外文翻譯--三輥卷板機上輥位置的分析建模及實驗驗證（英文）

1、journal of materials processing technology 1 9 7 ( 2 0 0 8 ) 268–278journal homepage: www.elsevier.com/locate/jmatprotecAnalytical and empirical modeling of top roller position forthree-roller cylindrical bending of plat

2、es and itsexperimental verificationA.H. Gandhi a,?, H.K. Raval ba C.K. Pithawalla College of Engineering and Technology, Nr. Malvan Temple, Via Magdalla Port,Surat-Dumas Road, Surat 395007, Gujarat, Indiab S.V. National

3、Institute of Technology, Ichhanath, Surat 395007, Gujarat, Indiaa r t i c l e i n f oArticle history:Received 28 January 2007Received in revised form26 May 2007Accepted 10 June 2007Keywords:Roller bendingSpringbackAnalyt

4、ical studyEmpirical modelingUncertainty analysisa b s t r a c tReported work proposes an analytical and empirical model to estimate the top roller posi-tion explicitly as a function of desired (final) radius of curvature

5、 for three-roller cylindricalbending of plates, considering the contact point shift at the bottom roller plate interfaces.Effect of initial strain and change of material properties during deformation is neglected.Top rol

6、ler positions for loaded radius of curvature are plotted for a certain set of data forcenter distance between bottom rollers and bottom roller radius. Applying the method ofleast square and method of differential correct

7、ion to the generated data, a unified correla-tion is developed for the top roller position, which in turn is verified with the experiments,on a pyramid type three-roller plate-bending machine. Uncertainty analysis of the

8、 empiricalcorrelation is reported using the McClintock’s method.© 2007 Elsevier B.V. All rights reserved.1. IntroductionLarge and medium size tubes and tubular sections are exten-sively in use in many engineering ap

9、plications such as theskeleton of oil and gas rigs, the construction of tunnels andcommercial and industrial buildings (Hua et al., 1999). Thehull of ships may have single, double or higher order cur-vatures, which can b

10、e fabricated sequentially; first by rollforming or bending (to get the single curvature), and thenline heating (to get the double or higher order curvature). Asroller bending is performed at least once in the sequential

11、pro-cess, its efficient performance is a prerequisite for the accurateforming of the double or multiple curvature surfaces (Shinet al., 2001). In view of the crucial importance of the bend-? Corresponding author. Tel.: +

12、91 261 6542507; fax: +91 261 2723999.E-mail address: anishgandhi2002@yahoo.co.in (A.H. Gandhi).ing process, it is rather surprising to find that roller-bendingprocess in the field has been performed in a very nonsym-metr

13、ical manner. Normal practice of the roller bending stillheavily depends upon the experience and skill of the opera-tor. Working with the templates, or by trial and error, remainsa common practice in the industry. The mos

14、t economicaland efficient way to produce the cylinders is to roll the platethrough the roll in a single pass, for which the plate roller-forming machine should be equipped with certain featuresand material-handling devic

15、es, as well as a CNC that can han-dle the entire production process (Kajrup and Flamholz, 2003).Many times most of the plate bending manufacturers experi-ence low productivity due to under utilization of their availablee

16、quipment. The repeatability and accuracy required to use the0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2007.06.033270 journal of materials processing technology

17、1 9 7 ( 2 0 0 8 ) 268–278Fig. 1 – Schematic diagram of three-roller bending process.thickness (t), plate width (w), material properties (E, n, K, and ?),center distance between two bottom rollers (a), top-roller posi-tio

18、n (U), top-roller radius (rt) and bottom-roller radius (r1)(Raval, 2002). The capacity of the plate bender is defined by theparameters such as tightest bend radius with the maximumspan and designed thickness of the plate

19、 and the amount ofstraight portion retained at the end portions of the plate.2. Bending analysisBending analysis is based on some of the basic assumptionssummarized below:? The material is homogeneous and has a stable mi

20、crostruc-ture throughout the deformation process.? Deformation occurs under isothermal conditions.? Plane strain conditions prevail.? The neutral axis lies in the mid-plane of the sheet.? Bauschinger effect is neglected.

21、? Analysis is based on power law material model, i.e. ? = Kεn.? Pre-strain is neglected.? Change of material properties during deformation isneglected.? Plate is with the uniform radius of curvature for supportedlength b

22、etween bottom rollers.2.1. Geometry of bendingIn thin sheets, normal section may be considered to remainplane on bending and to converge on the center of curva-ture (Marciniak and Duncan, 1992). It is also considered tha

23、tthe principal direction of forces and strain coincide with theradial and circumferential direction so that there is no shearin the radial plane and gradient of stress and strain are zeroin circumferential direction. The

24、 middle surface however mayextend. Fibers away from the middle surface are deformed asshown in Fig. 2. Initially the length of the fiber AB0 is assumedFig. 2 – Deformation in fiber AB0.as l0 in the flat sheet. Then, unde

25、r the action of simultaneousbending and stretching the axial strain of the fiber AB0 is ofthe formεl = ln ? lsl0?+ ln ?1 + y??= εa + εb (1)where εa is the strain associated with the extension of middlesurface, εb the ben

26、ding strain and ? is the radius of curvatureof the neutral surface.2.2. Moment per unit width for bending withouttensionIn the case of simple bending without applied tension andwhere the radius of curvature is more than

27、several times thesheet thickness, the neutral surface approximately coincideswith the middle surface. If the general stress–strain curve forthe material takes the form?f = Kεn eq (2)Then, for the plastic bending, applied

28、 moment per unitwidth can be of the form (Marciniak and Duncan, 1992)M = 2K? ? 1?n(n + 2)2n+2?tn+2 (3)2.3. Elastic springback in plates formed by bendingIn practice, plates are often cold formed. Due to springback,the ra

29、dius through which the plate is actually bent mustbe smaller than the required radius. The amount of spring-back depends up on several variables as follows (Raval, 2002;Sidebottom and Gebhardt, 1979):? Ratio of the radiu