Effect of Ball Size and Properties on Mill Grinding Capacity
Current ball milling theory suggests that grinding capacity is influenced by the size of balls charged to the mill. In selecting the appropriate ball charge, the first objective is to determine that ball size which will grind the coarse particles most efficiently. This size should be the largest ball size charged to the mill. The second objective is to provide the correct ball size distribution to grind the finer particles in the composite ball mill feed. This objective may necessitate charging a second, smaller ball size with the maximum ball size. The practice of charging a pre-determined ratio of two or more ball sizes to a mill is called rationed ball charging.
Maximum ball size is determined by several factors, including composite feed size, Bond Work Index, mill speed, mill diameter, and circulating load. An empirical equation was published by Azzaroni in 1981 to describe the relationship between these variables. The Azzaroni equation indicates that the correct ball size for the 2.93 m mill is 81 mm. Years of experience show that a 76 mm ball grinds the coarse particles most effectively.
Ball size distribution is governed by the wear law of the mill and by the wear characteristics through the cross-section of the balls charged to the mill. With this in mind, it is interesting to make a qualitative comparison of the ball size distributions which should be generated by 76 mm pearlitic carbon steel balls versus 76 mm martensitic alloy steel balls in the 2.93 m mills.
The 76 mm pearlitic carbon steel balls used have a relatively flat hardness gradient from surface to center. Therefore, the inherent wear characteristic of these balls should be nearly constant during their life in a mill.
Martensitic alloy steel balls are much harder, than pearlitic carbon steel balls throughout their cross-section. However, 76 mm martensitic balls generally have a hardness gradient. This gradient reflects varying amounts of soft transformation products such as bainite and pearlite in the ball micro-structure. The wear rates of these products are higher than that of martensite at equivalent carbon content. As a result, the inherent wear rate of martensitic balls increases slightly at the ball becomes smaller. Therefore, for a given ball mill with a constant wear law, the resultant seasoned 76 mm martensitic ball chart should contain more large balls, fewer small : balls, and less surface area than a seasoned charge of 76 mm pearlitic carbon steel balls. The reduced number of small balls, combined with a lower ball charge surface area, might explain the 6% lower grinding efficiency of a 76 mm martensitic ball charge compared to a 76 mm pearlitic ball charge.
We analyzed the ball size distributions resulting from charging 76 mm pearlitic carbon steel balls versus charging 76 mm martensitic alloy steel balls. This analysis was made using a computer simulation program that Lorenzetti et al described in 1977 to assess ball size distributions. Results for the 2.93 mills indicated that the martensitic steel ball charge should reduce consumption by at least 30%. However, the surface area of the charge should decrease 5% compared to the pearlitic , steel ball charge because of the hardness gradient effect described above.
The apparent correlation between lower ball charge surface area and decreased grinding capacity for martensitic balls warranted further investigation. We recommended a mill test using a rationed charge of martensitic alloy steel balls. The martensitic balls would reduce consumption. The rationed charge would increase the surface area of the ball charge.
The following experimental program was developed:
Conduct preliminary studies to determine a rationed charge.
Conduct a plant test in a 2.93 m production mill.
Compare grinding efficiency (tons ground per hour at a given grind) and ball consumption in the test mill with efficiency and consumption in two adjacent 2.93 m mills.