistics or weapons symposium or conference from an accuracy (cut rifle) barrel maker.
There are contributions from the larger corporate outfits who tend to make hammer forged or mass produced barrels for government and commercial use. Those kinds of barrels and shooting are different than the interests of folks in the context here.
This kind of study was/is generally done by government arsenals, large corporations, or university studies that were funded by one or both of those two.
The vast majority of the work is done for heavier weapon systems, but the general science generated by those studies was roughly applicable to the cut rifle barrels used for accuracy work.
Unfortunately, the most of that work is not free/public domain. The text books are crazy expensive, and the open symposium papers are behind pay walls. Occasionally, you can find some of the lesser work with a literature search when it comes out of a university thesis paper or open literature.
A simple question.
Is barrel wear just a function of velocity or is it based on energy?
You can say it is a simple question.... but that doesn't force Mother Nature to agree. It is not a simple question in reality. Not even close.
Energy in your question is assumed to either be the chemical energy you supply with the primer and propellant, or it can mean the effective muzzle energy that includes both the mass of the projectile and the velocity. So, that isn't going to help with your question till we drill down a little deeper.
In general
So should I increase velocity or increase bullet weight to minimise barrel wear.
You do the opposite on both. Increased velocity is worse, and so is increased projectile weight when the energy level is kept identical.
For example, if we took a 223 using a 55 grain bullet and ran the system at 1300 ft*lbs, and then ran the same system at the same energy but with a 77 grain projectile, the 77 will have higher wear.
Since we are this far down the rabbit hole, let me add that double base powders are worse, and shot tempo that makes a barrel hot is worse.
The simple answer isn't the one you want, but faster is worse than slower. Higher energy is worse than lower.
Anything more specific means we have to get more specific about the question context and details, but that spreadsheet macro that was shared above in post #12 is roughly correct and helps you understand how to compare parameters.
