A refined energy ratio method based on ultrasonic echoes for measuring short bolt axial stress

Ultrasonic stress measurement methods play an important role in measuring bolt axial stresses. Traditional Time of Flight (TOF) approaches have accuracy limits when applied to short-bolt stress measurement. This paper proposes a Refined Ultrasonic Echo-based Energy Ratio (RUEER) method for bolt stress measurement that considers internal nonlinear scattering attenuation effects, transmission-reflection effects at the interface area, and energy loss in the transition region. The ultrasonic wave inside the stressed bolt is decomposed into different components to better evaluate the energy attenuation of ultrasonic echoes. The proposed method is verified with stress measurement experiments. Results show that the average error of the proposed RUEER method is less than 2.5% for different bolts and clamping lengths. Through comparative testing, the accuracy of the proposed method demonstrates improved performance over the TOF and Energy Attenuation Method (EAM). Additionally, the RUEER method is more robust to variations in equipment performance than the TOF method.