Abstract

This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate drilling-induced vibrations, by considering idealized drag bits characterized either by multiple angular offsets between the blades or by a combination of full and partial blades, a departure from the symmetric bit of the RGD model consisting of multiple continuous blades. The RGD model is built on a two-degrees of freedom discrete representation of the drillstring combined with a rate-independent bit/rock interaction law. By relaxing the original constraints on the bit geometry, the coupled state-dependent delay differential equations governing the angular and axial motions of the bit now contain multiple state-dependent time delays. A linear stability analysis leads to explicit expressions for the critical rotational speed(s) defining two different regimes of stability of the coupled dynamics. Stability maps indicate that both groups of bits have a better axial stability than their RGD counterparts. It is also found that multiple critical rotation speeds exist for certain bit geometries, in contrast to the single axial stability boundary of the original RGD model. Time simulations confirm the predictions of the linear stability analysis and show evidence of the existence of different types of quasi-periodic responses before the establishment of a limit cycle characterized by both axial and torsional stick-slip events.

中文翻译：

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钻头设计对旋转钻井系统稳定性的影响

摘要

本文扩展了Richard等人最初提出的RGD模型。（J Sound Vib 305（3）：432–456，2007，https ://doi.org/10.1016/j.jsv.2007.04.015）通过考虑理想化的阻力钻头来研究钻井引起的振动，这些阻力钻头的特征在于叶片之间的多个角度偏移或全部和部分叶片的组合，这与包括多个连续叶片的RGD模型的对称钻头不同。RGD模型建立在钻柱的两自由度离散表示以及与速率无关的钻头/岩石相互作用定律的结合上。通过放宽对钻头几何形状的原始约束，控制钻头角向和轴向运动的耦合的与状态有关的延迟微分方程现在包含多个与状态有关的时间延迟。线性稳定性分析得出用于临界转速的明确表达式，这些转速定义了耦合动力学的两种不同的稳定性状态。稳定性图表明，两组钻头均比其RGD同类钻头具有更好的轴向稳定性。还发现，与原始RGD模型的单个轴向稳定性边界相反，对于某些位几何形状，存在多个临界旋转速度。时间模拟证实了线性稳定性分析的预测，并显示了在建立以轴向和扭转粘滑事件为特征的极限环之前存在不同类型的准周期响应的证据。