In the metal cutting industry it is well known that milling processes can be stabilized by applying different strategies in order to destroy the pure single delay regeneration that arise in case of conventional milling tools when high material removal rates are used either at low or at high cutting speeds. To achieve this goal, variable pitch angle, variable helix angle and serrated tools are already available in the market and serve alternative solutions for process designers to enhance milling process stability. Regeneration can occur and can cause instability on the tip of the deep drilling equipment when the drill bit is driven across hard earth crust materials. This work shows that theories introduced for milling processes can be implemented to improve the stability properties of deep drilling processes, too. Unlike in case of most milling processes, however, the stability properties of deep drilling are affected by the longitudinal and the torsional vibration modes. In this paper, the geometrical and mechanical models are derived for drill bits with general shapes of cutting edges and it is shown that the two DOF dynamics can be described by distributed state dependent delay differential equations. The stability properties are characterized in stability diagrams that can help to select the optimal drilling process parameters.

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