Energy Method in Stretch Reducing Process of Steel Tube

Available online at www. sciencedirect.comScienceDirectJOURNAL 0F IRON AND STEEL RESEARCH, INTERNATIONAL. 2008, 15(6); 3943Energy Method in Stretch Reducing Process of Steel TubeZHANG Fang ping,WANG Jian- mei .(Shanxi Provincial Modern Rolling Engineering Center, Taiyuan University of Science andTechnology, Taiyuan 030024, Shanxi, China)Abstract; According to the theories for stretch reducing process and steel tube plastic deformation, the energy meth-od was used to mesh the rolled deformation zone of the steel tube into the upper limit elements, and an admissible ve-locity field was constructed to deduce a series of formulas of the inner virtual power consumption of deformed bodies.The rlling force during the stretch reducing process could be obtained by optimizing the upper limit power, whichcould provide guidelines for a proper choice of the stretch reducing process and devices for steel tube companies, 8swell as new products and devices.Key words: upper limit power; rlling force; velocity fieldOn the basis of the ordinary reducing process,for enterprises to properly choose the processes andthe stretch reducing process aims to increase thedevices for reducing mills.stretching force. Because the tube body is deformedOnly in this way can qualified and high- qualityin a hollow condition, the wall thickness of the tubeproducts be produced. Thus, to obtain more exactwill be thinner under the stretching force (Fig. 1).solutions, the upper finite element method (FEM)The stretching force is produced by the frictionalhas been successfully used to calculate the rollingforce between the roll and steel tube, and the addi-force, owing to its advantages, such as affordabilitytional velocity speed difference between the twoand convenience. Moreover, some creative techno-stands as well,logical methods in upper FEM also give good guid-A set of stretch reducing machines usually con-ance to plastic deformation analysis. Therefore, thesists of 20一30 stands, for which the main functionresearch on upper FEM is meaningful not only inis to properly decrease wall thickness, as the radiustheory, but also in practice.is greatly decreased. The variation of wall thicknessElement Mesh by Upper FEMis determined by the vertical stretching force ( ten-sional force) on the tube during the stretch reducingThe principle of upper FEM is to divide the plasticprocess. The rolling force is an important parameterdeformation region of blank into numerous elements, asduring the stretching process, which provides a basisshown in Fig. 2. For symmetrical forming problems,starting from some chosen point on the line or theintersecting point on the contour boundary of the由workpiece, parallel lines can be drawn in both direc-tions. Thus, the deformed body is meshed into nu-merous loop elements with simple and normalizedcross sections, shaped by a group of lines parallel toFIg 1 Schematic diagram of working principle ofthe coordinates. The loop elements include rectan-the three-roll stretch reducergular elements and triangular elements.Foundation Item: Item Sponsored by National Natural Science Foundation of Chi中国煤化Inaization Poie onScience and Technology Project of China (200707071)Biography :ZHANG Fang ping(1971-), Female, Lctureship; E-mall: zhangfa:MYHCNMH G。, Aurz2. 20Journal of Iron and Steel Research, InternationalVol 15gular element is uniformly distributed along theboundary, and defined as ui,j, u;+1,j, wij, andw,j+1, respectively, on the basis of the serial num-ber of each line' s start number. Meanwhile, r, z,u, and w are accordingly defined as the geometrical|coordinates and velocity components of any point inthe element.The volume of the annular cylinder rectangularelement, V, is as follows:V= π(+1-r7)(z;+1-z;)(1)Each point in the rectangular element has threevelocity components, wherein the tangent compo-nent is zero. According to the incompressible vol-ume assumption, the sum of each node' s strain rateis zero, that is,Fig2 Mesh of rlling deformation areaε, +eo+i.=0(2)where, e, eo, and e. are the strain rates inr, 0, and2 Establishment of Kinematically Admissiblez directions, respectively.Velocity Field of Rectangular ElementFor axial symmetrical problems, the equationcan be written as:To construct upper FEM elements, some as-“+"+∞-0.sumptions are made as follows:(3)(1) The deformed material belongs to an idealJu+. u__ aw)zrigid, plastic body of isotropy, and also obeys theMises yield criteria;For this equation, the right side can be only(2) The inner element is regarded as a contin-thought of as the function of variable z, and the leftuous velocity field;side can be only thought of as the function r. Both(3) The normal velocity component of the ver-sides are irrelevant to each other and thus can be regar-tical element is uniformly distributed along theded as two independent ordinary differential equations,boundary;Next the velocity field of the rectangular ele-(4) The normal velocity component of adjacentment can be solved as follows:elements along the common boundaries is also con-u=-JMr+Ntinuous.(4)As shown in Fig.3, r，r;+1，别;，and zj+1 arew=Mx- Mz; +w.,;,defined as the four geometrical boundary coordinateswhereof the rectangular element. Based on these assump-M= 0i;+1 Wistions, the normal velocity component of the rectan-%j+1-名(wij+1”一Cwij2▲3 Establishment of Kinematically AdmissibleVelocity Field一"4JThe aligned edge BC is always supposed to liein the constant direction of the coordinate system asthe right triangle deforms, meaning BC is neitherd its boundary velocity4,;does中国煤化工straight line can be11下seenIY片CN M H Go this assumption,the rigid line can be extended as a rigid triangle asFig 3 Establishment of kinematically admissiblevelocity field of rectangle elementshown in Fig.4.Issue 6Energy Method in Stretch Reducing Process of Steel Tube●41●z4w.=J号oJ,√et+e+e:+2h.du= =nK|"1| .ri+1十r I「，“，,[1+号+字+5”1”drdr(8)where-u41.,=0f(r)=z;+u+(3,二号+1)(r- -r,) .r41tr;zwhere Yn is shear strain rate; and K is a constant re-lated with plastic status.0,4.2 Power consumption of velocity interval on adja-cent boundaries between elementsFig 4 Establishment of kinematically admissible(1) Rectangular elementsvelocity field of triangle elementThe sliding power between two rectangular ele-Taking the kinematically admissible velocityments with the same boundary can be shown as fol-lows:field of the rectangular element as a reference, thekinematically admissible velocity of the triangular el-W,= |r|Ou |dSp=πr●ement can be deduced as follows:|号Mrt+1-rn>(r+1+2r)+2Nr.(r+.-r)| wows+-+ru.,(z;-z)+(9)1i 1+T+1 1where, Sp is the interruption plane of velocity fieldu;$ t is the shear stress component on Sp; and Ou; isthe velocity interruption quantity on SD. .4 Total Power(2) Rectangular element and triangular elementW=ws+W.+W;(6)w.=2xr,K| |w.coE 一wABC |dz(10)where, Ws is the plastically deformed power of theelement; W, is the power consumption of velocity4.3 Frictional powerinterval between elements; and W; is the power con-(1) Power consumption of contact surfaces be-sumption of contact surfaces between element andtween rectangular element and tooltool.During the process of metal plastic forming, africtional resistance force will be produced when the4.1 Plastically deformed powerdeformed metal slides on the velocity surface, S..(1) Rectangular elementAccording to the principle of metal plastic form-The calculating formula is depicted as follows:ing, the plastically deformed power of the annularW= j。r{Ov|dS. .(11)loop of a rectangular element can be ilustrated aswhere Ov is the frictional sliding velocity, mm/s; τifollows:is the frictional stress, MPa, and if it is considered√3,X2r(z;+1-z,)Xas frictional constant, then τ=nO; and m is thefrictional factor.，V是Mr+李rdrTherefore, the following equation can be ob-whereo, is the yield limit of the material in simple tained.tension, MPa; and Er is the strain rateatr, 0, and z_1W:= =mo,r;+1，|M(zj+1-z,)* +2w.,(zj+1-z;)|directions, k=r, 0, orz.(2) Triangular element中国煤化工(12)YHC N M H G of contact surfacesing, the plastically deformed power of the annular between the angular loop of triangular element andloop of a triangular element can be obtained,●42●Journal of Iron and Steel Research, InternationalVol. 15fieldis to obtain a function of the upper limit ele-W;=mK。| Ov| dS;= rmK(1 +tan'q)●.ment boundary normal velocity component as an op-rit1+r;|u,|(r+i-n)(r,+3Xr+1) (13)timized variable of the whole upper limit power, thestagnation point or the minimum value, that is, thewhole upper limit power, can be obtained. Accord-5 Optimization of Upper Limit Powering to the upper limit theorem, the forming force de-No matter how the upper element is construc-duced from the minimum whole upper limit power isted, Ws, W,, and W( are all represented as the func-the most approachable to the real external force.tion of the geometrical location parameters of the el-Some technological methods in the upper FEMement boundary and normal velocity parameters,have deeply inspired many aspects, for example, thethat is, if only the location coordinates and normaldefinition of forming limit in the plastic machiningvelocity components on the boundary are given, notprocess, the simulation of metallic flow status dur-only the velocity of any point in the element, but al-ing metal plastic formation, the determination ofso each upper limit power component of the elementpre-forming work step, the study on the reasotscan be obtained. After getting the upper power com-that result in flaws during the reducing process, theponent of all the elements, the whole upper powermeasures to prevent the production of flaws, and thecan then be subsequently obtained, and finally theanalyses of other plastic deformation methods as well.forming force is calculated by the principle of virtual6 Calculating Sampleswork.When the deformable body is meshed into theThe reducing mill of hybrid-driven three-rollupper limit elements, the geometrical locations oftype in some中180 MPM units ( whose nominal rolleach element can be subsequently defined; however ，diameter is 360 mm), has reduced the base tube,not all the boundary normal velocities of each ele-164 mm in diameter, into a final tube, 60. 6 mm inment can be obtained， and thus, numerous unde-diameter. The corresponding initial data is shown infined parameters of element boundaries are containedTable 1.in the solution of the whole upper limit power of theThe contrast curves between calculated anddeformable body. Therefore, the optimization calcu-measured results are shown in Fig. 5.lation must be performed on these parameters. Al-As is shown in Fig. 5, the contrast curves showthough the optimization of the upper limit velocitythat the calculated results are in accordance with theTable 1 Initial data of cealculationWall thickness of base tube3.958 mm/sInlet velocity1.1 mm/sOutlet temperature765 CInlet temperature880 CThe total extension amount 3. 597Wall thickness of final tube3. 17 mmFrictional coefficient0. 0226.0measured results, and only smaller relative errorsexist. Therefore, such a method can not only meet22.0the fundamental requirements of production, but canalso be widely applied in engineering practice.18.0by upper FEM7 Conclusions14.0 I(1) The stretch reducing process has been the-10.0Experimental rllig curveoretically analyzed by using upper FEM. According6.to the virtual kinematically admissible velocity field,31620 2the中国煤化工the safety require-Stand numberFlg.5 The curve of product rlling forcementMH.CNM H Ghi-hich provide a basisfor the apμrourrale ciuitts UI une stretch reducingIssue 6Energy Method in Stretch Reducing Process of Steel Tube●43process, device, and the development of new prod-Machine Press, 1989 (in Chinese).[2] ZHAO Zhi-ye. Metal Plastic Deformation and Roling Theoryucts and devices.[M]. Beijing: Metallurgical Industry Press, 1980 (in Chi-(2) The comparison between the theoreticalresults and measured ones show that the theoretical [3] SUN Bin yu, ZHANG Hong. The Estabishment of Calculationresults are approximate to the measured ones withFormulas of Rolling Force on Skew Rolling Tube With Energylittle relative error, which could meet the basic de-Method [J]. Heavy Machinery, 1998, (3); 22 (in Chinese).LI Sheng -zhi, ZHU Cheng xu. Analysis of Interstand Tensionmands in production. Therefore, such a method canand Deformation of Steel Tube in Stretch Reducing Mill [J].be widely applied in engineering practice.Journal of East China Institute of Metallurgy, 1993, 10(2): 26(in Chinese).References:[5ZHANG Fang-ping. The Theoretical Analysis on Stretch Re[1] WANG Zu-tang, GUAN Ting dong, XIAO Jing rong, et al.ducing Process [D]. Taiyuan; Taiyuan Heavy Machinery InrThe Principle of Metal Plastic Forming [M]. Beijing: Chinastitute, 2002 (in Chinese).中国煤化工MYHCNMHG