The drilling of deep holes with small diameters remains an unsatisfactory technology, since its produc-tivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alterna-tive response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropri-ate conditions of use. A dynamic high-speed spindle/drilling head/tool system model is elaborated on the basis of rotor dynamics predictions. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. Investigations are focused on the drill’s torsional–axial cou-pling role on instability predictions. A generic accurate drilling force model is developed by taking into account the drill geometry, cutting parameters and effect of torsion on the thrust force. The model-based tool tip FRF is coupled to the proposed drilling force model into an analytical stability approach. The stability lobes are compared to experimentally determined stability boundaries for validation purposes.68739

1.  Introduction

The drilling of deep, small-diameter holes is an unsatisfac-tory machining operation that results in poor surface quality and low productivity. These drawbacks are mainly related to diffi-culties in evacuating the chips through the drill flute during the cut. Non-productive retreat cycles and the use of high-pressure lubrication are the current industrial solutions used to evacuate chips, but present respectively productivity and environmental problems. New drilling techniques have emerged, based on the tool’s axial vibration, in order to fragment the chips and enhance their evacuation without the need for lubricants and retreat cycles. The self-vibratory drilling technology uses the cutting energy to generate tool axial vibration (Guibert et al., 2008). A specific self-vibratory drilling head (SVDH) excites low-energy chatter vibration for specific process parameters by using a combination of a low-rigidity axial spring and an additional mass located between the spindle and the tool. By tuning both the stiffness of the spring located between the SVDH body and the SVDH vibrating subsystem i.e. the drill-holder, and the additional SVDH mass, the regenerative axial vibrations can be controlled for adequate cutting parameters. These self-excited vibrations must have a magnitude greater than the feed per tooth, which enables the fragmentation of the chips without external adjunction of energy. Changes brought about by controlled vibratory cutting include decreased average force and temperature. The challenge is to tune and keep operating condi-tion in stabilized self-excited vibration at a suitable frequency and magnitude for a good quality of cutting. So, instead of many tradi-tional manufacturing processes, the cutting parameters are chosen to be in the unstable domain.

In this paper an original approach to establishing accurate sta-bility lobes diagram in self-excited drilling operations is proposed. The predicted speed-dependent transfer function of the overall sys-tem, composed of spindle–SVDH–twist drill, is then integrated into an analytical chatter vibration stability approach to calculate the associated dynamic stability lobes diagram.

In Section 2, the spindle–SVDH rotor dynamics model is pre-sented. A special rotor-beam element, developed by Gagnol (Gagnol et al., 2007a,b) in a co-rotational reference frame is implemented. The rolling bearing stiffness matrices are calculated around a static function point on the basis of T.C. Lim’s formulation (Lim and Singh, 1990) and then integrated into the global finite element model. The rotating system is derived using Timoshenko beam theory.