Bifurcation and Stability Analyses on Stick-Slip Vibrations of Deep Hole Drilling with State-Dependent Delay

Abstract

To avoid stick-slip vibration, one of the most important forms of self-excited vibrations in deep hole drilling, this paper studies the stability and bifurcation characteristics of a drilling system based on a two-degree-of-freedom discrete model. It is a state-dependent delay model that could describe the non-linear dynamic characteristic of drilling systems more accurately, compared with the traditional constant delay models. In this paper, linear stability analyses of both the state-dependent delay model and the traditional constant delay model are carried out. Hopf bifurcation analyses are then performed by the method of multiple scales. The results show that the state-dependent delay model can provide more precise stability boundaries and more desirable supercritical Hopf bifurcation properties compared to the constant delay model. The control parameters (rotational velocity and feed velocity) will affect these results. It is noted that the method is reliable for deep hole drilling stability prediction and can provide a reference for dynamic optimization design.

Keywords

• stick-slip vibration
• self-excited vibration
• state-dependent delay
• method of multiple scales
• Hopf bifurcation analysis