A computational method to predict strip profile in rolling mills

Malik, Arif; Grandhi, Ramana V.

doi:10.1016/j.jmatprotec.2007.12.026

Cited by 59 publications

(29 citation statements)

References 11 publications

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“…Previous examples of static roll stack deflection calculations for 4-high and 20-high mills were most recently given by Malik and Grandhi [11]. It should be noted that even though the rolling process is dynamic, static models are typically applied to predict the expected roll stack deflection under steady-state rolling conditions to determine roll profiles and pass reduction schedules.…”

Section: Relevance Of Nonlinear Coupled Beam Methods To Cold Rolling Mmentioning

confidence: 99%

“…Besides the work of Malik and Grandhi, several other static physics-based methods to predict the shear, bending, and flattening deflections in rolling mills were also developed in past decades, as discussed in Ref. [11]. These other static methods, however, require iteration even for fully continuous contact conditions.…”

Section: Relevance Of Nonlinear Coupled Beam Methods To Cold Rolling Mmentioning

confidence: 99%

“…Research in past decades has focused on beams connected at their ends, and resting on discrete springs or underlying elastic foundations of the Winkler or elastic-solid type. Developments for this class of problem have been summarized by Aydogan [1] and Gendy and Saleeb [2], and are outhned in Table 1 [1][2][3][4][5][6][7][8][9][10][11]19]. …”

Section: Introductionmentioning

confidence: 99%

“…Figure l(a) illustrates the conventional single beam on single underlying elastic foundation problem. The special class of problem considered in this work-that of multiple, shear-deformable beams coupled with nonlinear, Winkler-type elastic stiffness is Differential equation for single Euler-BemouUi beam on elastic foundation [3] Solution to Hetenyi's equation in terms of functions for deflection, slope, moment, shear force [4] Foundation as elastic half space using Hamant equation, with flexibility matrix for cubic Euler-BemouUi beam element [5] Stiffness matrix for Euler-Bemoulli beam element with discrete end springs [6] Generalized contact stiffness matrix for external elastic restraint [7] Exact stiffness matrix for Euler-Bemoulli beam element on Winkler elastic foundation [8] Shear-deformable beam elements on elastic foundations [9,19] Shear and membrane locking [10] Exact stiffness matrix for shear-deformable beam element on Winkler elastic foundation [I] Hybrid-mixed formulation to avoid shear-and foundation-locking [2] Inexact formulation for multiple beams with coupled, linear Winkler elastic foundations [11] Hetenyi(1946) Miranda and Nair (1966) Cheung and Nag (1968) Bowles (1974) Mohr(1980) Ting and Mockry (1984) Bathe (1982) and Cook Referring again to the elastically coupled, multiple beam structure in Fig. 1 (h), it is noteworthy that the foundations may be integral to the beams themselves, or they may result from dissimilar media used to join or separate them.…”

Section: Introductionmentioning

confidence: 99%

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Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills

Malik

Hinton

2012

Journal of Manufacturing Science and Engineering

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Introduced is an efficient numerical method to calculate the displacements of structures involving multiple, shear-deformahle beams in lengthwise nonlinear elastic contact. Applicability of the method is general, and includes structures such as stacked beams, pipes, or machine components. A particularly relevant application, which is discussed and demonstrated in this paper, is the prediction of deflections and contact conditions between the rolls and strip in rolling mills used to process flat metals. The presented nonlinear displacement calculation method involves iteration using an efficient, simplified mixed finite element formulation. Nonlinearities in the general coupled beam problem can arise either from changing contact conditions between the lengthwise-coupled sheardeformable beams (opening/closing of gaps) or from nonlinear elastic coupling-stiffness between the beams. Unlike the conventional problem of end-connected beams resting on elastic foundations, this work presents an element stiffness matrix formulation and sample nonlinear solution techniques for the problem involving multiple beams that are mutually coupled along their lengths by intervening, nonlinear elastic foundations. Important practical examples of the method are given, based on production cold rolling mill data for type 301 stainless steel on a four-high mill. The examples demonstrate efficiency and value of the nonlinear coupled beam formulation in identifying appropriate machined roll profiles to produce desired strip flatness quality. The cold rolling applications presented are characterized by nonlinear Hertz foundations with stiffnesshardening, and by discontinuous contact conditions arising from nonuniform, machined roll diameter profiles. Solution efficiencies for the new formulation are compared using modified Newton-Raphson, average stiffness, and direct substitution techniques. While the average stiffness method is relatively slower, its characteristics may make it beneficial for transfer function development in flatness control systems. Application of the method to cold rolling mills illustrates the importance of including discontinuous contact nonlinearities, and enables reduced trial and error to determine suitable roll profiles. Presented is a new efficient variational formulation for computing displacements in structures involving multiple beams laterally coupled with nonlinear elastic foundations and changing contact conditions. Practical value of the method is demonstrated for identification of machined roll profiles in cold rolling mills in order to achieve desirable flatness of rolled products.

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Section: Relevance Of Nonlinear Coupled Beam Methods To Cold Rolling Mmentioning

confidence: 99%

Section: Relevance Of Nonlinear Coupled Beam Methods To Cold Rolling Mmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills

Malik

Hinton

2012

Journal of Manufacturing Science and Engineering

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“…[20] proposed a mathematical model in the form of transfer function matrix for the flatness control of strip mills. [21] presented a new compact, flexible, and efficient method to predict the deflection and resulting strip profile for both cluster-type and non-cluster-type rolling mills.…”

Section: Process Descriptionmentioning

confidence: 99%

Decoupling based decentralized robust control for combined shape and gauge system in tandem cold rolling process

Peng

Tong

Xiao

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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In this paper, we proposed a new control scheme of decoupling based decentralized robust control for a typical two-input two-output system in tandem cold rolling process. A dynamic coupled model of shape and gauge system was developed based on some field data. Then we proposed a new control scheme for the combined system. The controller consists of a decoupler and a set of robust controllers. The interactions could be mainly dealt with by the decoupler, and robust controllers could guarantee good performance of decoupling control and the robustness of each isolated subsystem. An example was given to illustrate the proposed control strategy. Simulation results showed excellent decoupling effectiveness, input tracking, disturbance rejection and parameter perturbation rejection.

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Analysis of Hot Rolling with Simplified Weighted Velocity Field and My Criterion

Zhao¹,

Cao²,

Zhang³

et al. 2013

Pricm

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A computational method to predict strip profile in rolling mills

Cited by 59 publications

References 11 publications

Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills

Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills

Decoupling based decentralized robust control for combined shape and gauge system in tandem cold rolling process

Analysis of Hot Rolling with Simplified Weighted Velocity Field and My Criterion

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