Evaluation of contact stress during rolling process, by three dimensional analytical inverse method

A fully analytical three-dimensional inverse method has been developed in order to evaluate contact stress in the roll bite during rolling process. Stress measurements can be done by inserting fibre optics inside the roll body, (however no real measurements were available and simulations have been used instead). The inverse method takes as inputs three independent measured (or simulated) components of the stress tensor under the surface of the roll, and evaluates surface tractions of the roll especially in the contact in the roll gap. Stress, deformation and displacements can be obtained in the whole roll as well. This approach uses the theory of 3D isotropic elasticity and relies on displacement harmonic and bi-harmonic potentials expanded into a double Fourier series along the circumferential and axial directions. The identification of the solution involves matrices of size (3 × 3) computed off-line. This simple solution involves mainly the on-line computation of Fast Fourier Transform (fft) of three inputs, which takes 0.5 s for each (processor 2.8 GHz, time displayed by Scilab 5.3). Good accuracy is obtained, and the number of sensors along the axial direction is studied. Thus, this work encourages the development of an on-line industrial tool.