Dynamic Simulation and Analysis of Plate Roll Bending Process for Forming a Cylindrical Shell Yogesh Srivastav Development Engineer Heavy Engg. Division Larsen and Toubro limited Mumbai-40007 yogesh.srivastav@hed.ltindia.com Suyog Shinde Asst.Manager Heavy Engg. Division Larsen and Toubro limited Mumbai-40007 suyog.shinde@hed.ltindia.com Keywords: Roll bending Simulation, Pyramidal three roll, Radioss analysis Abstract A simulation methodology is developed to study the dynamic process of plate roll bending using finite element method. The continuous three roll pyramidal bending configuration with cylindrical rolls is used to form thick plate into a cylindrical shell. Plate details, roll bending process parameters & machine data are taken as inputs. The forming of plate during process and stress as well as strain variation in work piece with respect to time can be visualized during the course of simulation. This is a 3D, elastic-plastic, explicit dynamic simulation and performed using FEA tool RADIOSS. The methodology has been evaluated and customized into user friendly simulation tool. 1 Introduction The roll bending process is an efficient technique for forming a metal plate into a cylindrical shape. This is a continuously local plastic forming process as shown in Fig. 1. In this, plate is passed through the set of rolls to get the desired formed shape. Over the last two decades, extensive research and development have been dedicated to roll bending process [1,, 3, 4, 5, and 6]. Unfortunately, even though some publications on analyses of three roll bending process in cylinder roll bending can be found, investigation of roll bending process with three dimensional models are not yet available for the manufacturing industry. The methods published are mostly analytical and used for the purpose of understanding the process. The roll bending is tedious iterative method which requires lot of skill which dramatically affects the productivity. This paper presents a dynamic simulation work on the plate roll bending process for the production of a cylindrical shell. This includes three roll pyramidal configuration of roll bending machines with cylindrical rolls. The simulation has been carried out based on the elastic plastic explicit dynamic finite element method using Radioss Explicit solver. Objective of this work is to develop the simulation methodology and simulation tool to study and optimize the complete process. This will help reduction of various defects while manufacturing the cylindrical shell. Fig. 1 Basic Principle Of Roll Bending Process
FEA Simulation Methodology Detailed study of roll bending is carried out to understand the overall process. Simulation methodology involves application of finite element method to the basic process understanding. Number of roll bending cases has been analyzed. Methodology has been developed by gradual refinement of different aspects from modeling the roll-plate configuration, application of loads and boundary conditions & analyzing the final results..1 Development of methodology Considering the mechanics involved in the process, roll bending is an extension of basic wide plate bending. The roll bending process can be considered as combination of displacement of the top roll in downward direction followed by rotation of all the rolls and governed by three point bending principle. So, normal bending equations (Plane strain bending as width of the plate is much greater than thickness of the plate) can be applied to analyze the roll bending. Ratio of bend radius and plate thickness (Bend ratio) & minimum bend radius are typical forming limits regarding roll bending process. Being a continuous bending process, strain hardening also plays important role in analysis. It is found that strain hardening need to be considered if bend ratio is less than 50. Hence selected material model should incorporate all the effects such as strain hardening, elastic behavior and large plastic deformation. Friction between rolls and plate is another very important parameter in roll bending. It depends on plate & rolls surfaces, local surface pressure between rolls and plate and the temperature in active interface. Study has been carried out to understand the effect of friction on formed shape to optimize friction value that can be considered during analysis. It is assumed that the temperature of plate and rolls throughout the process is constant. Vertical feed of top roll is one of the governing parameters in roll bending operation. A typical equation (1) is derived to calculate the total vertical feed required for forming a plate into a cylindrical shell and it has been used to provide actual vertical feed for the analysis. It is also found that peripheral velocity of the rolls affect the actual vertical feed required for forming. This effect has been considered for the analysis. = r ( R + r) d d R d R R R R r f y (1) Where, f y =Vertical feed R=Shell Radius r =Bottom roll radius d =Distance between bottom rolls ( ) ( ) R + r R + Relevant FEA concepts such as effect of mass scaling have been studied to perform the analysis. This helps to reduce the overall simulation time without affecting the accuracy of result. Roll bending concepts mentioned above are combined with FEA aspects to develop suitable methodology for the simulation. Necessary user defined subroutines have been developed and used in combination with RADIOSS solver.. FEA Model As shown in fig., finite element model includes four parts as one top roll, two bottom rolls and a plate. The finite element model is constructed in HyperMesh. Plate is modeled with 3D SOLID elements where as all rolls are modeled with 3D SHELL elements. In the analysis, all rolls are defined as rigid bodies. Contact surfaces are defined between top roll and upper surface of plate and between bottom rolls and bottom surface of plate. Fig. Finite Element Model Of Roll Bending Process
.3 Loads and boundary condition During the process, initially the top roll moves downward to bend the plate and control the curvature. After that all the rolls rotate with same peripheral velocity to drive the plate in the forward or backward direction. Top rolls are constrained in all direction except rotation and downward direction and motions of bottom rolls are constrained in all directions except rotation, Plate is in contact with all the rolls. Parameters listed in table 1 used for a typical simulation discussed in this section. Table1 Input Parameters Properties Parameter Values Material Properties Process parameters Geometry Parameters Modulus of Elasticity(E) 190000N/mm Yield Strength(YS) 50N/mm Tensile Strength(TS) 380 N/mm Vertical Feed 3mm/sec Roll Peripheral Velocity 54mm/sec Coefficient of Friction(µ) 0.3 Span of Bottom Rolls(d) 1100mm Plate Length 5900mm Bottom Roll Diameter 850mm Roll Length 3500mm Top Roll Diameter 950mm Plate Width 505mm Thickness of Plate(t) 60mm.4 Results Simulation methodology has been developed with above loads and boundary conditions in such a way that all the three rolls rotate to form the plate into cylindrical shape. As a result of simulation, parameters like deformation, plastic strain and von-mises stress distribution can be determined and seen throughout the plate with respect to time as the roll bending process proceeds. Similar results for one of such cases are as shown in figure 3, 4 & 5. The animation of the simulation can be also seen to understand the overall roll bending process. Reaction forces, coming on the rollers can also be determined with respect to time. Based on the visual inspection of the contour display, one can conclude that the final formed shape is very close to a cylindrical shape. For a manufacturer, the challenge is to minimize the deviation between the final shape and desired cylinder. The simulation provides a lot of information about this process. Fig. 3 Contour Display Of Deformed Shape At Different Stages
(Front View) (3-D View) Fig. 4 Contour Display Of Plastic Strain At Different Stages (Front View) (3-D View) 3 Validation of the Methodology The methodology is validated by simulating a practical roll bending case in which a plate has been formed into cylindrical shape in workshop. All the practical data is used for the simulation. It is found that the deformation of formed shape in simulation is very close to the actual deformation. As noted in table, the reaction force coming on top roll obtained by simulation is also in good agreement with the reaction forces in actual case. The reaction forces obtained from the finite element simulation are time varying. So the average value of the same has been calculated. For the comparison with practical case, reaction force data have been converted into equivalent cylindrical pressure in rolling machine. Table Comparison Of The Reaction Force On Top Roll In Terms Of Equivalent Hydraullic Cylider Pressure Side Simulation Result(avg.) Actual Value Front 70.5 bar 70 bar Rear 73. bar 70 bar Fig. 5 Contour Display Of Von Mises Stress At Different Stages (N/Mm ) 4 Application of developed methodology - Optimization simulation package The developed methodology is customized as a user friendly simulation package. Plate details, roll bending process parameters and machine data are taken as inputs and forming of plate during process and stress as well as strain variation in work piece with respect to time can be visualized during the course of
simulation. This provides optimization and visualization of the roll bending process before working on actual job. Hence will save time and rework of shell forming process. 5 Conclusion Methodology for simulation of roll bending process has been developed and validated. The same has been customized into user friendly simulation tool which helps in saving time; energy and rework in overall roll bending process. REFERENCES 1. Yang, M., Shima, Simulation of pyramid type three roll bending process. Int. J. mech. Sci. 30 (1988) 877-886. W. Johnson, P.B. Meller, Engineering Plasticity 1973 3. M. Hua, D.H. Sansome, K.P. Rao, K. Baines, Continuous four-roll plate bending process: it s bending mechanism and influential parameters, J. Mater. Process. Technol. 45 (1994) 181-186. 4. M. Hua, The mechanics of continuous roller bending of plates, Ph.D. Thesis, Aston University, U.K., 1986. 5. J.H. Liu, W.J. Stronge, T.X. Yu, Large deflections of an elastoplastic strain-hardening cantilever, J. Appl. Mech. 56 (1989) 737-743. 6. N.E. Hanson, O. Jannerup, Modelling of elastic-plastic bending of beams using a roller bending machine, Trans. ASME, J. Eng. Ind. 101 (1979) 304-310.