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This paper proposes a theory of cold rolling that considers roll deformation into a noncircular profile, for the analysis of temper rolling or the rolling of thin hard strips. Although models of this kind were presented by Matsumoto & Uehori in 1988, and more recently by other authors, the computation often fails when there is a large “neutral zone”, where plastic deformation is not proceeding because of roll flattening near the neutral point. In this paper, the elastic deformation of the strip being rolled is considered in order to ensure that the computation is accurate and stable even for a reduction ratio as small as 0.1%. The formulation of the strip is similar to Orowan’s rolling theory, but is modified with elastic deformation. The computing time is instantaneous. The computed rolling force and forward slip are compared with experimental results of wet temper rolling. It was found that there may be such a case as the backward-slip zone disappears and the entry elastic zone merges with the neutral zone into an integrated neutral zone when the exit tension is large compared with the entry tension.

Elastic-Plastic Theory of Temper Rolling with Noncircular Roll Flattening