With the development of high-pressure, high-temperature wells, the sealability of premium connections is being threatened by heavy loads. For the sake of researching the sealability of premium connections at the microlevel on the sealing surface, a rough profile was characterized according to a fractal function, and the influence of the fractal parameters of contact behavior on the rough surface was analyzed. A full-size premium connection model with a fractal surface FEM was established using ABAQUS software to analyze the Von Mises stress and contact pressure, and the sealability was then analyzed using contact strength theory. It was found that utilizing fractal functions to describe the rough morphology on the sealing surface of premium connections could reveal the contact behavior of the sealing surface more realistically. The premium connection’s fractal FEM was closer to the actual situation, considering the effect of the asperities’ elastic–plastic deformation on the sealability. The fractal dimension D had a greater influence on the contact area and contact pressure than the scale coefficient G. When the fractal dimension D was less than 2.5, the maximum Von Mises stress and maximum contact pressure on the sealing surface were 8.81 × 10⁸ Pa and 1.20 × 10⁹ Pa, respectively, making the surface prone to gluing. The sealability of the premium connection was primarily affected by the axial tension. When the axial tension was 1.2 × 10⁶ N, the sealing surface experienced significant displacement along the axial direction, the effective contact length reduced from 2.72 × 10⁻³ m to 2.24 × 10⁻³ m, and the maximum contact pressure reduced from 8.10 × 10⁸ Pa to 6.39 × 10⁸ Pa, which led to a 30% decrease in sealing strength, which may pose a high risk of sealing failure. When the internal pressure reached 1 × 10⁸ Pa, the effective contact length increased from 9.08 × 10⁻³ m to 1.06 × 10⁻² m, the maximum contact pressure increased from 8.67 × 10⁸ Pa to 1.37 × 10⁹ Pa, and the sealing strength increased by 23%.

Traditional static analysis cannot effectively explain the issue of the sealing performance of the premium connection being decreased due to the vibration of the tubing, leading to the failure of the connection sealing. In this paper, based on the energy dissipation theory and considering the influence of the micro contact slip of the sealing surface under the vibration of the tubing, a finite element model of the premium connection is established. The natural frequency and vibration mode are obtained through modal analysis experiments, and the accuracy of the finite element model is verified. The results show that the first five natural frequencies are mainly concentrated in the axial direction of the tubing, with the amplitude of the radial vibration mode being small. The vibration mode results are applied to the model as boundary conditions. It is found that an increase in the axial displacement amplitude leads to an increase in the energy dissipation of the sealing surface of the premium connection, which reduces the normal contact pressure and the effective length of the sealing surface, ultimately leading to a decrease in the sealing performance.

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.