This two-part paper is aimed at developing a theoretical and numerical simulation basis for initial penetration phenomena that profoundly influence hole tolerances and shape. In Part 1, dynamic force models are developed followed by models of the drill’s dynamic behavior in Part 2. Next, these models are combined and used to predict initial penetration behavior and hole shape. A comparison of simulated and experimental results concludes Part 2. In this part, by considering the effects of drill grinding errors and drill deflections, dynamic cutting chip thickness models are developed which, in combination with workpiece surface inclination effects, allow the formulation of expressions for the dynamic chip thickness and cutting chip cross-sectional area. By using these quantities to replace their static counterparts, static drilling force models are extended to facilitate the prediction of dynamic cutting forces. Separate thrust, torque, and radial force models for the major cutting edges, secondary cutting edge, and for the indentation zone are formulated. The effects of drill installation errors on the radial cutting forces acting on the chisel edge and the major cutting edges are also included.

Micro-drills were modeled as long twisted beams. Models for the critical speeds and the critical buckling loads were developed based on the finite element method of analysis. The effects of transverse shear, rotary inertia and gyroscopic moments were included in this analysis. The models have the capability of analyzing a wide variety of geometrical cross-sections. A computer program was developed for the calculation of the variations of the critical speeds and of the buckling loads. The effects of drill geometry, boundary condition, rotational speed, and cross-sectional area on the buckling loads and the critical speeds were analyzed.

Based on the developments in the first part of the paper, numerical algorithms for the evaluation of the engagement models have been formulated. Computational examples are given to demonstrate the validity of the developed models and algorithms. As a problem of pragmatic significance, the sensitivity of the resulting helical groove with respect to the machine setting parameters and tool profile errors has been investigated by means of a mapping from the machine setting or tool profile error space to the resulting helical profile error space.

The problem of helical groove machining in practice is still predominantly approached from an empirical trial and error standpoint. For the analytical resolution of this problem through a CAD approach, a generalized helical groove machining model, utilizing the principles of differential geometry and kinematics, has been formulated. The approach is based on the establishment of the fundamental analytical conditions of engagement between the generating tool surface and generated helical groove surface. The general mathematical relationships established facilitate the determination of the resulting tool or helical groove profile for a given helical groove or cutting tool profile, respectively.

A new drill point geometry, termed the helical drill point, specifically intended for micro-drills, is developed in order to alleviate the disadvantages of existing planar micro-drill points. A mathematical model for this new drill point has been established. It is shown that this model is more general than existing drill point models. The commonly used conical, cylindrical and planar drill point models are only special cases of the helical model. For uniquely determining the grinding parameters of the new drill point as well as guiding the grinder design, the characteristics, the controllability and the sensitivity of the grinding parameters have been analyzed. Finally the geometric characteristics of this new drill point are investigated.

A sensitivity analysis and toierance analysis/allocation of the grinding parameters is presented to guide the design of pianar micro-drill point grinders. The mapping from the desired micro-planar drill point geometry parameter space to the grinding parameter space of the drill grinder has been established to determine a unique grinding parameter set for the desired planar micro-drill point geometry. By means of the sensitivity analysis (variations of the drill point geometry parameters with respect to the grinding parameters), it is indicated which parameters are the most important and most profoundly affect drill point geometry. To specify the upper and/or lower limits of grinding parameter tolerances, and to assure that the total tolerance of the drill point geometry is maintained throughout the desired range, two methods are presented. Tolerance analysis shows the maximal tolerances of the drill point geometry parameters in terms of the maximal tolerances of the grinding parameters. This method requires the tuning of the tolerances ot the grinding parameters until the tolerance ot point geometry are satisfied. As an inverse problem to tolerance analysis, a rational tolerance allocation algorithm is investigated to assigr. the unknown grinding parameter tolerances from the known maximal allowable tolerances of the drill point geometry.