Abstract: Simulating Rotary Draw Bending and Tube Hydroforming Dilip K Mahanty, Narendran M. Balan Engineering Services Group, Tata Consultancy Services Tube hydroforming is currently an active area of development in the automotive industry on account of the advantages it offers in comparison to other manufacturing processes presently under use to produce similar components. The majority of hydroformed tubes must be pre-bent using some bending process. Rotary draw bending is one of the most commonly used tube bending processes, incorporating the use of a universal flexing mandrel and wiper die in case of thin tubes. Simulation of the rotary draw bending and subsequent tube hydroforming is an active area of development. These simulations help establish the feasibility of the hydroforming process for specific components and have the potential to reduce the number of forming trials required to standardize the process for production of a high quality hydroformed component. In addition, they provide a more accurate representation of the hydroformed component during analysis carried out for validating the component design when subject to in-service loads. In this paper, a method is developed for the simulation of rotary draw bending and subsequent tube hydroforming using ANSYS/LS-DYNA. This method employs two finite element models. The first of these is a parametric finite element model with more than 50 parameters used to simulate the rotary draw bending process. This model is created directly as an LS-Dyna input deck, using MATLAB. The second model, which includes the tube with the residual strains, stresses and thickness at the end of the rotary draw bending process, is used to model the tube hydroforming process. Numerical results are obtained for different tubes and can be used to predict feasibility of hydroforming of a specific tube to a given cross section, as well as to examine the residual tube strains and thicknesses at the end of the composite process. Introduction: Rotary Draw Bending: A typical rotary draw bending setup comprises of the tube to be bent along with the associated tooling - the clamp, the bend die, the pressure die, the wiper die and a mandrel. The type of mandrel to be used is influenced by various factors, including the tube diameter to thickness ratio. According to Reference 1, a typical sequence of operations once the tube is loaded into the bending tools is as follows: 1. The clamp closes to grip the tube between the clamp and the bend die. 2. The mandrel advances to the correct position. 3. The clamp and bend die rotate and draw the tube around the bend. 4. The pressure die simultaneously advances forward. 5. The mandrel is withdrawn. 6. The clamp opens to release the bent tube. In keeping with the typical rotary draw bending setup, the finite element model for the simulation of rotary draw bending is also comprised of various components including the tube, the bend die and clamp, the pressure die, the wiper die and a universal flexing mandrel. The scope of the current work is limited to the simulation of a single bend in a circular tube. With reference to the sequence of operations mentioned above, the simulation starts from the point when the bend die and clamp start rotating, thereby drawing the tube around the bend, and terminates when the bend die and clamp stop rotating.
Tube Hydroforming: A generic tube hydroforming setup comprises of the tube to be hydroformed, along with the hydroforming die halves and mechanisms for end sealing as well as for axial feed of the tube ends. Figure 1 - Schematic of Tube Hydroforming shows a schematic of the hydroforming process. Many tubular hydroformed components require the tube to be pre-bent to the general shape of the component so that it can be accommodated into the die cavity. Figure 1. Schematic of Tube Hydroforming A typical sequence of operations comprising the tube hydroforming process is as follows: 1. The tubular blank is placed in the lower die. 2. The upper die is brought partially down to engage the end seals. 3. The seals are advanced to sealing position. 4. The tube is filled with liquid and pressurized to hydroforming pressure. 5. The upper die is brought to closed position. 6. Pressure in the tube is increased to calibration level. 7. If axial feed is required, the end seals are simultaneously advanced to push the required amount of material into the die cavity. 8. Pressure in the tube is reduced to atmospheric level. 9. The end seals are withdrawn to the starting position. 10. The upper die goes up. 11. The hydroformed part is withdrawn from the lower die. The finite element model for simulation of hydroforming comprises of the tube with residual stresses and strains from the pre-bending operation along with the hydroforming die halves. The hydroforming die halves are assumed to be separated by an initial separation distance, and the possibility of contact between the die and the tube during the process of die closure is taken into account. No end seal mechanisms are modeled, and the axial feed is directly applied to the tube ends.
Procedure Modeling Rotary Draw Bending: A finite element model of rotary draw bending as developed in ANSYS/LS-Dyna during this work is shown in Figure 2 - Schematic of Finite Element Model for Rotary Draw Bending. The model comprises of the tube, the bend die and clamp, the pressure die, the wiper die and a universal flexing mandrel with three mandrel balls. The co-ordinate system adopted for the simulation has its origin located on the symmetry plane of the bend and along the axis of rotation of the bend die. Each component is assigned a range of node and element numbers, in order to facilitate easy identification of specific nodes and elements for any post-processing that would need to be carried out. Figure 2. Schematic of Finite Element Model for Rotary Draw Bending The tube is modeled using 4-noded fully integrated Hughes-Liu shell elements (Reference 2) located at the tube mid-surface. A minimum of five integration points across the thickness are used for the elements comprising the tube. The tube is divided into four parts axially - a forward free portion, a clamped portion, a bend portion and an aft free portion. The forward free portion of the tube is the portion of the tube ahead of the clamp, which does not participate in the bending process. The clamped portion of the tube is held between the bend die and the clamp during the bending process. The bend portion of the tube actually undergoes bending, while the aft free portion of the tube is behind the bend portion, and only translates axially during the bending process. The number of nodes on the tube in the circumferential direction constitutes the controlling factor for the total number of tube elements, since the number of nodes in the axial direction is computed for each of the tube portions by assuming an aspect ratio of one for the elements in that portion. Various material models are available for the tube, including the transversely anisotropic elastic plastic material model as well as the commonly used power law plasticity model. All the external (bend die and clamp, pressure die and wiper die) and internal (mandrel shank, mandrel balls) tooling is modeled using 3- or 4-noded shell elements located at the contacting surface. The default Belystschko-Tsay element formulation is used for this purpose. The bend die is modeled over 180 degrees, thereby limiting the maximum bend angle for the simulation to 180 degrees. Further, the minimum bend center line radius is constrained to be equal to the outer diameter of the tube. The clamp is modeled along with the bend die. The bend die and clamp, pressure die and wiper die are modeled assuming a uniform
clearance between the tube and the external tooling. The universal flexing mandrel is modeled as comprising a mandrel shank and one or more mandrel balls, with spherical joints between the mandrel shank and the first mandrel ball and between successive mandrel balls. Figure 3 - Schematic of Mandrel Cross Section shows a schematic of the mandrel including the mandrel shank and mandrel balls. All tooling (external and internal) is modeled as rigid. Figure 3. Schematic of Mandrel Cross Section Contact between various pairs of surfaces: tube-bend die, tube-pressure die, tube-wiper die, tube-mandrel shank, tube-mandrel balls is defined using the *CONTACT_SURFACE_TO SURFACE contact option, which allows for sliding between these surfaces with a Coulomb friction model. Different static and dynamic friction coefficients can be prescribed for different contact interfaces. Contact between the tube and the clamp is modeled using the *CONSTRAINED_EXTRA_NODE_SET option which allows for the nodes in the tube clamped region to be added to the clamp nodes, thereby constituting an ideal clamp. The bend die is constrained to rotate about the global z-axis, while the pressure die is constrained to translate along the global x-axis. The wiper die and mandrel shank are constrained along all degrees of freedom, while translation along the z-direction and rotation about the x- and y- directions are constrained for the mandrel balls. A trapezoidal profile is used to define the angular velocity of the bend die and clamp during the process of rotary draw bending as shown in Figure 4 - Angular Velocity Time History of Bend Die. This ensures a smooth angular rotation profile for the bend die - clamp - tube combination. In a similar manner, a trapezoidal profile is used to define the motion of the pressure die, with due care taken to ensure that the pressure die and bend die do not collide during the process of rotary draw bending.
Figure 4. Angular Velocity Time History of Bend Die Modeling Tube Hydroforming: A finite element model for hydroforming of a bent circular tube into a square die is shown in Figure 5 - Representative Finite Element Model for Tube Hydroforming. This model comprises of the bent tube with the residual stresses, plastic strains and thicknesses resulting from the rotary draw bending process, as well as the hydroforming die halves. As in the case of the external tooling for rotary draw bending, the hydroforming die halves are modeled at the contacting surface, using 4-noded Belystschko-Tsay shell elements. The same material model that was used for the tube during the rotary draw bending process is carried over to the tubular hydroforming process, while the hydroforming die halves are modeled as rigid. The practice of assigning specific node and element number ranges for different components is also adopted for the tube hydroforming process model.
Figure 5. Representative Finite Element Model for Tube Hydroforming Contact between the tube and the hydroforming die is modeled using the *CONTACT_SURFACE_TO_SURFACE option. Axial feed of the tube ends during the hydroforming process is modeled using either a force based approach or a displacement based approach. The displacements at one end of the tube are completely constrained, and an axial force/axial displacement is applied to the nodes at the other end of the tube. Analysis Rotary Draw Bending: Figure 6 - Deformed Configuration for Bent Tube shows the deformed geometry for a circular tube bent through 90 degrees, as obtained through the simulation. The tube outer diameter was 60 mm and the tube thickness was 1 mm. The bend centerline radius for the tube was one and a half times the tube outer diameter. The simulation was carried out without a mandrel. It can be seen that tube collapses on the outer side of the bend, while wrinkles develop on the inner side of the bend. This is a consequence of the relatively large ratio of tube outer diameter to tube thickness and the relatively small centerline radius of bend. Increasing the tube thickness was observed to result in a reduction in the wrinkling on the inner side of the bend as well as a reduction of the collapse of the tube on the outer side of the bend.
Figure 6. Deformed Configuration for Bent Tube In order to validate the finite element model developed for rotary draw bending, simulation results were obtained for rotary draw bending of a circular tube through an angle of 90 degrees. A three-ball universal flexing mandrel was used for this purpose. The tube material was Al 6061-T4, and the tube had an outer diameter of 69.85 mm. The tube thickness was 3 mm, and the tube was bent through a bend centerline radius of 2D, where D is the tube outer diameter. A power law plasticity material model was used for the tube. A default clamp length of twice the tube outer diameter was used for the simulation, along with pressure die and wiper die lengths equal to the tube bend length. The rotation of the bend die was adjusted so as to obtain a maximum linear velocity of 2 mm/ms on the bend die, while the pressure die was not allowed to move. Friction factors for various contact interfaces as well as the penalty stiffness scale factor for the interface were adjusted appropriately. Figure 7 - Energy Time History for Rotary Draw Bending Simulation shows the time histories of kinetic energy and total energy during the simulation. It is clear from this figure that the total energy is at least two orders of magnitude greater than the kinetic energy over most of the process, thereby ensuring that the process is being modeled as quasi-static.
Figure 7. Energy Time History for Rotary Draw Bending Simulation Tube Hydroforming: Figure 8 - Deformed and Undeformed Configurations for Hydroformed Tube shows the deformed and undeformed configurations for a hydroformed tube which was pre-bent through an angle of 90 degrees, and hydroformed from a circular to square cross section. The finite radii of the tube near the corners result from a combination of factors which include the density of the finite element mesh on the tube in the circumferential direction as well as the pressure-time history during the hydroforming process.
Figure 8. Deformed and Undeformed Configurations for Hydroformed Tube As a preliminary validation of the modeling approach adopted for the simulation of tubular hydroforming, a tube free expansion simulation was carried out, wherein a straight circular tube was allowed to expand freely over a given length. The unsupported tube length was 175 mm, the tube outer diameter was 76.2 mm and the tube thickness was 3.5 mm. A power law plasticity material model was used for the tube. A linearly increasing hydrostatic pressure was applied on the inside of the tube. Simultaneously, the ends of the tube were subject to an axial force which varied as a linear function of time, or to an axial displacement, which was measured from the experiment and provided as input to the simulation. The former approach is termed the force based approach, while the latter is termed the displacement based approach. Analysis Results & Discussion Rotary Draw Bending: Figure 9 - Major Strain in Longitudinal Direction for Bent Tube shows the major strain in the axial direction on the outer side of the bent tube as obtained through simulation. It can be seen that the major strain is relatively low at both ends of the tube bend, and reaches a maximum of about 40 % at an angle of about 80 degrees, as well as a relative maximum of about 38 % at an angle of about 50 degrees. Figure 10 - Major Strain in Circumferential Direction for Bent Tube shows the major strain in the circumferential direction at an angle of 45 degrees along the bent tube. The major strain is seen to change sign at a circumferential angle of about 125 degrees - indicating the angular location of the neutral axis of the bent
tube. In a pure bending case, the angular location of the neutral axis of the tube would be 90 degrees. For the present simulation, the change in angular location of the tube neutral axis can be attributed primarily to the drawing action whereby the tube is pulled by the bend die and clamp, in addition to being bent during the process of rotary draw bending. Figure 9. Major Strain in Longitudinal Direction for Bent Tube
Figure 10. Major Strain in Circumferential Direction for Bent Tube Tube Hydroforming: Figure 11 - Tube Radius Time History during Free Expansion Simulation shows the radius of the tube undergoing free expansion as a function of time as obtained through simulation, at the center of the unsupported length of tube. Simulation results for both force based and displacement based approaches are shown in this figure. Both these curves show similar qualitative trends, indicating that the tube radius expands at an increasing rate as the pressure increases. The difference between the force based and displacement based approaches can be attributed primarily to modeling only the supported length of tube, without including the end seals and/or the supported length as well.
Figure 11. Tube Radius Time History during Free Expansion Simulation Conclusion In this work, a method was developed to simulate the rotary draw bending and/or subsequent hydroforming of seamless circular tubes. Preliminary results obtained indicate that the modeling approach adopted for rotary draw bending is adequate, in that simulation results obtained using this approach can be adequately explained in terms of the physics of the process. The modeling approach adopted for hydroforming also appears to be adequate, in that the essential features of the process are captured by the simulation. References 1) Harry Singh, Optimising the Hydroforming Process and Tool Design by the Use of Computer Simulation, TPA Tube and Pipe Fabricating Conference, Tube and Pipe Association International. 2) Bradley Maker N., Input Parameters for Metal Forming Using LS-Dyna, 6th International LS-Dyna User's Conference, Dearborn, Michigan, April 9-11 2000.