ON THE MATHEMATICAL MODEL OF DEEP-HOLE DRILLING

A closed system of nonlinear differential equations describing the process of deep-bole drilling is derived, Torsional and longitudinal vibrations of the cutting part of a drill due to the parameters being distributed along the drilling tube are taken into account. The formation of cutting forces is considered with the shearing angle calculated on the basis of the minimum supplied power and elementary forces integrated over the entire cutting perimeter taking the specific features of each segment operation into account. The force interaction betvreen the blade and the workpiece is described by the Zener model, and the thermal phenomena are taken into account by introducing the thermal resistances of the channels. Thermal influence on a point of the workpiece surface is viewed as a time-dependent process.