THE MATHEMATICAL MODEL OF THERMAL PROCESSES OCCURRING DURING INTERACTION BETWEEN ROCK MASS AND ROCK CUTTING ELEMENTS OF DRILLING BITS

摘要

A two-dimensional numerical model of temperature field in the rock mass-cutting element-bit body system is put forward. It is based on the use of the finite element method and the time differential scheme and involves three stages. At the first stage, the calculation is performed in the framework of an axisymmetric model to determine dissipation of heat generated in a bit body and rock mass by heat sources in the cylindrical cutting element-rock mass contact zone. At the second stage, the calculated power of heat sources in the contact zone is corrected using the two-dimensional model in Cartesian coordinates on the strength of the results obtained at the first stage. Finally, at the third stage, the thermal state of the rock mass-cutting element-bit body system in view of the motion of a cutting element of a drilling bit relative to rock mass is calculated in the framework of the two-dimensional model in Cartesian coordinates on the basis of the corrected power of heat sources in the contact zone. The cutting element motion with respect to rock mass is taken into consideration by direct modeling of it. In doing so, temperature in the cutting element-rock mass contact zone is recomputed at each time increment. The results of numerical calculations performed using the proposed model agree well with laboratory measurements of temperatures in a drilling bit cutting element.