Danil L. Schwartz, Arkady M. Mikhailenko, Ekaterina I. Ustinova

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METHOD OF OPTIMIZATION OF ROLL CALIBRATION FOR CHANNELS. GROOVE SPACE

Danil L. Schwartz, Arkady M. Mikhailenko, Ekaterina I. Ustinova

ABSTRACT

The universal “concept of two-stage optimization”, consisting of two successively carried out optimization stages developed at Metal Forming Department of Ural Federal University in relation to optimization of the roll calibration for channels is considered in this article. Common features of these shapes classification and their variation levels are identified and justified. This developed structure is the basis for the formation of spaces of groove schemes. In the software implementation the groove space is represented as a “groove database”. In the future this database will be used to form the space of calibration schemes that are fundamentally suitable for these shapes rolling.

Keywords: rolling of sections, section bar, rolling mill machine, mill roll calibration, grooves, systems theory, system analysis, optimization of the roll calibration, channel, optimization space, criterion of optimality, objective function.

Received 31 October 2019Accepted 16 December 2019

Journal of Chemical Technology and Metallurgy, 55, 3, 2020, 657-665

Ural Federal University named after the First President of Russia B. N. Yeltsin Yekaterinburg, RussiaE-mail: ustinova1694@gmail.com

INTRODUCTION

One of the main directions of rolling production development is the task of range expanding, improving quality and increasing of economical types of rolled products production. This problem can be solved by individual technological operations optimizing. One of the most flexible elements of rolling production is the calibration of rolling rolls. Optimal calibration will allow you to get a finished profile with the specified size, shape and surface quality, while ensuring high productivity of the rolling mill and low production costs.

A fairly large number of scientific and practical works, articles, monographs, and textbooks [1 - 6] are devoted to the study of issues related to the optimization of rolling rolls calibrations, and moreover, the intensity of such work is increasing, and the range of issues ad-dressed is becoming wider. This confirms the relevance of the topic.

At Metal Forming Department of Ural Federal Uni-versity the universal “Concept of two-stage optimiza-tion” was developed [7 - 10]. In the framework of this article, its application to search for optimal calibration of rolls for channel rolling is considered.

Concept of two-stage optimizationThe channel profile makes up a significant part of

the volumes from the rolled products profiles [11 - 12]. The range of channels and channel profiles (U-shaped) is very wide and diverse, it is usually divided into general channels (most are produced according to GOST 8240-97, 8278-83) and special channels (most are produced according to technical specifications or others types of standards). The principles of various profiles of channel shapes production are technologically the same. Two types of channel profiles are produced - hot rolled and bent from sheet material. Despite the increase in the share of cheaper bent channels [3], a complete rejec-tion of hot-rolled channels production is not expected. Therefore, studies aimed to the technology improving of high-quality rolling of channels do not lose their relevance and given the technological uniformity of various channels production, it is advisable to carry out such studies from the general standpoint applicable to different types of channels.

The so-called system approach formulated in “System Theory” [13 - 15 and others] and “Theory of Optimal Control” [16, 17 and others] was chosen as the ideological basis of the methodology creating for

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optimal calibrations design. This is due to the fact that rolls calibration considered as a variable groove system is fully consistent with all the features of generally ac-cepted concept of “system”.

In accordance with the systematic approach two main fundamentally different cases of system variability are distinguished:

option 1 - structural difference of the system through the use of different subsystems or changes in the direc-tions of the subsystems connections (the elemental com-position of the system and/or the types and directions of its elements connections are different);

option 2 - a change in the quantitative characteristics of the subsystems relationships and the system relation-ships together with the environment (i.e., a change in the system controls).

During the system optimizing due to two variants of its variability (for one or different optimization purposes) you can get two different optimality options:

for option 1: the system that best suits the purpose of this class of systems will be the optimal system;

for option 2: the control that provides the best way to achieve the goal when the system of the unchanged structure is functioning, is the optimal control.

The best optimization result will be achieved pre-cisely due to the simultaneous achievement of these two optimality options.

In the technical system “calibration of rolling rolls” both of these options for variability and optimization are available and quite simply and not expensive can be im-plemented, both together and separately. The first variant

of variability corresponds to a change in the calibration scheme, and the best-selected calibration will correspond to the concept of “optimal calibration scheme”.

The second variant of calibration variability (change of controls) in practice translates into a change in the distribution of reduction along the passes. The reduction mode that best suits the optimization goal will be called the “optimal reduction mode.”

An analysis of the known solutions showed that during optimizing calibrations, either the first [5, 6] or the second [1 - 4] options for complex work optimizing using both optimization possibilities are unknown. It seems to us, however, that enough theoretical knowledge has already been accumulated on rolling calibration and practical experience, and it is time to use both of the optimization options considered above to design the technology for long sections rolling. The developed concept provides for a two-stage procedure: at the first stage, the optimal calibration scheme is revealed, and then, at the second stage, the optimal reduction mode is revealed.

The phased approach in addition to the process of solving the problem simplifying has additional advan-tages, in particular, makes it possible to use its optimality criterion at each stage, which, on the one hand, simpli-fies the procedures for the objective functions of each of the criteria generating, and on the other hand, allows precisely take into account the realities of the industrial section rolling mill. The block diagram of the universal “Concept of two-stage optimization” for rolling channels is shown on Fig. 1.

Fig. 1. Structural flowchart of two-stage calibration optimization.

Danil L. Schwartz, Arkady M. Mikhailenko, Ekaterina I. Ustinova

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Space of groovesIn the framework of this article we will consider the

formation of such an extensive block as the “Space of grooves” (block 5). However, before this it is advisable to consider the previous steps, the formation of this space, displayed in blocks: the goal of optimization, initial data and limitations, the criterion of optimality.

There can be a great many “optimization goals” (block 1) in real conditions of an actual rolling mill. A feature of the “Two-stage optimization concept” is a possibility to use two optimality criteria, each at its optimization stage and consider two diverse optimization goals accordingly (for example, maximum accuracy of finished products and minimum energy costs) “Optimi-zation goal” (see block 1 in Fig. 1).

“Initial data and restrictions” (block 2) contains information about the workpiece, profile, mill specifica-tions, technological limitations, etc.

The term “Optimality Criterion” (block 3) is under-stood as a uniquely defined method of the best solution obtaining that meets the optimization goal.

The “Space of grooves” (block 5) is a space con-taining all possible grooves, which are fundamentally applicable for the rolls calibrations formation for rolling channels. Filling this space is based on the analysis of well-known literature and factory documentation for channel calibrations. Further, for brevity, by the term “groove” we mean an unambiguous diagram or structure characteristic of a certain group of known calibers of the same type, for some features different from another group of grooves, or, for brevity, “from another groove.” The division of all known channel grooves into groups was carried out in the process of their classification according to the selected geometrical and technologi-cal properties. The selected classification features are subsequently used as measurements (coordinates) of

the “Space of grooves” (block 5). “Space of grooves” is an information space that includes all grooves that are fundamentally suitable for high-quality rolling of channel shape profiles (virtual channel grooves). To date a great deal of experience has been gained in the production of different channels on different rolling mills using a large number of different calibrations [21 - 25]. The typification of the characteristic forms of grooves used in industrial calibrations made it possible to dis-tinguish the characteristic features of channel grooves that satisfy to the requirements formulated above. We attributed to such features: C - type of wall; D - type of actual flanges; L - type of false flanges; P - type of caliber closure and the number of rolls forming of the groove. The designations of the corresponding channel profile elements are shown in Fig. 2.

Groove feature “C - type of wall”. In the well-known industrial channel calibrations calibers with a wall of four types are found: straight, notched, curved and wavy (Fig. 3, Table 1).

Groove feature “D - type of actual flanges”. In industrial calibrations grooves are used with only four types of shelves, also called “real flanges”: direct actual flanges with a small slope (1 - 5 % taper), direct actual flanges with an increased slope (10 % to 40 % taper), curved actual flanges, actual flanges without slope. However during the formation of the groove space and the combination of different levels of variation the idea came up of using a groove with actual flanges bent in-ward (with extended calibration), which would provide the best conditions for the strip to enter the groove, reduce the depth of cut into the rolls, and, therefore, reduce their wear.

Examples of such grooves are shown in Fig. 4, and the corresponding classification groups are given in Table 2.

Fig. 2. The division of channel into elements in two-roll pass (a) and four-roll pass (b).

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The groove feature L is “Type of false flanges”. After some generalization of the forms of false flanges known from the literature only three significantly different types of channel grooves can be distinguished: with triangular false flanges, with trapezoidal false flanges and without false flanges (Fig. 5, Table 3).

The groove feature P is “Type of groove closure and the number of rolls forming the groove”. The term «groove closure type» generally refers to a method for locating the rolls space relative to the position of the roll cross section. We will use the generally accepted classification of two-roll grooves on this basis [18, 19]. In the manufacture of channels two-roll grooves with all methods of groove closing are used.

Currently, the channel is also being rolled in uni-versal stands using four-roll grooves. From the point of view of metal forming in groove the method of groove closure affects, first of all, to the coverage ratio of the rolled metal by groove, the ratio of metal control by rolls. A similar controlling effect of the groove on the metal is also exerted by a change in the number of rolls forming the groove. With the increase in the number of rolls the ratio of metal control by rolls usually increases. With this in mind, outwardly different, but functionally similar, attributes “type of groove closure” and “number of rolls forming a groove” were combined into a single characteristic of groove “P” (Fig. 6, Table 4).

Each of the combinations of features variation levels

Table 1. Levels of characteristics variation С – “Neck type “.

Fig. 3. Neck type: a - straight, b - curved, c - cut, d – wavy.

Name Level Description Example

С1 Straight Straight

С2 Cut Formed by two split wedges

С3 Curved Center curved

С4 Wavy The wall has several bends

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C, D, L, and P given in Tables 1 - 4 defines a specific unique type of channel groove, and all possible combina-tions of levels is the channel groove space, presented in the form of a 4-dimensional matrix of channel grooves. Formally in order to designate each type of channel groove we introduce the concept of “groove code”, by which we mean a four-digit number made up of digital

designations of groove feature levels given in Tables 1 - 4. We fix the following order of occurrence of the characteristic levels in the groove code: 1st position - C - view of the wall; 2nd position - D - type of actual flanges; 3rd position - L - type of false flanges; 4th position - P - type of groove closure and number of rolls forming the groove. Based on this order the groove code will be

Table 2. Levels of characteristics variation D - “Real flanges”.

Fig. 4. Real flanges: a - straight with a small incline, b - straight with an increased incline, c - outward curved, d - no incline.

Name Level Description Example

D1 Straight with a small

incline

Straightforward with a small groove

taper.

D2 Straight with a

increased incline

Straightforward with the groove taper

from 10 to 40%

D3 Outward curved Curved outward

D4 No incline Straight, parallel to the groove wall

D5 Inward curved Bend about 1/3 of the flange into the

inside of the groove

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Table 4. Levels of characteristics variation Р - «Groove closure type and the number of rolls forming the groove».

Fig. 5. Counter flanges: a – trapezoidal, b – triangular.

Table 3. Levels of characteristics variation L - “Counter flanges”.

Name Level Description Example

L1 Triangular Non-equilateral triangle

L2 Trapezoidal Type of isosceles trapezoid

L3 No flanged No flanges

in the form of SDLR. For example, if the groove has a code of 4312, then, in accordance with Tables 1 - 4, the groove has a wavy wall, curved and triangular false flanges, half-closed type.

Considering the characteristics of the grooves C, D, L and P have, respectively, 4, 5, 3 and 5 levels of vari-

Name Level Description Example

Р1 Open The groove space is located approximately in the middle of the groove.

Р2 Half closed The groove space is offset down but in the groove area

Р3 Closed top The groove space shifted up off the groove area

Р4 Closed bottom The groove space shifted down off the groove area

Р5 Four-rolls The groove is limited to four working rolls

ation, the total number of combinations of such levels will be 4 ∙ 5 ∙ 3 ∙ 5 = 300 pcs. With a detailed study of the compatibility of different levels of characteristics C, D, L and P, it was found that a number of their combina-tions are either geometrically impossible or not applied in practice due to obvious technological inappropriate-

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Table 5. Matrix of channel grooves.

№

Classification characteristics Groovec

ode Example

С D L Р

1

Straight

Straight with a small incline Triangular Open 1111

22 Straight with a

increased incline

Trapezoidal Half closed 1222

44 Outward curved No flanged Closed bottom 1334

49

Cut

Straight with a small incline Triangular Closed bottom 2114

66 Straight with a

increased incline

Trapezoidal Open 2221

85 Outward curved

Trapezoidal Four-rolls 2325

92

Curved

Straight with a small incline Triangular Half closed 3112

115 Straight with a

increased incline

Trapezoidal Four-rolls 3225

132 Outward curved No flanged Half closed 3332

140

Wavy

Straight with a small incline Triangular Four-rolls 4115

159 Straight with a

increased incline

Trapezoidal Closed bottom 4224

179 Outward curved No flanged Closed bottom 4334

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ness. 94 such special combinations revealed. For the remaining 206 real combinations of performance levels, a table has been compiled, called the “Channel Groove Matrix”. In this table, each particular combination of performance levels is associated with a specific groove of a particular type and its code designation identifying this groove. Due to the hugeness of the «Channel Groove Matrix», only a fragment is shown in Table 5.

CONCLUSIONSAnalysis of the overall calibration structure of the

rolls showed the possibility of its description from the standpoint and in terms of modern systems theory, as a typical technological system. Using the principles known from the theory of systems, the possibility of constructing a two-stage optimization model intended for the design of optimal calibrations of section-rolling rolls using one or two optimality criteria is revealed. A general block diagram of such a model is developed.

One of the components of the optimization model for calibrating rolls intended for rolling the channel profile is considered - the space of channel grooves. As measurements (coordinate systems) of the groove space, the obvious technological and geometric characteristics of the channel grooves are used: C - view of the wall; D - type of actual flanges; L - type of false flanges; P - type

Fig. 6. Groove closure type and the number of rolls forming the groove: a - open, b - half closed, c - closed top, d - closed bottom, e, f - four-rolls.

of groove closure and the number of rolls forming the groove. To simplify the optimization procedures using the classification method the groove space discretization was carried out for fixed levels of the characteristics of the channel grooves C, D, L and P used in industrial channel calibrations. The filling of the groove space was carried out in the process of structural analysis of the working calibrations of the rolls, known from the litera-ture and factory calibration specifications. The groove space is presented in the form of a four-dimensional table, reflecting in a structured form the complete set of all possible rail grooves. It was found that for each of the selected groove features (C, D, L and P) there is a limited number of variation levels (4, 5, 3 and 5, respectively). Geometrically it is possible and technologically feasible only 206 combinations of grooves characteristics levels. Each combination of levels uniquely determines the type of a specific channel groove, which is assigned to the unique four-digit code.

The developed structure is the basis for the spaces formation of groove schemes. In a software implemen-tation, the groove space is represented as a “grooves database”. In the future this database will be used to create a space of calibration schemes, which are funda-mentally suitable for rolling of these profiles. The space of calibration schemes will be the space of optimization.

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