Application of the Finite-Element Analysis to the Pass Rolling Process

1. KOMMEK Applicationof the Finite-Element Analysisto the Pass Rolling Process Moscow State Instituteof Electronics and Mathematics (Technical University),Dep. Mathematical Simulation www.miem.edu.ru mmkaf@miem.edu.ru Professor, D.Sc. Chumachenko E.N. General Director KOMMEK Ltd. www.kommek.ru kommek@miem.edu.ru IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

2. KOMMEK Introduction The basic ratios and results of pass rolling process simulation using the SPLEN computing system developed based on the finite-element method (FEM) are discussed. The computing system allows setting any configuration of a roll profile, and presently it is used for studying isothermal and non-isothermal rolling processes with two symmetric rolls. In this model a rigid-ductile statement of the problem and special system of friction implementation are used. The computer system simulating the process of metal deformation in passes allows avoiding labor-consuming and expensive industrial experiments and reduces the time of developing technological solutions. Besides, at the design stage already, one can reveal defects of the rolled product form and working degree of the metal and thereby maximally approach a technological draft to the working one. To increase a solution algorithm speed, the half-analytical finite-elements method was used. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

3. Mathematical model of form changing hot materials KOMMEK Boundary conditions on the on the(1) on the - velocity of particles of continuum; - mill roller speed; - normal pressure; - normal to mill roller; - tangent stress; - directional cosines; - orthonormal frames; - constant of friction. (2) (3) Then and condition entry (4) IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

4. KOMMEK Heat exchange The heat exchange of the strip with rolls and with environment is described by the following variational equation: (5) where - is heat conductance coefficient; - is thermal capacity and density of the strip material; - is a generalized parameter dependent on the temperature difference of the strip and environment, Stephen-Boltsman constant, blackness coefficient of the body and on relative position of the surfaces when radiating; - is linear expansion coefficient for environment and rolls;; - is relative speed module of the movement with friction; - is a coefficient taking into account the part of released heat energy. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

5. KOMMEK For an arbitrary element of the strain focal point of a little enough thickness, the value characterizing relative elongation speed of the fibers in an element of the thickness dz, is constant: . In this case constant C in each section has its own value. Speed components of particles movement in any fixed element relative to the rolls surfaces look like: (6) a) b) A diagram of a focal point of strain at a longitudinal rolling (a) and stresses (b) applying to a layer of an infinitesimal thickness. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

6. KOMMEK Half-analytical of finite-elements method Thus, the three-dimensional speed field of an element is divided into two components. The speed field of in the section perpendicular to the rolling direction is determined from a finite-element approximation. The speed component along the rolling direction is calculated using an iterative procedure with a search of the constant C. So an initial volume problem for an element was reformed into a "generalized" two-dimensional problem which can be solved using the finite-element method. For a spatial stress-deformed state to be constructed, the length focal point of strain is divided into m parts by means of cross sections, and the value in each section at is determined. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

7. KOMMEK A spatial problem solution algorithm for each individual element is based on a minimization of the functional: (7) Finally the longitudinal movement speed of the particles in an arbitrary section can be determined by the ratio: , (8) where ; is the movement speed of an element at the focal point of strain input . IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

8. KOMMEK Experimental verification For model verification the experimental data obtained in expertises on study of a tension at rolling in smooth rolls, obtained earlier by professor Tarnovskiy I.J. utilized. Н0 , W0 -initial height and width of a strip; WF- averaged finite width of a strip. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

9. KOMMEK Experimental verification IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

10. KOMMEK Compare 3D and2.5D simulators A comparison of the considered model with a three-dimensional pass rolling version of J.J.Park and S.I.Oh accomplished in the SHPROL program based on the finite-elements method was carried out. SHPROL ▲Distribution of strain intensities on the surface of a rolled square section strip into oval at a stable mode. ◄ Diagrams of normal stresses at a focal point of strain when rolling a square section strip into oval.. SPLEN IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

11. KOMMEK An experimental test of the calculation results showed a high enough accuracy of forecasts for passes fillability at a profile rolling. The maximum error of the values characterizing geometrical parameters of a strip at a focal point of strain output in laboratory and industrial conditions did not exceed 6.4 per cent. Axial section of rolls when rolling a strip of square section in oval pass: - initial section of the strip; - section of the deformed strip. System SPLEN allows: - to model the rolling in groove; - to analyze the groove for optimal the ultimate article with respect to of process productivity filling the groove, the friction, the drawing, influence of roller temperature. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

12. KOMMEK When developing a new industrial calibration of rolls at the profiled rolling mill 320/250 ("Serp&Molot“ Works) for rolling strip steel of the 18x36 mm size of Steel 35, they decided to carry out a preliminary analysis based on imitating simulation using the SPLEN computing system. In conformity with the algorithm of numerical calibration test, of search and correction of the intermediate passes form, we accomplished a sequential change of initial calibration and solved problems of imitating simulation. Technological diagram of check and change of calibration IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

13. KOMMEK Change of a leader pass to product the most qualitative profile IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

14. Change of a leader pass to product the most qualitative profile KOMMEK IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

15. KOMMEK Physical simulation as result the mathematical simulation According to the changed calibration, a rolling was carried out, as a result of which a strip satisfying all preset requirements was manufactured. The deviation of the calculated results from the contour of a real template at the same mill adjustment did not exceed 1.5 per cent. The templates of a finish strip manufactured when rolling according to an initial (a) and changed (b) calibrations, and also according to a new calibration when rolling strips with cross sections of 18 x 36 (c), 20 x 32 (d) and 16 x 36 mm (e) a) b) c) d) e) IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

16. KOMMEK A trial test of the SPLENsystem during real calibrationsof the profile mills 500,300-2, 250-1 and the wiremill 250-2 is accomplishedin the Calibration Bureauof the MagnitogorskyMetallurgical Works.Specialists of the Worksmade the conclusion thatthe received results hada high degree of reliability,and graphic possibilities of the calculation results presentation are convenient to operate with. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

17. Resume KOMMEK The mathematical model and algorithms define a simulation of steadied calibrating process is designed. The response rate of designed systems on the degrees exceeds response rate of existing algorithms of spatial simulation calibrating process that is the important advantage at problem solving of optimization. On the basis of the above-stated method of application the operations on creation of a service system of simulation and optimization of manufacturing processes of rolling calibrating process are carried on. IKI Seminar «Mechanics, Control and Informatics» Moscow 2005

18. KOMMEK We employ the positive scientific results which came aboutdue to our extensive cooperation with: • National Institute of Aviation Technology (NIAT), Moscow, Russia • Research Institute of Metallurgical Machinery (VNIIMetmash), Moscow, Russia • Moscow Institute of Heat Technic (MIT), Russia • Harkov's Plant of Malushev, Ukraine • Joint Stock Corporation "Technomash", Moscow, Russia • Miass's Design Department of Machinery, Russia • Zlatoust's Machinery plant of V.I.Lenin, Russia AIRBUS INDUSTRY Aerospatiale Societe Nationale Industrielle, FranceDaimler-Benz Aerospace Airbus GmbH, GermanyConstrucciones Aeronauticas S.A., SpainBritish Aerospace (Operations) Ltd., England • Research and Industrial Company "Igsteel", Igevsk, Russia • Research and Industrial Aviation Company, Kazan, Russia • Bearing plants (Vologda, Kursk, Volgskiy), Russia • REINZ Dichtungs GmbH, Germany • Rolling plant “Serp&Molot”, Moscow, Russia • Magnitogorsky Metallurgical Works, Russia IKI Seminar «Mechanics, Control and Informatics» Moscow 2005