G=gdVt

Where G—the number of ore to be ground, tons;
Gd———the unit production capacity of the grinding machine according to the finished grain size d, t/m ³ • hour;
V———the volume of the grinding machine, m ³ ;
t———grinding time, hour.
From the cited formula, it can be concluded that the decisive parameters for grinding in the mill are unit production capacity and grinding time.
The unit production capacity of the mill is dependent on the variation of the original product and the finished product size and grinding conditions, which can be calculated as follows:

Where Q is the grinding machine production capacity according to the original product, ton / hour;
^-- and α-- are the yields of grinding in grinding products and original products, respectively.
The unit production capacity of the mill depends on the amount of newly produced product calculated from the difference between the content of the qualified product in the original product and the ground material, and is independent of the absolute value of this content. The effect of the yield in the ground material on the unit production capacity is not considered. In calculations, the effects are usually corrected by correction factors or line maps. [next]
Analyze another understanding of the concept of unit production capacity. Since the material in the mill consists of a mixture of the finished product and the product to be ground, the grinding energy of the steel ball or steel bar is proportionally distributed to each product in the mill. In this case, the destruction of the coarse material is only caused by the increase of the finished product, and the other energy and the volume of the mill are not utilized. Therefore, the more coarse material in the grinding machine, under the same other conditions, the grinding machine The total unit production capacity is also larger.
The production capacity of the mill in terms of finished product in relation to the effective utilization of the volume of the mill is referred to as the actual unit grinding capacity of the finished product. In this case, the amount of ground material in the specified particle size can be calculated as follows:

G=qVtβ ⁺ (2)

Where β ⁺ - the material rate to be ground, decimal;
q——The actual unit production capacity of the grinding machine grinding, t/m ³ • hour;
V——milling machine volume, meter ³ ;
T——grinding time, time.
The difference between the unit production capacity of grinding and the total unit production capacity is that the quantity of newly produced qualified materials during grinding is not related to all the ore being ground, but only related to the material to be ground. The ratio of the actual unit grinding capacity to the total unit grinding capacity can be written as follows according to equations (1) and (2):

Both the total unit grinding production capacity and the actual unit grinding capacity indicate the unit growth rate of qualified products during grinding. However, the general unit production capacity is the value that varies along the length of the mill, as the rate of unground material decreases, while the actual unit grinding capacity takes into account the unground material in the mill. The rate, therefore, is based on the belief that the unit grinding production capacity value is close to a constant.
Therefore, the material grinding process represented by formula (2) can be written as a differential equation of the form: [next]

dG=β ^V qdt (3)

In order to simplify the mathematical discussion, we first analyze the open-grinding process plan without prior grading.
The unground product rate (β ⁺ ) in the material ground at the instant of time t can be expressed by the following equation:

Where Q _и - the amount of raw ore to be ground, tons;
a——Qualified milled product rate in raw ore, decimal.
Then the differential equation (3) becomes the following form:
According to the newly grinded material:

Computer numerical control Most CNC milling machines (also called machining centers) are computer controlled vertical mills with the ability to move the spindle vertically along the Z-axis.

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