This thesis presents the mathematical modeling of drilling mechanics and dynamics in order to improve hole shape accuracy, optimize the drill tool geometry and drilling operations.

The thesis presents prediction of cutting forces, torque, power, vibrations and hole shape as a function of drill edge geometry, work material dependent cutting coefficients, drill structure and drilling conditions. The forces and torque are expressed as a function of chip load distribution along the cutting edge and cutting force coefficients. As the drill rotates and thrusts into the material, it experiences torsional, lateral and axial vibrations. The coordinates of the cutting edges, which generate the cut surface, are predicted by applying cutting forces and torque on the drill's structural dynamic model. The generated surface is digitized, and the chip distribution along the flute is calculated by subtracting it from the surface generated by the previous flute. Hence, the exact model of drilling kinematics and structural dynamics are considered, which leads to integrated simulation of static, dynamic and regenerative chatter vibrations of the drilling process and generated hole surface. The model is also used to investigate the mechanism of whirling vibrations and the hole wall formation by imposing commonly observed whirling motion on the drill. The simulation shows good similarity with experimentally measured cutting forces and hole geometries.

Although it is computationally costly, the numerical model of the drilling process considers the full physical model with true kinematics, dynamics and nonlinearities such as cutting coefficients and tool jumping out of cut due to excessive vibrations. As an alternative, an analytical frequency domain stability analysis for drilling is proposed for efficient generation of stability charts. The stability lobes predicted by the numerical and linear frequency domain models agreed well. Although the models agreed well with the experimental results published in the literature, a sigii nificant discrepancy is observed at practical drilling speeds where the high frequency modes of the drill led to chatter. It is shown that the unmodeled rubbing of the drill's flank with the wavy surface finish and chisel edge contact, i.e. process damping, remains a fundamental challenge in further research.