Determination of the actual deflection of the cutting tool ın turning by the Castigliano theorem

Abstract

The turning method is a widely utilized technique in machining. The effect of machining parameters on the machining quality in turning is quite high. A longer tool overhang reduces tool rigidity, leading to increased tool deflection and subsequently, a decrease in machining quality. The tool overhang should be as short as possible in order to reduce tool deflection and eliminate the negative effects of vibration. Another critical factor affecting machining quality, as much as the tool overhang length is the distance between the main cutting edge and the tool holder axis. In the turning process, the alteration of the main cutting-edge position significantly influences the amount of tool deflection. When the main cutting edge is positioned farther from the tool holder axis, it generates a greater torsional moment effect, which negatively impacts machining quality. However, although the main cutting edge position of the turning tool has a great effect on the machining quality, it has not been adequately explored in the existing literature.This study examines how deflection values vary concerning the deviation of the main cutting edge from the tool holder axis using various methods and compares the results. In contrast to the commonly used deviation equation, this research applies the Castigliano theorem, which provides results much closer to actual tool deflection values. The outcomes derived from the Castigliano theorem are then compared with finite element analysis (FEM) and experimental studies. The proposed theoretical approach aligns well with the experimental results, highlighting the significance of considering torsional moments alongside bending moments as they both play a substantial role in tool deflection.