Study on Mechanical Behavior of Thin-walled Member during Precision Straightening Process

Transcription

1 2014 by IFSA Publihing, S. L. Study on Mechanical Behavior of Thin-walled Member during Preciion Straightening Proce Ben Guan, Yong Zang, Diping Wu, Qin Qin School of Mechanical Engineering, Univerity of Science and Technology Beijing, No. 30, College Road, Haidian Ditrict, Beijing, , China Tel.: , fax: Received: 2 July 2014 /Accepted: 4 Augut 2014 /Publihed: 30 September 2014 Abtract: Thi paper introduce the mechanical behavior of precie traightening thin-walled member ytematically. A a reult of it cro ection characteritic of the thin-walled member, traditional traightening theory doe not work well in the traightening proce of thi kind of metal bar tock. Conidering the tre evolvement of ection during the traightening proce, a model wa built to analyi the traightening proce like thin-walled member with great ection height. By making a thorough analyi of the traightening proce, the ection deformation law and the relationhip between ectional ditortion and traightening parameter ha been matered. An analytical model wa built for macrocopic energetic parameter of the traightening proce and the parameter wa optimized baed on thi model. Then loading mode of thin-walled member traightening wa dicued. Copyright 2014 IFSA Publihing, S. L. Keyword: Straightening, Thin-walled member, ectional ditortion, Stre analyi, Loading mode. 1. Introduction With the rapid development of the contruction, railway tranportation, offhore exploration and bridge aviation indutry, the thin-walled member ha been popularized and applied in recent year a a new green material becaue of it uperior performance in mechanical property and economic advantage. For the large gradient of tre-train and temperature variation in the procee of metal forming, the exit of geometric imperfection and reidual tre cannot be avoided in the product. So traightening i an important finihing tep in the procee of metal forming, namely relieve reidual tre and eliminate geometrical imperfection through repeated elaticplatic reverely bending produced by pecial traightener [1]. Metal component traightening proce ha been tudied and dicued by many cholar with method of theoretical analyi and numerical calculation [2-8]. However, a a reult of it pecial cro ection characteritic, the mechanical and geometrical propertie of thin-walled member are different from other member and traditional profile. The main difference are a follow [9]: (a) Becaue of it large ection height, evolvement of the deformation and longitudinal reidual tre produced by the former working procedure and traightening roll have an important influence on it behavior during the traightening proce, which i not taken into conideration in the traditional traightening theory. (b) The thin-walled member i enitive to loading mode pecially, for it tructure and poor performance of bearing tranvere load. In addition, it technological requirement alo differ from member 36

2 with olid ection. Therefore, the optimization of traightening parameter, uch a bending deflection and traightening force, i particularly important. Meanwhile, in order to control the ection tre and geometric hape during the traightening proce, it mut be done to find a reaonable path along which the traightening force i delivered on the ection. (c) On account of the complex cro-ection mechanical propertie of thin-walled tructure, there mut exit cro-ection ditortion caued by platic deformation or intability during the traightening proce, no matter how the load i applied, which affect the etting and control of the parameter during the traightening proce. Therefore, traditional traightening theory ha great limitation when it i ued to decribe the mechanical behavior of large-cale thin-walled tructure during the traightening proce. Conidering the tructure characteritic, thi article make a deep and ytematic reearch of the mechanical behavior of thin-walled tructure during traightening proce and come up with a complete et of preciion traightening theory that work well with thin-walled member. 2. Stre Evolvement and it Influence In eence, the roller traightening proce i a repeated elatic-platic bending proce of the cro ection, which i a typical inhomogeneou croection deformation tate and reult in macrocopic reidual tre in the cro ection [10]. During the proce, new reidual tre i generated while exiting ection tre i reditributed, o the next bending proce would inherit the reidual tre generated by the previou bending proce which will give an impact on the anti-bending characteritic of the next bending proce. For thin-walled member with larger ection height, the impact of uch an act on traightening proce will be highly viible. Therefore, a cro-ection elatic-platic bending and traightening model for thin-walled tructure hould be etablihed with the tre evolvement taken into conideration Solution of the Model According to the reidual tre uperpoition principle, the tatic equilibrium relationhip and cro-ection yielding condition of baic elaticplatic theory, numerical analyi of the n+1th elaticplatic bending proce of the cro ection traightening can be achieved with the ue of MATLAB oftware. The main proce i a follow: a) dicretization of dimenionle cro-ection tre ditribution Divide the height range from -1 to 1 into N ection and dicrete tre which i continuouly ditributed in dimenionle cro ection. The tre value of the ection point i ued for calculation and analyi intead of real tre continuouly ditributed in the ection. b) calculation of the tre in cro-ection during bending loading ( n + By calculating bending tre w of every ection point according to curvature and uperimpoing the ( n) previou bending reidual tre c, we can achieve the tre value of the ection point: And then carry out the criteria for : > if, then = ±. ( n ( n ( n) < if, then + + = w + c. c) calculation of the reidual tre in cro-ection after unloading platic-bending ratio: rebounding tree: reidual tre: = + ( n ( n ( n) w c 6 1 M = z dz 1, = M c = + ( z, (2), (3) After achieving the platic-bending ratio and rebounding tree according to ( and (2) repectively, reidual tre of the ection point can be calculated with (3), namely = M ( = z The logic block diagram of the numerical analyi for tre of ingle ection point during the bending proce i hown in Fig. 1. We have to run thi program repeatedly for a roller traightening proce during which the rolled tock would be bended reverely many time Stre Evolvement During the Straightening Proce Take example of the 8 roller traightening baed on the principle of mall deformation. Suppoe that the maximum initial curvature of the dimenionle rectangular metal material C 0max =±3.5. With the ( + n+ n+ c 37

3 numerical method dicued above, the parameter C w of every bending proce can be obtained under the condition of mall deformation according to claical traightening theory, a hown in Table 1. tart ection have different bending characteritic a a reult of the different tre evolvement hitory, which ha an overall impact on the convergence of the M-C curve. Therefore, the behavior of the thin-walled member would have many great change during the traightening proce [11]. In addition, the model can be ued to analyi the cro ection reidual tre of the bar tock, a hown in Fig. 3. given:curvature C n+ 1,reidual w = z Cn+ 1 S M ( n) = w + c > no ( n) = w + c ye = ± (a) Value of claic theory 3 1 M = z dz 2 1 M c = M z Fig. 1. Logic block diagram of the numerical analyi for elatic-platic bending. Table 1. Convere bending parameter of C0max=±3.5 bar tock under mall deformation traightening theory. Number of roller Revere curvature Cw Compare the M-C curve of the tre evolvement model with that of the traditional traightening model, a hown in Fig. 2, it i eay to find that without taking the tre evolvement into conideration, the claic traightening model hold that the ection alway have the ame bending characteritic and the reidual bending curvature tend to be the ame and finally can be eliminated if bending parameter are et reaonably [1]. Thi can be een a the M-C curve continuouly tend to be convergent. However, the M-C curve of the tre evolvement model i not convergent becaue the dimenion-ection height h (b) Numerical olution of new model. Fig. 2. M-C curve of traightening reidual tre c /MPa Fig. 3. Ditribution of reidual tre in ection with different initial curvature of bar tock after traightening. 38

4 3. Simulation Analyi for the Mechanical Behavior of Member Straightening Proce The mechanical proce of thin-walled member traightening i extremely complicated, involving many iue related to geometric and material nonlinearity, multi-point contact, and heredity of reidual tre, ection deformation and imperfection enitivity. Numerical method uch a finite element method are ued to analyze the mechanical behavior of member during traightening proce in thi paper, becaue the exact analytical reult can t be got through claical theoretical method Stre Evolution in the Straightening Proce Two dynamic finite element imulation model for thin-walled member traightening proce of H-beam and bra tube (a hown in Fig. 4) are etablihed repectively by uing finite element analyi oftware, focuing on the introduction of the original geometric and phyical imperfection, the proceing method of geometric and multiple contact nonlinear in model, the friction decription between the member and traightening roller, the decription and introduction of thermal-mechanical coupling characteritic. Taking variable roller pacing traightening with nine roller for example, the equivalent tre evolution of the pecific ection ite in H-beam traightening proce i hown in Fig. 5. The imulation reult how that the equivalent tre in the ection fillet change moothly during the traightening proce, but the it value are quite high, and the equivalent tre in the web change everely. The imulation alo reveal the formation mechanim of platic hardened zone at the root of web (a hown in Fig. 6). Meanwhile, to reearch the heredity of the reidual tre during H-beam traightening proce, the reidual thermal tre when cooling end i introduced uccefully to the multi-roller traightening model a the initial tre before traightening. The tudy found that the longitudinal tree in mot region of the flange and web after traightening remain almot unchanged comparing with the value before traightening, but the root of web are influenced everely by traightening proce, the initial tenile tre before traightening change to compreive tre whoe tre gradient i very high. The tre heredity during traditional traightening i not conducive to improve the performance of the beam [12]. (a) finite element imulation model of H-beam Fig. 5. The equivalent tre evolution in H-beam during traightening proce. (b) finite element imulation model of bra tube Fig. 4. Finite element analyi model of the traightening proce. Fig. 6. The hardened zone produced in H-beam web. 39

5 In hort, after the finite element analyi of H- beam and large-cale pipe, we have got more comprehenive undertanding to thin-walled member traightening proce. The evolution of tre and train in the thin-walled member during traightening proce ha been graped and ome geometric and mechanical behavior of thin-walled member in traightening proce have been interpreted uccefully Section Deformation Problem The ection deformation i the characteritic of thin-walled member in traightening proce. The reaon why the ection deformation arie i that the lateral bearing capacity of thin-walled member ection i weak. Thi kind of ection deformation ha an ignorable effect on the etting of traightening parameter. By the finite element imulation, we have matered the ection deformation of H-beam and large-cale bra tube. The ection deformation of H-beam i hown in Fig. 7. The main form of ection deformation of H-beam appear a web falling. In thi cae, the actual bending deflection hould be the um of the theoretical one and the web falling. The ection deflection of H-beam in roller traightening i analyzed in theory by implified model. The reult can be concluded that the maximum web falling appear at the center of the web and it i related to the ection dimenion, the roll gap and the collar width. Through the imulation for multiple working condition a regreion formula ha be obtain, which how the relationhip between the web falling and typical H-beam traightening parametric variable. Taking H200*100 H-beam for example, the influence of lateral gap S to the web falling i hown a Fig. 8, from the curve a coefficient A can be concluded a follow [13] : A ( S ) = 0.44( S + 1.7) Fig. 8. The influence of lateral gap on the web falling. Fig. 9. Section flattening of thin-walled tube in traightening proce. The imulation how that the ection flattening i related to the traightening force, geometric characteritic and longitudinal curvature. The ection flattening become higher with the increae of the traightening force, and the trend i approximate to a part of quadric curve. So a regreion formula which how the relationhip between the ection flattening of tube and the traightening force can be decribed a follow: δ = A( R, t, p, a) F m Here the coefficient A i related to the pecification of tube, roller pacing p and roller inclination a [14] Optimization of Energetic Parameter and Loading Mode of Straightening Fig. 7. Section deformation of H-beam in traightening. The ection deformation of tube i imilar to that of H-beam (a hown in Fig. 9). The main ection of a tube i flattening which conit of overall ection flattening and local deformation. The lower lateral bearing capacity of the thinwalled ection make it more trict requirement to control the macrocopic energetic parameter of traightening, otherwie, the traightening force poibly caue uncontrollable ection deformation and urface breakdown. Hence, the relation between bending moment, traightening force and bending deflection hould be analyzed firtly in order to implement effective optimization of the macrocopic energetic parameter of traightening proce. 40

6 Here i taken the traightening proce of H-Beam with 9-roller variable pacing machine a example. Baed on the elatic-platic theory, the relation between the moment, traightening force and deflection of pacing-adjutable roller wa olved, and then a more reaonable ditribution range of the traightening moment wa acquired. The analytical mechanical model i hown in Fig. 10. Thi work provide a completely mathematical method to analyze energetic parameter of variable roller pacing traightening. Meanwhile, for convenient computing and a better undertanding, implified olution of the continuou traightening i given baed on a model of traightening element. An univeral deflection formulae i deduced a well which can be ued in multi-roller traightening. The analytical model of a traightening uint i hown in Fig. 11 [15]. maximum traightening force emi-ymmetric rollerpace traightening i reduced by 13 % than that of equal roller-pacing traightening, and the percentage rie to 22.1 % in the cae of random roller-pacing traightening. If the total traightening force i et a target, the reduction percentage are 1.3 % and 2.1 % repectively. Another poible way to control the urface quality and ection deformation in the traightening proce i to find new loading mode and change the tranmiion path of traightening force in tranvere ection of thin-walled member. Finally ideal multidimenional traightening i achieved. Some exploratory have been done in thi hand, uch a building a finite element imulation model and tudying the feaibility of traightening by preing the flange of H-beam (SPF) (Fig. 12). The reult how that the SPF method can avoid the web falling caued by the force preed on web. Beide, the SPF method can effectively olve the problem of the hedding of oxide film caued by fillet tre concentration when traightening the web. However, the SPF method may caue tre concentration and platic deformation at the end of flange. The overall height of the flange reduce obviouly. It not atifying than the traightening by preing the web when ue the ame reduction rule. However, thi doe not mean that SPF method i not feaible. Taking the platic deformation of the top of flange into conideration and giving a certain compenation, it i till more likely to realize the goal of beam traightening with SPF method. Fig. 10. Analytical model for continuou traightening. Fig. 12. FEM model of SPF method. Fig. 11. Analytical model of a traightening unit. Baed on the analyi of the macrocopic energetic parameter, an optimizing model i built. Taking the minimum of maximum traightening force and total traightening force a target function and the roller pacing a the variable, the optimized roller layout were obtained under three condition: equal roller-pacing, emi-ymmetric roller-pacing and random roller-pacing traightening. If taking the maximum traightening force a target, the optimization reult how that the theoretical 5. Concluion 1. For thin-walled profile with high ection uch a large cale H-beam, the heredity of longitudinal tre hould be taken into conideration when theoretical model of traightening i built. The reidual tre make the ection have very different bending characteritic. 2. Through finite element numerical calculation, the evolution of the tre and train during traightening of the thin-walled member ha been acquired, thi work give a comprehenive undertanding to the deformation behavior of the member. 41

7 3. The ection deformation ha an ignorable effect on the etting of traightening parameter. A regreion formula of ection ha been conclude baed on a erie of imulation on traightening proce. 4. A complete analytical model ha been built to calculate the macrocopic energetic parameter in traightening proce. Baed on thi model, the traightening parameter of thin-walled member ha been optimized and ome probably reaonable loading mode for traightening H-beam have been dicued. Acknowledgement Thi work i upported by the National Science Foundation of China (No ). Reference [1]. Cui Fu, Straightening and traightening machine (Second Edition), Metallurgy Indutry Pre, Beijing, China, [2]. Kawai K, Tatuki Y, Kudo H, Rotary traightening of curved hape near both end of eamle pipe, Journal of Material Proceing Technology, Vol. 140, 2003, pp [3]. Chen Min, Jiang Xiaomin, Zhao Zuxin, Innovation in the computing ytem of traightening force, Chinee Journal of Mechanical Engineering, Vol. 23, Iue 1, 2010, pp [4]. Zhang Mei, Yang He, Huang Liang, Spring back analyi of numerical control bending of thin-walled tube uing numerical-analytic method, Journal of Material Proceing Technology, Vol. 177, Iue 1-3, 2006, pp [5]. Schleinze G, Ficher F D, Reidual tre formation during the roller traightening of railway rail, International Journal of Mechanical Science, Vol. 43, Iue 10, 2001, pp [6]. Li K Y., Profile determination of a tube-traightening roller by envelope theory, Journal of Material Proceing Technology, Vol. 94, Iue 2-3, 1999, pp [7]. Maeda Y, Morimoto Y. Reidual tre control in teel plate by leveling proce, Current Advance in Material and Procee, Vol. 16, Iue 2, 2003, pp [8]. Doege E., Menz R., Huinink S., Analyi of the leveling proce baed upon an analytic forming model, Annal of the CIRP, Vol. 51, Iue 1, 2002, pp [9]. Yong Zang, Ben Guan, Diping Wu, Qin Qin, Preciion traightening theory of thin-walled member, in Proceeding of the 10 th International Conference on Frontier of Deign and Manufacturing, June 10-12, 2012, Chongqing, China (not publihed, oral preentation). [10]. Yonetani Shigeru, The engender theory and countermeaure of reidual tre, China Machine Pre, Beijing, China, [11]. Guan Ben, Zang Yong, Qu Weizhuang, Stre evolvement and it influence on bending behavior during roller leveling proce, Journal of Mechanical Engineering, Vol. 18, Iue 2, 2012, pp [12]. Cui Lihong, Reearch on the Characteritic of Stre and Heredity rule of Reidual Stre in H-beam during traightening, PhD Thei, Beijing Univerity of Science and Technology, Beijing, [13]. Gao Yan, Zang Yong, Finite element imulation of ection deflection during H-beam roller traightening, Journal of Univerity of Science and Technology Beijing, Vol. 28, Iue 12, 2006, pp [14]. Zang Yong, Dai Chun-fa, Li Li-min, Finite element imulation of ection deflection during the cro-roll traightening of the large diameter thin copper tube, Journal of Platicity Engineering, Vol. 16, Iue 4, 2009, pp [15]. Wang Hui Gang, Study on H-beam Straightening Mechanim and Dynamic FEM Simulation, PhD Thei, Beijing Univerity of Science and Technology, Beijing, Copyright, International Frequency Senor Aociation (IFSA) Publihing, S. L. All right reerved. ( 42