Stochastic and robust modeling of vibration level attenuation in a column drill

Pneumatic column drills are widely used in industrial manufacturing, where vibration significantly affects machining accuracy, equipment durability, and operator safety. This study proposes an uncertainty-aware probabilistic framework for vibration analysis and robust optimization of pneumatic column drilling systems operating under fluctuating industrial conditions. A reduced-order stochastic dynamic model was developed to investigate the influence of parameter variability associated with structural stiffness, damping behavior, spindle rotational speed, and excitation forces on vibration amplification and operational stability. Monte Carlo simulations and Sobol-based global sensitivity analyses identified stiffness and damping variability as the dominant contributors governing stochastic vibration-response dispersion and resonance-sensitive amplification behavior. A robust optimization strategy was subsequently implemented to reduce vibration amplitudes and improve dynamic reliability under uncertain operating conditions. The optimized stochastic configuration reduced the mean RMS vibration amplitude from 2.84 m/s 2 to 1.91 m/s 2 , decreased the response standard deviation by 44.3%, and improved the dynamic reliability index from 1.84 to 2.71. Experimental validation performed on a pneumatic column drill confirmed the physical consistency and predictive capability of the proposed framework, with a mean relative prediction error of 4.6% and a correlation coefficient of 0.94 between stochastic predictions and experimental measurements. These results demonstrate that uncertainty-aware probabilistic methodologies provide a more realistic representation of vibration behavior than deterministic approaches and offer an effective framework for vibration attenuation, reliability improvement, and robust design of pneumatic drilling systems operating under uncertain industrial conditions.