粉砕仕事指数の測定における第3法則の適用
1973 年 89 巻 1023 号 p. 301-305
詳細
1973 年 89 巻 1023 号 p. 301-305
Work index based on the third theory of comminution, presented by F. C. Bond in 1952, has been widely accepted in industry. Bond's method to determine standard ball mill work index Wis was adopted in Japanese Industrial Standard in 1969. According to the method Wis kWh per metric ton is determined by the laboratory grindability test using the following equation:
Wis=44.5×1.1/P10.23×Gbp0.82×(10/√P-10/√F).(1) whereP1 is the opening in microns of the sieve size tested, Gbp is the net grams of sieve undersize produced per mill revolution, Fis 80% passing size in micronsof the new feed, andPis 80% passing size in microns of the sieve undersize product.
Eq.(1) gives practically good results as far as minus 6 meshfeed samples with natural size distribution are concerned. To finer feed, however, eq.(1) may not be apllied. A grindability test which simulated a two-stage grinding indicated that eq.(1) gave an unreasonable value for minus 65 mesh feed (table 1). Applying the third theory to the grindability test, the auther derived a new equation which would be applicable to wide range of feed.
The grindability test is a model which simulates a closed circuit grinding with a circulating load of 250%. According to the third theory, Wis should be calculated from the following equation:
Wis=K/(10/√P-10/√F)×Bp(4)
where Bp is the grams of the sieve undersize product per mill revolution, and K is work input mWh per mill revolution to the test mill on the assumption that its grinding efficiency is equivalent to the standard commercial ball mill, which is an average overflow ball mill of 8 ft inside diameter grindig wet in closed circuit.
Grindability tests on typical minus 6 mesh feed samples informed the following relationship (fig. 1)
K=14+4×Bp×(10/√P-10/√F).(7)
From eqs.(4) and (7), the third theory equation to determine Wis obtained:
Wis=14/Bp(10/√P-10/√F)+4...(8)
It is demonstrated that eq.(8) is equivalent to Bond's equation (1) on standard minus 6 mesh feed (fig. 1), and gives a reasonable value for minus 65 mesh feed as well (table 2). Eq.(8) is considered to be applicable to wider range of feed than eq.(1).
Besides, eq.(8) is considered theoretically to reduce the influence of inaccuracy of sieving. In consequence, eq.(8) is expected to improve the accuracy of Wis determination.
Derivation of eq.(8) revealed that grinding efficiency of the standard commercial' ball mill would vary depending on grinding resistance of feed ores. It is suggestedthat the efficiency is considered to decrease as the grinding resistance decreases.
