Model for the prediction of low-frequency lateral vibrations in drilling process with pilot hole

Abstract

A model that predicts the appearance of low-frequency lateral vibrations in drilling with pilot hole is proposed in this work. These vibrations, called whirling in the literature, are responsible for the generation of lobe-shaped holes during drilling. The present model considers both the influence of the regenerative effect of vibrations on the cutting forces and the influence of the process damping phenomenon that appears along the main cutting edges. In order to model cutting forces, cutting edges are divided into discrete elements and for each of them oblique cutting model is employed. Specific cutting forces at each cutting edge element are calculated as function of cutting speed and normal rake angle value. A new methodology is developed to analyze the motion equation of the drill in the frequency domain in order to predict the appearance of whirling vibrations during drilling with pilot hole. Regarding the depth of cut and the spindle rotational speed, drilling stability limits against low-frequency lateral vibrations are obtained. Moreover, in the presence of vibrations, the model can predict the whirling frequencies that are excited depending on the established cutting conditions. In addition, the stability model is experimentally validated via drilling tests over pilot holes of different diameters for a wide range of cutting conditions. In order to study the appearance of low-frequency vibrations and to avoid the appearance of other vibrations such as regenerative chatter, the analysis is focused on low spindle speed values. A comparison between predicted vibration frequencies and actual frequencies in measured cutting forces during drilling tests is carried out and a good correlation between them is observed.