Abstract

Continuous models for a fluted twist drill are developed to study its static and dynamic bending characteristics. The static model is numerically simulated within Matlab for point loads at the free end of a twist drill. The bending curves are plotted and the bending stiffness of a twist drill is estimated. Effect of orientation of the spirally fluted cross-section at the fixed end on end deflection is studied. Characteristic bending curves for one pitch length of drill are plotted and region of minimum deflection is identified. Dynamic model is numerically simulated in Matlab over a range of rotating speeds and the first two natural frequencies and corresponding mode shapes are identified for the twist drill. New formulation for estimation of work stiffness is proposed considering the interaction of drill with the hole-wall. A new lumped mass model for studying lateral vibration behavior of the twist drill is developed using this work stiffness. The bending stiffness and fundamental natural frequency estimated using continuous models above and work stiffness calculated using proposed formulation are used in this new model. This model is numerically simulated in Matlab for different set of parameters and drill orbital motions are obtained. Results are analyzed to study the influence of various parameters on dynamics of drill and an explanation is given for generation of lobed holes and drill wandering phenomenon and surface roughness. Torsional stiffness of set of twist drills in clockwise and counter clockwise directions are measured experimentally in order to verify the stiffness symmetry. Appearance of cutting resistance when direction of twist coincides with the direction of cutting leads to periodic change in torsional stiffness of the twist drill during actual drilling. Lumped mass model is developed wherein the effect of this periodic change in torsional stiffness on torsional vibration is studied. Numerical simulations are carried out in Matlab for stiffness change of bilinear and combined linear and half sinusoidal nature. Lateral deflection of drill against hole wall is always associated with a small amount of angular twist. Lumped mass model to study bending-torsional coupling is developed. Numerical simulations are carried out in Matlab and results are compared with results for uncoupled torsional model.