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This article proposes a semi-analytical solution of von Karman's rolling equation on the elastic foundation. The roll indentation is considered as the spring compression of the elastic foundation of the work roll. A non-circular contact arc is obtained naturally as a part of the solution of the governing equation. Two elastic zones and four plastic zones are included. Hooke's law is applied in elastic zones, von Mises' yield criterion is used in plastic yielding and unyielding zones, and material stress-strain curves are employed in plastic loading and unloading zones. The solution of each zone was derived separately and a computer program was designed accordingly. The computing time is very short and the required core memory is very small. The results show that the compressive stress curves form a "friction hill" while the shape of the normal stress curve depends on the rolling parameters. A typical cold rolling case is selected as the basic study case. The results of this proposed model and the popular Bland-and-Ford model are shown to make comparison between these two models. Key rolling parameters included in the comparison results are the entry gage, the exit gage, the entry tension, the exit tension, the work roll diameter, the yield stress, and the friction coefficient. Rolling feasibility derived from this proposed model is not only on the existence of the convergent solution but also on whether or not the solution can follow the properties of the rolled material. Source


A new rolling model was developed directly from a von Karman equation using von Mises and Tresca yield criteria, and a new friction hill was revealed. The roll bite is composed of nine characteristic nodes in elastic deform, plastic deform and elastic recovery zones. This paper will describe this new theory and its associated solving routine. Comparison with other traditional and modern rolling models will also be presented. Source


Guo R.-M.,Tenova I2S
Iron and Steel Technology | Year: 2013

Rolling technology includes he rolling force model, the crown and shape model, the control and system response model, the thermal-related models, the pass schedule model, the chatter vibration model, the wear model, the component life expectancy model, and other analytical and empirical models. Conventional investigation assumes the roll gap to be a circular arc generated by an equivalent work roll diameter which can be estimated by the Hitchcock equation with the calculated rolling force. The shear stress r on the strip/roll contact interface obeys Coulomb's law of friction to become the product of the normal stress s and the friction coefficient. The original work roll provides the initial roll gap. The slip friction is enforced so that the shear stress changes with the normal stress proportionally. The calculation steps start from two sides of the roll bite. The normal stress increases continuously from both sides approaching the core of the roll bite. The intercept of two normal stress curves is defined as the neutral point where the strip speed matches with the roll speed, the normal stress reaches maximal and the shear stress vanishes. Source


Guo R.-M.,Tenova I2S | Dinellc P.,Tenova I2S
Proceedings of the 10th International Conference on Steel Rolling | Year: 2010

Nowadays, in the very competitive market place, metal producers deserve an optimal mill to fully cover the desired product mix with a minimum mill cost. Different product mixes with specified quality requirement lead to different mill configurations. With available control tools and versatile mill configurations, it is difficult to determine the optimal mill configuration for particular product mix requirements. The mill designer needs to take reliability and marketability into consideration. This article proposes an analytical method to optimize the mill design based on the given product mix. As described in this article, the optimal procedure starts with a method to select the work roll size by applying a force model. Most rolling parameters - force, torque, power, energy, speed, tension, and run time - are determined at this stage. The backup roll is then selected using the crown/shape control model and an associated cost function. The mill type (2hi, 4hi, 6hi, or cluster mills) can be realized using the determined work and backup rolls. The mill housing can be optimized with a given housing weight. The crown/shape control devices and associated control ranges can then be determined after the mill is designed based on the proposed procedure. Source


Malik A.,Saint Louis University | Sanders J.,Saint Louis University | Grandhi R.,Wright State University | Zipf M.,Tenova I2S
ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011 | Year: 2011

Optimal pass-scheduling on cluster-type cold rolling mills, use to process flat metals, presents added challenges over conventional (vertical-stack) mills due to the complexity of roll arrangements. Cluster-type rolling mills not only pose difficulties in modeling deflections occurring in the multi-roll stack, they also impose the burden of modeling more sophisticated mechanisms used to adjust rolling force distribution and achieve desired strip flatness. In a competitive global market for very thin gauge strip, an advantage is gained through use of efficient mathematical set-up models that can adequately optimize the flatness actuators according to the target gauge reductions for each rolling pass. The mill's process control computer should therefore determine a gauge reduction schedule leading to minimum number of passes, while simultaneously assigning nominal flatness control actuator set-points. Although recent developments in roll-stack deflection modeling using simplified, mixed finite element techniques have enabled more efficient roll-stack deflection modeling in 20-high and other cluster mills, the optimal pass-schedule problem is still complicated by the abundance of geometric and mechanical property variations in the strip or sheet to be processed. Furthermore, problems with strip flatness frequently arise because of uncertainties in roll diameter profiles resulting from variations in the roll grinding and roll wear patterns. In this paper, we extend recent work in pass schedule optimization (through improved rollstack deflection) by applying First Order Reliability Methods to rigorously account for various rolling process uncertainties. The results allow predictive probability constraints for strip flatness to be included in the optimization problem, thus enabling mill operators some insight and control into the likelihood of achieving desired strip flatness for a given rolling pass schedule. Copyright © 2011 by ASME. Source

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