Detail carving

Today was my first time doing a two bit carve. The rough carve went flawless using a 1.7 mm straight cut then went to 1.2 mm . The depth setting were the same in each carve but the 1.2 mm seemed to not go as deep leaving a step in the design.
After that I added wording to the design and removing the original design so as not to carve a second time. I used the 1.2 mm for the rough cut and then down to a 0.8 mm for detail at a 60% feed rate Things seemed to be going fine then the bit broke
I am curious is there a formula to determine feed rate with bit size to avoid breaking of bits?