They found that the theory and experimental models were in good agreement, indicating  
Figure 1: Flange fastening device: (**a**) disassembled, (**b**) assembled. that fluid layer thickness can be measured with acoustic reflection technology, providing some technical guidance for measuring air layer thickness in subsequent measurements. [PERSON] et al. [10] successfully measured the thickness of layered materials using the phase of the ultrasonic reflection coefficient spectrum and the particle swarm optimization inversion algorithm, demonstrating the application of the ultrasonic reflection coefficient in material thickness measurement. [PERSON] et al. [11] successfully measured the thickness of porous material coatings using ultrasonic complex reflection coefficients, successfully applying acoustic reflection coefficients in engineering measurements. Currently, domestic and foreign scholars mainly analyze the change in interface acoustic reflection coefficients under different contact states based on the acoustic theory between multilayer media [12]. With the continuous development of acoustic and finite element theories, the coupling calculation of multiple physical fields in finite element simulation software is more accurate and efficient, enabling acoustic reflection technology to be widely used in engineering practice. The previous studies were mainly conducted under the condition of vertical incidence. However, in practical industrial applications, it is difficult to ensure the vertical contact between the ultrasonic transducer and the tested workpiece due to mechanical structure and working environment constraints. As a result, the incidence angle varies with different working conditions. To enhance adaptability, it is necessary to establish a functional relationship between the air gap thickness and the resonant frequency at any incident angle. This can help to overcome the limitations of vertical incidence and provide more flexible and accurate measurements in non-destructive testing for mechanical engineering, acoustics, and other related fields. This article proposes a multi-angle incidence measurement method suitable for practical engineering applications based on previous research on the measurement method of the reflection coefficient, which greatly solves the inconvenience caused by the geometric dimensions and positions of the objects being tested. This study focuses on the separation state of the interface between the flange cover and the silicone sealing gasket in the flange fastening device, and establishes a finite element simulation model for vertical incidence. The first-order resonance frequency under different air layer thicknesses is solved by the theory of sound reflection, and the results show good consistency between theoretical calculations and finite element simulation results, indicating the effectiveness of the vertical incidence finite element simulation model. Furthermore, a multi-angle incidence measurement simulation model is established, and analytical expressions for the air layer thickness and its first-order resonance frequency under different incidence angles are derived to verify the reliability of the multi-angle incidence measurement model, providing a new approach for subsequent practical engineering testing methods.