By hay rings I'm assuming that you're talking about the round metal/galvanized type that are just put around a standing round bale of hay....
A couple of observations:
First, hay rings are mainly designed to save hay; as in not let cows trample and urinate/deficate all over it. I've read/and seen when hay rings can save as much as a third of the hay put out.
Second, if your calves are getting in the hay rings, is the ring serving it's purpose (to keep animals from wasting hay)?
And third, is the amount of hay you may (or may not be saving) worth the expense of losing calves? As we all know, calves are sky high now... Not like 5 years ago. Today one lost calf could well cost you $500 to $1,000.
There are other type of "hay savers" that will keep the hay off the ground.
Just trying to offer some friendly advice.....
I had posted a hay sled a year or so ago, and it's still working fine.
My homemade example: