Is there a formula for determining the correlation between kiln feed rate and kiln speed?

No, there is no precise formula for the relationship between kiln speed and feed rate. This depends on the degree of preparation (calcination) of the feed at the kiln inlet and the progression of this feed preparation along the kiln length. However, there are "rules of thumb" and guidelines you can use for various kiln process types. What type of kiln are you operating?

We are having to stop our kiln at frequent intervals because of ring build-ups. When we raise the alumina modulus to 1.7 we have better results. Secondly what's the difference between a snowman and a ring formation.

: Ring formation is caused by the formation of liquids in the kiln at a particular position. These penetrate the refractory lining and cause a localised thickening of the coating. Fe₂O₃ can be a cause of these problems and I am not surprised that raising the alumina modulus has solved the problem. Many cement factories operate with higher alumina modulus than 1.7 and I would recommend keeping the kiln feed mix design with the higher alumina modulus. A snowman is the formation of a large build-up on the first grate of the cooler where the clinker falls from the kiln rather than a build-up in the kiln.