The magnetostrictive guided wave technology as a non-contact measurement can generate and receive guided waves with a large lift-off distance up to tens of millimeters. However, the lift-off distance of the receiving coil would affect the coupling efficiency from the elastic energy to the electromagnetic energy. In the existing magnetomechanical models, the change of the magnetic field in the air gap was ignored since the permeability of the rod is much greater than that of air. The lift-off distance of the receiving coil will not affect the receiving signals based on these models. However, the experimental phenomenon is in contradiction with these models. To solve the contradiction, the lift-off effect of receiving the longitudinal mode guided waves in pipes is investigated based on the Villari effect. A finite element model of receiving longitudinal guided waves in pipes is obtained based on the Villari effect, which takes into account the magnetic field in the pipe wall and the air zone at the same time. The relation between the amplitude of the induced signals and the radius (lift-off distance) of the receiving coil is obtained, which is verified by experiment. The coupling efficiency of the receiver is a monotonic decline with the lift-off distance increasing. The decay rate of the low frequency wave is slower than the high frequency wave. Additionally, the results show that the rate of change of the magnetic flux in the air zone and in the pipe wall is the same order of magnitude, but opposite. However, the experimental results show that the error of the model in the large lift-off distance is obvious due to the diffusion of the magnetic field in the air, especially for the high frequency guided waves.
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