Physical statistical modelling of bending vibrations

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes holes with several lobes. One explanation for the occurrence of spiralling is the intersection of time varying bending eigenfrequencies with multiples of the rotational frequency of the boring bar leading to a regenerative eect. This eect results from the periodical tilt of the drillhead cutting in each lobe after each revolution and continues in a self exciting manner even when the original causing eigenfrequency keeps changing. We propose a physical-statistical model consisting of a system of coupled dierential equations and allowing the explicit Maximum Likelihood estimation of the modal parameters and by this the implicit estimation of the bending eigenfrequency courses. An extensive simulation for the evaluation of the properties of these estimators and tted courses has now been conducted. It is shown that the results of the model can be improved by tting polynomial local regressions frequency band wise. With the tted eigenfrequency courses it is possible to set up the machining parameters in a way that intersections of specic eigenfrequencies with multiples of the rotational frequency and spiralling correspondingly get unlikely.