A shape factor based ultrasonic measurement method for determination of bolt preload

The existing ultrasonic testing models cannot accurately measure bolt preload due to the non-uniform distribution of axial stress in the effective stressed region of bolt and cannot rapidly complete the calibration of detection coefficients due to the difficulty to determine the key parameters such as effective stressed length. In order to eliminate the impact of non-uniform distribution of axial stress on the measurement, realize rapid and accurate calibration of detection coefficients and further improve the measurement accuracy of bolt preload, the concept and determination method of shape factor are proposed. Based on the shape factor, a combination of longitudinal and transverse waves is adopted to establish a mathematical model for measuring the preload applied to a bolt during assembly, avoiding the need to measure ambient temperature. The calculation method of shape factor is obtained by statics simulation of a bolted joint. Through the combination of finite element simulation and experimental calibration, the material factors and temperature factors of 45# steel as well as the shape factors of M20 and M16 bolts are obtained. The experiments show that the relative error of this method is within 5%, which meets the requirements of engineering applications. •The shape factor expresses the non-uniform distribution of stress in the bolt.•Temperature only affect the change in time-of-flight of ultrasonic waves.•A combination of longitudinal and transverse waves can avoid testing temperature.•Effective stressed length is related to the grip distance and bolt specifications.•Material factor and shape factor can be obtained by a small amount of tensile test.