Multi-response Optimization of Ultrasonic Case Depth Measurement

This paper presents a methodology for optimizing the parameters of the immersion ultrasonic backscattering technique used in measuring the case depth of induction-hardened parts. The accuracy of an immersion ultrasonic backscattering technique is governed by two major parameters: the probe angle and probe distance from the part surface. The required equations are derived to calculate the probe distance based on the focal length of the probe. A design of experiments (DOE) process is also performed by conducting 81 tests on three surface-hardened steel shafts, to identify the significant factors affecting the measurement results. The findings demonstrate the effectiveness of the probe angle, probe distance and their interaction in the backscattering technique. The desirability function approach is then used to optimize the multi-response results of case depth measurements. The optimal settings for this specific case are determined as a probe angle of 16° and a probe distance of 10 mm, resulting in a desirability function value of 0.90. The methodology introduced in this paper can be applied to other backscattering applications, providing optimal configurations for ultrasonic testing, and improving measurement accuracy.