# An Interface Pressure Detection Method of Cable Silicone Rubber-XLPE Based on Nonlinear Ultrasound
## 3 Materials and Methods
### Experimental Setup  
The test system consists of a RAM-5000 SNAP nonlinear, high-energy ultrasonic test system, a 50 \(\Omega\) impedance matcher, a duplexer, a low-pass filter bank, a band-pass filter bank, an oscilloscope, and a computer. In order to receive more harmonic components from the reflected waves at the interface, a longitudinal ultrasonic transducer from Olympus from Changsha Pengxiang Electronic Technology Co. (Changsha, China) with a central frequency of 2.25 MHz was selected for this test, and the bandwidth of the transducer met the test requirements. The pressure measurement device consists of a pressure transducer and a power supply. The pressure platform consists of a hydraulic press, bolts, nuts, springs, and an epoxy resin plate. The pressure value at the silicone rubber-XLPE interface is the product of the pressure sensor indication and the force area of the silicone rubber, as shown in Figure 10.  
Figure 10: Nonlinear ultrasonic test stands. (**a**) Diagram of the test platform. (**b**) View of the test site.  
Figure 9: Experimental materials. (**a**) Silicon rubber and (**b**) XLPE.  
The signal source excited by the system host is passed through a low-pass filter bank, in which the high-frequency signals are filtered out to ensure that the harmonic signals in the interface-reflected waves are not related to the input signal. The primary echo signal containing all frequency components is transmitted directly back to the system host reception port 1 through the duplexer, and the harmonic signal is transmitted back to the system host reception port 2 through the band-pass filter bank.  
Silicone rubber is a high acoustic attenuation material, and for the same frequency of ultrasound, the longitudinal wave has less attenuation and better penetration than the transverse wave, so the longitudinal wave was chosen for the test. In order to receive more of the harmonic components of the reflected waves at the interface, an Olympus longitudinal ultrasound transducer with a central frequency of 2.25 MHz was chosen for this test.  
The system was setup by computer software to generate a Hanning window-modulated signal of 2.25 MHz and 8 cycles. Glycerol was uniformly applied to the surface of the ultrasonic transducer and the sample under test to reduce the energy attenuation of the ultrasonic waves and the nonlinearity introduced by the coupling agent. The hydraulic device was controlled so that the pressure transducer indicated a gradient from 0 MPa to 0.2 MPa, in 0.05 MPa increments. Since it takes at least 30 min for the actual cable attachment to stabilize at the interface, a wait of 30 min was needed after each gradient before performing ultrasonic testing.  
Since the coupling between the ultrasonic transducer and the pattern surface, the test equipment, and other factors will affect the test results, it is necessary to verify the reliability of the test system. Keeping the silicone rubber-XLEE interface pressure unchanged at a certain value, the excitation voltage of the system was gradually increased, and the relationship between the fundamental amplitude, A\({}_{1}\)\({}^{2}\), and the harmonic amplitude, A\({}_{2}\), under different excitation voltages was obtained, as shown in Figure 11. The fitting curve formula was: A\({}_{2}\) = 1.2584103A\({}_{1}\)\({}^{2}\) + 0.0592, and the correlation coefficient, R\({}^{2}\), was 0.993. It can be seen that when the excitation voltage increased, A\({}_{2}\) and A\({}_{1}\)\({}^{2}\) had a good linear relationship, and the stability of the test system was high.