The first two Grinding Efficiency Measurement examples are given to show how to calculate Wio and Wioc for single stage ball mills. Figure 1. The first example is a comparison of two parallel mills from a daily operating report. Mill size 5.03m x 6.1m (16.5′ x 20′ with a ID of 16′).
This example shows that Mill 2 is slightly more efficient than Mill 1 even though it has a higher power consumption per tonne. This shows the use of the work index equation taking into account the differences in feed and product sizes. The calculation is only part of the total plant performance study and must be tied into the total plant operation.
The next example covers an in-plant study on the effect of mill speed on mill performance. The two speeds being studied are 68% and 73% of critical speed in 5.03m (16.5′ diameter inside shell 16′ inside liners) ball mills. This study was over a period of four months. Grindability tests were run on monthly composite samples of the feed to each mill. The operating data, test data and calculations are given in Table III.
The data given in Table II can be compared in several ways. A comparison based upon power per ton consumed is given in Table IIIA. This shows the difference in power per ton of mill circuit feed consumed without taking into account the variations in mill circuit feed, mill circuit product and grindabilities as shown in data tabulated in Table III.
Eliminating variations in mill circuit feed and product, Table IIIB shows the comparison based upon the work index calculated from the operating data (Wio).
The next comparison eliminates the variations caused by differences in the grindability of the ore. This is the more accurate comparison as it compares grinding circuit performance as referred to a cannon base or reference. Table IIIC gives the comparison based upon Wioc/Wi.
The next two examples are for rod mill ball mill circuits. Figure 2 shows a conventional rod mill-ball mill circuit. The data for this circuit and Wi0 calculations are:
- Rod mill size 3.5m x 4.88m (11.5′ x 16′ diameter inside shell 3.35m-11′ 4.72m 15.5′ rods)
- Ball mill size 4.72m x 4.88m (15.5″ x 16′ diameter inside shell 4.57m-15′)
- Rod mill feed produced by closed circuit crushing micrometers 14,500
- Rod mill product micrometers 1300
- Ratio of reduction 11.15
- Rod length to mill diameter ratio 1.409
- Optimum ratio of reduction 15.05
- Power per metric tonne motor input Kw 4.2
- Motor efficiency % 95.6
- Calculated operating work index Wi0 21.62
- On basis motor output x 0.956 20.67
- On basis short ton x 0.9074 18.76
- Diameter factor ÷ 0.939 (EF3) 19.98
- Low ratio of reduction EF6
1 + (11.15 – 15.05)²/150 = 1.101 (divide) 18.15
Wioc 18.15 - Rod mill grindability test results Wi 15.0
- Efficiency factor Wioc ÷ Wi 1.21
- Grinding Efficiency in % 82.6
- Ball mill feed micrometers 1300
- Ball mill product micrometers 115
- Ball mill ratio of reduction 11.3
- Power per metric tonne motor input Kw 9.2
- Calculated operating work index Wio 15.75
- On basis motor output
4.2 x 0.956 + 9.2 x 0.947 = 12.73 Kw/tonne
15.75 x 12.73 ÷ 13.4 14.96 - On basis short ton x 0.9074 13.58
Diameter Factor ÷ EF3
9.2/13.4 x 0.914 – 0.925 to = 0.925 14.68 - Rod mill low ratio of reduction
1 + .101 x 4.2/13.4 = 1.032 14.22
wioc 14.22 - Ball mill grindability test results Wi 14.3
- Ball mill grindability test results Wi 15.0
- Combined 15.0 x 4.2/13.4 + 14.3 x 9.2/13.4 14.52
- Efficiency factor Wioc ÷ Wi 0.979
- Grinding efficiency in % 102.11
This shows the rod mill is inefficient while the ball mill is performing efficiently better than indicated from the grindability test results, with the overall circuit operating in line with grindability test results.
Figure 3 shows a rod mill-ball mill circuit with a concentration step between the rod mill and the ball mill with the tailings being removed from the circuit. There is also a concentration step between the ball mill and the classifier. In determining grinding efficiency, each stage is considered as a single stage. The power per tonne for rod milling is determined from the rod mill feed rate and the power per tonne for ball milling is determined from the ball mill feed rate.
Note the efficiency factor of 1.22 lines up with the 1.2 factor recommended for selecting rod mills for rod milling circuit when feed is produced with closed circuit crushing.
The four examples were given to show how the Bond work index equation can be used to evaluate grinding mill performance, report mill operating data and evaluate in-plant grinding studies.
