STRIP THICKNESS ESTIMATION IN ROLLING MILLS FROM ELECTRICAL VARIABLES IN AC DRIVES

Latin Ameican Applied Reseach 39:353-359(2009) STRIP THICKNESS ESTIMATION IN ROLLING MILLS FROM ELECTRICAL VARIABLES IN AC DRIVES N.S. MARCELLOS, J.F. DENTI and G.C.D. SOUSA Pof. Eletotécnica, CEFETES, ES, Basil;. nilson@cefetes.b, Pof. Depto Eng. Elética, UFES, ES, Basil; j.denti@ele.ufes.b, g.sousa@ele.ufes.b Abstact The lage-scale utilization of steel in the moden society highlights the impotance of the lamination pocess, and poses new demands fo advanced technologies in the electomechanical equipments as well as fo the contol systems. Seveal pocess paametes, such as stip thickness, fiction, tension, tempeatue, and olling speed have a stong influence in the quality of the final poduct, and stategic impotance in the contol system. This pape intoduces a method to obtain the toque and olling mechanical powe estimates in eal time, without utilization of lamination pocess models. In contast to existing techniques, in this wok these estimates ae deived fom stato electical vaiables, eadily available in AC dives. This wok also discusses the utilization of the toque and olling mechanical powe estimates to detemine input and output stip thickness, by means of a neual netwok. Simulation esults ae pesented and compaed to eal industial data to demonstate the validity of the poposed technique. Keywods Stip thickness estimation, olling dive system. I. INTRODUCTION A olling mill system is typically fomed by olls that educe the stip dimension by lamination foces, and ae commonly equipped with seveal instuments, actuatos, and contol devices. Cuent olling mills employ complex compute pogams which equie the knowledge of oll foce, and ely on micopocesso contol to povide seveal infomation, equied fo nomal opeation, as well as fo inputs to new olling mills design. Vaiables such as oll load, toque, powe, and vibation ae deived by mathematical models, and play a fundamental ole in the pocess pefomance. Seveal opeating paametes ae monitoed and contolled to waant poduct quality. Fig.1:Rolling mill and moto dive. Some vaiables such as stip thickness, yield stess, 353 fiction coefficient, stip tension between stands, tempeatue, and oll speed all have intense influence in the end poduct quality, and stategic impotance in the contol system pefomance. Roll foce, toque, and mechanical powe obtained by diect measuement o calculation ae fundamental to pocess contol system. The knowledge of the toque magnitude enables the identification of seveal pocess paametes, and can be decisive in the identification of fatigue effots that the mechanical components ae subjected to. The olls can pesent pematue failue in thei mechanical components even when the opeating load is bellow the design limits. The solution to this poblem nomally involves a modification in the powe tansmission geomety and the selection of mateials with bette mechanical popeties, which allows an impovement in the components lifetime. The lack of the knowledge of the toque magnitude in eal time has pevented futhe development in this aea. Engineeing design nomally utilizes safety factos lage that unity to waant lage components lifetime. Even with all safety pecaution in place, the dive component still fails pematuely (Chan, et al., 1999). This emphasizes the impotance of a technique to obtain the oll toque in eal time to waant a safe opeation. This pape pesents a methodology to obtain, in eal time, the toque magnitude and olling mechanical powe, fom an open loop obseve, based on the machine dynamic model. Next, a neual netwok is tained to povide the input and output stip thickness fom thee inputs: toque magnitude, olling mechanical powe, and measued oll foce. The synchonous machine dynamic model, convete model, and Oowan pocess model wee initially utilized fo simulations studies. Finally, eal olling stand data wee utilized to validate the poposed methodology. II. PROCESS DESCRIPTION A. Rolling Pocess A olling mill is fomed by seveal mechanicals components connected to poduce the desied thickness eduction in a steel stip. A typical hot stip mill stand is pesent in Fig. 1. Two AC motos dive both sides of a oll stip. The mateial flows between the olls to obtain the desied thickness, as show in Fig 2, at a tempeatue nea 1000ºC. In hot olling mills, the stip thickness is educed, fom an input thickness h 1 to an output thickness h 2 by the lamination foce of the two paallel olls while moving the uppe wok oll to achieve the desied

Latin Ameican Applied Reseach 39:353-359(2009) Fig. 2: Input and output thickness stip. thickness. B. Electo Mechanical Dive System The olling mill is a geneal stuctue of electomechanical dive system as shown in Fig. 3. The basic equipment can be divided into the following components: powe souce, convete, electic moto, and the mechanical components. The oll stand is the main pocess component. The moto contol system is typically fomed by a speed contol loop with a seconday cuent loop (Monse, 1998). The toque equied by the mateial that is being olled is tansmitted to the electic moto shaft by the mechanical components composed of mass, geas, couplings, and joint shaft. Cycloconvete synchonous o induction moto dives have been extensively utilized in moden olling mills. They nomally opeate unde vecto contol to delive the high powe and low speed equied by these mills. The DC moto dives that wee used fo seveal decades have been gadually substituted fo AC machine dives in news pojects, as well as in etofitting pesent plants. C. Toque and Powe Estimation The Oowan Model was employed to epesent the hot olling stip pocess, and to demonstate the possibility to obtain the toque magnitude and lamination powe fom the electic signals eadily available in the powe convete that feeds the AC machine in the dive system. The full ode dynamic model of the AC synchonous machine was employed to demonstate the feasibility of such scheme. Figue 4 shows a typical input olling opeating data, which ae fed to the Oowan model, in ode to obtain an estimate of the olling powe and toque. The lamination toque (T q ) fom the Oowan model acts as the load toque that is fed to the synchonous moto model. The developed electomagnetic toque (T sinc ) and mechanical powe (P sinc ) estimates fom the output data. It is indispensable to veify if the magnitudes of the estimates fom the machine estimato ae in ageement with the values deived fom the Oowan model. If so, these values can be employed to tain a neual netwok, fom which opeating paametes such as thickness, yield stess, fiction coefficient, stip tension between stands and othes. Initially, in this pape, it is poved that the pocess vaiables such as toque and lamination powe can be obtained fom the electic vaiables. The models pesented ae simulated in MATLAB/SIMULINK. D. Rolling Model Seveal olling pocess models ae available in the liteatue. These models seve diffeent puposes, and ae suitable fo specific applications, such as stip thickness computation, dynamic pocess studies, mechanical components specification, and contol system implementation Some models ae employed to detemine a olling load P, the olling toque Tq and olling powe Pot, which ae elated to the stip thickness. The load P can be elated to seveal opeating paametes, and can be expessed by nonlinea equations (Denti, 1994) such as: P = f µ S, t, t, h, h,, (1a) (, 1 2 1 2 θ ) ( µ S, t, t, h, h, ) p v L Tq = f, (1b) Tq, 1 2 1 2 θ v L Pot = Tq v L (1c) whee µ is the fiction coefficient; S is the aveage yield stess; t 1 is the stip tension in the back stand; t 2 is the stip tension in the font stand; h 1 is the input stip thickness; h 2 is the output stip thickness; is the tempeatue and v L is the olling speed. The Oowan model is adopted to obtain the olling load P, olling toque Tq and olling powe Pot, and makes use of the following input vaiables: h 1, h 2, t 1, h 2, Fig. 3: Electo mechanical dive system. Fig. 4: Toque and olling powe estimation. 354

N.S. MARCELLOS, J.F. DENTI, G.C.D. SOUSA Fig. 5: Inputs and outputs in Oowan model. Fig. 6: Synchonous moto model: input/outputs vaiables. S, V L, as show Fig 5. The Eq. (3) is utilized to calculate the olling load with application of stip tension between stands. α N = α P wr' p ( φ) dφ p ( φ) dφ (2) 0 α N whee w is the stip width; R is the olling adius defomation; p (φ) (p - (φ)) is the stip vetical pessue in input (output) aeas; is the angle in stip and olling contact and N is the angle in stip and olling contact whee p (φ)=p - (φ). The olling toque is detemined by Eq. 3 bellow, which takes into account the olling defomation and the input and output stip tensions. α t1h1 t2h2 Tq = w R R' φ p( φ) dφ (3) 0 2R' whee t 1 is the stip tension fowad; t 2 is the stip tension back; h 1 is the input thickness; h 2 is the output thickness. E. Powe Convesion and AC Moto Models The electic motos applied in moden olling mill dives have ated powe in the MW ange, and ae pedominantly AC motos, in substitution to the DC motos utilized in olde olling mill dives. One eason fo such substitution is the maximum cuent limitation imposed by the DC machine commutato. In ode to cicumvent such limitation, olde DC olling mill dives wee composed of many DC motos, assembled in the same shaft. As a consequence, these assemblies occupy a lage space, and had a detimental effect on the plant efficiency. In moden olling mill dives, both induction and synchonous motos ae utilized, and aea fed by digitally contolled AC powe convete. The pime advantage of synchonous motos ove induction motos in a cycloconvete dive system is its ability to opeate at unity powe facto in all opeating conditions. With the minimum kva equiement at the moto teminals, cuent equiements at the convete, tansfomes and moto cables ae also educed (Jackson, 1993). The suitable epesentation of a synchonous moto to simulate its dynamic pefomance is done by means of the Pak tansfomation. This tansfomation efes the stato vaiables to a oto efeence fame (d -q ), which emoves the time vaying inductances pesent in the oiginal voltage equations. The epesentation of a thee-phase synchonous moto with its input and output vaiables is shown in Fig. 6. The equivalent cicuit of a thee-phase synchonous machine with the efeence fame fixed in the oto by the Pak equations (Bose, 1986) is shown in Fig. 7. Equations (4), (5) and (6) ae deived fom the d -q equivalent cicuit. Equation (4) epesents the electic dynamics, whee flux linkages ae the state vaiables. The vaious flux linkage definitions ae pesented in Eq. 5, wheeas the electomagnetic toque Te is obtained fom Eq. 6, whee Pol is the numbe of poles. The vaiables indicated by v and i and subscipt s, ae associated with the stato windings. The tems L mq and L md epesent the magnetizing inductance in the quadatue (q axis) and diect axis (d axis). The tems with subscipt l epesent the leakage inductances v qs = qs w λ ds p λ qs s v ds = ds w λ qs p λ ds v' v' v' s kq = ' kq ' kq p λ' kq (4) fd = ' fd ' kd = ' kd ' fd p λ' fd kd p λ' kd Fig. 7: Roto fame equivalent cicuit fo a synchonous moto. 355

Latin Ameican Applied Reseach 39:353-359(2009) Fig.8: Vecto contolled cycloconvete-fed synchonous moto dive. Fig. 9: Neual netwok with taining vaiables λ qs = L λ ds = L ls ls ds qs Lmq ( i qs i' kq) Lmd ( i ds i' kd i' fd ) ' kq Lmq ( i qs i' kq) fd Lmd ( i ds i' fd i' kd ) ' kd Lmd ( i ds i' fd i' kd ) ( λ ds qs qs ds) λ ' kq = L' (6) lkq λ ' fd = L' ' lfd λ ' kd = L' lkd 3 Pol Te = λ (7) 2 2 whee kq, kd and fd denote the q and d dampe winding vaiables, and field vaiables, espectively. These equations wee employed to deive the Matlab/ Simulink dynamic model fo the synchonous moto dive utilized in oveall olling mill model. The electic vaiables necessay to implement the vecto contol ae amatue cuents I a, I b, I c, field cuent I f, and oto angle position. The output vaiables of inteest ae the electomagnetic toque and the mechanical powe at the AC moto shaft (Tqsinc and Pqsinc). The moden olling mill dives ae fed by cycloconvetes o invetes, and utilize field-oiented contol, also known as vecto contol. A simplified linea convete model was selected fo convenience, as shown in Fig 8. The speed contolle geneates the cuent toque efeence (I T *) fom the speed eo, that is esponsible fo the toque poduction. Duing tansients, a compensating flux efeence is pesent (I M *), to ensue fast dynamics, and to maintain the vecto conditions between field flux and amatue MMF (Bose, 1986). The cuents ae conveted to stato efeence d s -q s, and then to a,b,c stato efeence fame. By pope cuent loop contol (denoted by block G), the thee phase cuents ae foced to follow the efeence cuents by action of the efeence voltage vecto v abc *. This efeence voltage vecto is then applied to the cycloconvete contol. F. Neual Netwok Based Thickness Estimation As peviously stated by Eqs. 1(a) and 1(b), the olling foce (P) and toque (Tq) ae dependant on seveal opeating paametes and pocess vaiables. It is thus necessay to establish a mathematical elation among these paametes vaiables. A neual netwok is well suited to epesent such elation, since it can automatically deive the elation fom measued data. The Multilaye Pecepton Backpopagation (MLBP) was chosen to povide values such as input and output thickness, as well as othe paametes, if necessay. This choice of a MLBP can be seen as a pactical tool to ealize a non-linea input-output mapping between input and output vaiables. This netwok is shown in Fig. 9 and was used as a function appoximato to eplace Eqs. 1(a) and 1(b). In Fig 9 R epesents the numbe of elements in the input vecto, S is the output vecto, IW and LW ae, espectively, the input and hidden laye weights. The sum of the weighted inputs and the bias fom the input to the 356

N.S. MARCELLOS, J.F. DENTI, G.C.D. SOUSA tansfe function f. A netwok of two layes, being the fist laye with a sigmoid tansfe function, and a second laye with a linea tansfe function, can be tained to appoximate any function (with a finite numbe of discontinuities) abitaily well. P, Tq and Pot wee utilized to tain the netwok, and the output S is equal the thickness h 1. These vaiables ae obtained fom the Oowan Model, as show in Fig. 5. Afte adequately tained, the inputs to the neual netwok wee P, Tqsinc and Pqsinc, wheeas these two last vaiables obtained by means of the dynamic model of the synchonous machine dive system, as shown in Fig. 10, and ae the electomagnetic toque and mechanical powe of the moto. The pupose hee is to estimate the input thickness h 1est o othe opeation paametes. G. Simulation Results The olling mill model pesented in this pape was calibated with measued data fom in a eal olling pocess, and constucted with paametes povided by Sidea S.A. Company. The vaiables utilized to obtain the olling load (P), olling toque (Tq) and olling powe (Pot), wee: h 1, h 2, t 1, t 2, V L and tempeatue. Initially, the Oowan model was tuned by adjusting the yield stess S. Fig. 11 shows the input and the output stip thickness of the eal olling mill, that wee applied to the model to test the poposed methodology. Figue 12 shows the oll foce obtained fom the Oowan Model, in compaison with the eal foce. It was next veified if the toque and mechanical powe values of synchonous moto wee well coelated with the coesponding toque and olling powe obtained fom Oowan Model. In Figs. 13 and 14 can be obseved, espectively, the electomagnetic toque and the mechanical powe fom the moto, compaed with the values calculate fom the Oowan Model. In Fig. 13 the peak toque occued at t=2s, and coesponds to the synchonous moto stat up, befoe the intoduction of the stip in the oll gap. The electic vaiables ae in accodance with the pocess vaiables in the time ange above 4 s. These vaiables ae utilized as input vaiables to the neual netwok in ode to obtain the input and output thickness. The taining data ae obtained fom Oowan Model as shown the Fig. 9. Then, the simulation esults ae compaed with the eal data pocess set as shown in Fig. 15. As shown in Fig. 16 and 17, the eal data input thickness h 1 is quite close to the estimated value h 1EST. Fig. 18 shows the output thickness estimate h2est along with the actual thickness (h 2 ). It can be seen that they ae closely elated, although not identical. III. CONCLUSION This pape demonstates the possibility to obtain, in eal time, the toque and olling powe fom the eadily available electic stato vaiables (stato voltages and cuents) of the AC moto in olling mill dives. The poposed technique makes use of a toque estimato, based on the electomagnetic toque dynamic Eq. (6). Fig. 11: Input opeating vaiables fo the simulation study (input and output thickness magnitudes). Fig. 12: Real data olling foce and olling foce fom the Oowan model. Fig. 10: Neual netwok with sampled vaiables. 357

Latin Ameican Applied Reseach 39:353-359(2009) Fig. 13: Developed electomagnetic toque and olling toque. Fig. 14: Electomechanical powe in AC moto and olling powe Fig. 15: Data set used to compae the pedictions. Anothe possibility to be pobed the featue, is the utilization of the electomagnetic toque estimate povided by the dive pocesso, via seial pot (suck as RS485).These vaiables can be used in on-line olling contol, in substitution to the values obtained fom simplified models, avoiding additional computation effots. Moeove,they avoid the use of toque sensos in the pocess. By means of electic vaiables and the oll foce, and a neual netwok tained with opeational conditions, elevant pocess vaiables such as input an output thickness can be obtained with necessay pecision. Othe vaiables can be similaly obtained to supevise the olling pocess, if necessay. 358 REFERENCES Bose, B.K., Powe Electonics and AC Dives, Pentice- Hall, Englewood Cliffs, New Jesey (1986). Chan, W., A. Wang and J.M. Shoup, Real Time Toque Measuement of Rolling Mill Dive, Alcoa Technical Cente, 557-564 (1999). Denti, J.F., Um Método de contole Dinâmico de Laminadoes Revesíveis, Tese de Doutoado, Escola de Engenhaia da UFMG (1994). Jackson, W. J., Mill Motos fo Adjustable Speed AC Dives, IEEE Tansactions on Industy Applications, 29, 566-572 (1993). Monse, M., V. Mulle, H. Cev and S. Schulze, Modeling and Dynamic Simulation of Electomechanical

N.S. MARCELLOS, J.F. DENTI, G.C.D. SOUSA Systems of Equipment in the Rolling Mill Field, IEEE 5 th Intenational Wokshop on on Advanced Motion Contol, 469-474 (1998). APPENDIX A) Equivalent Cicuit Paamete in oto efeence fame: Rs=0.3 Ohm, stato winding esistance; Rq=2.2 Ohm, amotisseu oto winding esistance diect axis quadatue axis; Rd=2.2 Ohm, amotisseu oto winding esistance diect axis; Rf=0.064 Ohm, winding field esistance diect axis; J=0.1 kgm 2, oto inetia; B=0.001, amotisseu coefficient; Poles=4; Llf=0.0017 H, leakage inductance in field winding diect axis; Lls=0.001H, leakage inductance in stato windings; Llq=0.00086H leakage inductance in amotisseu oto winding quadatue axis: Fig.16: Estimate Thickness h1=h1est. B) Roll s Phisiques Chaacteistics Roll s diamete= 300 mm Tip width= 500 mm Roll s Poisson Coefficient = 0,305 Stip s Poisson Coefficient = 0.305 Roll s Young modulus=21000 kgf/mm 2 Stipl s Young modulus=21000 kgf/mm 2 Fiction Coefficient=0.1 Fig. 17: Estimate Thickness h1=h1est. Fig. 18: Estimate Thickness h2=h2est. Received: Januay 24, 2007 Accepted: Octobe 6, 2008 Recommended by Subject Edito: Albeto Cuitiño 359