Determination of contact temperature on cutting disc during rock destruction

. During the destruction of rocks by disc cutters the question of their operation without water cooling is arising. To implement this an approach to determining the temperature of the disk cutter is considered in the article. The calculations of heating of the disc cutter with various geometric parameters (diameter, sharpening angles, blunting edge radius) and geological conditions under different cutting conditions (cutting depth) are presented. The disc cutter temperature and comparison with a critical one is given. The results allow to increase wear resistance and thereby determine the modes of operation in which forced cooling of the cutting disc is not required.


Introduction
The most common cutting tool used in roadheaders and shearers is a cutting pick. Cutting picks are well proven in the destruction of weak and medium-strength rocks. At the same time, it was proven that when operating mining performs in difficult geological conditions (the presence of solid inclusions and highly abrasive rocks) it is advisable to destroy the rocks using disc cutters [1][2][3][4]. Different types of cutting drums equipped with such tools are shown in the fig.1. One of the advantages of cutting discs is that the destruction of the rocks occurs in large fractions without the formation of dust. That makes it possible to refuse to supply water under each disc and use only an external spraying system. However, the rejection of local spraying requires the thermal calculation of the disk. The purpose of this calculation is to check for exceeding the critical temperature at which the properties of the metal of the cutting disc can deteriorate.

Materials and Methods
The determination of tool heating is truly relevant for metalworking and in this area has been studied in [5][6][7][8]. There are no detailed studies to determine the heating temperature of cutting disc during rock destruction have been identified. To determine the highest value of the contact temperature at the cutting disc, the formula for determining the temperature at the pick cutter with steady heat flow and free cooling is used as the basis: where q3 -heat-flux density on a contact area, W/cm 2 , Vr -cutting speed, m/min, S -surface contact area of cutting disc and rock, mm 2 , ∆i -linear wear of the tool (for cutting disc is equivalent to the depth of cut h), mm, λr -heat conduction coefficient of cutting disc, W/(cm·K), λp -heat conduction coefficient of rock, W/(cm·K), αp -thermal diffusivity coefficient of rock, см 2 /с.
Heat-flux density on a contact area is where Pf is the friction force on a contact area, N.
where V is the feeding speed of cutting disc, m/min, R is the cutting disc radius, mm. The friction force is determined by Equation where μ is the cutting resistance coefficient, Pk -contact strength of rock, MPa.
where 0 4 is the coefficient of the disk friction on the rock, P -breakaway force, kgf, D -cutting disc diameter, mm, d -cutting disc joint-pin diameter, mm, G -loading force, kgf.
The function 3 S A can be determined by equation where b is the average width of the area contact area of cutting disc and rock, mm.
where ρ is blunting cutter disc edge radius, mm, φ1 and φ2 angles of inclination of generatrix to the axial section for cutting disc with asymmetric cutting-point angles ( fig. 2). To determine the temperature on the tool according to equation (1), it is necessary to determine the contact area of the cutting disc with the rock S. We introduce the coordinate system and find the coordinates of points A and B ( fig. 3). The origin will relate to the center of the disc of radius R.
The contact area of the disk cutter with the rock is part of the conical surface, cut off by a plane + �� ������ � − = 0.
Given that the disc cutter is two conical surfaces inclined at different angles to the axial section, it is necessary to determine the contact area for the angle (fig. 4).
where φ = φ1 + φ2 is angle to the axial section, and expression (12) will look like this: Considering that the asymmetric disc cutter has angles of inclination to the axial section � d � ,, the total, the bilateral surface area will be equal to Thus, the contact area depends on the main parameters of the disc cutter: � � , and the depth of cut h.
To analyze the obtained equations, we determine the temperature of the disc cutter heating for certain conditions and parameters indicated in the Table 1.

Conclusion
The presented calculations of heating the disc cutter with various geometric parameters (diameter, sharpening angles, blunting edge radius) and geological conditions under different cutting conditions (cutting depth) allow us to determine the disc cutter temperature and compare it with a critical one that affects the structure and properties of the disc cutter material, which could lead to a decrease in wear resistance, and thereby determine the modes of operation in which forced cooling of the cutting disc is not required.