Energy-balance equations for in-roll stresses for anisotropic materials in wound rolls

This Thesis concerns itself with the thorough investigation of the effects of core material parameters on the structural behaviour of wound rolls in core-roll winding systems. The underlying theme in this work is the derivation, based on the theory of elasticity, of an analytic expression for the core material's elasticity modulus as a function of only material parameters and geometry.The approach undertaken herein is purely theoretical and encompasses the rigorous analysis of principally two models; linear isotropic and anisotropic. As for the former, both planar and axisymmetric geometries are investigated; and in the case of the anisotropic model, an axisymmetric plane stress situation is studied. Moreover, finite-element modelling and analysis for the isotropic condition is carried out to confirm the theoretical findings. The objective is then to apply the results; namely, the inclusion of Poisson's ratio and elasticity modulus of the core material, to modify existing energy-balance roll structure formulae. This undertaking is called for if the aim is to have a valid winding model that simulates the actual winding process; i.e., one which incorporates sensing the presence of the core through layers of wound material. Results are further compared with existing winding models and conclusions are given