How does the content of chromium have influence in quality and performance of grinding balls? Is it better a low content of this metal to improve hardness in balls?

If the grinding balls contain chromium then they are forged, hard grinding balls. If the balls don't contain chrome then they are softer mild steel and the wear rate will be higher. Balls containing chrome cost more but last significantly longer and maintenance of the optimum media loading in the mill is easier. Many cement companies use soft media for raw grinding as the wear on the steel simply increases the iron content of the raw mix slightly. Most cement companies use hard media for cement grinding as the wear rate on soft media when grinding clinker is too high and the mills need continuous recharging.

What are the relationships between clinker hard burning and grindability of clinker. Is hard burned clinker hard to grind? Finally what is the relation between silica mudulus(SM), iron modulus, time of storage of clinker, size of the clinker.

When clinker is hard burnt the amount of liquid phase increases and the clinker becomes very dense and fused together. This is the reason why hard burnt clinker is hard to grind. High silica modulus means low liquid content therefore softer clinker. High iron content means more liquid so possibly denser and harder clinker. If clinker is stored for a long time then it can become hard to grind due to "relaxation" of the clinker. Large clinker implies hard burning and agglomeration into large balls so might well be hard to grind.