In this paper, we show how the approach of nonsmooth dynamical systems can be used to develop a suitable method for the modelling of a rotary oil drilling system with friction. We study different kinds of frictions and analyse the mathematical properties of the involved dynamical systems. We show that using a general Stribeck model for the frictional contact, we can formulate the rotary drilling system as a well-posed evolution variational inequality. Several numerical simulations are also given to illustrate both the model and the theoretical results.

中文翻译：

---

具有摩擦的机械旋转钻井系统建模的非光滑方法

在本文中，我们展示了如何使用非光滑动力系统的方法来开发一种适用于带有摩擦的旋转式石油钻井系统建模的方法。我们研究了各种摩擦，并分析了所涉及动力系统的数学特性。我们表明，使用一般的Stribeck模型进行摩擦接触，可以将旋转钻探系统公式化为良好的演化变分不等式。还给出了一些数值模拟，以说明模型和理论结果。