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On-line calculation of time optimal pass sequences for cold rolling on Sendzimir mills

86 pages
Industrial research and development
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ISSN 1018-5593
* *
European Commission
technical steel research
Mechanical working (rolling)
On-line calculation of time optimal pass
sequences for cold rolling on Sendzimir mills
Edith CRESSON, Member of the Commission
responsible for research, innovation, education, training and youth
DG XII/C.2 — RTD actions: Industrial and materials technologies —
Materials and steel
Contact: Mr. J.-L. Martin
Address: European Commission, rue de la Loi 200 (MO 75 1/10),
Β-1049 Brussels — Tel. (32-2) 29-53453; fax (32-2) 29-65987 European Commission
i eß&k jø&t
Mechanical working (rolling)
On-line calculation of time optimal pass
sequences for cold rolling on Sendzimir mills
O. Davies, P. Yates, J. Woodisse
British Steel, Swinden Technology Centre
Rotherham S60 3AR
United Kingdom
Contract No 7210-EA/823
1 August 1990 to 31 July 1993
Final report
Science, Research and Development
Neither the European Commission nor any person acting on behalf of the Commission
is responsible for the use which might be made of the following information.
A great deal of additional information on the European Union is available on the Internet.
It can be accessed through the Europa server (
Cataloguing data can be found at the end of this publication.
Luxembourg: Office for Official Publications of the European Communities, 1998
ISBN 92-828-3127-2
© European Communities, 1998
Reproduction is authorised provided the source is acknowledged.
Printed in Luxembourg
2.1 Schedule Optimisation g
2.2 Evaluation of the Objective Function 11
2.3 Operational Constraints4
2.4 Software Testing 15
3.1 The Temperature Dependence of Stainless Steel Yield Stress 1
3.2 Annealing Treatment7
3.3 Investigation of Anisotropy of Stainless Steel Yield Stress8
3.4 Conclusion and Implications to Rolling Mill Scheduling 19
4.1 Measurement of Roll Separating Force 21
4.2 Monitoring Sendzimir Mill Rolling using Torque Telemetry 24
1. Data used in Optimisation Program OPTI
2. Cold Rolling Model Input Parameters
3. Optimised Schedule Results and Computation Times
4. (a) Percentage Chemical Analyses ofType302XD Hot Band Material
(b)els of Type 302AA Hot Bandl
5. Mechanical Properties of Softened and Descaled 302AA Grade Stainless Steel Hot Band
6. Details of Cold Rolling Experiments, Starting Hardness 139-141 VPN
7.s of Cold Rolling, Starting Hardness 145-162 VPN
8. Details of Cold Rolling Experiments, Starting Hardness 160-182 VPN
9. 302XD Bright Annealed Rolling Schedules LIST OF FIGURES
1. Schematic of Optimisation Programme Modules
2. Total Strip Gauge Reduction Displayed as a Function of the Individual Pass Reductions
3. Schematic of Optimisation Search Space
4. True Stress ν Natural Strain Type 302XD Longitudinal Results of Tensile Tests
5.e Stress ν Natural Strain Type 302XD Transverse Results of Tensile Tests
6. True Stress ν Natural Strain Type 302XD Transverse Results of Tensile Tests at Different
7. True Stress ν Natural Strain Type 302XD Longitudinal Results of Tensile Tests at Different
8. Proportion of Martensite in the Tensile Test Specimens Against Test Temperature - Values
Determined by Ferriscope Measurement
9. Graph of Annealing Time in Furnace ν Final Hardness Values
10. Comparison of Cumulative Roll Separating Force with Initial Hardness
11. True Stress ν Strain Curves for Various Initial Hardnesses
12. Yield Stress of Grade 302AA Stainless Steel Obtained by Compression Testing
13. Ratio of Compressive and Tensile Yield Stress ν % Reduction
14. Sketch of a 63 inch Sendzimir Mill Housing
15.h of simplified Geometry Developed for Mathematical Modelling
16. Undeformed Mesh
17. Deformed Mesh (Magnified Displacement)
18. Vertical Strain Component (E22) as Viewed from the Front of the Mill
19.l Straint (E22) as Viewed from Mill Interior
20. Prototype Load Sensor
21. Gauge Output ν Applied Strain
22. Strain Sensor Output During Rolling
23. Screwdown Pressure Signal ν Gauge Output for Bottom Back-Up roll Eccentric Positions
24. Sendzimir Mill Torque and Speed Signals
25. Weighted Histogram of Torque Output for a Six Pass Schedule
26. Fourier Spectrum for Single Pass Torque Measurement 27. Work Roll Torque per Unit Width ν Input Gauge
28.k Roll Torque per Unit Width ν Total Fractional Reduction
29. Work Roll Torque per Unit Width ν Front Tension Stress for First Passes
30.k Roll 'Fitted' ν Measured Torque per Unit Width
31. Histogram of Residual Error/Mean Measurement Error
32. Calculated Yield Stress ν Reduction
33. (a) Fit to 40 Passes Residual Error for Remaining 25 Passes in Sample
(b) Fit to 50 Passes Residual Error for Remaining 15 Passes in Sample
(c) Fit to 60slr forg 5s ine
British Steel pic
ECSC Agreement No. 7210.EA/823
The aim of this project has been to test the feasibility of implementing the on-line calculation of time
optimised rolling schedules for Sendzimir rolling mills. Cold rolling is a complex physical process, which is
further complicated by the fact that hot rolled coils of stainless steel can have individual characteristics.
The variability in the properties of processed strip is generated by the natural fluctuations in processing
parameters that occur during casting, hot rolling, annealing, descaling and grinding. The variability of
hot rolled coil properties necessitates that on-line adaptive schedule calculations are performed during
subsequent cold rolling. The schedule calculations are therefore repeated after each pass. The new
calculations are based upon measurements of coil properties obtained during cold rolling, such that the
material in question is always rolled in an optimum manner.
Scheduling can be implemented in a number of different ways. Firstly, one can use a model to predict the
mill loadings and adjust the schedule until maximum rolling force and the minimum number of passes
have been achieved. The mill speed is free to vary from pass to pass at the discretion of the mill operators.
Adaption of the schedule is achieved by measuring roll separating force, from which the yield stress is
inferred and subsequent more accurate roll separating force are predicted. This approach is favoured for
reversing hot rolling mills, where rolling speed is limited. It would also be suitable for application on four-
high or Z-high cold rolling mills which have limited reduction and speed capability.
Alternatively, one can generate a model which predicts both the mill rolling force and maximum mill
speed throughout a schedule. A time optimum schedule may then be calculated which seeks to find the
balance between heavier draftings and faster rolling speeds. This approach is deemed to be applicable to
rolling on Sendzimir mills. These mills are generally equipped with powerful motors which allow rolling
speeds in the range 500-1000 m/min to be achieved. However, the rolling of quality stainless strip also
requires that certain criteria are obeyed regarding drafting, strip speed and tension. To achieve maximum
productivity of a high quality product, the schedule required must respect the rules applied, yet exploit the
available mill power. Schedule adaption can be implemented by using measured load data as a means of
refining the predictions made. However, it must be realised that adaption is also a means of error
correction. One cannot claim to have time optimised scheduling if the result on rolling requires
continuous large error correction. One must therefore aim to achieve suitable accuracy in the predictions
of the model such that adaption represents a small perturbation to the predictions.
The proposed solution to this problem is a computer software package capable of providing calculated
schedules within the time required to roll one pass. Thee developed must therefore contain all the
information required to predict the rolling forces generated at the work roll for any proposed reduction
sequence. The main elements of the proposed system are shown in Fig. 1. Essentially the system consists
of an optimising procedure, a model of the mill mechanics, and a model of cold rolling describing the
behaviour of stainless steel strip during rolling reduction.
The approach sought is both theoretical, in that the aim is an improved understanding of the cold rolling
processes, and practical, in that a focus has been retained on the overall aim of the project and its
importance to stainless strip manufacturers. Hence, both theoretical and empirical models of material
behaviour under deformation have been included in the design of the software package. More details of
the software and its functionality are given in Section 2. The optimisation procedure can be successful only if it can accurately predict the behaviour of the strip
under any given processing conditions. Therefore, the mechanisms which control the yield stress of rolled
stainless steel strip have been investigated. This work is described in Section 3 below.
In order for adaptive scheduling to be implemented, a measure of a coil's properties during rolling must be
obtained; this is best achieved by measuring rolling load. Great effort has therefore been expended in
attempting to sense the roll separating force generated by a production Sendzimir mill. This work is
detailed in Section 4 of this report.
Alarge suite of software has been developed for the calculation of optimised rolling schedules. The
program has been written in FORTRAN 77 and consists of numerous subroutine modules. Great care has
been taken to ensure that the code operates in an efficient manner, both in terms of the number of
calculation steps required and the memory allocation demanded. Figure 1 shows the connectivity of the
main program modules; the function of these routines is discussed below. The source code requires a
storage capacity of 100 kb. The program can therefore be operated on a personal computer of reasonable
capacity. The code can be thought of as comprising two parts, the optimisation algorithm, which locates
the minimum of the function, and the function algorithm, which computes the objective function to be
minimised. In Fig. 1, the routines which comprise the function evaluation are located within the large
box. The two components are discussed more fully below.
2.1 Schedule Optimisation
The optimisation routine provides the main driving force of the programme. This module has been
significantly developed since first reported. The aim has been to develop an algorithm that calculates the
rolling schedule which minimises the total processing time, and which completes the required calculations
within a time suitable for on-line mill application. To ensure these aims are met the structure of the
problem have been exploited to the maximum. The function to be minimised is the total rolling time T,
this is given by:
Τ = V t. ··■(!)
wheret¡isthetimetorollthe ith of η passes. Τ does not include the inter-pass delay time. Thistimeisnot
afunctionoftheparameters which control the schedule and thus would only be presented asanegligible
additiveconstantifincluded in the above equation.
The values t¡ are dependent upon the reductions and tensions used for each pass. The rolling time is thus
dependent upon the variables x¡, Sf¡, Sb¡, where Sf¡ and Sb¡ are the front and back tensions respectively. The
parameter x¡ is defined as:
h. , - h.
x. = -^ l- ..-(2)
1 h0­hn
where ho is thestartingstripthicknessand h, is the thickness after rolling pass i. This variablehasbeen
specifically choseninpreferencetothe fractional reduction achieved at each pass. This isbecausethe
values of x¡ mustsatisfy:

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