Axial force measurement of the bolt/nut assemblies based on the bending mode shape frequency of the protruding thread part using ultrasonic modal analysis

Bolt/nut assemblies are commonly used in machines and structures to enable easy assembly and disassembly. However, the axial force (i.e. the fastening force) of such assemblies decreases due to recursive external loading on the bolt/nut assemblies or chronic progressive wearing of the assemblies. Consequently, axial force monitoring is essential in preventing serious failure due to loss of functions in the assembly or fatigue. This study proves that the axial force on bolt/nut assemblies can be measured by investigating changes in the bending mode natural frequency of the bolt's threaded portion that protrudes from the nut (hereinafter referred to as the “protruding thread part“). This method is postulated on the observation that a reduction in the axial force decreases the joint stiffness of the bolt/nut assembly at the protruding thread part, leading to a shift in the characteristic peak frequency of the bending mode. A bolt/nut assembly is formed and its bending mode shapes and bending mode frequencies are obtained by impact tests. A series of tests are performed to define a quantitative measure of the correlation between the shift in the bending mode frequency and the axial force on the bolt/nut assembly. This method enables to perform measurement of the axial force on the bolt/nut assembly of −40 to −50% in the frequency range between 25 and 35 kHz. Dependency of the accuracy of this method on bolt aspect ratio (protruding length/nominal diameter) shows that lower aspect ratios are better suited for measuring axial force via bending mode frequency variation.