In the paper the theoretical modeling of ultrasonic testing of railway rails with high scanning speed is considered. The model for the calculation of the ultrasonic field generated by the ultrasonic transducers and the pulse echo amplitude received after wave reflection at the defect is developed. The model is based on well-established principles of elastodynamic theory: the Rayleigh-Sommerfeld integral, the Auld reciprocity relation, and the Kirchhoff approximation. It forms the basis for design of computer program to simulate ultrasonic inspections of railway rails with automated mobile systems. The major innovation introduced in the model is taking into account the high scanning speed of the ultrasonic probes over the rail head and the limited repetition rate of the ultrasonic system. The mentioned aspects of the high-speed rail testing require the revision of one of the basic paradigms of the current ultrasonic models, which assume that the scanning speed of the ultrasonic probe is negligible in comparison to the speed of ultrasonic waves propagating in the tested material. Actually, when scanning rails at a speed of 120 km/h, the ultrasonic probe can change its position up to 5 mm between transmitting and receiving ultrasonic pulses reflected from defects located in the rail foot. Such a shift in probe position is not negligible and should be considered in calculations. As a consequence, the ultrasonic system's slow repetition rate and fast scanning speed can make it less likely that certain rail flaws will be found. To quantitatively examine the severity of these phenomena, the new ultrasonic model and related simulation software was developed.
Mackiewicz et al. (Tue,) studied this question.