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Study of Hakiel's Nonlinear Model for Wound Roll Stress Implementations

Alexei Azarov
Organization: ZINK Imaging, Inc
Chien Liu
Organization: ZINK Imaging, Inc

2007 Wolfram Technology Conference
Conference location

Champaign, IL


The quality roll winding problem has been studied for a long time. It was found that the quality of a wound roll depends on the intensity and the distribution of in-roll stresses. Hakiel's nonlinear model reduces the problem of finding the stress distribution to the sum of the solutions of a nonlinear second-order ordinal differential equation (ODE) boundary problem for each loop wound on the roll. The algorithm is very sensitive to the boundary problem solution accuracy as the error is summed at each step. In this work we present an implementation of the Hakiel's algorithm in Mathematica 6. For the case of a constant in-roll radial modulus of elasticity, an explicit analytical formula of the Hakiel's model was derived in Mathematica. We also implemented the Hakiel's algorithm in Matlab and in COMSOL Script systems. We compare the Hakiel's algorithm implementations in these three computational tools in terms of accuracy obtained and computational time for both constant and variable in-roll radial modulus of elasticity cases.

*Mathematics > Calculus and Analysis > Differential Equations
*Wolfram Technology
*Wolfram Technology > Kernel > Numerics

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HakielsNonlinearModel.nb (2.2 MB) - Mathematica Notebook [for Mathematica 6.0]