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.
Highlights
Delay differential equations (DDEs) often appear in various fields of science and engineering, such as control systems [1], lasers [2], neuroscience [3] and cutting process dynamics
This paper mainly studies the non-linear dynamic stability of the deep hole drilling in coal seam gas exploitation
In order to study the influence of non-linear state-dependent delay on deep hole drilling systems, this paper studied and compared the stability of constant delay (CD) and SDD models through the lobes diagram
Summary
Delay differential equations (DDEs) often appear in various fields of science and engineering, such as control systems [1], lasers [2], neuroscience [3] and cutting process dynamics. In order to study the influence of non-linear state-dependent delay on deep hole drilling systems, this paper studied and compared the stability of CD and SDD models through the lobes diagram. Liu and Balachandran [36,37] carried out a stability analysis using a semi-discretization and constructed a stability volume in the three-dimensional parameter space of spin speed, cutting depth and a cutting coefficient They used a two degree-of-freedom model and a multisegment model of drill strings with state-dependent delay. A two-degree-of-freedom model considering axial and torsional vibration was established, and the linear stability and the characteristics of Hopf bifurcation of the drilling system were studied by using the method of multiple scales.
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