Nonlinear Evolution of Natural Frequencies in Premium Threaded Connections Under Varying Contact Stiffness: An Experimental Study

This study experimentally investigates the evolution of natural frequencies of premium threaded connections under varying interface contact stiffness, aiming to establish a non-destructive vibration-based method for evaluating sealing contact conditions. The sealing interface features a sphere-on-cone configuration, and Hertzian contact theory is used to derive the contact pressure distribution, which shows a nonlinear increase in peak pressure with increasing normal load. Modal experiments were conducted under free–free boundary conditions using an impact hammer on a Φ88. 9 mm × 6. 45 mm P110 premium threaded connection. Three make-up torque levels (4081 N·m, 4393 N·m and 4691 N·m) were applied to create distinct contact states, and the first five orders of natural frequencies were extracted from the measured acceleration responses, using frequency response function (FRF) analysis with peak-picking identification. The results demonstrate that natural frequencies increase significantly with make-up torque, following a power-law relationship f = αT^β with R2 > 0. 97 for the first three modes. A critical torque range of 4200–4400 N·m is identified, below which frequencies rise sharply and above which the increase slows due to contact stiffness saturation. Lower-order modes are more sensitive to contact stiffness variations than higher-order modes. The findings confirm that natural frequency can serve as an effective non-destructive indicator for assessing tightening quality and detecting loosening in premium threaded connections, offering practical guidance for torque optimisation and structural health monitoring in oilfield operations. Although only three torque levels are used, the observed trend is physically consistent with contact mechanics theory and widely reported joint stiffening behavior. Therefore, the fitted relationship should be interpreted as a physically guided empirical model rather than a purely statistical fit.