Estimation of the ultrasonic time-of-flight for evaluating the axial force acting on bolt/nut assemblies under various mechanical and thermal conditions

Abstract

The ultrasonic testing method is a prospective technique adopted for measuring the axial force acting on a bolt; the method is a nondestructive testing method employed for structural health monitoring. In ultrasonic testing, the ultrasonic time of flight (ToF) is obtained, and the axial force is computed using the mathematical relationship between the ultrasonic ToF and the axial force acting on the bolt. Therefore, it is essential to accurately compute the axial force from the ToF. However, existing theoretical equations do not reflect actual scenarios that bolt/nut assemblies may encounter under varying mechanical and thermal conditions. Therefore, the practical application of this method in engineering practices is limited. Establishing a mathematical relationship by considering mechanical and thermal deformation could serve as a fundamental solution for providing more accurate axial force measurement results in ultrasonic testing. In this study, we proposed calibration equations that could be applied to various types of bolts, which are primarily used in mechanical components. The calibration coefficients obtained from the experiments were substituted into the theoretical equations to improve the estimation accuracy of the ultrasonic ToF. Additionally, we compared the experimental results acquired using various types of bolts: M8, M10, M12, and M14, with the results obtained from the theoretical equations using the calibration coefficients. It was verified that it could make the axial force measurement of the bolt accurate as a calibration of the change of the ToF by the bolt deformation from the mechanically stressed region and the thermal conditions with 8.8% error. We expect that the theoretically and experimentally verified calibration equations can improve the reliability and robustness of mechanical components.