Evaluation of Friction Coefficient by Simulation in Bulk Metal Forming Process

Abstract

With the objective of evaluating the accuracy of the upper-bound theory for calculating the average Tresca friction coefficient m in the hot forging process, we performed simulations using different values of m in each compression process to high strain levels. It was found that the upper-bound theory is not applicable at high strain levels, because the contact surface of the cylindrical sample is composed of an originally flat end surface and the annular portion formed by the contact of the lateral surface with the anvil surface. The relation among $P = {\frac{{R_{m} H}}{{R_{t} H_{0} }}},$ true strain, and m could be expressed by $\left( {a^{\prime} + a^{\prime\prime}\varepsilon + a^{\prime\prime\prime}\varepsilon^{2} - P} \right) + \left( {b^{\prime} + b^{\prime\prime}\varepsilon + b^{\prime\prime\prime}\varepsilon^{2} } \right)m\,+ \left( {c^{\prime\prime}\varepsilon + c^{\prime\prime\prime}\varepsilon^{2} } \right)m^{2} = 0.$ Here, the m values obtained were in good agreement with the actual ones used in the simulations. The value of m of the arbitrary geometry cylindrical sample could also be directly read from a contour map with a relationship among nominal strain, parameter B of the corresponding standard sample, and m.