Research on the Whirling and Vibration Characteristics of Steel–Titanium Alloy Composite Drill Strings for Ultra-Deep Wells

To address whirling- and vibration-induced failures in ultra-deep well drill strings caused by high slenderness ratios and complex loading conditions, this study establishes a nonlinear dynamic finite element model for a steel–titanium alloy composite drill string. The model is discretized with Euler–Bernoulli beam elements and solved using Newmark time integration combined with an iterative node-based spatial solution. Weight on bit, torque, wellbore–wall friction, impact/contact force, and equivalent drilling-fluid damping are considered. The model is used to evaluate how titanium alloy section size, length, wall thickness, and installation position affect whirling, lateral vibration, and torsional vibration. The results show that increasing drill-string diameter reduces the whirling range and lateral vibration intensity; when the diameter exceeds 149.23 mm, wall-impact frequency decreases markedly. Although the titanium alloy section exhibits approximately 60% higher local lateral vibration intensity than the steel section, the upper steel section experiences an approximately 18% reduction in lateral vibration. Installing the titanium alloy section in the middle of the string rather than near the bit reduces the overall lateral vibration intensity by approximately 30% and torsional vibration intensity by approximately 40%. Based on comparative sensitivity analysis, a titanium alloy section length of 1000–2000 m, diameter not less than 139.7 mm, and wall thickness not less than 12.7 mm are recommended for the simulated ultra-deep well conditions. These findings provide quantitative guidance for safer and more stable composite drill-string design.