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12. Effectiveness of edge drop control of tapered work roll shifting during tandem cold rolling process

Author

Xiao-chen WANG, Xia-wei FENG, Dong XU, Quan YANG, and Ji-quan SUN

Subjects
strip rolling, preset, transverse flow, inter-stand post-rolling yielding, edge drop automatic control, Mining engineering. Metallurgy, TN1-997, Environmental engineering, TA170-171
Abstract

In the process of tandem cold rolling of nonoriented silicon steel strip, it is imperative to design the control strategy and initial values of the edge drop control efficiency coefficient to achieve automated control in the edge drop by shifting tapered work roll. To obtain these values, intensive modeling is needed to study not only the effects of work roll deformation, metal transverse flow, and inter-stand deformation on tapered work roll shifting at one stand but also the effects of different work roll shifting values at the upstream stand on the edge drop at downstream stand. These intensive calculations have to be performed by an accurate numerical model with a high cost/effective ratio. Based on the metal transverse flow theory at the edge drop zone, a numerical model was built in this study, in which the lateral flow was treated as a pure shear increment inside the rolling region, so that building a stiffness matrix in the lateral direction was not needed and modeling cost was saved. Additionally, inter-stand deformation was considered. Considering the proportional ratio of the strip was broken by the tapered work roll shifting, the longitudinal strain at the strip edge was considerably lower than the strain at the center, which leaded to shrinking and thinning near the edge. It was proved that the coupled model can provide results, which were obtained through industrial experiments, with higher accuracy compared with the original one. Successive calculations of two stands were conducted to reveal the control effectiveness of different tapered work roll shifting values at upstream stand on the downstream stand. It has been observed that the edge drop control region is the widest at the 1st stand, and its width successively reduces at the 2nd and 3rd stands. Based on this rule, a control strategy based on a three-point measure instead of a single point was proposed, and it was proved to be more effective than the one-point measure used in industrial applications.

Published
2020
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42. On Schur Convexity of Some Symmetric Functions

Author

Chu Yu-Ming and Xia Wei-Feng

Subjects
Mathematics, QA1-939
Abstract

For and , the symmetric function is defined as , where are positive integers. In this paper, the Schur convexity, Schur multiplicative convexity, and Schur harmonic convexity of are discussed. As consequences, several inequalities are established by use of the theory of majorization.

Published
2010

43. Inequalities for Generalized Logarithmic Means

Author

Xia Wei-Feng and Chu Yu-Ming

Subjects
Mathematics, QA1-939
Abstract

For , the generalized logarithmic mean of two positive numbers and is defined as , for , , for , , , , for , , and , for , . In this paper, we prove that , and for all , and the constants , and cannot be improved for the corresponding inequalities. Here , and denote the arithmetic, geometric, and harmonic means of and , respectively.

Published
2009

44. Schur-Convexity for a Class of Symmetric Functions and Its Applications

Author

Chu Yu-Ming and Xia Wei-Feng

Subjects
Mathematics, QA1-939
Abstract

For , the symmetric function is defined by , where and are positive integers. In this article, the Schur convexity, Schur multiplicative convexity and Schur harmonic convexity of are discussed. As applications, some inequalities are established by use of the theory of majorization.

Published
2009

45. Two Sharp Inequalities for Power Mean, Geometric Mean, and Harmonic Mean

Author

Xia Wei-Feng and Chu Yu-Ming

Subjects
Mathematics, QA1-939
Abstract

For , the power mean of order of two positive numbers and is defined by . In this paper, we establish two sharp inequalities as follows: and for all . Here and denote the geometric mean and harmonic mean of and respectively.

Published
2009

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