# PROCESS CHANGING MODEL of STRIP CONTINUOUS HEAT TREATMENT FURNACE and its APPLICATION

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2 Proceedngs of the 1st Internatonal Conference on Computers & Industral Engneerng knd of transent operatons as process changng. For the process changng s very common and mportant n heat treatment process of strp steel, so dervng a mathematcal model to forecast or even control the transents that occur n such a change s a fundamental problem for the steel strp ndustry [1]. hs paper focuses on the forecastng the temperature of steel strp durng the process changng by mathematcal model. Lots of expermental and numercal smulaton data were presented and compared, the results ndcate that the present mathematcal model s feasble. (a) Vertcal type furnace (Left: Electrcal resstance furnace; Rght: Radant tube furnace) Burner n operatng sde Burner n drvng sde teel trp Outlet Inlet oakng secton Drect fre heatng secton Pre heatng secton (b) Horzontal type furnace Fgure 1. Dagram of steel strp contnuous heat treatment furnace 1. Mathematcal Model of Heat ransfer ome assumptons and smplfyng methods are presented here to smplfy the heat transfer n furnace: (1) Usually the carbon or stanless steel strp s very thn, the temperature dfferences n thckness drecton can be neglected. (2) he radant tubes (see Fgure 1(a)) and burners (ee Fgure 1(b)) are equpped n alternate drectons n furnace, and steel strp movng forward along longtudnal drecton of furnace. o the temperature dstrbuton of each radant tube or furnace chamber s smplfed as unform temperature profle. (3) he surfaces of radant tubes, steel strp, wall of furnace and gas are grey bodes n the calculaton of radaton heat transfer, and the emssvty keep constant. he equaton descrbng the temperature of steel strp s gven as Equaton (1), whch s a smple one dmensonal Fourer heat conducton equaton. s ( x, ) s ( x, ) s Cps s (1) x x Where: ρ s s densty of strp, kg m -3 ; C ps s specfc heat of strp, W m -2 K -1 ; s s temperature of strp, K; x s the axs n lateral drecton of strp, m; τ s tme, s. Fgure 2 shows the thermal boundary condton of strp. he heat flux dstrbuton along the lateral drecton of strp s not unform, and they are the functon of strp wdth, radant tube and wall temperature. he functons of heat flux q r, q l are: 1058

4 Proceedngs of the 1st Internatonal Conference on Computers & Industral Engneerng 2. Mathematcal Model of Process Changng he calculaton method of process changng mathematcal model s as shown n Fgure. In the movng drecton of steel strp between nlet and outlet of contnuous heat treatment furnace, n trackng nodes have been set. Every trackng node s not movng wth steel strp, but t stores the steel strp s message at ts poston,.e. the steel grade, sze, temperature and col number. 1 q r -1 q l q -1, =q r +q l +1 Fgure. he dstrbuton of trackng nodes along the strp movng drecton he dstance between neghbourng trackng node -1 and s defned as Δ, here and n the followng dscusson the regon of s 2 to n. he number of trackng node usually large enough to keep Δ smaller than 1.0 m, whch means that the poston of weld between new col and prevous col can be easly tracked based on the fact that f the neghbourng trackng nodes have dfferent steel strp s messages there must be a weld between ther locatons. And the error of weld s locaton calculated by ths method s smaller than Δ. Based on the mathematcal model of radaton and convecton heat transfer, the average heat flux q -1, of steel strp between neghbourng trackng nodes -1 and can be obtaned. he steel temperature at trackng node s: q 1, 1 (6) scpshs, 1Bs, 1 Vs Here s new temperature of steel at trackng node ; -1 s prevous temperature of steel at trackng node -1; H s,-1 and B s,-1 s thckness and wdth of steel at trackng node -1; ρ s and C ps s densty and specfc heat of steel at trackng node -1; V s s the movng velocty of steel strp, m s -1. he temperature of trackng node 1 s the nlet boundary condton of process changng model, and usually 1 s a constant value such as the envronmental temperature ( 1 = 20 n the followng dscusson). he calculaton of process changng model s start from trackng node 1 and end at trackng node n. o after n-1 tmes calculaton of Equaton (6), all the trackng node wll get new temperature of steel strp. hen the steel strp s message (except temperature) stored n trackng node -1 s coped to, whch corresponds wth the movng of steel strp n realty. he above calculaton s repeated every Δτ = Δ/V s seconds, and the results (e.g., the temperature of steel strp, poston of weld) are out put every Δτ seconds too. Here a note should be declared that V s can t be zero, else Δτ wll be a nfnty number and lead to ncorrect results. 3. Expermental and Numercal Results In the followng we take a radant tube furnace (see Fgure 1(a)) as an example to analyze the process changng model buld n ths paper. able 1 shows the expermental data of a typcal process changng. In n 1060

5 hckness (mm) Velocty (m/mn) ths process changng there are knds of steel grades A, B, C and reject col. he reject col s transton steel but not producton. Input the data of able 1, temperature of furnace and radant tubes nto process changng model, Fgure 5(a) shows the expermental and numercal results. he relatve error analyss n Fgure 5(b) shows that the relatve error between expermental and numercal results of steel strp temperature s wthn ±2% n a probablty of 93%. able 1. Expermental data of a process changng mode me (mn) Relatve error (%) Relatve error (%) Proceedngs of the 1st Internatonal Conference on Computers & Industral Engneerng teel Grade hckness (mm) Emssvty Heat reatment Grade trp movng Velocty (m/mn) 0 A CA B CA B CA B CA B CA Reject Col Reject Col C 7 5-3CA C 7 5-3CA C 7 5-3CA C 7 5-3CA 583 hckness (mm) emperature ( ) trp emp. Cal. trp emp. Exp. hckness Velocty Furnace emp. of zone 1 Radant ube emp. of zone 1 Furnace emp. of zone 2 Radant ube emp. of zone me (mn) me (mn) (a) Expermental and Numercal Results (b) Relatve error of strp temperature Fgure 5 Expermental and numercal results of process changng of vertcal furnace Fgure 6 shows another result of process changng of vertcal furnace, and the relatve error s wthn ±2% n a probablty of 91%. hckness (mm) emperature ( ) trp emp. Cal. trp emp. Exp. hckness Velocty Furnace emp. of zone 1 Radant ube emp. of zone 1 Furnace emp. of zone 2 Radant ube emp. of zone me (mn) (a) Expermental and Numercal Results hckness (mm) Velocty (m/mn) me (mn) (b) Relatve error of strp temperature 1061

6 Velocty m/mn Proceedngs of the 1st Internatonal Conference on Computers & Industral Engneerng Fgure 6. Expermental and Numercal Results of Process Changng of Vertcal Furnace Fgure 7 shows a set of expermental and numercal result of drect fred horzontal furnace (see Fgure 1 (b)), the steel strp s stanless steel. In Fgure 7 the process changng s not very clear (the steel grade and sze keep constant), and only the furnace temperature of zone 6 and zone 7 has fluctuaton wthn a narrow range. he maxmum relatve error of expermental and numercal result of steel strp temperature s less than 0.5%. hckness (mm) emperature ( ) teel temp. Exp. teel temp. cal. Velocty hckness Furnace temp. of zone 5 Furnace temp. of zone 6 Furnace temp. of zone 7 Furnace temp. of zone 8 Furnace temp. of zone me (mn) Fgure 7. Expermental and numercal result of drect fred horzontal furnace From the results as shown n Fgure 5 and Fgure 6, the relatve error of process changng model exceeds 3% around the weld poston (the weld between prevous and new col s at the step change of the strp thckness, see hckness lnes n Fgure 5 and 6). But Fgure 7 does not have ths phenomenon. o t means that there may be some shortage n the process changng model. Although the relatve error analyss shows that process changng model s relable and applcable, but we stll try to check and cover the shortage n ths mathematcal model.. Conclusons Based on heat transfer model of steel strp contnuous heat treatment furnace, the process changng model was buld for strp contnuous heat treatment process. And the model s able to predct strp temperature under multform varyng factors such as strp velocty, strp sze (wdth and thckness), steel grade and furnace status. In ths paper numerous expermental data obtaned from vertcal and horzontal furnace are present, and the smulaton results of the process changng model match well wth expermental data, the relatve error s less than 2.0% n a probablty above 90%. All the results ndcate that the process changng model s precse and relable. But there are stll some shortages n ths process changng model, and more work should be pay to check and cover these shortages. Reference [1] Davd O. Marlow. Modellng drect-fred annealng furnaces for transent operatons [J]. Appl. Math. Modellng, , Vol.20: 3-0. [2] Dou Rufeng, Wen Zh, L Wen, et al. Radaton heat transfer calculaton and analyss of tower furnace by Monte-Carlo method [J].Energy for Metallurgcal Industry, , 27(6): 19-21,

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