Chemical and Metallurgical Institute named after Zh. Abishev (Republic of Kazakhstan):

Malyshev V. P., Doctor of Engineering Sciences, Professor, Head of Laboratory
Makasheva A. M., Doctor of Engineering Sciences, Professor, Chief Researcher
Zubrina Yu. S., Assistant

E-mail (common): eia_hmi@mail.ru

The purpose of the study consists in substantiation of a possibility for direct simulation of laboratory and commercial mills operation. In the context of the probabilistic theory of grinding it was established that, because with mill diameter increase collision frequency decreases, and grains breaking increases, scaling factor of grinding rate is determined by counter effect of mill diameter on required collision frequency of balls and grains and upon grains breaking with impact. As a result, extremal dependence of grinding rate constant on mill diameter is formed, permitting to substantiate the maximum identity with respect to grinding rate of laboratory and commercial mills of certain size. It was established that, laboratory mills of smaller diameter simulate operation of larger diameter commercial mills better, owing to equality of frequency and activation factors product with regard to them. Maximum identity with respect to grinding rate falls on batch-laboratory and commercial mills of 1.8–1.9 m in diameter. Stricter correspondence of operational results of both types of mills may be established by additionally taking into account the starting fractional makeup of grinding bodies and ground mill feed material. In the general case, direct calculation of current fractional makeup of ground mill feed material is expedient by means of immediate probabilistic model of grinding with respect to commercial mill’s operational conditions.

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