Evaluation of straightening capacity of plate roll straightener

Transcription

1 J. Cent. South Univ. (0) 9: DOI: 0.007/s Evaluation of straightening caacity of late roll straightener WANG Yong qin( 王勇勤 ), LIU Zhi fang( 刘志芳 ), YAN Xing chun( 严兴春 ) State Key Laboratory of Mechanical Transmission (Chongqing University), Chongqing , China Central South University Press and Sringer Verlag Berlin Heidelberg 0 Abstract: Straightening machine is widely used for imroving the quality of the defective mild steel lates. In general, the caacity of straightening machine is affected by material roerties, the initial shae of the incoming late and the lastic ratio. The mechanics model describing the caacity of the machine was develoed. The deviation of the straightening caacity curves was studied. Then, the resented model was evaluated by comarative study to filed roduction data. Finally, the influences of overstretch, straightening seed, strengthening coefficient, elastic modulus, width of the late on the straightening caacity were studied. It is convenient to determine whether the late can be straightened or not by a series of straightening caacity curves. The straightening seed, width of the late and elastic modulus of the material are more sensitive to the straightening caacity than the strengthening coefficient. Key words: lastic ratio; straightening caacity; strengthening factor; late Introduction Straightening is an imortant rocedure in the roduction line of the late. It is used to eliminate the common late defections such as curl, gutter, middle waves and edge waves which are generated in the rocess of the rolling and cooling []. There are many reorts on the straightening rocess rediction for a secific roll straightener. For examle, PARK and HWANG [] and HUH et al [3] develoed a FEM rogram for the analysis of roller straightening rocess and designed a FEM to calculate the quantitative level of curl, resectively. BEHRENS et al [4] develoed an analytical 3D simulation model to find a suitable adjustment of the leveler to reach a flat sheet metal. Also, the analytic model had been studied to redict the curvature distribution in the thickness [5 9]. The equiment which can carry out this rocedure is called the roll straighter. In connection with the exanded range of roducts made from lates and the increasingly stringent requirements on the quality of the lates, various modern straightening machines have been resented. MATSUZAKI et al [0] studied a hot leveler which could be changed into a erfectly stable system by two dynamic absorbers by numerical analysis so that the olygonal wear of the rollers was not generated at all. BELOBROV et al [] and TITARENKO et al [] introduced the new modern straightening machines with world class erformance characteristics of the Novokramatorsky Mashinostroitelny Zavod (NKMZ) Comany. Also, BELOBROV et al [3] gave the main design features of the new in line late straightening machines (PSMs) of the Severstal Comany. In other words, the new generation straighteners have exanded the range of late thicknesses, width and yield stress, automated the straightening oeration, imroved the reliability of the comonents and mechanisms, and reduced residual internal stresses in the late. The resent work was focused on the rocess technology how to imrove the residual stress and flatness of the late well. But it is rare to have reorts on the evaluation of the straightening caacity based on a detailed theoretical analysis for a secific roll straightener for a late. For filling u this ga, it is necessary to study the basic rincile of evaluating the caacity of the late straightener. In this work, the mechanics model describing the strengthening caacity was resented. To verify the mechanics model, the results of roosed model were comared to the field roduction data. The factors affecting the caacity of the straightener were discussed by using the roosed model. Caacity evaluation model of straightening rocess The new owerful straighter owns strong ability to level the extensive range late, but the caacity of a secific leveler with the definite structure and ower is Received date: ; Acceted date: 0 8 Corresonding author: WANG Yong qin, Professor; Tel: ; E mail: wyq@cqu.edu.cn

2 478 limited. The straightener shown in Fig. consists of nine, 0 mm diameter rollers, with a searation between contiguous rollers of 30 mm. The lower rollers are fixed and certain vertical dislacements are alied on the uer rollers. The maximum straightening force and the motor ower are 40 MN and 800 kw, resectively. The equiment builder has sulied the design caacity and set for its machine for given materials, yield strength and thickness. In general, the caacity of a leveler is constrained by the following conditions. J. Cent. South Univ. (0) 9: where A t is the elastic limit curvature, At = σ s, i / EH, σ s,i is the yield stress of the late, and D is the diameter of the rollers. Fig. Definition of overstretch Fig. 3 D model of nine roller leveler. Plastic ratio The straightening rocess is very comlicated with the elasto lastic deformation in the late. The ercentage that the thickness of the lastic deformation accounts for the whole thickness is called the lastic ratio. The lastic ratio R, as shown in Fig., is described as R H = 00% () H where H is the thickness of the lastic region and H is the total thickness of the late. The overstretch (S) is usually used to reflect the lastic ratio in the engineering. It is defined as S = R () The lastic ratio is an imortant arameter in the straightening technologies [4 5]. The quality of the late can be imroved well if R increases to 70% 80% (S=3.3 5). The late cannot be leveled well if the lastic ratio is less than the exected value even though it is winded around the rollers (ρ=d/). So the geometry model of overstretch can be summarized as EH S R σ s, i (3) A DS t. Maximum straightening force The maximum force is a constant value when the straighter is designed over. So its straightening caacity is constrained by its maximum force and its structure. The straightening forces, as shown in Fig. 3, are generated by the rollers with the action of the roller ga. They can be deduced by the three moment equation of multi suorted beam as Fi = ( M i + M i + M i + ) (4) where M i, M i and M i+ are the inner moments of the late under roller i, i, i+, resectively. So, the sum straightening force is calculated as 8 M F = F F M F σ Σ N N t, i i sum i sum (5) i= i = Equation (5) can be simlified as 3 F sum s, i N 4 BH i = M i (6) where N is the roll number, is the roll itch, M t,i is the elastic limit inner moment of the late under roller i, M t, i = BH σ s, i / 6, M i is the moment ratio, M i = M i / M t, i, M i is the inner moment of the late under roller i, F i is the straightening force of the late under roller i, and F sum is the maximum straightening force.

3 J. Cent. South Univ. (0) 9: Fig. 3 Straightening forces.3 Total motor ower Similar to the maximum straightening force, the total motor ower is also a constant for a secific straighter. The torque that the transmission system needs to overcome includes the friction resisting moment at the roller journal, T =F (μd/), the friction resisting moment between the roller and the late, T =F (μd/), and the lastic deformation resisting moment, n 3 = J, i. So T R u the relationshi between the motor ower and the inner moment can be summarized as µ d 8 M P η D f + M + u v N n t, i D sum i J, i i = (7) where v is the straightening seed; u J,i is the lastic energy in erlength of the late; u BH σ s, i 3 J, i ζ i ζ i ζ i 6E ζ i 4 = ( ) [ + ( )(3 + )], ζ i is the elastic ratio, and ζ i = R ; η is the total efficiency of the transmission system; d is the diameter of the rollers journal; f is the coefficient of the rolling friction between the roller and the late; μ is the friction coefficient between the roller journal and the bearing. So, Eq. (7) can be simlified as n DBH 3 σs, i ( ζ i ) [ + ( ζ i )(3 + ζ i )] + E i = ζ i 4 µ d 4 BH σ s, i[( f + ) ] 3 N Psum η D M i (8) i = V The arameters of P sum, D,, d, η, J and μ are constants for a definite straighter. The straightening force, the inner moment in the late and the lastic energy in er length of the late can be calculated according to the straightening rocess technology. All rograms are carried out in Matlab software. 3 Verification Using the in house rogram, simulation results are obtained under the conditions listed in Table. It can be seen from Fig. 4 that the straightening caacities are a series of family curves. The greater the lastic ratio is, the narrower the straightening range is. Actually, any of the curves is surrounded by three arts. For examle, as for the caacity curve of the case of S=3, Section B C is controlled by the lastic ratio shown in Eq. (3), Section C D is the maximum yield strength of all the late, Section E F is contained by the maximum straightening force and Section D G is restricted by the motor ower. Section E F and Section D G intersect at Point A. Finally, the straightening curve (S=3) is generated by the Section B C, C D, D E and E F. Table Straightening conditions of late Parameter Value Number of work rollers 7 (to: 3, bottom: 4) Roller diameter/mm 0 Roller itch/mm 30 Maximum straightening force/mn 8 Motor ower/kw 30 Diameter of roller journal/mm 0 Width of late/mm 50 Fig. 4 Exlanation of straightening caacity In order to verify the roosed model, it is necessary to comare the results of the roosed model with some other credible data. It can be seen from Fig. 5 that the simulation result can match the field roduction result well. When S changes from 3 to 7 (lastic ratio changes from 66.7% to 85.7%), the straightening caacity changes obviously. 4 Discussion The roosed model is used to research the influence of elastic modulus, strength coefficient and straightening seed on the straightening caacity. The straightening conditions are listed in Table.

4 480 J. Cent. South Univ. (0) 9: Fig. 5 Results comarison of roosed model and field roduction data Table Straightening conditions of late Parameter Value Number of work rollers 9 (to: 4, bottom: 5) Roller diameter/mm 0 Roller sace/mm 30 Maximum straightening force/mn 40 Motor ower/kw 800 Diameter of roller journal/mm 0 Maximum straightening force/mn 40 Motor ower/kw 800 Diameter of roller journal/mm 0 It can be found that the larger the straightening seed is, the narrower the range is in the same overstretch condition, as shown in Fig. 6. The late (H=30 mm, σ s =800 MPa) located at oint A, is above all the curves. This means that this late is beyond the caacity of the straighter listed in Table and it cannot be leveled in this straighter. Otherwise, the total straightening force or the total toque is larger than the allowable value of the machine. In other words, this straighter will be in danger. But if its yield strength decreases to 50 MPa, as shown at oint A, it can be leveled well. The late (H= mm, σ s =700 MPa) located at oint B is secial because whether it can be leveled or not deends on its straightening seed and overstretch at the same time. If the straightening seed v=60 m/min and S=3.3 (R =70%), it can be leveled. But it is dangerous if v=0 m/min and S=5 (R =80%). In other words, whether it can be leveled deends on its straightening seed and defection degree. The lated located at oint C (H=3 mm, σ s =500 MPa) is similar with that located at oint B. Their difference is that the late located at oint C largely deends on overstretch. Contrast to the late located at oint A, the late located at oint D can be easily and safely leveled because it is below all the caacity curves. Fig. 6 Straightening range under condition of B=3 000 mm, λ=0 and E=5 GPa Considering the strengthen effect of the material, it is necessary to study the influence of strengthen coefficient on the straightening caacity. It can be found that the straightening caacity decreases to some degree when the material of the lates has the strengthening effect when comaring Fig. 6 with Fig. 7. Also, the straightening caacity is influenced by elastic modulus and width of the late. The greater the elastic modulus E is, the smaller the u J,i is. So, the caacity shown in Fig. 8 is wider than that in Fig. 7. Fig. 7 Straightening range under condition of B=3 000 mm, λ=0.0 and E=5 GPa Fig. 8 Straightening range under condition of B=3 000 mm, λ=0.0 and E=0 GPa

5 J. Cent. South Univ. (0) 9: Similarly, the caacity shown in Fig. 9 is wider than that in Fig. 8. M i f μ η Elastic limit moment Rolling friction coefficient between roller and late Friction coefficient between roller journal and bearing Total efficiency of transmission system References Fig. 9 Straightening range under condition of B= 000 mm, λ=0 and E=5 GPa 5 Conclusions ) The straightening caacity model is roosed and there is a good consistence when the simulation result is comared with the field roduction data. ) The influence of overstretch, straightening seed, strengthening coefficient, elastic modulus, width of the late on the straightening caacity is studied. The research results indicate that the greater the straightening seed, strengthening coefficient and width of the late are, the smaller the straightening caacity is, and the larger the elastic modulus is, the larger the straightening caacity is. 3) The leveling ossibility of a late can be determined quickly and conveniently for a given shae and material roerties. Nomenclature H Thickness of late B Width of late H Plastic deformation thickness of late E Elastic modulus σ s,i Yield stress of late S Overstretch R Plastic ratio ζ i Elastic deformation ercentage A t Elastic limit curvature R Radius of roller D Diameter of roller d Diameter of roller journal Roller itch sum Motor ower F Maximum straightening force F i Straightening force under roller i F sum Sum of straightening force Inner moment of late under roller i M t,i [] TOMITA S, FUJITA Y. Recent trend and roblems of straightening technologies of thick lates [J]. Journal of the Jaan Society for Technology of Plasticity, 999, 40: 408. (in Jaanese) [] PARK K C, HWANG S M. Develoment of a finite element analysis rogram for roller straightening and alication for removing blanking bow defects of thin steel sheet [J]. Iron & Steel Institute of Jaan Journal, 00, 4: [3] HUH H, LEE H W, PARK S R, KIM G Y, NAM S H. The arametric rocess design of tension straightening with an elasto lastic finite element model [J]. Journal of Materials Processing Technology, 00, 3: [4] BEHRENS B A, NADI T E, KRIMM R. Develoment of an analytical 3D simulation model of the straightening rocess [J]. Journal of Materials Processing Technology, 0, : [5] DOEGE E, MENZ R, HUININK S. Analysis of the straightening rocess based uon an analytic forming model [J]. Manufacturing Technology, 00, 5: [6] KADOTA K, MAEDA R. A method of analysis of curvature in straightening rocess numeric study of roller straightening rocess [J]. Journal of the Jaan Society for Technology of Plasticity, 993, 34: (in Jaanese) [7] HIGO T, MATSUMOTO H, OGAWA S. Effects of numerical exression of stress stain curve on curvature of material of roller straightening rocess [J]. Journal of the Jaan Society for Technology of Plasticity, 00, 43, 496: (in Jaanese) [8] XUE Jun an, CUI Li, HU Xian lei, LIU Xiang hua. Effect of lastic deformation rate on late steel during roller leveling [J]. Journal of Northeastern University, 009, 5(5): (in Chinese) [9] CUI Li, HU Xian lei, GUO Qiang, LIU Xiang hua. Analyzing roller leveling strategies for high strength steel lates [J]. Journal of Northeastern University, 0, 3(5): (in Chinese) [0] MATSUZAKI K, SUEOKA A, RYU T, MORITA H. Generation mechanism of olygonal wear of work rolls in a hot leveler and a countermeasure by dynamic absorbers [J]. International Journal of Machine Tools & Manufacture, 008, 48: [] BELOBROV Y N, SMIRNOV V G, TITARENKO A I. Modern straightening machines [J]. Metallurgist, 00, 46(9/0): [] TITARENKO A I, BELOBROV YU N, SMIRNOV V G, EVGINENKO I A, SHESTOPALOV A V, SATONIN A V, SATONIN A A, BEGUNOV A A. New advances at the Nvokramatorsk machine lant in the technology and equiment used for straightening lates [J]. Metallurgist, 006, 50(/): [3] BELOBROV Y N, SMIRNOV V G, TITARENKO A I, PEREKHODCHENKO V A, SINEL NIKOV I L. Automating the Control of modern equiment for straightening flat rolled roducts [J]. Metallurgist, 004, 48 (7/8): [4] MATSUO A, FUJITA M. Various roblems in leveling the lates and sheets with roller leveling [J]. Iron & Steel Institute of Jaan Journal, 006, 9(): (in Jaanese) [5] MATSUO A, YOSHIKAZU S. Mechanism of roller leveling [J]. Iron & Steel Institute of Jaan Journal, 00, 5(5): 00. (in Jaanese) (Edited by YANG Bing)