CC BY
5S. Spuzic
The University of South Australia
A CASE OF DIGITIZING THE DEFORMATION ZONE IN UNIVERSAL MILL1
Abstract. It is widely recognised that digitizing industrial records is a precondition for implementing the system optimisation based on the industry 4.0 (I4) methods such as big data analytics, digital twins, and machine learning (ML). While many variables in the processes such as forming of solids are already recorded in a suitable digital format, i.e. temperature, velocity, forces etc, are readily measured online, the information about the morphometry of the deformation zone needs to be translated into a digital format that is more suitable for embracing the broad variety of geometries. In this manuscript, one approach to resolving this task for the deformation zone observed in rolling the universal sections is presented.
Keywords: digitizing, universal rolling, deformation zone.
Introduction
Since the 1st universal beam mill appeared in Luxembourg in the early 1900s, efforts have been made to establish satisfactory models of the main factors, such as flange spread, roll separating force and a forward slip [1].
However, the traditional empirical analysis models that were derived from the plate and strip rolling theory cannot meet the increasing requirements of high precision, high quality, and high productivity. Analysis of the universal rolling process is more difficult than that of a 2-high mill because of the more complicated deformation zone.
The process designers are aiming at the ideal combination of the morphometric components in the series of subsequent passes illustrated in Fig. 1. If the morphometry of the bar coming out of the break-down (2-high) mill is designed correctly, the bar will be shaped without the cross-section distortion in the subsequent series of passes in the universal mill and the edger mill.
Fig. 1. Series of passes in rolling universal beams: a) break-down shape coming out of the 2-high mill; b) the profile rolled in the universal mill;
c) the profile obtained in the edger mill [2]
In addition, the deformation zone in the universal mill also needs to be appropriately designed with regard to all aspects of the morphometry (Fig. 2).
However, it is well known that universal rolling of H-beams and columns shows complicated behaviour of material flow between the web and the flange. For example, so-called bulging (Fig. 3) occurs when the flange height hf (see Fig. 2) in the roughing universal mill becomes in the practice larger than predicted.
1 Acknowledgment: The author acknowledges support by the STEM organisational unit operating within the University of South Australia that provided the resources needed for realising the related research.
Consequently, an uncontrolled increase in the flange height reduction (Ahf) during the subsequent pass conducted in the edger leads to the excessive flow of the rolled material in the lateral direction (parallel to the edger roll axis). Bulging leads to rapid wear of the vertical roll during the rolling in the universal mill and to the flange tip distortion in the final products [2].
Fig. 2. Universal beam groove and the rolled profile [3]
Fig. 3. Deformation of the flange tops after edger rolling [2]
A number of researchers attempted to predict the material flow in this rolling configuration by using various analytical methods, including FEM as well [3, 4]. However, the recent strategies based on big data analysis of the records collected in the actual rolling mills are shown to be more promising [5].
To this end there is a need to translate the industrial records into digital format as shown by the way of the following examples. In this manuscript it is illustrated how the universal mill deformation zone records can be converted into a format suitable for the big data analytics, ML and digital twins.
Digitizing procedure
A number of the process variables such as chemical composition, velocities, temperatures, and forces, are recorded in a digital format that is already suitable for statistical analyses. This, however, is not the case with the deformation zone morphometry (geometry and dimensions). Typically, this category of records is stored in the form of technical drawings such as shown in Fig. 2, 4, and 5.
As it can be observed in Fig. 5, for x > 422.52 mm there are two corresponding points on the red coloured contour. To avoid this the contour is transformed from the y — x system into x — L system of coordinates. To maintain the database structure consistency, the same transformation is applied to the antecedent and the posterior passes as well.
Tables 1 and 2 show an excerpt for the Fig. 4 points translation between the two coordinate systems. Note that the L values are calculated backwards starting with xmax = 448.5.
Fig. 4. The technical drawing defining the cross-section of the bar at the entry into the universal mill; the cross-section is double symmetrical, hence the 1st quadrant is shown only
(the linear dimensions are in mm)
Fig. 5. The technical drawing defining the cross-section of the bar after rolling in the universal mill as indicated in Fig. 1b, and Fig. 2 (the linear dimensions are in mm)
Table 1
Excerpt of the equations used for the Fig. 4 points translation between two coordinate systems
X у AI l X
448.5 0 0 0 =P2
448.5 0.77956458866404 =SQRT((Q3-Q2)A2+(P3-P2}A2) =S2+R3 =P3
448.5 1.55912917732851 =SQRT((Q4-Q3)A2+(P4-P3)A2) =53+R4 =P4
448.5 2.33869376599298 =SQRT((Q5-Q4)A2+(P5-P4)A2) =S4+R5 =P5
448.5 3.11825835465745 =SQRT((Q6-Q5)A2+(P6-P5)A2) =S5+R6 =P6
448.5 3.89782294332237 =SQRT((Q7-Q6)A2+(P7-P6)A2) =S6+R7 =P7
448.5 4.67738753198662 =SQRT((Q8-Q7)A2+(P8-P7)A2) =S7+R8 =P8
448.5 5.45695212065108 =SQRT((Q9-Q8)A2+(P9-P8)A2) =S8+R9 =P9
448.5 6.23651670931578 =SQRT((Q10-Q9)A2+(P10-P9)A2) =S9+R10 =P10
448.5 7.01608129798025 =SQRT((Q11-Q10)A2+(P11-P10)A2) =S10+R11 =P11
448.5 7.79564588664472 =SQRT((Q12-Q11)A2+(P12-P11)A2) =S11+R12 =P12
448.5 8.57521047530942 =SQRT((Q13-Q12)A2+(P13-P12)A2) =S12+R13 =P13
448.5 9.35477506397389 =SQRT((Q14-Q13)A2+(P14-P13)A2) =S13+R14 =P14
448.5 10.1343396526383 =SQRT((Q15-Q14)A2+(P15-P14)A2) =S14+R15 =P15
448.5 10.913904241303 =SQRT((Q16-Q15)A2+(P16-P15)A2) =S15+R16 =P16
448.5 11.6934688299675 =SQRT((Q17-Q16)A2+(P17-P16)A2) =S16+R17 =P17
448.5 12.473033418632 =SQRT((Q18-Q17)A2+(P18-P17)A2) =S17+R18 =P18
448.5 13.2525980072967 =SQRT((Q19-Q18)A2+(P19-P18)A2) =S18+R19 =P19
448.5 14.0321625959609 =SQRT((Q20-Q19)A2+(P20-P19)A2) =S19+R20 =P20
448.5 14.8117271846258 =SQRT((Q21-020)A2+(P21-P20)A2) =S20+R21 =P21
448.5 15.5912917732901 =SQRT((Q22-Q21)A2+(P22-P21)A2) =S21+R22 =P22
Table 2
Excerpt of the numerical values for the Fig. 4 points translation between two coordinate systems
X У Л1 i X
448.50 :.:эоооо :.:эооо с.:эооо 448.50
44B.50 0.779565 0.77956 0.77956 44В. 50
448.50 1.559129 0.77956 1.55913 44850
¥ 448.5 D 2.33B694 0.77956 2.33869 44850 X
SM 448.5 D 3.11S258 0.77956 3.11S26 448.50 5D0.HJ 45D.D0
448.5 D 3.897823 0.77956 3.89782 448.50
250 448.5 D 4.6773BB 0.77956 4.67739 44В. 50
448.50 5.456952 0.77956 5.45695 44850 ¿DDOO
2öD 448.5 D 6.236517 0.77956 6.23652 44850 35D.HJ
448.5 D 7.016081 0.77956 7.0160S 448.50 5DD.D0
ISO 448.50 7.795646 3.77956 7.79565 448.50 гэпш
448.50 B.57521 0.77956 B.57521 44В. 50 ÎDD.DO
lOD 448.50 9.354775 0.77956 9.35478 44850
SO 448.50 10.13434 0.77956 10.1343 44850
448.50 10.9139 0.77956 10.9139 448.50 1DQ.DG
448.50 11.69347 0.77956 11.6935 448.50 5D.D0
448.50 12.47303 0.77956 12.473 44В. 50 D.DD
□ 1DD 200 300 4DD 500
448.50 13.2526 0.77956 13.25 26 44850 и 1UU 2UU SiXJ ьш /ии ыии !
448.50 14.03216 0.77956 14.0322 448.50
448.50 14.81173 0.77956 14.8117 448.50
448 40 15 59134 0 77956 15 5Ч1Ч 448 50
Analogous translations applied to the contour in Fig. 5 resulted in the x - L diagram shown in Fig. 6.
л: L
Fig. 6. Translation of the red-coloured contour in Fig. 5 from the initial y — x into the blue-coloured contour defined in the x — L coordinate system
The following digitizing procedure defined in [6] and [7] and illustrated in Fig. 7 results in the 6x6 square matrix.
Magnification of the blue-contour segment on the left of the point 5. The points b and c are chosen analogously to capture the rapid changes in the derivations that can be observed between the points 6 and 7, and on the right-side of the point 8.
Fig. 7. Transformation from x-L coordinates into x— a data, and the 12 points resulting in 12 coefficients obtained by applying Chebyshev transform (N = 11)
The 1st quadrant representation of the cross-section shown in Fig. 4 to 6 is characterised by three distinct segments where the derivation of the contour graph undergoes a rapid change. This is illustrated in Fig. 7 by magnifying the portion in the vicinity of the point 5. Similar rapid changes in the derivations can be observed between the points 6 and 7, and in the vicinity of the point 8.
Analogous triple local changes can be identified in the case of all other passes used in rolling the universal beams. Therefore, to increase the digital precision, the density of the reading points need to be increased within such zones. One way of achieving this is to introduce additional Chebyshev transforms (N = 5). This is illustrated by capturing one of such segments within the green frame as indicated in the magnification in Fig. 7. The segment boundaries are defined by the LA and Xa coordinates of the point A which is an x - L representative of the fillet-arc-centre defined in the original y — x coordinate system. The Chebyshev transforms for the remaining two segments and the corresponding points B and C are defined in analogous fashion. This includes shifting the points A, B and C to the origin, and in the case of the point B, a rotation about the origin to bring the segment in the 1st quadrant.
This allows for structuring the matrix M:
M =
Q Ci C2 C3 C4 C5
Q C7 Cg C9 Ci0 Cii
xa La xb Lb xC Lc
C0 a c1a c2 a C3 a C4 a c5 a
C0 b c1b c2 b c3b c4 b c5b
Coc Cic c2c C3C c4c C5c
(1)
where Ci - coefficients of the Chebyshev polynomial of the first kind ( N = 11; i = 0, 1, 2, ... 11); Xj - the xi, Lj coordinates of the points A, B and C (see Fig. 7); j = A, B, C ; Cnj - coefficients of the Chebyshev polynomial of the first kind (N = 5; n = 0, 1, 2, ... 5).
Selected values for the case of the contour shown in Fig. 4 are presented in matrix Mx:
m1 =
309.1646 -304.446 1.369315 - 41.2972 3.745533 12.40607
- 20.67 43.12561 -48.0837 49.14705 - 21.2757 16.81446
209.2461 433.9052 xb Lb xc Lc
88.9853 3.636816 3.556178 2.946475 2.094483 1.086476
c0b C1B c2b c3b C4 b c5b
c0c Qc c2c c3c c4c C5c
(2)
The matrix N is defined for the contour shown in Fig. 5 following the analogous procedure. The deformation zone that takes place in the universal rolling configuration shown in Fig. 1b is digitally defined by the matrices M and N, and by the roll diameters.
Conclusions
While the above procedure allows for precise reproduction of the original contour by starting from the digital matrices, the statistical analyses of the large collection of digitized cases will result in extracting the patterns, trends and correlations. These extracts will result in obtaining clouds of the points dispersed along an average smooth contour which can be inferred within the boundaries defined by the standard errors of the estimates. One way of using these inferences is to observe whether the deformation zone of a process of interests falls too far from the inferred regression function, or even beyond the confidence limits.
Practical application of the above approach to actual rolling processes requires an access to the industrial records stored by the industrial corporations. The onus is on the organisations such as the institutions and associations of engineers and the steel industries to encourage the corporations to start sharing the relevant data and utilise the full potentials of the I4, ML, digital twins and the big data analytics to further optimise the actual rolling systems.
References
1. Jin X.G., Liu Y.L., Lian J.C., Wagoner R.H. A three-dimensional analysis of the universal beam tandem rolling process: Part I // Deformation analysis Journal of materials processing technology, 2000. Vol.102(1). P. 59-64.
2. Hayashi H., Saito S., Kataoka K., Nagayama E., Takahashi K. Mathematical Models for Setup Control System in H-beam Universal Rolling, Tetsu to hagane, 1993. Vol.79(12). P. 1338-1344.
3. Nepryakhin S.O., Shilov V.A., Shvarts D.L. Metal Flow and Forces when Rolling I Beams in Universal Grooves // Steel in Translation, 2014. Vol. 44. №11. P. 842-846. © Allerton Press, Inc. (original Russian text published in "Stal", 2014. №11).
4. Takashima Y., Yanagimoto J. Finite Element Analysis of Flange Spread Behavior in H-beam Universal Rolling // Steel research international, 2011. Vol. 82(10). P. 1240-1247.
5. Spuzic S. A Case of Application of Data Transforms // WSEAS Transactions on Computers, 2021. Vol. 20. P. 126-134.
6. Spuzic S., Kinzin D.I. A Contribution to Digitizing the Deformation Zone of Complex Geometry // Kalibrovochnoe Byuro, 2020. №18. P. 5-14. URL: http://passdesign.ru/namber18.
7. Spuzic S. Translating Morphometric Information About the Rolling Passes Into a Structured Database // Kalibrovochnoe Byuro, 2020. №17. P. 5-12. URL: http://passdesign.ru/namber17.
