A Three-Dimensional Inverse Problem of Estimating the Surface Thermal Behavior of the Working Roll in Rolling Process

Abstract

A three-dimensional inverse analysis utilizes a different perspective to estimate the surface thermal behavior of the working roll in rolling process. The inverse analysis is based on the temperature reading taken inside the roll at several different locations. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate the surface unknown conditions of the working roll. Then, the linear least-squares method is adopted to find the solution. The advantages of this proposed inverse analysis method are that no prior information is needed regarding the functional form of the unknown quantities, no initial guess need be used and the numbers of iterations for calculation process is limited to one. The results show that only few measuring points are sufficient to estimate the boundary conditions when measurement errors are neglected. When measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. [S1087-1357(00)70201-2]

Evaluation of temperature field and heat flux by inverse analysis during steel strip rolling

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“…The expression of u q (used for the numerical results) is appended in Appendix B (Eq.B.1). Therefore by plugging (17) in (18):…”

An Efficient Inverse Method for Determining the Material Parameters and Coefficient of Friction in Warm Rolling Process

“…In their recent paper (Weisz-Patrault et al 2014), they presented a fully threedimensional inverse analytical method for determining the temperature field and heat fluxes by measuring the temperatures at several locations in the rolls. Hsu et al (2000) predicted the thermal behavior of work-roll in rolling by three-dimensional inverse model. The temperature measurements are carried out at several locations inside the roll.…”

A model for evaluating thermo-mechanical stresses within work-rolls in hot-strip rolling

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