Oliver Webber

Varying bending eigenfrequencies in BTA deep hole drilling: mechanical modeling using statistical parameter estimation

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes a multi-lobe shaped distortion of the bore hole cross section. An important factor governing the occurrence of spiralling is the coincidence of a bending eigenfrequency of the boring tool with a multiple of the spindle rotation frequency. This article presents a discrete dynamic model of the tool/boring-bar assembly including a Lanchester-damper and containing free parameters for the unknown stiffness of the tools lateral supports. Furthermore, a method for estimating these parameters by determining the changing eigenfrequencies over the drilling depth from spectrogram data using the maximum likelihood method is proposed.

Statistics, Dynamics and Quality - Improving BTA-deep-hole drilling

In this paper we present how statistical experimental design, time series analysis and non-linear dynamic models have been applied to gain a deeper insight into BTA-deep-hole drilling process. BTA-deep-hole drilling process is used to produce long holes of a length to diameter ratio larger than 5. This process normally produces holes of high quality with regard to straightness, smoothness of the boring walls and roundness. However, two dynamic disturbances, chatter and spiralling, are sometimes observed in the process. While chatter mainly results in increased wear of the cutting edges of the tool but may also damage boring walls, spilling damages the workpiece severely. In our study we applied experimental design to gain insight into the connection between process parameters and quality measures like roughness and roundness, while at the same time creating a database for dynamic modelling of the processes. This turned out ot be a very helpful approach because we observed all kinds of dynamic disturbances. In this paper we will focus on chatter which turned out to be dominated by a few (eigen-) frequencies. Two models were proposed to describe the variation of the amplitudes of these frequencies, on the one hand a stochastic differential equation and on the other hand a descriptive model based on piecewise periodogramms. In the latter model the knowledge of the underlying experimental design was used to distinguish between the effects of the assembly of the machine, like damping by the starting bush on the tool, and effects of the dynamics and stochastic influences. Because this model is completely data-driven it can be used as a starting point for the development of a suitable dynamic model of a process.

Spiralling in BTA Deep-hole Drilling: Models of Varying Frequencies

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes holes with several lobes. Since such lobes are a severe impairment of the bore hole the formation of spiralling has to be prevented. Gessesse et al. (1994) explain spiralling by the coincidence of bending modes and multiples of the rotary frequency. They derive this from an elaborate finite elements model of the process. In online measurements we detected slowly changing frequency patterns similar to those calculated by Gessesse et al. We therefore propose a method to estimate the explanation of spiralling in practice because the finite elements model has to be correctly modified for each machine and tool assembly while the statistical method uses observable measurements. Estimating the variation of the frequencies as good as possible opens up the opportunity to prevent spiralling by e.g. changing the rotary frequency.

Koordinierter Einsatz von Sensorik und Statistik

Kurzfassung Das spezielle Verfahren des BTA-Tiefbohrens wurde entwickelt, um lange Bohrungen mit hoher Oberflächengüte herstellen zu können. Auf Grund der sehr geringen Steifigkeiten der dabei verwendeten schlanken Werkzeuge ergeben sich Probleme wie Rattern, Abweichungen im Mittenverlauf und Wellenbildung, die auch Drall genannt wird. Die Oberflächen- und Formfehler stellen eine erhebliche Schädigung des Werkstücks dar. Durch den Einsatz einer speziell an den schwer zugänglichen Prozess angepassten Sensorik wurde die noch weitgehend unbekannte Systemdynamik messtechnisch erfasst und mit Hilfe statistischer und mathematischer Methoden ausgewertet sowie modelliert.

Deriving a statistical model for the prediction of spiralling in BTA deep hole drilling from a physical model

One serious problem in deep hole drilling is the occurrence of a dynamic disturbances called spiralling. A common explanation for the occurrence of spiralling is the coincidence of time varying bending eigenfrequencies of the tool with multiples of the spindle rotation frequency. We propose a statistical model for the estimation of the eigenfrequencies derived from a physical model. The major advantage of the statistical model is that it allows to estimate the parameters of the physical model directly from data measured during the process. This represents an efficient way of detecting situations in which spiralling is likely and of deriving countermeasures.

Modelling and Understanding of Chatter

Recent analysis in chatter modelling of BTA deep-hole drilling consisted in phenomenological modelisation of relationships between the observed time series and appearance of chatter during the process. Using the newly developed MEWMA control chart [4, 5], it has even been possible to predict the occurence of chatter about 30 to 50 mm in advance (i.e. up to one minute before the chatter starts). Unfortunately, no relationships between the machine and model parameters have been detected. Therefore, in this paper a physical model of the boring bar is taken into account. Simulation studies of the regenerative process are performed. These simulated time series show the same characteristics as the data recorded during the drilling process and thus support the validity of our model. By running such simulations, we intend to find strategies for chatter prevention in future work.

Prediction of spiralling in BTA deep-hole drilling: estimating the system's eigenfrequencies

One serious problem in deep-hole drilling is the formation of a dynamic disturbance called spiralling which causes holes with several lobes. Since such lobes are a severe impairment of the bore hole quality the formation of spiralling has to be prevented. Gessesse et al. [2] explain spiralling by the coincidence of bending modes and multiples of the rotation frequency. They derive this from an elaborate finite elements model of the process. In online measurements we detected slowly changing frequency patterns similar to those calculated by Gessesse et al. We therefore propose a method to estimate the parameters determining the change of frequencies over time from spectrogram data. This significantly simplifies the explanation of spiralling for practical applications compared to finite elements models which have to be correctly modified for each machine and tool assembly. It turns out that this simpler model achieves to explain the observed frequency patterns quite well. We use this for estimating the variation of the frequencies as good as possible. This opens up the opportunity to prevent spiralling by e.g. changing the rotary frequency.

Modellierung der Bohrgüte in Abhängigkeit von den Fertigungsparametern beim BTA-Tiefbohren

Das BTA-Tiefbohrverfahren (Boring and Trepanning Association) wurde entwickelt, um Bohrungen mit grosem Verhaltnis von Bohrungstiefe zu Bohrungsdurchmesser bei gleichzeitig hoher Oberflachengute und geringer Abweichung im Mittenverlauf zu erzeugen. In Folge notwendigerweise geringer Steifigkeiten der Werkzeuge konnen Prozessstorungen wie Rattern oder Drallbohren auftreten. Diese Storungen konnen eine erhebliche Schadigung des Werkstucks zur Folge haben. Um eine Datengrundlage fur die Erforschung der Ursachen dieser Vorgange zu schaffen, ist zunachst eine Modellierung des BTA-Tiefbohrprozesses bezuglich zweier Gutemase fur die Bohrungen durchgefuhrt worden. Die Versuchsplanung fur diese Modellbildung und die Ergebnisse aus dem ersten Versuchsplan werden in diesem Bericht beschrieben.