Inverse Cauchy method with conformal mapping: Application to latent flatness defect detection during rolling process

Abstract

a b s t r a c tIn this paper a semi-analytical inverse Cauchy problem is presented for a finite cylinder with a cylindrical hole under the surface called the detecting roll. Applications to latent flatness defect detection during rolling process are considered. A steel strip wraps at a known angle around the detecting roll. The presented inverse method aims at evaluating the residual stress profile of the strip. The inputs are the displacements and free surface traction at the hole surface and the outputs are the resultant forces per unit length in the contact between the strip and the roll, thus by equilibrium of the strip the residual stress profile is inferred. This paper is based on plane complex elasticity with conformal mapping techniques. Several 2D-computations are performed at several axial positions. This work is theoretical, the measurement device is not available and technical issues are not broached. Some numerical examples with synthetic data are provided in order to evaluate accuracy and noise sensitivity. Results encourage further investigations and technical developments.

Quick Recognition and Elimination of an Additional Signal Caused by Deflection of an Integral Roller Flatness Meter

“…(Received on January 13,2021; accepted on June 29, 2021; J-STAGE Advance published date: August 18, 2021) Compared with the sectional roller flatness meter, the integral roller flatness meter is more suitable for products with higher requirements on surface quality, and thus becomes the trend of the contact-type flatness meter for cold rolling. Due to its structure design, some problems arise.…”

“…Guan, Ben et al 12) presents a novel contactless stress detection technology based on a magnetoresistance sensor and the magnetoelastic effect, enabling the detection of internal stress in manufactured cold-rolled strips. Weisz-Patrault, Daniel 13) presented a semi-analytical inverse Cauchy problem for a finite cylinder with a cylindrical hole under the surface called the detecting roll to evaluate the residual stress profile of the strip. Yoshito, Isei et al 14) developed a new shape meter which employed LED dot pattern projection method to realize accurate AFC (Automatic Flatness Control).…”

Modelling and Application of Signal Decoupling of Adjacent Channels of a Whole-Roller Seamless Flatness Meter

“…15) To evaluate residual stress profile of strips, a semi-analytical inverse Cauchy problem based on plane complex elasticity with conformal mapping techniques was presented by Daniel Weisz-Patrault for a measuring roll with cylindrical holes. 16) Liu Jiawei et al analyzed the stress of a measuring roll and obtained a deflection model of a measuring roll by using the influence function method. 17) YU Bingqiang et al analyzed the influences of measurement error of strip edges, transverse temperature difference in strips, deflection of measuring roll and the shape of the strip coil on the flatness measurement results and established a corresponding compensation models.…”

Imposed curvature of an elastic-plastic strip: application to simulation of coils

“…Many numerical simulations have been developed in order to predict the residual stress state in the strip as a function of rolling process parameters [1,2] (see [3] for a bibliographical review). Inverse methods dedicated to experimental validation of these models have been proposed (see [4][5][6] for the mechanical problem and [7][8][9] for the thermal problem) as well as a recent inverse method dedicated to residual stress evaluation using a hollow cylinder [10].…”