The bolt connection is formed by the bolt and nut to exert the axial pretightening force on two or more joints. The pretightening force determines the tightness of the connection. The bolt connection plays an important role in many fields of mechanical manufacturing. There are many micro-protrudes and pits irregularly distributed on the surface of the connecting parts. When the pre-tightening force is applied to the bolt, the micro-protrudes in contact between the upper and lower connecting parts will squeeze each other, and the micro-protrudes between the connecting surfaces will have a certain degree of elastic-plastic deformation under the action of external force, which leads to the increase of the real contact area between the micro-protrudes, and then the real contact area between the plates will also increase.

Based on the Hertz contact theory analysis, literature [13] finds that within a certain range of preload, the real contact area between the joint surfaces increases with the increase of axial preload. The ultra-sound wave propagates through the part where the micro-convex bodies between the bonding surfaces contact each other. Therefore, the actual contact area between the joint surfaces of the two connectors is in a positive proportional relationship with the transmitted signal energy of the ultrasonic wave. However, when the pre-tightening force increases to a certain extent, the contact area between the joint surfaces reaches the maximum because the micro-convex bodies between the connectors are basically flattened. The energy of ultrasonic transmission signal gradually approaches saturation state and does not change.

Here, ultrasonic surface wave transmission signal energy is used to detect the attenuation of bolt axial force, as shown in Figure 1. For the bolt-connected lap plate structure, the surface wave excitation signal is generated by the wave inclined probe on the surface of the upper plate, and transmitted to the lower plate through the micro-convex body contacting each other between the joint surface of the two connecting plates, and received by the surface wave inclined probe of the lower plate. The relationship between the axial force of the bolt and the transmission signal energy of the surface wave is obtained, and the actual contact state of the micro-convex body on the joint surface is known. Then the attenuation of bolt axial force can be detected quickly and the loosening of bolt connection can be monitored online in real time.