Determining Friction and Flow Stress of Material during Forging

Determination of flow stress and friction in cold forging is of paramount importance. In this work, an inverse procedure is developed for predicting the Coulomb’s coefficient of friction and strain-dependent flow stress simultaneously based on the measurement of bulge and forging load. It is also established that in cold forging Coulomb’s coefficient of friction can be approximated as half the friction factor in Tresca (or constant friction) model. In the inverse procedure, forging load is estimated analytically but bulging is estimated by developing an empirical relation. The efficacy of the inverse procedure is ascertained by the data obtained from finite element method simulations. Finite element method was implemented in ABAQUS and validated with the results available in literature. In most of the cases, inverse procedure provides less than 5% error in the estimates of friction and flow stress. A sensitivity analysis is also carried out to study the effect of measurement error. It is observed that error in the estimation of friction is proportional to error in the measurement of bulge. The novelty of the method lies in the quickness and simplicity of the method.

On the Applicability of Newton’s, Poisson’s and Stronge’s Collision Hypotheses

This paper deals with collision with friction. Equations governing a one-point collision of planar, simple non-holonomic systems are generated. Expressions for the normal and tangential impulses, the normal and tangential velocities of separation of the colliding points, and the change of the system mechanical energy, are written for three types of collision in connection with Newton’s hypothesis, and for five types of collision in connection with Poisson’s and Stronge’s hypotheses. These, together with Routh’s semi-graphical method and Coulomb’s coefficient of friction, are used to show that the algebraic signs of five, newly-defined, configuration-related parameters, not all independent, span eleven cases of system configuration. For each, the ratio between the tangential and normal components of the velocity of approach, called α, determine the type of collision which, once found, allows the evaluation of the associated normal and tangential impulses and ultimately the changes in the motion variables. The analysis of the eleven cases with Newton’s hypothesis indicates that the calculated mechanical energy may increase if sticking or reverse sliding occur, and that regions of α exist for which there is no solution or there are multiple solutions. Regarding Poisson’s hypothesis, there are regions of α, narrower than with Newton’s hypothesis, for which there is no solution. However, whenever a solution exists it is unique, coherent and energy-consistent. The same applies to Stronge’s hypothesis, however for a narrower range of application. It is thus concluded that Poisson’s hypothesis is superior as compared with Newton’s and Stronge’s hypotheses.