Analytical estimation of diametral error in turning process considering flexible supports

Abstract

Turning is a fundamental metal cutting process. Diametral accuracy plays a vital role while turning long and slender workpieces. Hence the estimation of diametral error becomes more important for work pieces generally with slenderness ratio greater than six. The diametral error during the turning process is caused mainly by radial cutting force component and tangential cutting force component. Apart from this, it is also affected by cutting conditions, rigidity of the machine tool and type of support condition of the work piece. The main aim of the present research work is to construct an analytical model of turning process and to estimate the diametral error of the work piece. The cutting tool edge deflection is determined based on Euler Bernoulli beam theory. The work piece is considered as propped cantilever beam with flexible supports at the ends. These flexible supports are introduced taking the rigidity of head stock and tail stock into consideration. The radial deflection of the work piece is estimated for different slenderness ratio. It was found that the diametral error was lesser near the head stock end when compared to the tail stock end. This is due to the fact that the rigidity of the head stock higher than the tail stock. The maximum diametral error was found almost in the middle of the work piece. This occurs due to the least rigidity at the center along the length of the work piece. The obtained results are also compared with the literature. A good match was found between the results of the analytical model and published literature.