Mathematical Approach for Drilling

Abstract

The present paper is on the study of whirling dynamics of the tool workpiece system in a deep hole machining process. An innovative analytical model is proposed in order to carry out simulation studies on the whirling vibrations of the tool workpiece system in a deep hole boring process. At the interaction point of the boring bar-workpiece system there will be an additional displacement in addition to the torque transmitted. This displacement is of a dynamic origin and could be simulated as a wedge introduced between the cutting head-workpiece assemblies. An assumed mode method with the Lagrangian equations was used to derive the mathematical model of the system.