Simplified theories of flat rolling .1. The calculation of roll pressure, roll force and roll torque

The classical theories of rolling continue to be widely used in practice although finite element methods can provide a more detailed analysis of the deformation during rolling. Both a homogeneous deformation solution and an inhomogeneous method for calculating the roll pressure are reformulated as a development of the classical theories of flat rolling. The new solutions do not require the gradient of the stress-strain curve d(2k)/d phi. This simplifies the computations, leads to consistent estimates of the main rolling parameters including the calculation of the roll torque and allows more general yield stress functions to be readily included in solutions for hot or cold rolling. Data for the rolling of annealed copper is used to establish the consistency and accuracy of the new solutions.