Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. ANALYSIS OF WORK ROLL THERMAL BEHAVIOR FOR 45MM HOT STRIP MILL WITH GENETIC ALGORITHM HONGBO LI, 2 JIE ZHANG, 3 YONGMEI ZHANG, 4 XUTAO ZHENG, 5 YI SU, 6 HONGLIANG CHEN Scool of Mecanical Engineering, University of Science and Tecnology Beijing, Beijing, Cina 2 Guofeng Iron and Steel Co.Ltd, Tangsan, Cina E-mail: liongbo@ustb.edu.cn, 2 zangjie@ustb.edu.cn, 3 zym_6@26.com, 4 tribe987@63.com, 5 efredsuou@63.com, 6 aricecen@yaoo.com.cn ABSTRACT Work roll termal contour is one of te important factors for roll contour design and configuration in ot strip rolling, for wic te temperature field calculation is a critical factor. To realize te work roll termal beavior for 45mm ot strip mill, te temperature field and termal contour calculation model was built wit finite different metods, and te genetic algoritm was introduced to te model parameter optimization in order to improve te simulation precision. It was proved tat te model can matc te engineering precision requirement by te comparison between several and measured values of te work roll temperature. Wit te model, te work roll termal contour variations in a rolling process, as well as te effect of rolling rytm and sifting strategy on te work roll termal contour were calculated. Te results sow tat te work roll termal crown varies relatively fast at te beginning of a rolling unit, and ten tends to be stable. In te rolling process, te rolling rytm sows great influence on te work roll termal contour, wile te sifting strategy sows little influence. Keywords: Hot rolling, Work roll, Termal beavior, Genetic Algoritm. INTRODUCTION A 45mm ot strip rolling production line as produced tin strips wit considerable good quality soon after its operation in 8. To furter improve te stability of te strip production and te profile quality of te strips, it is essential to analyze and optimize te configuration of te roll contour. Since te temperature field calculation is te critical factor in work roll termal contour, wic is one of te most important factors for work roll design. Domestic and foreign scolars ave paid a lot attention to te building of a rational work roll temperature field and termal contour forecast model wit ig calculation accuracy. Most models are based on te basic law of eat transfer and calculate wit modern numerical metod suc as te analytic metod [-2], te finite element metod [3-4] and te finite difference metod [5-9]. Among tem, te finite difference metod gains a wide range of application in engineering, because of its simple and quick calculation and ig calculation accuracy. For calculating te temperature field wit finite difference metod, te most critical problem is te building of different calculating model and te treatment of boundary conditions, especially te latter, wic aims to truly reflect te eat excange of te work roll in te rolling process. It is very difficult to give an accurate expression of te work roll eat excanging in te wole rolling process, so certain assumptions are necessary[5-9]. In addition, it is difficult to accurately determine te eat transfer coefficients in te simulated calculation, suc as te eat transfer coefficients between te work roll and te strip, te cooling water, and te air. Tis is mainly because of te complexity of te rolling process. Terefore, te work roll temperature field is still difficult to calculate accurately. So it is advisable to searc for eac eat transfer coefficient suitable for a certain rolling mill based on te actual production data to furter improve te calculation accuracy of te work roll temperature field. Applying genetic algoritm to te parameter optimization of te work roll temperature field contributes to improving te calculation accuracy of te temperature field and laying a good foundation for mastering te work roll termal beavior accurately. 76
Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. 2. THE TEMPERATURE FIELD AND THERMAL CONTOUR CALCULATION MODEL OF 45MM HOT STRIP MILL Heat conduction equation & difference equation. Te work roll is geometry symmetrical and te variation of its termal boundary is strictly cyclical. In te study of termal contour caused by temperature, te circumferential temperature fluctuation tat occurs in te roll surface can be simplified and te variation along te circumference can be neglected, tus te temperature field can be converted to a two-dimensional problem. For tis reason, te eat conduction equation in cylindrical coordinate system can be express as: 2 2 T λ T T T = + + 2 2 t ρc r r r x () Were, T is temperature; t is time; λ is termal conductivity of te material; ρ is te density of te roll material; c is te mass eat capacity; r is te radius coordinate; x is te axial coordinate. First a mesing model sould be built, te axial space step noted as x and te radius space step noted as r. Via te metod of controlling volume balance, te relevant differential equations were establised based on te caracteristics of te boundary conditions. And ten based on te energy λ t ρc( x) 2 conservation law, noted ρc λ t ( r) 2 as fx and fr a te internal grid point s differential equation turned to be: T = T + frt + fxt + fxt n+ n n n n i, j i, j i, j i, j i, j+ r n r n + fr + Ti +, j 2 fr + fr + 2 fx Ti, j r r (2) Similarly, te differential equations of te surface boundary, te side element, te end region element, te corner element, te core element and te core element of te end region can be establised. Te determination of influencing factors. Te main factors of te boundary eat transfer are te contact eat transfer between te work roll and te strip, as well as te convective eat transfer between te work roll and te cooling water accompany wit te air. In order to simplify te engineering calculation, te equivalent eat transfer coefficient metod is used in te model. Wit te equivalent contact eat transfer coefficients between te work roll and te strip, te work roll and te cooling wate, as well as te work roll and te air noted as a, te relationsip of te ot-flow density and te equivalent eat transfer coefficients can be acquired via te tird type of boundary conditions. Te parameters of te temperature field model can be classified into two categories: te first category is te known parameters wic can be acquired directly or via certain formula suc as ambient temperature, te temperature of cooling water, te pysical parameters of te work roll, te strip widt and te rolling rytm, tey are all noted as parameter E; te second category is te undetermined parameters, namely te equivalent contact eat transfer coefficients a.ten te temperature field defined as T( t) f ( E,,,, t) s w a at moment t can be Te optimization of te model parameters wit genetic algoritm. Te initial value of a can be acquired by te traditional teory formula and experience. In order to make te simulation model matc te actual condition and meet te need of engineering simulation analysis, te genetic algoritm was introduced into te optimization of te tree parameters. Noted te design variables to be optimized as vector to be H = (,, ), ten te T( t) f ( E, H, t) s w a. turned Wit te 45mm ot strip mill F5 stand as te study object and te of work roll temperature as te calculation foundation, te temperature field model parameters were optimized. Wit te Genetic Algoritm and Direct Searc Toolbox in MATLAB, te objective function is defined as: Nm Nt F = ( T (, i, t ) T (, i, t )) Were, i= Nm optimization; c n m n 2 (3) is te number of te rolls used in te N t is te number of te points 77
Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. Tc measured in te temperature field; is te actually measured value of te work roll surface T temperature field; m is te value acquired from te model. Te calculation model of te termal contour. Te termal contour of te work roll can be solved by using te analytic metod after te temperature distribution is acquired. Te work roll could be assumed as a cylinder wit infinite lengt because its axial lengt was long enoug. Te displacement was irrelevant to te direction of te axis and te temperature field was symmetric about te center section of te roller. Based on te simultaneous basic stress and strain equations of te termo u( x, t) elasticity teory, te diameter expansion of te roll at moment t was described as follows [9]: + νβ u x T r rdr c r r 2 ( ) = ( ) + + ν r (4) r Were, ν and β are Poisson's ratio and te coefficient of te linear expansion respectively, r is te radius. Ten te termal contour D( x, t) calculated via te following formula: (, ) = u ( x, t) u ( x t ) u ( x t) D x t w, + d, / 2 c can be (5) Te validation of te simulation model. Te parameter vector H gained in te genetic algoritm optimization was validated by te 5 series of data. Te comparison between te model results and te actual results was sown in Figure. It reflected tat te calculation value generally coincided wit te actual value but tere was also relatively large deviation at some points, especially te calculation value of te 5t series. Tere may be some reasons suc as: Te rolling rytm used in te model calculation is not te actual rolling rytm, in oter words, te input is not te actual rolling time and intermittence time, but te average value of te rolling rytm. After a rolling unit and before unloading te work roll, tere were still cooling water works on te rolls about ~2 minutes, wic is difficult to measure accurately. After work roll unloading, te cooling water remains on te surface of te work roll wic influences te test results. It is difficult to make every series of data to be te optimal parameters. All te factors mentioned lead to te difficulty in te consistence between te off-line simulated calculation and te actual condition. So it is feasible to use a model tat can just meet te need of engineering calculation. 5 3 5 3 5 3 5 3 5 3 33 6 99 3 65 33 6 99 3 65 33 6 99 3 65 33 6 99 3 65 33 6 99 3 65 Figure Te and te calculated values of te work roll temperature 78
Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. 3. ANALYSIS OF THE WORK ROLL THERMAL BEHAVIOR FOR 45MM HOT STRIP MILL After te validation, te simulation model can be used to analyze te work roll termal beavior for 45mm ot strip mill, in order to improve te strip profile control tecnologies. Te variation of te termal contour in te rolling process. In a service period of a work roll, if tere is no work roll sifting, te rolling rytm is 8s (rolling time)/45s (intermittence time) and te strip widt is mm, te variation of te termal contour is sown in Figure2. It can be seen tat te termal contour is increasing gradually wit te proceeding of rolling. Te variation of te termal crown is sown in Figure3. In te rolling process of te first strips, te termal crown increases rapidly, and ten te increasing rate of te termal crown decreases gradually and tends to be stable. Te effect of te rolling rytm on te termal contour. Wile te rolling time remains 8s, and te intermittence time is 45s, 65s and 85s, te corresponding termal contours are sown in Figure4 (te sifting step is 5mm and te sifting stroke is 8mm) after pieces of strips ave been rolled. It can be seen tat te termal contour varies obviously wit te cange of te rolling rytm. Te variance of te termal crown of te work roll is about µm wen te intermittence time canges from 45s to 65s; and it is about µm wen te intermittence time canges from 65s to 85s. Te termal contour doesn t vary linearly wit te cange of te intermittence time, and te faster rolling rytm as greater influence on te termal contour. Te effect of te sifting strategy on te termal contour. Te sifting strategy mainly as two factors: te sifting stroke and te sifting step. Te effects of te two factors on te termal contour are analyzed as follows. Cange te sifting step and keep te sifting stroke constant Using te same rolling parameters just mentioned, te variation of te termal contour is analyzed wen te sifting stroke was ±8mm and te sifting step was 5mm and mm respectively. In order to make te work rolls ultimate axial position unanimous, 97 pieces of strips are rolled and te strip widt is mm. After te work roll service period, te termal contours are sown in Figure5. termal contour/µm termal crown/µm termal contour/µm 8 t t t 8t t 33 6 99 3 65 Figure 2 Work roll termal contour variation in a rolling process 8 8 strip No. Figure 3 Work roll termal crown variation in a rolling process 8 8s/45s 8s/65s 8s/85s 33 6 99 3 65 Figure 4 Work roll termal contours wit different rolling rytm It can be acquired tat wen te sifting stroke remains uncanged, te cange of te sifting step as little influence on te temperature field and te termal crown, and only causes te translation along te axial direction of te roll. It is mainly influenced by te strip distribution probability along te axial direction wic is caused by te cange of te sifting strategy. Cange te sifting stroke and keep te sifting step constant Te sifting step remained 5mm and te sifting stroke was canged from ±8mm to ±mm. Te influence on te termal contour is sown in Figure6. It can be acquired tat te cange of te sifting stroke also as little influence on te termal contour wen te sifting step remains uncanged. 79
Journal of Teoretical and Applied Information Tecnology 3 t September 2. Vol. 43 No.2 5-2 JATIT & LLS. All rigts reserved. termal contour/µm 8 sifting step 5mm sifting step mm 33 6 99 3 65 Figure 5 Work roll termal contours wit different sifting step termal contour/µm 8 sifting stroke 8mm sifting stroke mm 33 6 99 3 65 Figure 6 Work roll termal contours wit different sifting stroke 4. SUMMARY () Wit te equivalent contact eat transfer coefficients between te work roll and strip, te work roll and te cooling water, as well as te work roll and te air as te optimization objects, te genetic algoritm was used in te parameter optimization of te temperature field calculation model, making te temperature field and termal contour model meet te demand of engineering calculation precision. (2) Wit tis model, te work roll termal contour variation in a rolling process of 45mm ot strip mill is calculated. In te earlier stage of te rolling process, te termal crown of work roll increases rapidly, and ten te increasing rate decreases gradually and tends to be stable gradually. (3) Te effect of te rolling rytm on te work roll termal contour is calculated. Te results sow tat te termal contour doesn t vary uniformly wit te cange of te intermittence time. It can be concluded tat te faster rolling rytm as greater influence on te termal contour. (4) Te effect of te sifting strategy on te work roll termal contour is calculated. Te results sow tat te sifting strategy ad little influence on te termal contour. Foundation Item : Item Sponsored by te Metallurgy Researc Foundation of USTB (YJ-) REFERENCES [] S.Jarrett and J.M.Allwood. Ironmaking and Steelmaking, Vol.26, no6, 999 pp439 [2] D.F. Cang. Journal of Materials Processing Tecnology, Vol.94, no,999, pp45 [3] B. G. Cen, X. L. Cen and A.K.Tieu. Iron and Steel, Vol.26, no8, 99 pp [4] P. A. Atack, Robinson I S. Iron Making and Steel Making, Vol.23, no, 996 p.69 [5] V.B. Ginzburg. Iron and Steel Engineer, Vol.74, no., 997 P.38 [6] X. L. Zang, J. Zang and G.Wei et.al. Metallurgical Equipment, 2, no33, pp [7] L. P. Yang, Y. Peng and H. M. Liu. Journal of Iron and Steel Researc, Vol., no4, 4 pp29 [8] Z. F. Guo, J. Z. Xu and C S,Li et.al. Journal of Norteastern University (Natural Science), Vol.29, no4, 8 pp57 [9] L. S.Wang, Q. Yang and A. R. He, et al. Journal of University of Science and Tecnology Beijing, Vol.32, no7, pp922 8