Preform design in metal forming refers to the design of an initial shape of the workpiece that, when it has undergone an associated forming process, forms the required product shape with desired property successfully without formation of defects and without excessive waste of materials. A carefully selected preform can contribute significantly to the reduction of the production costs. Preform design problems are encountered in various metal-forming processes, such as closed-die forging, shell nosing, rolling, and sheet-metal forming. Design of an optimal preform shape requires simultaneous determination of optimal process conditions. However, we are here concerned with the determination of the best preform shape under a given set of process conditions. In this chapter, a new method of “backward tracing” is introduced as an alternative approach to the solution of preform design, and the applications of this method to some specific processes are discussed. Similarly to the forward simulation technique, the backward tracing method uses the finite-element method. The forward simulation technique has been discussed in the previous chapters. Backward tracing refers to the prediction of the part configuration at any stage in a deformation process, when the final part geometry and process conditions are given. The concept is illustrated in Fig. 15.1. At time t = t0, the geometrical configuration x0 of a deforming body is represented by a point Q. The point Q is arrived at from the point P, whose configuration is given as x0–1 at t = t0–1, through the displacement field during a time-step Δt, namely, x0 = x0–1 + u0–1 Δt, where u0–1 is the velocity field at t = t0–1. Therefore, the problem is to determine u0–1, based on the information (x0) at point Q. The solution scheme is as follows: taking a loading solution u0 (forward) at Q, a first estimate of P can be made according to P(1) = x0 – u0 Δt.
Static Friction in Oil Lubricated Cold Forming Processes
