Rapid solution of Orowan´s equations using a hybrid computer

This paper describes a method of obtaining a rapid solution of Orowan´s equations using a hybrid computer complex. A PDP8 4 K-store digital computer, an analogue computer and associated interface provide the necessary hybrid system. The normal approach to Orowan´s equations is to obtain values of roll force and torque for a known reduction, with no reference to such mill constants as mill elasticity etc. By using the Newton-Raphson convergence technique on three rolling variables, a solution to the equations is obtained in about 500 ms. A simple modification to the hybrid system gives a near-dynamic solution, and the effects of slow variations in the input variables can be studied. By including the input and output tensions to the stand as entry and exit values for the horizontal force, the effects of slow variations in tension can also be established.