1100 ISSN 0036-0295, Russian Metallurgy (Metally), Vol. 2016, No. 11, pp. 1100–1105. © Pleiades Publishing, Ltd., 2016. Original Russian Text © E.A. Garber, M.A. Timofeeva, 2016, published in Metally, 2016, No. 6, pp. 111–117. Improvement of the Technique of Calculating the Energy–Force Parameters of Pinch-Pass Mills for Increasing the Efficiency of Producing Cold-Rolled Strips E. A. Garber and M. A. Timofeeva Cherepovets State University, pr. Pobedy 12, Cherepovets, 162606 Russia e-mail: mamz2011@mail.ru Received December 9, 2015 Abstract⎯New propositions are introduced into the technique of energy-force calculation of pinch-pass mills in order to determine the energy–force and technological parameters of skin rolling of cold-rolled steel strips at the minimum errors. The application of these propositions decreases the errors of calculating the forces and torques in a working stand by a factor of 3–5 as compared to the calculation according to the well- known technique, saves the electric power in the existing mills, and demonstrates the possibility of decreasing the dimensions of working stands and the power of the rolling mill engine. Keywords: skin rolling, cold-rolled strips, energy–force parameters DOI: 10.1134/S0036029516110082 The aims of skin rolling, which is the final defor- mation operation of the process of production of cold- rolled steel strips, are to provide the possibility of deep and complex drawing in stamping of ready sheets and to ensure their minimum nonf latness and the required surface microgeometry, which influences the adhe- sion of a sheet to a corrosion-resistant coating. To achieve these aims at the minimum energy con- sumption, it is necessary to apply the modern methods of the theory of skin rolling, which can be used to cal- culate the energy–force parameters of this process at the minimum errors, to calculate the technological conditions of pinch-pass mills. Skin rolling is performed after annealing of strips cold-rolled in a continuous or reversing mill. The pur- pose of annealing is to remove the high work harden- ing of the strip that was induced by cold rolling, since, for the problems to be solved, the material of the strip supplied to a pinch-pass mill should have the mini- mum yield strength, i.e., the yield strength before cold rolling. Thus, skin rolling is a certain type of cold rolling and is performed in working stands, which usually have a design that is similar to that of the working stands in a cold-rolling mill. Therefore, to calculate the energy–force parame- ters of pinch-pass mills, we can use most methods of the modern theory of cold rolling described in [1]. This theory develops a number of points of the classi- cal theory of rolling [2–4], is based on a large body of industrial experimental results, and was tested on operating mills for a long time. In contrast to the classical theory, the stresses in the deformation zone in the new theory are separately calculated in elastic and plastic regions, and elasticity equations rather than the plasticity condition are used for calculation in the elastic regions. In [1], we presented reliable expressions for calcu- lating all contact stresses and the length of each region in the deformation zone, namely, the first elastic region, the backward and forward creep zones in the plastic region, and the second elastic region. The laws of contact friction in the deformation zone were con- sidered in a separate section in [1]. It was proved that these laws are radically different for hot and cold roll- ing: in hot rolling, no slip between a strip and rolls exists, which is characteristic of friction of rest in the stick zone. In contrast, in cold rolling, contact sliding friction is operative over the entire deformation zone and the stick zone is absent. We presented reliable expressions to calculate the friction coefficients in the deformation zone for both hot and cold rolling. Based on the developed new propositions, we [1] developed a technique and new formula to calculate the energy–force parameters of rolling, namely, the forces operating between a strip and rolls and the torques and the powers of the rolling mill engines in working stands. Our comparative analysis of the state of stress (SOS) in a strip during cold rolling and skin rolling showed that the methods developed in [1] cannot be