Manufacturing Processes  MFRG 315  3.2.3 Work and Efficiency in Metal Forming 

Introduction
Because of the difficulty of accurately estimating friction effects it is sometimes convenient to use a method which gives the minimum stresses and work necessary to perform a process (a lower bound solution) and a different method which gives the maximum likely stresses and work. The true value will lie between these two extremes. The next sections show some of these methods. Note in the above that presenting the expressions (eg: L_{1}/L_{0})so the largest value is on the top, when natural logs are taken gives a positive numerical value whereas with the smaller value on the top when natural logs are taken gives the same numerical value but with a negative sign. As the work done must be positive, it is common to present the ratio so that the larger value is on top. The actual total work per unit volume in a deformation process is significantly greater than that shown above. In addition to the ideal work of plastic deformation, U_{p}, work must be done to overcome friction at the metal  tool interface, U_{f} and to do redundant work, U_{r}. The redundant work is the work involved in internal shearing processes due to non  uniform deformation that does not contribute directly to the change in shape of the body. U_{r} depends upon the geometry of the process and on the friction. The total work per unit volume is given by: Rolling is typically 75  95% efficient whereas extrusion is typically 30  60% efficient. The simple (lower bound) analysis above, which assumes no work hardening, friction or redundant work, gives a theoretical maximum reduction in area of 63.2%. However in practice reductions are usually below 20% in any one stage as friction work and redundant work absorb a significant amount of the work per unit volume and to enable production to run smoothly a safety margin must be allowed in the wire tension to prevent frequent breakage. David J Grieve, 29th October 2008. 