You can often substitute not any for none. Sometimes you can't. Some old-fashioned grammarians cling to the idea that none is singular because of its etymology, and insist that you have to say none is. Most Americans would say None of my friends are wealthy, and most grammarians agree that this is perfectly fine.
In None of this cheese is any good, "none" means the opposite of "all": All of this cheese is good/None of this cheese is good.
"Any" is an adverb modifying the adjective good.
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