Elementary Theory Of Rolling

THE PURPOSE OF THIS PAPER is to lay a foundation of elementary theory that might be useful in the discussions which it is hoped will be evoked during this Symposium. It is not my purpose to try to expound the details of the most complete theories as that would be impossible in the time at our disposal and, even if time were available, would probably be of less usefulness than a discussion of the principles underlying the advanced theoretical treatment. I shall try to discuss the fundamental bases for these advanced theories. There exists at the present time very much less need for a detailed description of complete theory than existed when this Symposium was being organized. The reason for this is that a series of papers by L. R. Underwood has been appearing in the magazine Sheet Metal Industries. It is understood that this series will he published soon in the form of a book. Dr. Underwood's articles are complete, critical and well written and it would be hopeless to try to do better in less space. The need, then, is for a brief treatment of basic theory. The objective of any theory of plastic forming- is to enable one to calculate the force and power requirements for the process, and where the deformation is not uniform, to calculate the distribution of strains- In the formed object. We need as the basis for the calculation the relationship between stress and strain in the metal, particularly for the combination of stresses imposed by the forming process. We need to know the stress-strain curve for some simple state of stress, and we need in addition some theory