Calculation of Rolling Load and Torque in the Hot Planetary Rolling Mill

Abstract

This paper presents a completely new approach to the mechanics of the Sendzimir hot planetary rolling mill. Previous work on this subject, by R. Tovini, included determinations for the distribution of the advance of the strip, the draft, the rolling load, the torque and the horizontal backthrust for the whole range of positions which the planetary rolls made, whilst contacting the hot metal. The new approach differs vastly from that of Tovini, the main four differences being as follows. First, whereas the method of Tovini is based upon the forward displacement of surface metal, as a ripple, along the surface of a rigid core which extends in the central portion of the metal for the full length of the working arc, the new approach assumes that the plastic zones between the planetary rolls extend from each roll to the centre of the material. The effect of this assumption is that the local deformation due to a pair of planetary rolls can be considered as an extension which is effectively uniform throughout the thickness of the strip which is instantaneously between the planetary rolls. Secondly, the method used by Tovini is one of successive approximations to obtain values for the advance of the strip, whereas the new method finds a close approximation for the advance of the strip by direct analysis. Thirdly, Tovini neglects the friction hill in roll load and torque calculations and uses the mean strain rate for the equivalent simple roll in order to calculate the mean yield stress, whereas the new method defines and uses both local and overall mean strain rates, these being necessary to obtain a realistic value for the resistance to deformation. Fourthly, in Part 1 of Tovini's paper, intermittent advance of the strip was assumed, whereas in the present method uniform entry speed is assumed and it is then shown how the results for any distribution of entry speed can be obtained by superposition. (In Part 2 of Tovini's paper continuous advance of the slab is briefly considered but, the process is not analysed in detail.) Appendix I shows a method of tabular calculation, which gives results for the distribution of roll separating force, torque and backthrust for the whole range of angular positions during which a pair of planetary rolls contact the strip or slab. From these results the back-up roll separating force, the horizontal backthrust and the horsepower for the process can be derived.