# An Interface Pressure Detection Method of Cable Silicone Rubber-XLPE Based on Nonlinear Ultrasound
## 4 Conclusions  
In this paper, nonlinear ultrasonic detection of the pressure at the silicone rubber-XLPE interface was performed by simulations and experiments, and the results showed that:  
1. As the interface pressure increased, the time domain amplitude of the reflected waves at the interface slightly decreased, the fundamental amplitude of the interface-reflected wave frequency domain decreased, the second harmonic amplitude increased, and the ultrasonic nonlinear coefficient increased. Figure 16: XLPE–silicone rubber interface ultrasonic nonlinearity coefficient as a function of pressure. Figure 17: Comparison of theoretical and experimental interface nonlinearity coefficients. 2. For contact interfaces composed of two different materials, ultrasound waves were vertically incident to the interface from both sides, and the nonlinear ultrasound detection results were approximately the same. 3. The use of the relative nonlinear coefficient could effectively achieve evaluation of the pressure state of the flat silicone rubber interface, which provided a new idea for the pressure detection of the interface between the actual cable accessories and the cable body. The authors' use of nonlinear ultrasound techniques allowed for the detection of flat silicone rubber-XLPE interfacial pressures, which provides a basis for research into the detection of interfacial pressure in real products. The shape of the real product resembles a cylindrical shape, and the ultrasonic transducer needs to use a curved probe when performing nonlinear ultrasonic inspection. Alternatively, a device that can be fully coupled to the curved surface of the real sample can be designed so that the curved coupling device is paired with a planar ultrasound transducer for detection. Based on the relationship between the nonlinear coefficient and the interfacial pressure, the magnitude of the interfacial pressure can be deduced from the nonlinear coefficient. However, in the simulation, the authors used equally spaced and sized semicircles to characterize the roughness of the silicone rubber surface, which simplified the silicone rubber-XLPE interface contact state to some extent. The modeling of the silicone rubber-XLPE interface can be improved later to bring it closer to the real situation. During the actual operation of the cable intermediate joint, factors such as interface roughness, temperature, ageing, overfill, and the coupling agent all affect the interface pressure between the cable attachment and the body. The authors have only studied one sample of roughness value in this article so far, and the relationship between the interfacial pressure and the nonlinear coefficient needs to be continued to be investigated for different roughness values. There is also a need to continue to explore the effects of temperature, ageing, and other factors on the nonlinear ultrasonic detection of silicone rubber-XLPE interfacial pressure. In this paper, only a simplified model of 110 kV integral prefabricated cable accessories was investigated. Subsequent studies on cable intermediate joints for medium- and low-voltage distribution networks (e.g., wrapped, cold-shrink, heat-shrink cable intermediate joints, etc.) can be carried out. Conceptualization, C.F. ; methodology, C.F., A.S. and J.L. ; validation, A.S. and J.W. ; formal analysis, A.S.; investigation, C.F., J.L., A.S. and J.W. ; data curation, C.F., J.L., A.S. and Y.Z. ; writing--original draft preparation, A.S., Y.Z. and F.L. ; writing--review and editing, C.F., J.L. and J.W. ; visualization, C.F., R.X. and F.L. ; supervision, C.F., J.L., R.X. and B.O. ; project administration, C.F. and J.L. ; funding acquisition, J.L. and R.X. All authors have read and agreed to the published version of the manuscript. This research was supported by the Open Fund of the State Key Laboratory of Power Grid Environmental Protection (GYW51202201415). All relevant data are included in the paper. This research was supported by the State Key Laboratory of Power Grid Environmental Protection.