Forming characteristics of thin-walled tube bending process with small bending radius

  LI Heng(李 恒) , YANG He(杨 合), ZHAN Mei(詹 梅), GU Rui-Jie(谷瑞杰)  

Department of Materials Forming and Control Engineering, Northwestern Polytechnical University,Xi’an 710072, China

Received 10 April 2006; accepted 25 April 2006

Abstract: Currently requirements of thin-walled tube with small bending radius cause the defects such as wrinkling, overthinning and cross-section distortion more prone to occur in bending process. Based on the analysis of the forming characteristics by analytical and experimental methods, a complete 3D elastic-plastic FEM model of the process was developed using ABAQUS/Explicit code, including bending process, balls retracting and unloading process, and thus the plastic deformation characteristics with small bending radius were investigated. The main results show that: 1) The utmost deformation feature of the NC bending process is its continuous progressive deformation. 2) The occurring conditions of the defects such as wrinkling and tension instability in the process are obtained. The wrinkling is traditional on the double compressive stresses state and the tension instability is on the double tension stresses state. 3) The enhanced non-uniform deformation in thin-walled tube with small bending radius is demonstrated by comparing the stress/ strains distributions under the 1.5D and 1D bending conditions. 4) For 1D small bending process, a new method—“stepped mandrel retraction” is proposed to improve the bending quality in experiment according to the FE simulation. The simulation results are verified by experiment.

Key words: tube bending; forming characteristics; small bending radius; ABAQUS/Explicit

1 Introduction

Thin-walled tube NC bending technology has been attracting more and more applications in aviation, aerospace, ship and automobile, etc, due to its satisfactory high efficiency, high precision and good flexibility[1]. There are increasing requirements of complex and precise components in the above areas. But there occur many defects such as wrinkling at the intrados, over thinning at the extrados and cross-section distortion. Especially, the often needed bent tube with small bending radius enlarges the deformation degree and enhances the imbalance forming degree, which makes the defects and forming parameters difficult to be controlled. So it is of great significance to investigate the plastic deformation mechanism and thus the characteristics of defects in realizing the effective control of the above various defects, especially for small bending conditions.

However, the process is a tri-linearity physical process with multi-factor coupling interactive effects. Many researches have been carried out by using analytical, experimental or numerical methods, respectively. But most of them focus on only the effect of wall thickness change in NC bending process as the pre-bending operations for the subsequent hydroforming. Little literature has been published on aspects of the plastic bending deformation mechanism, not to say the small thin-walled tube bending with small bending radius [2-13]. Due to the build-in complication, few studies are carried out to investigate the plastic bending deformation deeply by analytical and/or experimental methods. And compared with the static implicit FE method, the dynamic explicit algorithm can simulate the complex process and wrinkling phenomenon with dynamic contact conditions and large deformation without any convergence problem. So in the study, the deformation characteristics such as stress/strain distributions and some special phenomena are studied by using the commercial FE code ABAQUS/Explicit combined with analytical and experimental methods.

2 Mechanical analysis of NC bending process

For NC bending process, the rotary draw bending method is used (shown in Fig.1). Pulled by bend die and clamp die, the tube goes past the tangent point and rotates along the groove of bend die to desired bending degree and bending radius; then the mandrel retracts and the tube is unloaded.

Fig.1 Forming principle for NC tube

The essential toolings and the cooperation between them are needed to accomplish the thin-walled tube bending process to ensure the free-wrinkling and allowed thinning and cross-section distortion degrees. The pressure die is to apply enough pressure force and bending moment to the tube and push it against the wiper die tightly ensuring the free-wrinkling bending tube. Meanwhile, the moving pressure die helps push the materials into bending regions reducing the thinning degree. The wiper die and/or proper mandrel (with one or more flexible balls) are used to prevent the tube from wrinkling and over cross-section distorting. The wiper die nest in the bend die groove with its very thin tip extending to the bend tangent point (the point where the tube will begin to bend). In doing so, it fills up the gap normally left by the bend die. Therefore, the tube is completely confined and does not have space in which to wrinkle. The roles of various dies are different each other affecting the stress and strain distribution and materials flow state.

The forces subjected to tube are analyzed.Fig.2 shows that the pressure force N_c is applied to the front tube by the bend die and clamp die, which introduces enough friction force f_c to drag the tube past tangent point and be bent; The pressure die exerts the pressure force N_p to the tube against wiper die to avoid wrinkling, meanwhile it applies the forward friction force f_p to the tube to push the materials into the deformation areas; Both the mandrel and wiper die exert the normal force N_m, N_w to restrain wrinkling and cross distortion, while they induces the backward friction force f_mb, f_mf, f_w. In some bending cases with small bending radius, the optional boost block may apply the forward boosting force F_b to the ending face of the tube directly. The above forces change the local or the whole stress/strain distribution of the bent tube in NC bending process.

Fig.2 Resultant forces subjected to tube in NC bending

So it can be seen that the process is influenced not only by the tube materials properties m (including work hardening exponent n, strength coefficient K and anisotropic exponent R, etc), geometrical parameters such as relative bending radius R/D and relative diameter D/t, toolings parameters (including mandrel extension e and/or balls number n, etc) and process parameters (including bending speed v, push assistant speed v_p and boosting speed v_bp), but also the dynamic contact conditions (including friction conditions c and clearance f between tube and various dies). It is concluded that the NC bending process has so many controlling freedoms, especially the boundary conditions. Under the interaction between the above factors, the tube is formed steadily. And the steady forming T influenced by many factors is demonstrated by

            (1)

The field distribution with small bending takes on obvious 3D characteristics. Fig.2 shows that node A in the extrados is under tension stress in both tangent and hoop directions and compressive stress in radial direction, meanwhile node B in the intrados is under three-dimensional compressive stress states. According to the volume constancy rule of plastic deformation, the extrados nodes are under tangent tension strains, hoop and radial compressive strains. While the intrados nodes are under the states with tangent compressive strains, hoop and radial tension strains. Because the tube bending forming mainly depends on the tube material’s compression and elongation deformation, the tangent stress σ_θ and strain ε_θ on the compression (intrados) and elongation (extrados) regions are regarded as the maximum principle stress and strain. Due to the large relative tube diameter D/t, the normal stress can be neglected. So the plane-stress state is assumed.

But the steady compressive deformation of the tube in the intrados is prone to transfer to the out-plane bifurcation state-wrinkling instability due to tangent compressive stress. Meanwhile, it is evitable to become thinner in wall thickness at the extrados and become thicker at the intrados due to the tangent compressive stress or tangent tension stress. Also, the cross-sections of the tube are distorted by the resultant forces induced by the bilateral compressive stress at the intrados and bilateral tension stress at the extrados. However, it is noted that among the above three defects, the wall thickness change and cross-section distortion are natural phenomenon and consequences of plastic deformation in bending. The wall thickness change and cross-section distortion can not be prevented and only be controlled to allowed extent, but the wrinkling can be avoided.

But from geometrical point of view, the deformation has been accomplished with the scheduled bending radius once the tube materials are drawn past the bending tangent point, and the subsequent deformation is regarded as the repeated similar deformation to desired bending angle. The materials finished deformation transfers the bending force exerted by clamp die to the bending areas. So compared with other bending methods, the period of approaching the steady deformation state is smaller. It is concluded that the utmost characteristics of NC bending process is continuous progressive deformation, which may determine the bending deformation and the occurring of defects to some extent.

3 Experimental

The experiment can study the bending process directly and verify the FE modeling. In the authors’s lab, the PLC controlled hydraulic tube bender W27YPC-63 is used with the same bending principle as the NC bender. The material is aluminum alloy LF2M and stainless steel (1Cr18Ni9Ti). Tube OD is 38 mm, wall thickness t is 1 mm, the length L is 600 mm and the bending radius R is 57 mm and 38 mm, respectively. The relative bending radius is 1.5D and 1.0D, which are regarded as the small bending conditions. The bending speed is 0.15 rad/s, and the pressure die’s pushing assistant speed is the same as the centerline tangent velocity of the bend die. For 1.5D and 1D bending radius, the pressure die linear speed is 8.55 mm/s and 5.7 mm/s, respectively. The bender is without boost device. The tooling parameters are shown in Table 1 and Table 2[14].

Table 1 Tooling geometry dimensions

Table 2 Mandrel geometry dimensions

Different friction conditions are set to lubricate the various contact interfaces. The lubricant is stainless steel extrusion oil. The interfaces with tube/mandrel and tube/wiper die should be lubricated well; the ones with tube/pressure die should be set as dry lubrication; the one with tube/bend die should be set as generally large, while the one with tube/clamp die should not be lubricated.

It is found that even more factors may cause the bending fail, such as toolings rigidity and bender’s stability, which is up to the quality of the bender and toolings. It is observed that the tooling rigidity influences the wrinkling instability greatly. The low rigidity of the toolings such as wiper die may cause the wrinkling to occur. Also, the wear of the toolings such as wiper die may cause the wrinkling instability. It is known that the smaller R/D and larger D/t, the tighter the bending conditions and the more carefully to set up the toolings. The experiment proved this point. It is observed that for thin-walled bending process with 1D relative bending radius, the wrinkling frequently occurs. It is found that the relative slipping between tube and clamp die is the critical problem to induce the wrinkling occurring for small bending radius bending process.

The grid method is used to analyses the strain. The mesh with 15 mm×14.92 mm scaling is marked in the tube outer surface, and the trammel is employed to measure the mesh length.

As shown in Fig.3, the six lengths in the tangent bending direction for six cross-sections are measured at 0?, 90? and 180? respectively and the tangent strains ε_θ are calculated by ε_θ=lg(1+Δl/l); Next, the hoop thickness at the fifth cross-section is measured by 45? intervals to obtain the normal strain ε_r by ε_r=lg(1+Δt/t).

Fig.3 Schematic of locations for strain measurement

Fig.4 shows that the tangent strain at the extrados increases gradually from the back end to front end of the tube, while it decreases when reaching the maximum magnitude at the fifth cross-section. And the front end refers to the straight parts clamped by the clamp die and bend die, and the back end refers to the straight parts contacted with the wiper die. It is seen that the maximum tangent strain at the extrados locates at the front end of the tube. So the most thinning and cross-section distortion occur at the front end of the tube. Meanwhile, it is also observed that the maximum compressive strain locates at the back end of the tube, so the wrinkling and thickening occur in the area near the bending tangent point. Fig.5 shows that the neural layer of the normal strain moves inward obviously. It is found that the normal strains at the extrados are much larger than the ones at the intrados, namely the thinning degree at the

Fig.4 Tangent strains at different locations of cross-section

Fig.5 Normal strain at fifth cross-section

extrados is much than the thickening degree at the intrados.

4 Explicit FEM modeling

Based on the above research, a 3D elasto-plastic FE model for the process is developed using the explicit FE code ABAQUS/Explicit, which includes bending, ball retracting and unloading process altogether shown in Fig.6[14].

Fig.6 Plane symmetry FE model for NC bending process

Due to the plane-stress assumption, four-node doubly curved thin shell S4R is used to model the tube: reduced integration and hourglass control. The toolings are modeled as discrete rigid bodies with 4-node 3D bilinear quadrilateral rigid element R3D4.

The uniaxial tension test is used to obtain the properties (shown in Table 3). Strain hardening behavior was described by SWIFT’s equation as

                                   (2)

Table 3 shows five kinds of contact interfaces. “Surface-to-surface contact” method is used to define the contact between tube and dies. “Kinematic constraints” method is employed to describe mechanical constraints for contact pairs except for the tube/mandrel interface which is modeled with “penalty method”.

Table 3 Mechanical properties of tube

The boundary constraints and loading are applied by two approaches: “Displacement/rotates” and “Velocity/ angular”. Both bend die and clamp die are constrained to rotate about the global z-axis simultaneously. Mandrel’s speed along x-axis is zero during bending process, while when the bending finished, mandrel will be retracted. Wiper die is constrained along all degrees of freedom. “Connector element” is employed to define dynamic contact between mandrel shank and balls. The pressure die is constrained to translate only along the global x-axis. And the booster block is not considered in the study.

The trapezoidal profile is used to define the smooth loading process of bend die, clamp die and pressure die to ensure neglected inertial effects in explicit simulation of quasi-static process.

The classic COULOMB friction model is chosen to represent the friction behavior. According to the experiment, the different friction coefficients needed are shown in Table 4. The friction coefficient for tube/clamp die is assigned to be more than 0.6 to satisfy no slipping in the clamp interface, which causes wrinkling by experimental observation.

Table 4 Friction conditions in various contact interfaces

The FE model is verified[15]. Also in the study, the clearance between tube and wiper die is changed to provoke the wrinkling in the experiment and FE model. Fig.7 shows that the developed FE model can simulate the NC bending process well and can be used to study the forming mechanism of bending process reliably.

Fig.7 Simulation and experimental results-wrinkled tube

5 Results and discussion

It is found that the balls retracting operation has little effect on the wall thickness change and it improves the cross-section distortion degree a little in the curved regions. Furthermore, it is observed that whether wrinkling occurs is not related with the retracting process [12]. Additionally, the unloading process only influences the tube accuracy. So in the study, the stress/strain analysis is only limited to the bending period and the wall thickness change and cross-section distortion are calculated based on the geometrical configuration after retracting and uploading.

Because the deformation of nodes in the crest lines of both outside and inner side of the tube is the largest, these nodes can present the bending characteristics of the tube. Thus, the nodes along the both crest lines are selected to investigate the plastic deformation. Because the stress distribution of stainless steel tube is similar to the aluminum tube, the tube materials are aluminum alloy LF2M in the following without special declaration. Fig.8 shows the results with 1.5D and 1D. It is found that the wrinkling instability occurs with 1D bending conditions.

5.1 Bending characteristics with small bending radius

It is known that the wrinkling and other defects are most sensitive to the tangent compressive and tension stresses, so the distributions of the stresses are studied [16]. Fig.9 shows the tangent compressive stress distribution at the intrados along bending direction. It is found that, at the early stage, the tangent compressive stress value becomes larger and larger with the increasing bending angle. But when the angle reaches a certain value, the compressive regions reduce and the compressive stress fluctuates and even becomes positive (tension stress) at the curved regions. Also, it is observed that the tangent compressive stress distribution is uniform along the inside tube at the early bending stage.

Fig.8 Geometrical configuration of LF2M bent tube by FE simulation: (a) 1.5D; (b) 1D

Fig.9 Tangent stress of nodes along bending direction with 1.5D

But at the later forming stage, the distribution becomes un-uniform. The stress of the nodes near the bending tangent point is compressive and maintains uniform, while the stress of nodes at the curved regions turns tension at the latter stage. In addition, the maximum compressive stress is located near the bending tangent point. Because the wrinkling is sensitive to the compressive stress, the behavior near the bending tangent point is essential to the overall bending process wrinkling prevention.

Fig.10 shows the stresses along the hoop direction at 0? and 45?, respectively. It is observed that at 0? the tangent and hoop stresses are compressive at the intrados, and both stresses are tension stresses at the extrados. But at 45?, the bilateral tangent stresses at the intrados are tension stresses, and the tangent stress at the extrados fluctuates. It is found that at 45?, the hoop stress near the neutral layer becomes large and compressive. So in the thin-walled tube bending process, the stress distributions along the bending direction are uniform greatly. The shear stress is little enough to be neglected compared with the tangent and hoop stresses.

Fig.10 Stresses along hoop direction at different degrees with 1.5D: (a) 0?; (b) 45?

Fig.11 shows the plastic strain distributions of the tube along the bending direction. It is also shown that the strain distributions are non-uniform along the bending direction. It is shown that the maximum magnitudes of the tangent, hoop and normal plastic strains at the intrados are larger than those at the extrados generally, namely the deformation degree is larger than the materials at the intrados. Additionally, it is shown in Fig.11(b) that the magnitudes of the hoop plastic strains both at the intrados and extrados are much obvious, which confirms that the neglecting of the hoop strain of the tube is not reasonable for NC bending process in theoretical analysis[17]. Fig.11(d) shows that the shear strains at the crest lines of the tube is much minor compared with the tangent, hoop and normal strains. But from Fig.12, it is shown that the shear strains are large enough, especially at the nodes near the neural layer.

Fig.11 Distributions of plastic strain along both crest lines with 1.5D: (a) Tangent strain; (b) Hoop strain; (c) Normal strain; (d) Shear strain

Fig.12 Strains along hoop direction at different degrees with 1.5D: (a) 0?; (b) 45?

5.2 Comparison of bending behavior with 1.5D and 1D relative bending radius

Under the same conditions, the tight bending process with 1D relative bending radius is simulated and the deformation is discussed. Fig.8(b) shows that the slight wrinkling, over thinning and severe cross-section distortion are observed for 1D bent tube. First, the tangent compressive stress along the inside bending direction at different bending stages is demonstrated. Fig.13 shows that compared with 1.5D bent tube, the compressive tangent stress distribution for the smaller bending radius is more inhomogeneous. At the little bending stage 0.78 s, the tangent stress even turns tension in the curve regions, which is different from the 1.5D bent tube. Fig.14 shows comparison of the maximum tangent stresses for different bending radiis. It is seen that the tangent compressive stress for 1D is larger than the ones for 1.5D, as well as tangent tension stress. That is why the wrinkling occurs earlier and severer for smaller bending radius tube than for larger one.

Fig.13 Tangent stresses at different bending stages

Fig.14 Comparison of tangent stress of nodes along bending direction at different bending stages with 1D and 1.5D

Fig.15 shows the comparison of the wall thickness distributions of the bending tube along the crest lines at the intrados and extrados. It is found that the wall thickness change for 1D relative bending radius is much greater than the 1.5D bending operation. Meanwhile, Fig.16 shows the cross-section distortion degree along the bending direction. It is found that the cross-section distortion degree of the former bending operation is also greater than the latter.

Fig.17 is the distribution of plastic strain along the both crest lines with 1D. It is shown that the plastic strains at the extrados are larger than the ones at the intrados, which is also different from the smaller bending

Fig. 15 Wall thickness along bending direction

Fig.16 Cross-section distortion degree

radius bent tube. It is noted that the shear stresses are neglected for both cases, and the shear strains are almost equal to zero at the crest lines, but it approaches the maximum near the neural layer.

For 1D case, the slipping magnitude is about 3.1 mm. Fig.18 shows that for 1D bent tube, the RF of both pressure die and bend die is far larger than the ones for 1.5D at later period, which is the direct reason of slipping. So for the same materials, process parameter and boundary conditions, there is relative slipping between tube/clamp die for small bending radius, which causes wrinkling as demonstrated as Fig.8(b). For 1.5D case, there is no relative slip between tube/clamp die. In addition, the relative slip between tube/pressure die represents the materials amount involved into bending deformation. Thus, the relative slip between tube/pressure die under the two cases are compared, as shown in Fig.19. It is found that with bending angel increasing, the relative slip between tube and pressure die for 1D case increases sharply, while the slip distance

Fig.17 Distributions of plastic strain along both crest lines with 1D: (a) Tangent strain; (b) Hoop strain; (c) Normal strain; (d) Hoop strain

Fig.18 Reaction force(RF) of pressure die and bend die: (a) RF of pressure die; (b) RF of bend die

for 1.5D case increases little. It is known that the large relative slip between tube and pressure die means little effective materials into deformation zones, which induces the severe wall thinning degree.

5.3 New method to improve bending quality with 1D relative bending radius

As mentioned in both experiment and simulation, the key problem for small bending radius is the relative slipping between tube and clamp die, which causes wrinkling in the later bending period. And it is known that it is the large reaction force (RF) of bend die that causes the relative slipping. Here, a new method named “stepped balls retraction” is proposed to improve the bending quality for smaller bending radius.

The method refers to that the whole bending process is divided into multi-steps with fraction bending angles such as 5?, which is different from the balls retraction. Balls retraction means that when the overall bending deformation is finished, the mandrel and balls are retracted to unload. But the proposed method is positive to control the bending deformation. From the simulation, the effect mechanism of the method is obtained.

Fig.19 Relative slip for tube/clamp die and tube/pressure die: (a) Between tube and clamp die; (b) Between tube and pressure die

It is found that the RF of the bend die for “stepped balls retraction” increases step by step, which ensures no relative slipping between tube/clamp die shown in Fig.20(a). It is found that the new operation can realize the stepped local unloading, reduce the dragging force of mandrel greatly and then ensure no relative slipping between tube/clamp die, thus prevent wrinkling. Thus, the wrinkling does not occur with “stepped balls retraction” operation. Meanwhile, Fig.20(b) shows the relative slipping distance between tube/pressure die with new method is much smaller than the one under general bending conditions, which helps to make the materials into plastic bending regions and thus reduce over thinning degree shown in Fig.21. Fig.22 shows the cross-section distortion degree with “stepped balls retraction”. It is shown that the maximum cross-section distortion degree with “stepped balls retraction” is 10%, while for the general bending condition, it is 12%.

Fig.20 Relative slip distance: (a) Between clamp die and tube; (b) Between pressure die and tube

Fig.21 Wall thickness along bending direction

Fig.22 Cross-section distortion degree

To verify the above results, a series of 1Cr18Ni9Ti tubes with 1D are bent between 30? and 150? in the experiment. The “stepped balls retraction” method is used and the step angle is 5?. Fig.23 shows the simulation and experimental results with bending angle 90?. It is seen that the instability does not occur in both simulation and experiment. That is because there is no relative slipping for tube/clamp die in practice with new method. So the problem for smaller bending-relative slipping of tube/clamp die is conquered. Additionally, the thinning and cross-section distortion degree are compared. The cross-section distortion degree is within 5% and the maximum thinning is within 29%. By comparison of the wall thickness at the extrados of the bent tube with 1D between FE simulation and experimental results, it is found that the maximum wall thinning degree is nearly the same between FE and experimental results.

Fig.23 1D 1Cr18Ni9Ti bent tube by FE simulation and experiment: (a) Bent tube by FE simulation; (b) Bent tube by experiment

6 Conclusions

The non-uniform plastic deformation behaviors are studied. For the aluminum tube bending process, 1D is beyond its bend-ability due to the defects such as cracking and wrinkling occurring. But by simulation, the bending deformation of the virtual material can be studied to take insight into the thin-walled tube bending process. The feature of the bending process is continuous progressive deformation, which can be used to explain the plastic deformation behaviors. Also the non-uniform distributions of stresses/strains mean that the more carefulness should be taken and new methods such as “stepped balls retraction” is proposed to control the forming quality. The experiment verifies the above conclusions.

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(Edited by PENG Chao-qun)

Foundation item: Projects(59975076, 50175092) supported by the National Natural Science Foundation of China; Project(50225518) by the National Science Found of China for Distinguished Young Scholars; Project by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, PRC; Project(20020699002) by the Specialized Research Fund for the Doctoral Program of Higher Education of MOE, PRC; Project (04H53057) by Aviation Science Foundation

Corresponding author: YANG He; Tel: +86-29-88495632; Fax: +86-29-88495632; E-mail: yanghe@nwpu.edu.cn