FEM Modeling of Coupled Modes Vibrations and Rock-Cutting Elements Wear in Percussive–Rotary Drilling of Geological Materials

Downhole vibrations are a primary cause of premature wear and failure of rock-cutting elements (RCEs) during well drilling. This study develops an integrated finite element (FEM) model that couples axial and torsional vibrations with the evolution of the wear flat, friction, and temperature. The model is validated against laboratory experiments on a drilling stand using MEMS accelerometers. Two types of tungsten-cobalt (WC-Co) inserts were compared: uncoated and coated with a 3–5 nm titanium nitride (TiN) layer. Thirty tests were performed on granite and sandstone under varying single-RCE weight on bit (WOB = 1.0–2.2 kN) and rotation speed (RPM = 80–120). The TiN coating, by providing a low-friction running-in surface, reduced axial RMS acceleration by 18%, torsional amplitude by 24%, and the steady-state wear rate by 27% (from 0.154 to 0.112 mm/h) in granite. Frequency spectra revealed a resonant torsional peak at 55 Hz when RPM exceeded 120, with torque fluctuations increasing by 240%. A safe operating chart was constructed, defining green (WOB 1.0–1.6 kN, RPM 80–110), yellow, and red zones. The recommended regime (WOB = 1.7 kN, RPM = 105) gives 94% of maximum rate of penetration while reducing predicted wear by 35% compared to the red zone. The model prediction errors are 8–12% for axial and 10–15% for torsional vibrations. This work demonstrates that the proposed laboratory framework, combining nanoscale TiN-coated inserts with low-cost MEMS sensors, enables improved characterization of drilling vibrations and wear and supports the development of practical operating charts for drilling optimization.