A prediction of the friction factor for the forging process
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I. INTRODUCTION
FRICTION between the die and workpiece plays an important role in determining the quality of the finished product as well as the life of the die in metal-forming processes such as forging, rolling, extrusion, drawing, and sheet metal working. As a consequence, knowledge of frictional conditions during plastic deformation is essential for the optimum design of dies. From the viewpoint of CAD/CAE, better understanding of the friction behavior can lead to more precise numerical modeling, thus permitting designers to avoid the trial-and-error efforts currently typical of the intermediate stage of die development. In practice, the development of an accurate and efficient method to quantify and evaluate frictional conditions is one of the ways to achieve this goal. Although substantial advances had been made in the evolution of various tests for quantitative evaluation of friction factors in actual on-line forming processes, the procedures are very cumbersome. The need for a more systematic approach is evident, especially for processes conducted at high temperature and high strain rates.[1] With regard to direct experimental measurement of the friction factor, the most commonly used method is the embedded pin technique proposed by Backofen and coworkers.[2,3] In addition to the measurement of the friction factor, Backofen’s method can also measure variations of normal pressure and shear stress. These are determined by using a pair of pressure-sensitive pins installed in a platen. However, the associated experimental setup is elaborate and is also quite expensive to fabricate. Another frequently used technique, the calibration curve method, approaches the problem of friction factor measurement indirectly. This method measures a specific geometric parameter, the aspect ratio,[1,4–6] and from this measurement deduces the friction factor. This is an undeniably useful method, but requires stopping the forging process a number of times in midprocess to make measurements of workpiece deformation. These measured variations in width (radius) and thickness are compared with a set of calibration curves. Each individual calibration curve represents the theoretically predicted workpiece CHORNG-DER LEE, Graduate Student, CHENG-I WENG, Professor, and JEE-GONG CHANG, Postdoctoral Researcher, are with the Department of Mechanical Engineering, National Cheng-Kung University, Tainan, Taiwan, 701, Republic of China. Manuscript submitted September 22, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
dimensions for a given friction factor. The estimated friction factor of the experimental forging is then interpolated from the apparent position of the experimental data between the two closest-matching successive calibration curves. However, as pointed out by Goetz et al.[7] and Dutton et al.[8] empirical calibration curves depend on the actual strain, strain rate, and mechanical characteristics of the material. Thus, calibration curves derived on a theoretical or a semiempirical basis may not adequately include parameters, or
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