Oscillations of dynamical systems applied in drilling : analytical and numerical methods

Kiseleva, Maria Oscillations of Dynamical SystemsApplied in Drilling: Analytical andNumerical Methods Jyvaskyla: University of Jyvaskyla, 2013, 68 p.(+included articles) (Jyvaskyla Studies in Computing ISSN 1456-5390; 181) ISBN 978-951-39-5518-2 (nid.) ISBN 978-951-39-5519-9 (PDF) Finnish summary Diss. This work is devoted to the study of electromechanical models of inductionmotorpowered drilling systems. This is a current issue, as drilling equipment failures cause significant time and expenditure losses for drilling companies. Although there are many papers devoted to the investigation of these systems, equipment failures still occur frequently in the drilling industry. In this study, we continue investigations begun by researchers from the Eindhoven University of Technology, who introduced an experimental model of a drilling system. The model consists of two discs connected to each other by a steel string that experiences purely torsional deformation. The upper disc is connected to the driving part. The lower disc, representing the bottom end of the drill-string, experiences friction torque caused mainly by interaction with the shale. The key idea of the present study that distinguishes it from the previous model was the introduction of more complex equations of the driving part, in particular, considerations of the induction motor. Towards this end, two new mathematical models are considered. The first is a simplified one, its prototype being an electric hand drill. In this case it is assumed that the drill string is absolutely rigid and the friction torque acting on the lower part of the drill-string has asymmetric characteristics of the Coulomb type. The qualitative analysis of this model made it possible to obtain parameters on permissible loads (i.e., permissible values of the friction torque) in case the system remained in operational mode after the shale’s type changes. Using computer modeling, analysis of sudden load appearance was also performed. The second mathematical model focuses on the torsional deformation of the drill during operation. For the friction torque with Coulomb type asymmetric characteristic, local analysis of the system is provided. The author carried out computer modeling of the friction model created by the researches at the University of Eindhoven. In this model, we found an interesting effect represented by hidden stick-slip oscillations. The results of the study have been published in 11 papers.