TRANSLATING MORPHOMETRIC INFORMATION ABOUT THE ROLLING PASSES INTO A STRUCTURED DATABASE Текст научной статьи по специальности «Строительство и архитектура»

S.Spuzic

The University of South Australia

TRANSLATING MORPHOMETRIC INFORMATION ABOUT THE ROLLING PASSES

INTO A STRUCTURED DATABASE*

Abstract. Hot steel rolling is amongst the most important industrial techniques because of huge amount of consumed resources, immense environmental impact, and the significance of the long products in overall economy. Criteria for improving rolling operations include process efficiency, resource consumption, system reliability, product quality and ergo-ecological sustainability, all of which being critically influenced by roll pass design (RPD). With advances in computerised information processing, it becomes apparent that further progress is to be sought in intelligently combining different RPD strategies. The key to optimising rolling systems is to be found in hybrid modelling i.e. in combining stochastic, deterministic and evolutionary analyses. Evidence obtained by using small-scale chemo-physical modelling encourages the use of experimental rolling to study the RPD interactions. However, with the advent of data acquisition and processing systems, the large collections of industrial records can nowadays be analyzed within the real time, thus allowing for online extracting and applying useful knowledge. This leads to implementing I4 and I5 paradigms. A precondition for employing machine learning and big data analytics is to establish a suitable metrics including digitization of the RPD variables. Examples of roll pass deformation zone translation into vectors are presented along with an application of the inferred models to solve an actual RPD problem.

Keywords: steel rolling, roll pass design, knowledge, manufacturing, statistical analysis.

Intro

The increasing evidence of global warming, key resource decline, and consequent socioeconomic disruptions highlids the urgency for improving the sdustainability of large industrial systems such as rolling mills. Rather than focusing exclusively on developing more sustainable sources of energy there is also a need to rationalise resource consumption in operating large-scale industrial enterprises. These gigantic man-made systems are nowadays governed by multinational corporations that are too often driven by narrowly defined profit. The steel manufacturing plants are typical examples. The production of one tonne of steel product requires nearly 90 tonnes of fresh water. The whole metalworking sector is seething with sources of environmental hazard and pollution. On the average, about 1.8 tonnes of CO2 is emitted for every tonne of steel produced. Out of 30 groups of the largest industrial processes, steel industry is on 7th place in ranking based on total global emissions from 2005 [1-3].

However, awareness of this state of affairs must not overshadow the significance of metallic materials such as steel. Steel is a unique material in its capacity to be continually recycled. Moreover, the process of steel production results in the generation of sustainable co-products such as slag which is further used by the cement industry. And finally, the steel products, which are characterised by a very advantageous combination of elasticity, strength, plasticity and strain hardening, are versatile, durable and affordable.

Hot rolling industry is the key link in manufacturing steel products. About 90% of all steel, about 80% of all metallics, and at least some fraction of the remaining engineering materials, are at some stage processed by hot rolling. Hot rolling industry delivers the input products for most if not all other industries.

Present trends in efforts to further optimise large industrial systems, including rolling mills, converge to strategy called Industry 4.0 and its extension 5.0. This strategy is closely intertwined

* The Author acknowledges the support by the STEM, the University of South Australia.

with aproaches such as machine learning, big data analytics, and virtual factory, all requiring the digitization of industrial records.

A new method for translating the morphometric (geometric and dimensional) RPD records into a structured database is introduced. This new format allows for employing statistical analyses onto a wide spectrum of pass geometries defined in the same vector space.

Problem description

The actual practice of rolling production continues to outstrip our theoretical understanding of it [1-5]. This means that expensive corrections and trials must be undertaken at the resource consuming industrial scale.

Various deterministic methods, such as finite element/difference modelling and slip-line-fields continue to be used in attempt to optimise the process within the deformation zone. FEM-based mathematical modelling of hot rolling of long products remains inferior to modelling applications in closed-die forging. Many of FEM focused publications neglect the comparison with real-world rolling operations due to dealing with only selected aspects of actual rolling processes, while omitting others [5].

The output metrics for evaluating the sustainability of rolling system include yield, productivity, reliability, quality and costs.

Ideally, hot solid steel should plastically flow through a sequence of passes in such way to maintain an optimal level in all five above listed indicators. The current state of the art in RPD is characterized by availability of a variety of models that enable correlating the effects of factors such as pressure, temperature, velocity, chemical composition, mechanical strength etc. These variables are already recorded in a suitable digital format. However, the resulting synergy of these variables is significantly affected by the phenomena embodied within the deformation zone which, in turn, depends on its morphometry. Analysing the deformation zone requires transforming the existing RPD information into generic vectors that allow for intelligent structuring a database embracing broad variety of rolling passes and series.

In other words, to enable statistical analyses of the industrial RPD records, there is a need to employ one-to-one translation of information represented by the way of examples in Figures 1 to 3 into an n-dimensional vector space. Each specific contour needs to be represented by a unique n-tuple vector, and there need to exist a unique translation from such vector into the pass contour.

a) "Rhomb" b) "Parallelepiped" c) "Round"

Fig. 1. Simple pass contours shown in y-x coordinates

Fig. 2. Complex pass contours

Fig. 3. Another example of a complex pass contour

Simple geometries

Simple geometries of interest include double symmetrical two-dimensional shapes similar to rhombus, rectangle, round, oval, hexagon and octagon. Figure 1 is drawn with having in mind that is enough to draw these shapes in 1st quadrant only.

It has been found that a series of the N-th order Chebyshev polynomials of the first kind, Tn , defined e.g. in [3x], allow for sufficiently precise fitting of the shapes shown in Figure 1.

Tn(g) = cos(n• acosQ), -1 <£< 1. (1)

The groove contour is defined by

N

f (*)=! aTn (§). (2)

n=0

Additional transformation allows for further homogenization of the pass contour database. Geometries illustrated in Figure 1 can be translated in the y-a coordinate system. A one-to-one mapping from the y-x coordinates into y-a coordinate system, and vice versa is defined by Equation (3) and Figure 4.

a = tan 1

У

(3)

Fig. 4. Example of transform from y-x coordinates to y-a coordinates

Complex geometries

Complex geometries presented in this manuscript include a broad variety of double-symmetrical shapes that are more intricate than the above group and also the shapes with a single axis of symmetry only. Several typical extremes are shown in Figures 2 and 3. For such cases the pass contour needs to be broken into two segments by defining a separation point at which the con-tactless curve has the first derivative dy/dx = w. The contactless segment of the groove contour is the portion of the pass where there is no contact between the rolled material and the groove surface. Usually, this segment coincides with the roll clearance zone - a gap between the roll collars. (There are certain peculiar RPD cases where several points exist each satisfying the condition dyldx = w, however, the choice of the separation point can be governed by introducing intelligent conventions.)

The cases where one-to-one mapping is not maintained in the 1st quadrant of the y-x system are quite frequent in the group of complex geometries. Therefore, the first step is to convert graph from the y-x coordinates into the x-L coordinates, as shown by the way of an example in Figure 5. The contour length L is measured "backwards" starting with the intercept of the pass contour with the x axis in the original y-x version (point where y = 0). Hence, the graph in x-L coordinates is inverted, i.e. L= 0 at the separation point.

L

Fig. 5. An example of conversion of the pass contour from y-x into x-L graph

Once the contour of the type illustrated by means of the example in Fig 5 is created, the digitizing procedure is the same as in the cases of simple geometries described above. The statistical models inferred from the database created in this way will need to be transformed twice during the reverse translation into the contours in the y-x space.

Creating a structured RPD database

Final steps in constructing an ordered database comprise creating digital twins for the series of analogous rolling processes by using the records from numerous production campaigns. Ideally, this would include the information such as:

1. Product specification describing the morphometry, tolerances, chemical composition, mechanical properties and other requirements (e.g. surface quality).

2. Specification of a series of transition objects; this includes the morphometric measurements of the intermediate passes.

3. Tools specifications (roll diameters, hardness, surface finish, material specifications).

4. Complementary documentation including heating, cooling and finishing conditions.

5. Rolling operation records (temperatures, velocity, productivity, yield, statistical process control documentation, delay records, and operation costs).

6. Maintenance records that include roll redressing and roll changeover/reliability records.

For RPD analyses, the variety of the above records can be reduced in the cases where some specifications are common for otherwise different products. Structured database can be narrowed down to the morphometric records related to rolling products that fit into the same category with regard to their pass configurations and complexity, chemical compositions of processed materials, mill specifications, etc.

Tasks for structuring morphometric database include:

1. RPD records collection.

2. Translation of records into mathematical forms.

3. Structuring database by ordering the Chebyshev coefficients for series of passes and products.

4. Statistical analysis and knowledge extraction from structured database.

5. Reverse translation of inferences into technical documentation.

6. Defining and testing the resulting RPD improvements.

Case analysis

An example of a structured RPD morphometric database for finishing pass in rolling round wire rod and bars is shown in Table 1. Finishing pass for this type of products typically consists of an "oval" shaped cross-section ("leader oval") being rolled in the finishing groove resulting in a "round" cross-section of a final product. The observed chemical composition of the rolled product (mild carbon steel) and the types of rolling mills are quite similar for all observed cases in this database, and hence are considered to be constant.

Table 1

Extract from the structured database showing Chebyshev coefficients for the penultimate oval

and the finishing round cross-sections (a few rows are selected to illustrate the variety of coefficients) [7]

OVAL •

с. С] c2 С, c4 G Cft C7 Cg c9 Сю Cu C0

1 2.922Э4 -3.15481 0.20270 0.10354 -0.11852 0 06226 -0.02004 -0.00125 0.00906 -0.00864 0.00527 -0.00215 2.40B70

2 4.14005 -4.09062 -0.24301 0.28051 -0.09199 -0.01847 0.02311 0.00089 -0.00842 0.00287 0.00304 -0.00420 4 21536

3 10.81863 -10,33275 .... 0.33401

.... ....

100 5.10708 -5.0S898 .... 4.26956

Transformations to Chebyshev polynomials of order N = 11 were applied to 100 observations. Statistical analysis of polynomial coefficients for finishing rounds revealed that all coefficients of order 1 to 11 are linearly dependent on the coefficient C0ROUND. Moreover, the coefficient C0ROUND

can be very strongly correlated to the "ideal" hot diameter of the round cross-section exiting the final pass as shown in Equation (4) for which the coefficient of determination is over 0.99 and alpha risk is less than 0.001 [7].

C0ROUND = 0-3015 • 0 round . (4)

Therefore, further inferences were made by examining the trends, correlations and patterns between C0ROUND and the coefficients corresponding to ovals.

In the case of the leader oval, the significance of Chebyshev coefficients decreases with the coefficient's order i.e. the coefficients C0, C1, C2, etc. affect the curve fitting validity (accuracy) and reliability (precision) much more than the coefficient C6 to C11 ) - see Eqn (5) and (6) and Tables 2 and 3 [7].

The correlations for the oval coefficients C0 to C4 with C0ROUND are quite strong, as shown in Equation (5) [7].

For n < 5 CnOVAL = An + BnC0ROUND + Cn (C0ROUND ) . (5)

For regression (5) the coefficient of determination is about 0.9 and alpha risk is less than 0.05 [7].

For i > 4 Coval = 0-5 (- E, ±[(E, )2 - 4D, F - 0^)] ^ ) D1. (6)

Table 2

Numerical values for symbols used in Eqn (5) and (6); N = 11 [7]

n 0 1 2 3 4

A 0 0 0.159585 0 0

B 1.236525 -1.2975 0 0.053117 -0.04433

C -0.00826 0.016285 -0.00791 0.000852 0.001786

i 5 6 7 8 9 10 11

D 136.1786 310.0893 861.3844 1374.67 2967.924 2872.801 4150.1881

E -17.018 18.30036 29.18851 0 66.73392 23.1678 0

F 5.397462 4.66491 4.841182 4.773652 4.861556 4.773281 4.783724

Table 3

Statistics obtained for correlations in Eqn (5) and (6); N = 11 [7]

n, i 0 1 2 3 4 5 6 7 8 9 10 11

Correlation Coefficient 1.00 1.00 0.83 0.95 0.92 0.59 0.62 0.58 0.54 0.51 0.63 0.62

Standard Error of Estimate 0.27 0.43 0.27 0.12 0.08 2.39 2.32 2.40 2.48 2.55 2.31 2.32

Alpha risk % 0.1 0.1 0.1 5.00 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

The above correlations are used in a study dealing with the problems observed during rolling wire rod 7 mm in diameter. The rolling mill operators reported rapidly increasing instability and vibrations at the finishing block consisting of 10 roll sets in a succession of horizontal and vertical configuration [4, 7].

The RPD morphometric database allowed for analyzing the curvature for the leader oval. The range of curvatures measured in over 100 observations is shown in Figure 6 using normalized coordinates. The curvature inferred from Equations (4) to (6) allowed for suggesting the change in the current oval groove bottom radius 12 mm to radius 9 mm (see Fig 7) [4, 7].

Fig. 6. Leader oval bar curvature distribution Fig. 7. Leader oval groove bottom modification [7]

The suggested modification is implemented in the observed rolling mill and the results of the series of industrial rolling campaigns confirmed the decrease in the instability [4, 7].

Conclusions

The requirements for further rationalisation of large-scale manufacturing systems involving rolling process have been recently amplified by the global environmental crisis. However, the practice of rolling production continues outstripping our theoretical understanding of it. This means that expensive corrections and trials must be undertaken at the very costly industrial scale.

The companies operating rolling mills increasingly recognize the new generation factory (I4 and I5) potential to radically improve the sustainability of complex industrial operations. The primary driving force for such advance is in utilization of big data analytics. There is a well-accepted general understanding about the importance of analysing actual industrial records. The most valid evidence about the interplay of all variables in a rolling mill and the ultimate outcomes is a factual manufacturing process. Rolling mill operations generate immense quantities of records, the digitization of which is one of the key preconditions for extracting hidden knowledge from this treasure. Sustainable systems that continuously learn and improve the performance of rolling mills are extremely valuable for the overall economy.

In this manuscript methods for translating morphometric information about the rolling passes into a structured database are presented. The proposed approach helps overcoming the computing barriers that prevent taking advantages of big data accumulated in rolling mill repositories. A digitized database created from over 100 observations of finishing passes in rolling round wire rod and bar has been used to infer correlations describing RPD trends and patterns.

Finally, a case study of a problem from an industrial rolling mill has been presented along with a solution - a groove contour modification to mitigate excessive vibrations at the finishing stage of rolling. This solution, based on knowledge inferred from a digitized morphometric database, has been validated in full scale industrial rolling.

A challenge is how to mobilise disconnected metalworking concerns and integrate accumulated databases to take advantage of giant leaps in process control and information technology to further optimise the hot rolling operations.

References

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