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This study investigates the application of ultrasonic vibration-assisted turning (UAT) in machining hardened 9CrSi alloy steel, with a hardness range of 60-62 HRC. The research focuses on the effects of ultrasonic vibration frequency and amplitude on surface roundness and cylindrical accuracy during the turning of a cylindrical workpiece with dimensions of 63mm in diameter and 40mm in length. A piezoelectric transducer (PZT) operating at a frequency of 28kHz and an amplitude range of 5–10$\mu$m was employed to generate the ultrasonic vibrations. Experimental results were analyzed using a 2-sample t-test to evaluate the effects of UAT. The findings show a significant enhancement in surface quality, with surface roughness reduced by approximately half compared to conventional turning (0.705$\mu$m vs 1.302$\mu$m). Additionally, UAT achieved superior geometric precision, with roundness and cylindricity errors reduced by about two-thirds and one-half, respectively, compared to conventional turning (roundness error: 0.00556mm vs 0.01361mm; cylindricity error: 0.026mm vs 0.046mm). The ultrasonic vibrations facilitated the formation of shorter, intermittent chips, reducing the risk of surface scratching and contributing to a longer tool life. Furthermore, UAT demonstrated the potential to operate without lubrication, offering both economic and environmental benefits by reducing costs and minimizing pollution. These results highlight the potential of UAT to revolutionize machining processes by enhancing efficiency, precision, and sustainability. However, it is important to note that while UAT shows promising results, further studies are needed to explore its limitations, such as the impact on tool wear over extended periods of use and the scalability of the process for industrial applications.

Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.