The study of fracture theory focuses on the relationship between the work consumed by the fracture and the properties of the material being crushed.
In beneficiation plant, most of the electrical energy used for crushing and grinding operations. In order to gain a deeper understanding of the process of crushing and grinding ore, to evaluate the efficiency of crushing and grinding processes and machinery, in order to find effective crushing and grinding methods, many "theories" about the power consumption in the process of crushing and grinding have been proposed. hypothesis. At present, the more popular ones are: area theory, volume theory and crack theory.
1. Area Theory In 1867, PRRittinger proposed that the energy consumed during crushing is directly proportional to the surface area produced by the material during the crushing process. The area can be expressed by Equation 2-4:
(2-4)
Where A 1 - the work consumed by the fracture;
K 1 - constant;
D K - the average size of the material after it has been broken;
D o - the average size of the material before it is broken.
Broken ratio , then Equation 2-4 can be written as:
(2-5)
The average diameter of the material is determined by the method of adjusting the average diameter. It can be seen from Equation 2-5 that the energy consumption when crushing the material is proportional to the crushing ratio and inversely proportional to the feed size. At the same crush ratio, power consumption is inversely proportional to particle size.
The area says that the energy consumed during the crushing becomes the surface energy. It assumes that all the power consumption overcomes the cohesive force of the material, and only considers the separation work of the lattice surface cracking during the material crushing process, without considering the deformation work, so Incomplete.
2. Volume Theory In 1874, F. Kick proposed that the material was broken into small particles of similar geometry, and the required power consumption was proportional to the volume or weight of the material.
This theory is based on the analysis of the deformation of the material as it is squeezed. When an external force acts on the material, the reaction of the internal stress generated by the material increases as the external force increases. When the internal stress increases to the material strength limit, the material is destroyed and broken. The mathematical formula of volume is:
(2-6)
The size of the material particle size is calculated using the geometric mean diameter.
The volume theory considers the work that the material is subjected to deformation by pressure, that is, the work required to overcome the cohesion is considered. However, the bending strength limit and tensile strength of rock are extremely far apart, and the compressive strength limit cannot be simply considered.
3. Cracks In 1950, FCBond et al. proposed that the ore should be deformed under pressure. After accumulating a certain amount of deformation work, cracks are generated and finally broken. The work required for the fracture is proportional to the crack, which in turn is proportional to the square root of the particle size (diameter or side length). The mathematical expression of the crack is:
(2-7)
The particle sizes Do and Dk before and after crushing are expressed by the mesh size of the Taylor standard sieve in an amount of 80% by weight of the material.
The crack said that the material first deformed under the action of pressure, and the deformation work accumulated to a certain extent. The internal stress of some weak points or faces in the material reached the strength limit, thus causing cracks. At this time, the work (bit energy) of the deformation is concentrated near the crack, so that the crack is enlarged and becomes the work required to generate the fracture surface.
The above three theories respectively explain the certain stages of the crushing process, and therefore only reflect the energy consumption law at a certain stage, and thus each has a certain scope of application. The experimental research proves that the coarse crushing is more accurate in terms of volume theory, and the crack theory is not reliable enough. In the case of fine crushing (when it is broken below 10 μm), the data obtained by the crack is too small, and the area theory is more accurate. In the broad range of coarse and fine crushing, the crack theory is more applicable. The empirical formula of the crack theory is determined by the test of general crushing and grinding equipment , and it is mostly consistent with the medium crushing ratio.
Among the three power theory, the crack theory has great practical significance and application value, because K1 and K2 in the area theory and volume formula respectively represent the deformation work and separation work required to produce unit surface area and unit volume deformation, This is still unclear at the moment. Therefore, the application of these two doctrine formulas is limited, and the crack formula has a wider application value.

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