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Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending
CJA 1375 10 September 2019 Chinese Journal of Aeronautics, (2019), xxx(xx): xxx–xxx
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Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
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Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending
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Chunmei LIU a,b, Yuli LIU a,b,*
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7 8 9
10
a
Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China b
Received 2 April 2019; revised 12 August 2019; accepted 12 August 2019
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KEYWORDS
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Cross-sectional deformation; FE simulation; H96 double-ridged rectangular tube; H-typed rotary draw bending; Ridge groove fillers; Twice-springback stage
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Abstract The bent double-ridged rectangular tube (DRRT) with high forming quality is helpful to improve the microwave transmission accuracy. For reducing the cross-sectional deformation in the H-typed bending process, in addition to using rigid mandrel to support the inside of tube, ridge groove fillers are also added to restrict the deformation of ridge grooves. Because of the change of stress and strain state of bent tube in bending, rigid mandrel retracting and specially twicespringback stages, and the springback of fillers, the cross-sectional deformation of tube in each stage may be different. Therefore, based on the ABAQUS platform, the finite element models (FEM) for H-typed bending, mandrel retracting and twice-springback stages of H96 DRRT with fillers were established and validated. It is found that, for the height and width deformation of tube and spacing deformation of ridge grooves, retraction of mandrel can make the distribution of these deformations more uniform along the bending direction. The first springback can reduce these deformations significantly, which should be emphasized. But the second springback only increases them by less amount, which can be ignored. The smaller height deformation of ridge groove and filler can be neglected. Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
* Corresponding author at: Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China. E-mail address: [email protected] (Y. LIU). Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
1. Introduction
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With the advantages of lower cut-off frequency, wider working frequency bandwidth and smaller size, curved double-ridged rectangular tube (DRRT) has been widely used in aerospace microwave transmission and communication systems.1 The bent tube is usually obtained by high-precision and highefficiency rotary draw bending (RDB) technology.2 However, cross-sectional deformation of bent tube occurring in the bend-
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https://doi.org/10.1016/j.cja.2019.08.005 1000-9361 Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: LIU C, LIU Y Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.005
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ing process will change the shape and size of the inner cavity of tube, so that the electromagnetic wave transmitted in the bent tube is phase-shifted.3,4 It can be considered that the microwave transmission accuracy depends on the forming quality of the bent tube. For the H-typed bending process, which means the tube is bent along the narrower flanges and the ridge groove is located on the side wall, Xiao et al.5 and Liu et al.6 found that adding the I-shaped rigid mandrel or PVC elastic mandrel into the DRRT, the cross-sectional deformation can be effectively improved. But it is worth noting that the ridge grooves, where the electric field is more dense,7 are still deformed severely due to the large pressing force, as shown in Fig. 1(a). Therefore, while using the rigid mandrel, it is also considered to add fillers into the ridge grooves to restrict the deformation of ridge grooves, as shown in Fig. 1(b). The entire H-typed forming process of DRRT from the straight tube to the bent tube includes the following stages. Firstly, the bending stage, the ridge groove filler can be bent together with the tube and the cross-section deformation of tube and filler occurs in this stage. Secondly, the internal rigid mandrel retracting stage, which may change the cross-sectional deformation in the mandrel-support area. Finally, the special twice-springback stage after unloading the external bending dies, which is proposed due to the use of ridge groove fillers in this study. In the first springback of this stage, the fillers are still in the ridge grooves, that is the synchronous springback of bent tube and filler occurs. So except for the bent tube, the variation in the deformation of filler will also occur and the existence of fillers may also affect the springback of crosssectional deformation of bent tube. In the second springback, the fillers have been removed, the cross-sectional deformation of tube may continue to change. Therefore, it is found that the cross-sectional deformation in each stage of the entire H-typed forming process may be different. At present, some researches have been carried out on the cross-sectional deformation of DRRT in H-typed RDB with fillers. Chen et al.8 found that when the hardness of polymer materials is less than Shore D60, which is added into both the DRRT and ridge grooves, the forming quality of the cross section is difficult to ensure. Similarly, Xu9 used polyester carbonic acid (a kind of polymer material) as the filling material, which can suppress the cross-sectional deformation to improve the electrical performance of the bent tube. But as the filler, the strength and hardness of polymer material are required to be high, and the injection molding process is complicated and time consuming. Jiang et al.10 selected 3A21 aluminum alloy as the ridge groove filler, which can be processed easily to
Fig. 1
reduce the cross-sectional deformation of DRRT. It can be found from all the above researches that the use of ridge groove filler cannot only alleviate the uneven deformation of tube, but also significantly improve the deformation of the ridge groove. However, these studies only focus on the deformation in the bending stage, the effects of mandrel retracting and springback on the cross-sectional deformation are not taken into account. Zhang et al.11 obtained that the retraction of mandrel can make the cross-sectional deformation of the whole rectangular tube tend to be uniform. Li and many other scholars12–14 discovered the effect of springback on cross-sectional deformation of high-strength Ti-3AL-2.5V titanium alloy circular tube, 3A21 aluminum alloy and H96 brass rectangular tube of RDB. In these study, cross-sectional springback, that is the change in the amount of cross-sectional deformation before and after springback, is one of the characteristics of elastic recovery and it is found that the cross-sectional springback is beneficial to reduce the cross-sectional deformation. Using the theoretical analysis method, Liu et al.15 found that when considering the cross-sectional ovalization of circular tube after springback, the springback prediction model has higher accuracy. Zheng et al.16 found that during the Etyped bending of DRRT, cross-sectional deformation became larger after springback in cores-support zone while they all became smaller in no-cores-support zone. The above studies show that the mandrel retracting and springback will affect the final cross-sectional size accuracy of the bent tube, which are important stages that cannot be ignored in the forming process. Based on the above research status, it is found that different stages of the entire H-typed bending process all have the effect on cross-sectional deformation, which should be considered and studied. However, the research about the specific effect of each stage on cross-sectional deformation of DRRT with fillers in H-typed RDB has not been reported. Therefore, the finite element models (FEM) for H-typed bending, mandrel retracting and twice-springback stage of H96 DRRT with fillers were established based on the ABAQUS platform. With these models, the characteristics of cross-sectional deformation of tube and filler in the entire H-typed forming process, the effects of mandrel retracting, twice-springback, the springback of filler on the cross-sectional deformation of tube and which stage has the most significant effect on the cross-sectional deformation were studied to improve the forming quality of H-typed double-ridged rectangular bent tube.
Bending types and a method to restrict cross-sectional deformation of H96 brass DRRT for H-typed RDB.
Please cite this article in press as: LIU C, LIU Y Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.005
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2. FEM for H-typed RDB of DRRT with ridge groove fillers
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2.1. Definition of material models
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The fillers assembled in the ridge grooves are bent and deformed together with the tube during the H-typed bending process. The material of DRRT is H96 brass. Considering the stiffness and strength of polymer and metal materials and the requirement for manufacturing the filler, the 3A21 aluminum alloy10 is appropriate and chose as the filler for research in this paper. In the finite element simulation, the tube and filler are defined as continuous isotropic deformable solid element, and the material models of DRRT and filler should be defined respectively. The true stress–strain curves of H96 brass DRRT and 3A21 aluminum alloy filler are obtained by the uniaxial tensile tests, as shown in Fig. 2. The plastic strain ep of the materials needed in the simulation is calculated by subtracting the elastic strain from the true strain, as shown in Eq. (1), the constitutive equation as shown in Eq. (2) is used to describe the plastic deformation of material. ep ¼ e r=E r ¼ Kðe þ bÞ p
n
2.3. Establishment of the FEM for H-typed bending process
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The three-dimensional FEM for the actual entire H-typed bending process of H96 DRRT with fillers are composed of four sub-models, which are the H-typed bending model, the rigid mandrel retracting model, the first springback model after unloading the rigid dies and the second springback model after removing the fillers.
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The surface to surface contact model is used to define the contact between the non-deformable rigid dies, including the bending die, pressure die, mandrel and so on, and the tube which is selected as slave face. The height and width of filler are the same with those of ridge groove, which means that the clearance between filler and tube is set to be 0 mm in sim-
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60.2 99.8 0.330 0.145 225.3
ð2Þ
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3A21 aluminum alloy
92.8 70.0 0.324 0.425 588.0
168 169 170 171 172 173 174 175 176 177 178
p
2.2. Definition of contact models
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H96 brass
Modulus of elasticity E (GPa) Yield strength r0.2 (MPa) Poisson ratio m Hardening exponent n Strength coefficient K (MPa)
ð1Þ
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153
Parameters
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159
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Table 1 Main mechanical properties of H96 brass DRRT and 3A21 aluminum alloy ridge groove filler.
ulation. So the contact between the filler and tube is defined by two contact models of surface to surface contact and general contact, and their simulation results are shown in Fig. 3. It can be seen that, when using the surface to surface contact model, the penetration phenomenon occurs between the filler and tube, as shown in Fig. 3(a). But there is non-penetration found in Fig. 3(b) when the general contact model is used. This may be because in the surface to surface contact model, the master face of the contact pair can penetrate to the slave face, but as two deformable faces, the tube and filler should not be penetrated each other. So the general contact model is chosen to define the contact between the filler and tube.
where e is true strain, r is true stress, e is plastic strain, E is modulus of elasticity, K is strength coefficient, n is hardening exponent and b is a constant. According to Eq. (2), the mechanical properties of these two materials are achieved by fitting the obtained plastic stress–strain data and shown in Table 1. Then, the main mechanical properties and plastic stress–strain data are imported into the software to complete the definition of material models.
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(1) The H-typed bending model
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Except for the definition of the above material models and contact models, for improving the computational accuracy and efficiency of the models, based on the geometric model shown in Fig. 4(a), the element type of the tube and ridge groove filler are defined as a deformable 8-node hexagonal reduced integral solid element (C3D8R) with five integration points, meanwhile the rigid dies are defined as the bilinear quadrilateral rigid shell element with four nodes (R3D4). The mesh sizes of tube, filler and mandrel are all 1 mm 1 mm, and that of other rigid dies are all 3 mm 3 mm. The angular velocity of bending die is 0.5 rads1. After solving the above key technologies, based on the platform of ABAQUS/Explicit, the H-typed bending model of H96 brass DRRT with 3A21 aluminum alloy ridge groove fillers is established, as illustrated in Fig. 4(b). (2) The rigid mandrel retracting model When the bending stage is completed, the rigid mandrel retracting begins at the velocity of 60 mms1, and the time of this stage is one second. The rigid mandrel retracting model is shown in Fig. 4(c). (3) The first springback model
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Fig. 2 True stress–strain curves of H96 brass DRRT and 3A21 aluminum alloy ridge groove filler.
Because the fillers are still in the ridge grooves after unloading the rigid dies, so the first springback model after unloading
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Fig. 3
Fig. 4
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Comparisons of different contact models for tube and filler.
Models of the entire H-typed RDB of H96 brass DRRT with ridge groove fillers.
all the rigid dies, that is, the synchronous springback model of the double-ridged rectangular bent tube and deformed fillers. The springback is the release process of stress and strain of the double-ridged rectangular bent tube and fillers after bending process. The information such as stress and strain of the double-ridged rectangular bent tube and fillers in the result file, which is calculated by the previous step bending model, is introduced into the first springback model and defined as the initial field. The contact model of the tube and fillers is the
same as in the bending model. In order to avoid the rigid displacement of bent tube and fillers during the springback, it is needed to impose sufficient constraints on the formed tube and fillers. A encastre boundary is applied to end position of the DRRT where is not deformed during the bending process, so that the stress and strain of the double-ridged rectangular bent tube and fillers can be released freely. Based on the above analysis, the first springback model after unloading all the rigid dies is established and shown in Fig. 4(d).
Please cite this article in press as: LIU C, LIU Y Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.005
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(4) The second springback model
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The second springback model, as shown in Fig. 4(e), is built to simulate the final springback of tube after the fillers are removed, whose establishing method is similar to that of the first springback model.
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2.4. Experimental verification of the finite element models
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2.4.1. Description of the cross-sectional deformation of tube and filler
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In order to quantitatively analyze the cross-sectional deformation of DRRT and filler in H-typed bending, the description of deformation is given as follows: dHi and dhi are used to indicate the height deformation of tube and ridge groove; dBi and dbi are used to indicate the width deformation of tube and spacing deformation of ridge grooves; dh0 i and db0 i are used to indicate the cross-sectional height and width deformation of filler. These deformations can be calculated by Eqs. (3)–(8), respectively. dHi ¼
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ð4Þ
Bi B 100% dBi ¼ B
ð5Þ
bi b 100% dbi ¼ b dh0 i
ð6Þ
h0 h0 ¼ i 0 100% h
ð7Þ
b0i b0 100% b0
ð8Þ
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ð3Þ
hi h 100% dhi ¼ h
259 261
Hi H 100% H
db0 i ¼
where as shown in Fig. 5(a), the schematic diagram of certain cross section of DRRT before deformation, H = 18.29 mm and h = 4.39 mm are the original height of tube and ridge
Fig. 5
5
groove; B = 8.15 mm and b = 2.57 mm are the original width of tube and spacing of ridge grooves; as shown in Fig. 1(b), h0 = 1.85 mm and b0 = 2.75 mm are the original height and width of filler. Hi (i = 1(10 )–10(100 )), hi (i = 11(110 )–14(140 ), 15(150 )–18(180 )), Bi (i = 19(190 )–26(260 ), 32(320 )–39(390 )), bi (i = 27(270 )–31(310 )), hi0 (i = 41(410 )–44(440 )), and bi0 (i = 41 (44), 40(45), 410 (440 )) are those corresponding sizes at a certain node i (as shown in Fig. 5(b) and (c)) after deformation. According to the above expressions, the positive value of a deformation indicates that the size increases after deformation, and relatively the negative value indicates the decrease. For negative value, the greater the absolute value, the more severe the deformation.
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2.4.2. Experimental validation
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In order to ensure the credibility of the next research results, it is necessary to verify the reliability of the above established models by comparing result error between the experiment and simulation. The DRRT with ridge groove fillers and experiment process of H-typed RDB are shown in Fig. 6. The simulation conditions are consistent with the experimental ones, as shown in Table 2. Based on the experimental and simulation conditions shown in Table 2, the comparisons between the experimental and simulation results are carried out. The experiment is carried out with three specimens, the profiles of these experimental specimens are basically consistent. So one representative bent specimen is chosen to be shown in Fig. 7(a) and (b). As shown in Fig. 7(a) and (b) ignoring the smaller fillet of the real tube, the profiles of the bent tube after the fillers were removed and the deformation of a certain cross section of the final bent tube obtained from the simulation are basically coincide well with those from the experiment. Furthermore, based on the Eqs. (3) and (6), the distribution of dH of node 5(50 ) and db of node 27(270 ) in characteristic cross sections along the bending direction from the simulation bent tube and three experimental specimens are obtained and shown in Fig. 7(c) and (d). It can be seen that the results of these three experimental specimens are similar and their distribution laws are basically the same, so the average of these experimental results can be
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Schematic diagram of DRRT before and after deformation.
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Fig. 6
Table 2
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Experiment process of H-typed rotary draw bending of DRRT with ridge groove fillers.
Experimental and simulation conditions.
Parameters
Experimental
Simulation
Angular velocity of bending, x (rads1) Bending angle, h (°) Bending radius, R (mm) Boosting velocity of pressure, Vp (mms1) Velocity of retracting mandrel, V1 (mms1) Friction coefficient-tube (H96 brass)/filler (3A21 aluminum alloy) Friction coefficient-tube (or filler)/clamp die (45# steel) Friction coefficient-tube/mandrel (35CrMo) Friction coefficient-tube (or filler)/ other dies (45# steel) Clearance-tube/mandrel, Cm (mm) Clearance-tube/other dies and filler (mm)
0.5
0.5
90 60 35.21
90 60 35.21
60
60
A little lubricating oil
0.27
Dry friction
0.6
Large quantity of lubricating oil A little lubricating oil 0.2
0.01
0
0
0.17 0.2
used to compare with the simulation results. Then it can also be obtained that the distribution of deformations along the bending direction from the simulation results is in agreement with that from the average experimental results, the maximum errors between average experimental results and simulation ones of these two deformation are about 8.4% and 9.8%, respectively, and the average errors of them are both about 4.8%. The offset may be produced by many reasons, such as the error in measuring the experimental bent tube, the clearance between the tube and bending dies was not accurate to 0 because of the dimension tolerance allowed in machining the dies and so on. These errors of no more than 10% are acceptable, which means that the simulation and experimental results are highly consistent. Therefore, three-dimensional FEM including the H-typed RDB and mandrel retracting models of DRRT with 3A21 aluminum alloy ridge groove fillers and two springback models are reliable, and the next study can be conducted on this basis.
3. Cross-sectional deformation of DRRT and filler in the entire H-typed RDB
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3.1. Height deformation of tube
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In the H-typed bending process of DRRT, the outer flange and inner flange are depressed and deformed under the action of tangential tensile and compressive stress respectively. The different depressions of inner and outer flanges cause the height of tube to change, that is, the height deformation of tube dHi occurs. Based on the established bending, mandrel retracting and twice-springback models, different depressions of inner and outer flanges of section S1 in mandrel-support zone and section S6 in non-mandrel-support zone (as shown in Fig. 8) at each stage of the entire H-typed forming process have been obtained and shown in Fig. 9(a) and (b). And according to Eq. (3), dHi of section S1 and S6 are calculated and shown in Fig. 9 (c) and (d). It can be seen that the depressions of inner and outer flanges and height deformation of tube are both symmetrically distributed along the width direction. At any stage of the entire forming process, the maximum deformation is located at node 5 (50 ) in the middle of flanges. After bending stage, the depression of inner flange of sections S1 and S6 are almost the same, and due to the support of rigid mandrel, the depression of outer flange of section S1 is significantly smaller than that of section S6, which makes dHi of section S1 smaller than that of section S6. After the mandrel retracting stage, because the support of mandrel to section S1 is missing, only the outer flange depression of section S1 increases. So that dHi of section S1 increases, while that of section S6 remains basically unchanged at this stage. It is indicated that the use and retraction of the rigid mandrel affect the height deformation of tube in mandrel-support zone more significantly than that in nonmandrel-support zone, and the influence on the depression of outer flange is greater than that of inner flange. After the first springback, the outer flanges of sections S1 and S6 both move up, the inner flanges move down, which means that the depression of outer and inner flanges of these two sections decrease and tend to be gentle. That is, dHi of these sections are both reduced at this stage. After the second springback, the depression of outer flange of section S1 keeps substantially unchanged, but the depression of outer flange of section S6 continues to become smaller. The depressions of inner flange of these two sections both become larger slightly.
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Fig. 7
Fig. 8
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Simulation and experimental results after the fillers were removed.
Distribution of characteristic cross sections.
After calculating, dHi of these sections are slightly increased at this stage. Overall, the change of depression of outer flange of section S1 during the mandrel retracting stage is larger than that in the twice-springback stage. The influence of first springback on the inner flange depression of section S1 and outer and inner flanges depressions of section S6 are significantly greater than the second springback, and the mandrel retracting stage can be ignored. This is because only the stress in mandrel-support
zone is unloaded during the mandrel retracting stage, while the stress of whole bent tube is released during the first springback stage, then a slight springback of deformation is only caused by the removal of the fillers in the second springback stage. Therefore, for the height deformation of tube in mandrelsupport zone, the mandrel retracting and first springback stages should be emphasized and considered simultaneously. For the height deformation of tube in non-mandrel-support zone, focusing on the first springback stage is enough.
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3.2. Height deformation of ridge groove
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The height deformation of ridge groove dhi is caused by the change of the position of inner and outer walls of ridge groove. Based on the established models, the position of inner and outer walls of ridge groove of section S1 and S6 in the entire H-typed forming process is obtained and shown in Fig. 10(a) and (b). And according to Eq. (4), dhi of section S1 and S6 are calculated and shown in Fig. 10(c) and (d). It can be seen that, the deformation of the left and right ridge grooves is symmetrical, so only analyzing one side is enough. On these two sections, the inner and outer walls of ridge groove basically both move upward, the displacement of inner wall is larger than that of outer wall, which makes the height of the ridge
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Fig. 9 Depression of inner and outer flanges, height deformation of section S1 and S6 after bending, mandrel retracting and twicespringback process.
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groove reduced. The displacement and dhi of node 11 (110 ) located at the intersection of side wall and ridge groove are the largest at any stage of the entire forming process. After bending, although the displacement of inner and outer walls of ridge groove of section S1 is slightly larger than that of section S6, because of the supporting effect of fillers on ridge grooves, dhi of these sections are almost the same and both very small, the maximum dhi is less than 1.5%. After the mandrel retracting, the position of outer and inner walls of ridge groove of section S6 substantially unchanges. The outer and inner walls of ridge groove on section S1 move down slightly to the same position as the section S6, but the change of dhi is small and negligible. This shows that due to the introducing of filler, the influence of the use and retraction of mandrel on the height deformation of ridge groove in the entire bent tube is small and even not needed to be considered. Then during the first springback, the inner and outer walls of ridge groove on section S1 move downward slightly, while those on section S6 move up slightly, eventually reducing dhi of the two sections. But because the fillers are not removed at this stage, they still have a certain support effect to the ridge groove, dhi at this stage has little difference with that after mandrel retracting. After the second springback, because the fillers are removed, whose support function to the ridge grooves does not exist, the inner wall of ridge groove on these
two sections relatively move upward relatively larger, so that the height deformation of ridge groove increases. Overall, whether in the mandrel-support zone or the nonmandrel-support zone, only the second springback has a significant effect to increase the height deformation of ridge groove, other stages can be ignored.
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3.3. Width deformation of tube
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Since the deformations of the two side walls of bent tube are symmetrical, therefore, unlike the deformation in height direction studied above, only analyzing the width deformation of tube directly is enough. Based on the established models, the width deformation dBi of section S1 and S6 in the entire H-typed forming process are obtained and shown in Fig. 11(a) and (b). It can be found that after bending, under the support of mandrel, dBi of section S1 is much smaller than that of section S6. Especially in the outer area of neutral layer, where the deformation is bigger, dBi of each node on section S1 is relatively gentle. But on section S6, the closer to the ridge groove, the larger the dBi, and at the intersection of side wall and ridge groove, that is dBi on node 26(260 ) is the largest. After the mandrel retracting stage, dBi of section S6 is not changed, but dBi of section S1 is significantly increased, due to the support function of mandrel does
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Fig. 10 Position of outer and inner walls of ridge groove, height deformation of ridge groove of section S1 and S6 after bending, mandrel retracting and twice-springback process.
Fig. 11 448 449 450 451 452 453 454 455 456 457
Width deformation of section S1 and S6 after bending, mandrel retracting and twice-springback process.
not exist, and the distribution law of dBi is the same as that of section S6. At this stage, dBi of section S1 is even higher than that of section S6. It is shown that, except for the height deformation of tube, the use and retraction of the rigid mandrel also affect the width deformation of tube in mandrel-support zone more significantly, and the influence on the deformation of side wall in outer area of neutral layer is greater than that in inner area. After the first springback, in the outer area of neutral layer, dBi of these two sections are both reduced and dBi of each node
is basically the same. But in the inner area of neutral layer, dBi is changed from negative to positive, which makes a ‘‘bulk belly” phenomenon appear. After the second springback, dBi in the outer area of neutral layer of section S1 is slightly decreased, while in the inner area is slightly increased. The change of dBi on section S6 is exactly contrary to that on section S1. However, it can also be seen that the changes of dBi on these two sections are both very small and even negligible, that is, there is no need to study dBi during second springback stage emphatically.
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Overall, as same as the height deformation of tube, for the width deformation of tube in mandrel-support zone, the mandrel retracting and first springback stages should both be emphasized and considered. For the non-mandrel-support zone, focusing on the first springback stage is enough.
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3.4. Spacing deformation of ridge grooves
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Like the width deformation of tube, only studying the spacing deformation of ridge grooves dbi of sections S1 and S6 in the entire H-typed forming process, which are shown in Fig. 12. It can be obtained that at any stage of the entire forming process, the bottoms of ridge grooves move to the middle of tube, so that the spacing of ridge grooves is decreased. Along the height direction, from node 27(270 ) to 31(310 ), dbi is gradually decreased, the maximum dbi occurs at the node 27(270 ), so that the bottoms of the ridge grooves have a trapezoidal shape. Similar to the width deformation of tube, after bending, dbi of each node on section S1 is far smaller and more gentle than that of section S6. After mandrel retracting, dbi of section S6 can be considered to remain unchanged, dbi of section S1 is significantly increased to a greater value. After the first springback, dbi of these two sections are both notably reduced, and even the expansion deformation can be found in the inner area of neutral layer. After the second springback, the bottoms of ridge grooves of these two sections move toward the middle, which makes the spacing deformation dbi increased. The change of dbi on section S6 is slightly larger than that on section S1. However, it can also be seen that the variation of dbi during the first springback stage is much greater than that during the second springback. Overall, due to the bottoms of ridge grooves and side walls of tube may move together in the entire H-typed forming process, the law of change of the width deformation of tube and spacing deformation of ridge grooves between each stage is almost identical. Therefore, as the same as the width deformation of tube, for the spacing deformation of ridge grooves in mandrel-support zone, the mandrel retracting and first springback stages should be emphasized and considered. In the nonmandrel-support zone, focusing on the first springback stage is enough.
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Fig. 12
3.5. Cross-sectional deformation of filler
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During the bending process, the fillers are bent and deformed together with the tube, while in the first springback, they may also have springback synchronously. Therefore, it is necessary to obtain the cross-sectional deformation of bent filler to study whether the springback of filler has an effect on the crosssectional deformation of bent tube during the first springback. At the same time, for comparative research, without the bent tube, the springback of bent filler itself after the mandrel retracting process is also added. According to the previous analysis, it is found that the height deformation of ridge groove in the mandrel-support zone and non-mandrel-support zone is similar, it can be thought that the deformation of different positions of bent filler is almost the same. Therefore, the cross section of filler corresponding to section S6 of tube is selected for research. Fig. 13 shows the height and width deformation of filler on the chosen cross section at bending, mandrel retracting and springback process. It can be drawn that after the bending stage, the height deformation of filler is larger than the width deformation, and the dh’i at node 44(440 ) is the largest. This is because the filler is only squeezed by the ridge groove in the height direction, so the width deformation of filler can be ignored. The deformation of filler does not change after mandrel retracting, so the mandrel retracting process has no effect on the deformation of filler. It can also be seen from Fig. 13(a) that if without the bent tube, only the bent filler itself has springback, the height deformation of filler will decrease, but the change of height deformation in this condition is slightly larger than that in the first springback. This shows that during the first springback process, the springback of filler and ridge groove is interacted, there is still a small interaction between the ridge groove and filler at this time. So that the results are obtained and shown in Fig. 10(d) and Fig. 13(a): after the first springback, the height deformation of ridge groove and filler are slightly reduced. Overall, the distribution law of the height deformation of filler and ridge groove are basically the same at each stage. The deformation of filler is very small, the maximum height deformation and width deformation are only 1.8% and 0.8%, respectively. The springback of deformation can also
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Spacing deformation of ridge grooves of section S1 and S6 after bending, mandrel retracting and twice-springback process.
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Fig. 13
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Height and width deformation of filler at bending, mandrel retracting and first springback process.
Fig. 14 Distribution of maximum cross-sectional deformation of tube along the bending direction after bending, mandrel retracting and twice-springback process. 548 549 550 551
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be negligible. Therefore, the deformation of filler is no longer to be analyzed in the following research. It can also be considered that 3A21 aluminum alloy is a good choice as the ridge groove filler. 4. Distribution of maximum cross-sectional deformation of DRRT in the entire H-typed RDB In order to study the cross-sectional deformation of the whole bent tube more comprehensively, choosing the nodes obtained above where the maximum deformations of dHi, dhi, dBi and dbi
in the cross section occur, dHmax, dhmax, dBmax and dbmax represent the corresponding maximum deformations of each characteristic cross section. The distribution of dHmax, dhmax, dBmax and dbmax along the bending direction in the entire Htyped forming process are shown in Fig. 14. It can be known that, due to the use of filler, dhmax after bending and mandrel retracting process is same and evenly distributed along the bending direction, the difference between each characteristic cross section is very small. However, dHmax, dBmax, and dbmax in mandrel-support zone are significantly smaller than those in the non-mandrel-support zone after
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bending, especially the greater deformations in the width direction, that is, dBmax and dbmax both gradually increase along the bending direction. After mandrel retracting, the distribution of dHmax, dBmax and dbmax along the bending direction tend to be uniform. dHmax in mandrel-support zone increases, that in the sections S2–S5 decreases and that in other sections remains unchanged. Not only in the mandrel-support zone, dBmax and dbmax in sections S0-S6 increase significantly, and that in other sections are slightly decreases. Compared with the cross-sectional deformation after mandrel retracting, during the first springback, dhmax is still approximately constant, but other deformations are all reduced. Especially the deformations in the width direction, the average of dBmax is changed from 13.56% to 4.29%, while the average of dbmax is changed from 40.50% to 11.08%, these deformation are almost reduced by 2/3. After the second springback, dHmax, dBmax and dbmax increase slightly, but the changes of these deformations during the secong springback are much smaller than that during the first springback. Due to the fillers are removed, dhmax begins to be changed and increased at the second springback stage, but the change of dhmax is also very small, which is about 1.58%. This is because most stress of bent tube is released during the first springback stage, but only a small amount of remaining stress is required to be released during the second springback stage. The same results as the analysis of Section 3 can also be obtained from the above research that, for the height and width deformation of tube and spacing deformation of ridge groove, the retraction of mandrel has an obvious effect on these deformations in the mandrel-support zone, which makes the distribution of these deformations more uniform along the bending direction, especially the deformations in the width direction; the first springback makes them reduced significantly, but the second springback makes them increased slightly, the effect of the first springback on these deformations is significantly greater than the second springback. For the height deformation of ridge groove, only the second springback can make it increased slightly, the average of dhmax after the second springback is only 2.56%, which is still far less than dbmax. 5. Conclusions (1) The finite element models including the H-typed rotary draw bending, mandrel retracting and twice-springback stages of double-ridged rectangular tube with 3A21 aluminum alloy ridge groove fillers have been established, and validated by the experiment. (2) For the height and width deformation of tube and spacing deformation of ridge groove, the retraction of mandrel can make the distribution of these deformations more uniform along the bending direction; the first springback makes them reduced significantly, but the second springback only makes them increased slightly. For the smaller height deformation of ridge groove, only the second springback can make it increased slightly. (3) During the first springback process, the springback of cross section of filler and ridge groove is interacted in the height direction, so that the height deformation of
ridge groove and filler are slightly reduced. The distribution law of the height deformation of filler and ridge groove are basically the same at each stage. (4) In the subsequent research of controlling the crosssectional deformation in the entire H-typed forming process with fillers, the smaller height deformation of ridge groove and filler can be neglected. The bending, mandrel retracting and first springback stages, that significantly affect the cross-sectional deformation, should be emphasized and considered at the same time. The second springback stage with less change of cross-sectional deformation can be ignored.
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Acknowledgements
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The authors would like to thank the Science, Technology and Innovation Commission of Shenzhen Municipality of China (Nos. JCYJ20170306160003433 and JCYJ20180306171058717) and 111 Project of China (No. B08040) for the support given to this research.
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References
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1. Qiu D, Klymyshyn DM, Pramanick P. Ridged waveguide structures with improved fundamental mode cutoff wavelength and bandwith characteristics. Int J RF Microw Comput Aided Eng 2002;12:190–7. 2. Yang H, Zhan M, Liu YL. Some advanced plastic processing technologies and their numerical simulation. J Mater Process Technol 2004;151(1–3):63–9. 3. Lu M, Leonard PJ. Design of trapezoidal-ridge waveguide by finite element method. IEE Proc Microwave Antennas Propag 2004;151:205–11. 4. Chen XQ, Zhao X, Lu M, Ren EE. Study on effects of device deformations on the transmission characteristics of trapezoidalridge waveguides. Study Opt Commun 2008(1);54–6 [Chinese]. 5. Xiao YH, Liu YL, Yang H. Research on cross-sectional deformation of double-ridged rectangular tube during H-typed rotary draw bending process. Int J Adv Manuf Tech 2014;73(9– 12):1789–98. 6. Liu CM, Liu YL, Yang H. Influence of different mandrels on cross-sectional deformation of the double-ridge rectangular tube in rotary draw bending process. Int J Adv Manuf Tech 2016;91(1– 4):1243–54. 7. Chen XQ, Ren EE, Lu M, Wang T, Wang L. Analysis of the transmission characteristics of the inverted trapezoidal-ridge waveguide. J Infrared Milli Terahz Waves 2010;31(9):1005–14. 8. Chen Y, Xu YC, Yuan SJ, Du ZF, Xu XY. The influence of the high polymer void filler’s hardness in the I-section tube bending. Mater Sci Technol 2010;18(1):206–9 [Chinese]. 9. Xu XY. Inventor; a machining method of bending waveguide tube. China CN 102361153A; 2012 Feb 22 [Chinese]. 10. Jiang F, Liu YL, Yang H. Study on cross-sectional deformation of H-typed rotary draw bending of H96 brass double-ridged rectangular tube with different ridge groove filler materialsProceedings of the 7th international conference on tube hydroforming. p. 295–301. 11. Zhang K, Liu YL, Yang H. Influence of retracting mandrel on springback of H96 thin-walled rectangular wave-guide tube in rotary draw bending process. Mater Sci Technol 2013;21(1):56–61 [Chinese]. 12. Li H, Yang H, Song FF, Zhan M, Li GJ. Springback characterization and behaviors of high-strength Ti-3AL-2.5V tube in cold
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rotary draw bending. J Mater Process Technol 2012;212 (9):1973–87. 13. Zhu YX, Liu YL, Li HP, Yang H. Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube. Trans Nonferr Metal Soc 2012;22(9):2233–40. 14. Dong WQ, Liu YL, Zhao GY, Yang H. Establishment of springback prediction model for the rotary-draw bending of thin-walled rectangular tube considering variation of Young’s
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modulusThe 10th Asia-Pacific conference on engineering plasticity and its application. p. 182–8. 15. Liu YF, Daxin E. Effects of cross-sectional ovalization on springback and strain distribution of circular tubes under bending. J Mater Eng Perform 2011;20(9):1591–9. 16. Zheng XS, Liu YL, Liu CM, Yang H. Impact of springback on the cross-sectional deformation of H96 brass double-ridged rectangular tube in E-typed rotary draw bending. Int J Adv Manuf Technol 2017;89(9–12):3451–8.
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Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
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Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending
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Chunmei LIU a,b, Yuli LIU a,b,*
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a
Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China b
Received 2 April 2019; revised 12 August 2019; accepted 12 August 2019
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KEYWORDS
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Cross-sectional deformation; FE simulation; H96 double-ridged rectangular tube; H-typed rotary draw bending; Ridge groove fillers; Twice-springback stage
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Abstract The bent double-ridged rectangular tube (DRRT) with high forming quality is helpful to improve the microwave transmission accuracy. For reducing the cross-sectional deformation in the H-typed bending process, in addition to using rigid mandrel to support the inside of tube, ridge groove fillers are also added to restrict the deformation of ridge grooves. Because of the change of stress and strain state of bent tube in bending, rigid mandrel retracting and specially twicespringback stages, and the springback of fillers, the cross-sectional deformation of tube in each stage may be different. Therefore, based on the ABAQUS platform, the finite element models (FEM) for H-typed bending, mandrel retracting and twice-springback stages of H96 DRRT with fillers were established and validated. It is found that, for the height and width deformation of tube and spacing deformation of ridge grooves, retraction of mandrel can make the distribution of these deformations more uniform along the bending direction. The first springback can reduce these deformations significantly, which should be emphasized. But the second springback only increases them by less amount, which can be ignored. The smaller height deformation of ridge groove and filler can be neglected. Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
* Corresponding author at: Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518057, China. E-mail address: [email protected] (Y. LIU). Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
1. Introduction
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With the advantages of lower cut-off frequency, wider working frequency bandwidth and smaller size, curved double-ridged rectangular tube (DRRT) has been widely used in aerospace microwave transmission and communication systems.1 The bent tube is usually obtained by high-precision and highefficiency rotary draw bending (RDB) technology.2 However, cross-sectional deformation of bent tube occurring in the bend-
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https://doi.org/10.1016/j.cja.2019.08.005 1000-9361 Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: LIU C, LIU Y Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.005
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ing process will change the shape and size of the inner cavity of tube, so that the electromagnetic wave transmitted in the bent tube is phase-shifted.3,4 It can be considered that the microwave transmission accuracy depends on the forming quality of the bent tube. For the H-typed bending process, which means the tube is bent along the narrower flanges and the ridge groove is located on the side wall, Xiao et al.5 and Liu et al.6 found that adding the I-shaped rigid mandrel or PVC elastic mandrel into the DRRT, the cross-sectional deformation can be effectively improved. But it is worth noting that the ridge grooves, where the electric field is more dense,7 are still deformed severely due to the large pressing force, as shown in Fig. 1(a). Therefore, while using the rigid mandrel, it is also considered to add fillers into the ridge grooves to restrict the deformation of ridge grooves, as shown in Fig. 1(b). The entire H-typed forming process of DRRT from the straight tube to the bent tube includes the following stages. Firstly, the bending stage, the ridge groove filler can be bent together with the tube and the cross-section deformation of tube and filler occurs in this stage. Secondly, the internal rigid mandrel retracting stage, which may change the cross-sectional deformation in the mandrel-support area. Finally, the special twice-springback stage after unloading the external bending dies, which is proposed due to the use of ridge groove fillers in this study. In the first springback of this stage, the fillers are still in the ridge grooves, that is the synchronous springback of bent tube and filler occurs. So except for the bent tube, the variation in the deformation of filler will also occur and the existence of fillers may also affect the springback of crosssectional deformation of bent tube. In the second springback, the fillers have been removed, the cross-sectional deformation of tube may continue to change. Therefore, it is found that the cross-sectional deformation in each stage of the entire H-typed forming process may be different. At present, some researches have been carried out on the cross-sectional deformation of DRRT in H-typed RDB with fillers. Chen et al.8 found that when the hardness of polymer materials is less than Shore D60, which is added into both the DRRT and ridge grooves, the forming quality of the cross section is difficult to ensure. Similarly, Xu9 used polyester carbonic acid (a kind of polymer material) as the filling material, which can suppress the cross-sectional deformation to improve the electrical performance of the bent tube. But as the filler, the strength and hardness of polymer material are required to be high, and the injection molding process is complicated and time consuming. Jiang et al.10 selected 3A21 aluminum alloy as the ridge groove filler, which can be processed easily to
Fig. 1
reduce the cross-sectional deformation of DRRT. It can be found from all the above researches that the use of ridge groove filler cannot only alleviate the uneven deformation of tube, but also significantly improve the deformation of the ridge groove. However, these studies only focus on the deformation in the bending stage, the effects of mandrel retracting and springback on the cross-sectional deformation are not taken into account. Zhang et al.11 obtained that the retraction of mandrel can make the cross-sectional deformation of the whole rectangular tube tend to be uniform. Li and many other scholars12–14 discovered the effect of springback on cross-sectional deformation of high-strength Ti-3AL-2.5V titanium alloy circular tube, 3A21 aluminum alloy and H96 brass rectangular tube of RDB. In these study, cross-sectional springback, that is the change in the amount of cross-sectional deformation before and after springback, is one of the characteristics of elastic recovery and it is found that the cross-sectional springback is beneficial to reduce the cross-sectional deformation. Using the theoretical analysis method, Liu et al.15 found that when considering the cross-sectional ovalization of circular tube after springback, the springback prediction model has higher accuracy. Zheng et al.16 found that during the Etyped bending of DRRT, cross-sectional deformation became larger after springback in cores-support zone while they all became smaller in no-cores-support zone. The above studies show that the mandrel retracting and springback will affect the final cross-sectional size accuracy of the bent tube, which are important stages that cannot be ignored in the forming process. Based on the above research status, it is found that different stages of the entire H-typed bending process all have the effect on cross-sectional deformation, which should be considered and studied. However, the research about the specific effect of each stage on cross-sectional deformation of DRRT with fillers in H-typed RDB has not been reported. Therefore, the finite element models (FEM) for H-typed bending, mandrel retracting and twice-springback stage of H96 DRRT with fillers were established based on the ABAQUS platform. With these models, the characteristics of cross-sectional deformation of tube and filler in the entire H-typed forming process, the effects of mandrel retracting, twice-springback, the springback of filler on the cross-sectional deformation of tube and which stage has the most significant effect on the cross-sectional deformation were studied to improve the forming quality of H-typed double-ridged rectangular bent tube.
Bending types and a method to restrict cross-sectional deformation of H96 brass DRRT for H-typed RDB.
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2. FEM for H-typed RDB of DRRT with ridge groove fillers
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2.1. Definition of material models
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The fillers assembled in the ridge grooves are bent and deformed together with the tube during the H-typed bending process. The material of DRRT is H96 brass. Considering the stiffness and strength of polymer and metal materials and the requirement for manufacturing the filler, the 3A21 aluminum alloy10 is appropriate and chose as the filler for research in this paper. In the finite element simulation, the tube and filler are defined as continuous isotropic deformable solid element, and the material models of DRRT and filler should be defined respectively. The true stress–strain curves of H96 brass DRRT and 3A21 aluminum alloy filler are obtained by the uniaxial tensile tests, as shown in Fig. 2. The plastic strain ep of the materials needed in the simulation is calculated by subtracting the elastic strain from the true strain, as shown in Eq. (1), the constitutive equation as shown in Eq. (2) is used to describe the plastic deformation of material. ep ¼ e r=E r ¼ Kðe þ bÞ p
n
2.3. Establishment of the FEM for H-typed bending process
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The three-dimensional FEM for the actual entire H-typed bending process of H96 DRRT with fillers are composed of four sub-models, which are the H-typed bending model, the rigid mandrel retracting model, the first springback model after unloading the rigid dies and the second springback model after removing the fillers.
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The surface to surface contact model is used to define the contact between the non-deformable rigid dies, including the bending die, pressure die, mandrel and so on, and the tube which is selected as slave face. The height and width of filler are the same with those of ridge groove, which means that the clearance between filler and tube is set to be 0 mm in sim-
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ð2Þ
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3A21 aluminum alloy
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p
2.2. Definition of contact models
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H96 brass
Modulus of elasticity E (GPa) Yield strength r0.2 (MPa) Poisson ratio m Hardening exponent n Strength coefficient K (MPa)
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Parameters
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Table 1 Main mechanical properties of H96 brass DRRT and 3A21 aluminum alloy ridge groove filler.
ulation. So the contact between the filler and tube is defined by two contact models of surface to surface contact and general contact, and their simulation results are shown in Fig. 3. It can be seen that, when using the surface to surface contact model, the penetration phenomenon occurs between the filler and tube, as shown in Fig. 3(a). But there is non-penetration found in Fig. 3(b) when the general contact model is used. This may be because in the surface to surface contact model, the master face of the contact pair can penetrate to the slave face, but as two deformable faces, the tube and filler should not be penetrated each other. So the general contact model is chosen to define the contact between the filler and tube.
where e is true strain, r is true stress, e is plastic strain, E is modulus of elasticity, K is strength coefficient, n is hardening exponent and b is a constant. According to Eq. (2), the mechanical properties of these two materials are achieved by fitting the obtained plastic stress–strain data and shown in Table 1. Then, the main mechanical properties and plastic stress–strain data are imported into the software to complete the definition of material models.
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(1) The H-typed bending model
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Except for the definition of the above material models and contact models, for improving the computational accuracy and efficiency of the models, based on the geometric model shown in Fig. 4(a), the element type of the tube and ridge groove filler are defined as a deformable 8-node hexagonal reduced integral solid element (C3D8R) with five integration points, meanwhile the rigid dies are defined as the bilinear quadrilateral rigid shell element with four nodes (R3D4). The mesh sizes of tube, filler and mandrel are all 1 mm 1 mm, and that of other rigid dies are all 3 mm 3 mm. The angular velocity of bending die is 0.5 rads1. After solving the above key technologies, based on the platform of ABAQUS/Explicit, the H-typed bending model of H96 brass DRRT with 3A21 aluminum alloy ridge groove fillers is established, as illustrated in Fig. 4(b). (2) The rigid mandrel retracting model When the bending stage is completed, the rigid mandrel retracting begins at the velocity of 60 mms1, and the time of this stage is one second. The rigid mandrel retracting model is shown in Fig. 4(c). (3) The first springback model
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Fig. 2 True stress–strain curves of H96 brass DRRT and 3A21 aluminum alloy ridge groove filler.
Because the fillers are still in the ridge grooves after unloading the rigid dies, so the first springback model after unloading
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Fig. 3
Fig. 4
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Comparisons of different contact models for tube and filler.
Models of the entire H-typed RDB of H96 brass DRRT with ridge groove fillers.
all the rigid dies, that is, the synchronous springback model of the double-ridged rectangular bent tube and deformed fillers. The springback is the release process of stress and strain of the double-ridged rectangular bent tube and fillers after bending process. The information such as stress and strain of the double-ridged rectangular bent tube and fillers in the result file, which is calculated by the previous step bending model, is introduced into the first springback model and defined as the initial field. The contact model of the tube and fillers is the
same as in the bending model. In order to avoid the rigid displacement of bent tube and fillers during the springback, it is needed to impose sufficient constraints on the formed tube and fillers. A encastre boundary is applied to end position of the DRRT where is not deformed during the bending process, so that the stress and strain of the double-ridged rectangular bent tube and fillers can be released freely. Based on the above analysis, the first springback model after unloading all the rigid dies is established and shown in Fig. 4(d).
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(4) The second springback model
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The second springback model, as shown in Fig. 4(e), is built to simulate the final springback of tube after the fillers are removed, whose establishing method is similar to that of the first springback model.
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2.4. Experimental verification of the finite element models
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2.4.1. Description of the cross-sectional deformation of tube and filler
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In order to quantitatively analyze the cross-sectional deformation of DRRT and filler in H-typed bending, the description of deformation is given as follows: dHi and dhi are used to indicate the height deformation of tube and ridge groove; dBi and dbi are used to indicate the width deformation of tube and spacing deformation of ridge grooves; dh0 i and db0 i are used to indicate the cross-sectional height and width deformation of filler. These deformations can be calculated by Eqs. (3)–(8), respectively. dHi ¼
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ð4Þ
Bi B 100% dBi ¼ B
ð5Þ
bi b 100% dbi ¼ b dh0 i
ð6Þ
h0 h0 ¼ i 0 100% h
ð7Þ
b0i b0 100% b0
ð8Þ
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ð3Þ
hi h 100% dhi ¼ h
259 261
Hi H 100% H
db0 i ¼
where as shown in Fig. 5(a), the schematic diagram of certain cross section of DRRT before deformation, H = 18.29 mm and h = 4.39 mm are the original height of tube and ridge
Fig. 5
5
groove; B = 8.15 mm and b = 2.57 mm are the original width of tube and spacing of ridge grooves; as shown in Fig. 1(b), h0 = 1.85 mm and b0 = 2.75 mm are the original height and width of filler. Hi (i = 1(10 )–10(100 )), hi (i = 11(110 )–14(140 ), 15(150 )–18(180 )), Bi (i = 19(190 )–26(260 ), 32(320 )–39(390 )), bi (i = 27(270 )–31(310 )), hi0 (i = 41(410 )–44(440 )), and bi0 (i = 41 (44), 40(45), 410 (440 )) are those corresponding sizes at a certain node i (as shown in Fig. 5(b) and (c)) after deformation. According to the above expressions, the positive value of a deformation indicates that the size increases after deformation, and relatively the negative value indicates the decrease. For negative value, the greater the absolute value, the more severe the deformation.
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2.4.2. Experimental validation
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In order to ensure the credibility of the next research results, it is necessary to verify the reliability of the above established models by comparing result error between the experiment and simulation. The DRRT with ridge groove fillers and experiment process of H-typed RDB are shown in Fig. 6. The simulation conditions are consistent with the experimental ones, as shown in Table 2. Based on the experimental and simulation conditions shown in Table 2, the comparisons between the experimental and simulation results are carried out. The experiment is carried out with three specimens, the profiles of these experimental specimens are basically consistent. So one representative bent specimen is chosen to be shown in Fig. 7(a) and (b). As shown in Fig. 7(a) and (b) ignoring the smaller fillet of the real tube, the profiles of the bent tube after the fillers were removed and the deformation of a certain cross section of the final bent tube obtained from the simulation are basically coincide well with those from the experiment. Furthermore, based on the Eqs. (3) and (6), the distribution of dH of node 5(50 ) and db of node 27(270 ) in characteristic cross sections along the bending direction from the simulation bent tube and three experimental specimens are obtained and shown in Fig. 7(c) and (d). It can be seen that the results of these three experimental specimens are similar and their distribution laws are basically the same, so the average of these experimental results can be
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Schematic diagram of DRRT before and after deformation.
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Fig. 6
Table 2
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Experiment process of H-typed rotary draw bending of DRRT with ridge groove fillers.
Experimental and simulation conditions.
Parameters
Experimental
Simulation
Angular velocity of bending, x (rads1) Bending angle, h (°) Bending radius, R (mm) Boosting velocity of pressure, Vp (mms1) Velocity of retracting mandrel, V1 (mms1) Friction coefficient-tube (H96 brass)/filler (3A21 aluminum alloy) Friction coefficient-tube (or filler)/clamp die (45# steel) Friction coefficient-tube/mandrel (35CrMo) Friction coefficient-tube (or filler)/ other dies (45# steel) Clearance-tube/mandrel, Cm (mm) Clearance-tube/other dies and filler (mm)
0.5
0.5
90 60 35.21
90 60 35.21
60
60
A little lubricating oil
0.27
Dry friction
0.6
Large quantity of lubricating oil A little lubricating oil 0.2
0.01
0
0
0.17 0.2
used to compare with the simulation results. Then it can also be obtained that the distribution of deformations along the bending direction from the simulation results is in agreement with that from the average experimental results, the maximum errors between average experimental results and simulation ones of these two deformation are about 8.4% and 9.8%, respectively, and the average errors of them are both about 4.8%. The offset may be produced by many reasons, such as the error in measuring the experimental bent tube, the clearance between the tube and bending dies was not accurate to 0 because of the dimension tolerance allowed in machining the dies and so on. These errors of no more than 10% are acceptable, which means that the simulation and experimental results are highly consistent. Therefore, three-dimensional FEM including the H-typed RDB and mandrel retracting models of DRRT with 3A21 aluminum alloy ridge groove fillers and two springback models are reliable, and the next study can be conducted on this basis.
3. Cross-sectional deformation of DRRT and filler in the entire H-typed RDB
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3.1. Height deformation of tube
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In the H-typed bending process of DRRT, the outer flange and inner flange are depressed and deformed under the action of tangential tensile and compressive stress respectively. The different depressions of inner and outer flanges cause the height of tube to change, that is, the height deformation of tube dHi occurs. Based on the established bending, mandrel retracting and twice-springback models, different depressions of inner and outer flanges of section S1 in mandrel-support zone and section S6 in non-mandrel-support zone (as shown in Fig. 8) at each stage of the entire H-typed forming process have been obtained and shown in Fig. 9(a) and (b). And according to Eq. (3), dHi of section S1 and S6 are calculated and shown in Fig. 9 (c) and (d). It can be seen that the depressions of inner and outer flanges and height deformation of tube are both symmetrically distributed along the width direction. At any stage of the entire forming process, the maximum deformation is located at node 5 (50 ) in the middle of flanges. After bending stage, the depression of inner flange of sections S1 and S6 are almost the same, and due to the support of rigid mandrel, the depression of outer flange of section S1 is significantly smaller than that of section S6, which makes dHi of section S1 smaller than that of section S6. After the mandrel retracting stage, because the support of mandrel to section S1 is missing, only the outer flange depression of section S1 increases. So that dHi of section S1 increases, while that of section S6 remains basically unchanged at this stage. It is indicated that the use and retraction of the rigid mandrel affect the height deformation of tube in mandrel-support zone more significantly than that in nonmandrel-support zone, and the influence on the depression of outer flange is greater than that of inner flange. After the first springback, the outer flanges of sections S1 and S6 both move up, the inner flanges move down, which means that the depression of outer and inner flanges of these two sections decrease and tend to be gentle. That is, dHi of these sections are both reduced at this stage. After the second springback, the depression of outer flange of section S1 keeps substantially unchanged, but the depression of outer flange of section S6 continues to become smaller. The depressions of inner flange of these two sections both become larger slightly.
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Fig. 7
Fig. 8
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7
Simulation and experimental results after the fillers were removed.
Distribution of characteristic cross sections.
After calculating, dHi of these sections are slightly increased at this stage. Overall, the change of depression of outer flange of section S1 during the mandrel retracting stage is larger than that in the twice-springback stage. The influence of first springback on the inner flange depression of section S1 and outer and inner flanges depressions of section S6 are significantly greater than the second springback, and the mandrel retracting stage can be ignored. This is because only the stress in mandrel-support
zone is unloaded during the mandrel retracting stage, while the stress of whole bent tube is released during the first springback stage, then a slight springback of deformation is only caused by the removal of the fillers in the second springback stage. Therefore, for the height deformation of tube in mandrelsupport zone, the mandrel retracting and first springback stages should be emphasized and considered simultaneously. For the height deformation of tube in non-mandrel-support zone, focusing on the first springback stage is enough.
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3.2. Height deformation of ridge groove
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The height deformation of ridge groove dhi is caused by the change of the position of inner and outer walls of ridge groove. Based on the established models, the position of inner and outer walls of ridge groove of section S1 and S6 in the entire H-typed forming process is obtained and shown in Fig. 10(a) and (b). And according to Eq. (4), dhi of section S1 and S6 are calculated and shown in Fig. 10(c) and (d). It can be seen that, the deformation of the left and right ridge grooves is symmetrical, so only analyzing one side is enough. On these two sections, the inner and outer walls of ridge groove basically both move upward, the displacement of inner wall is larger than that of outer wall, which makes the height of the ridge
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Fig. 9 Depression of inner and outer flanges, height deformation of section S1 and S6 after bending, mandrel retracting and twicespringback process.
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groove reduced. The displacement and dhi of node 11 (110 ) located at the intersection of side wall and ridge groove are the largest at any stage of the entire forming process. After bending, although the displacement of inner and outer walls of ridge groove of section S1 is slightly larger than that of section S6, because of the supporting effect of fillers on ridge grooves, dhi of these sections are almost the same and both very small, the maximum dhi is less than 1.5%. After the mandrel retracting, the position of outer and inner walls of ridge groove of section S6 substantially unchanges. The outer and inner walls of ridge groove on section S1 move down slightly to the same position as the section S6, but the change of dhi is small and negligible. This shows that due to the introducing of filler, the influence of the use and retraction of mandrel on the height deformation of ridge groove in the entire bent tube is small and even not needed to be considered. Then during the first springback, the inner and outer walls of ridge groove on section S1 move downward slightly, while those on section S6 move up slightly, eventually reducing dhi of the two sections. But because the fillers are not removed at this stage, they still have a certain support effect to the ridge groove, dhi at this stage has little difference with that after mandrel retracting. After the second springback, because the fillers are removed, whose support function to the ridge grooves does not exist, the inner wall of ridge groove on these
two sections relatively move upward relatively larger, so that the height deformation of ridge groove increases. Overall, whether in the mandrel-support zone or the nonmandrel-support zone, only the second springback has a significant effect to increase the height deformation of ridge groove, other stages can be ignored.
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3.3. Width deformation of tube
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Since the deformations of the two side walls of bent tube are symmetrical, therefore, unlike the deformation in height direction studied above, only analyzing the width deformation of tube directly is enough. Based on the established models, the width deformation dBi of section S1 and S6 in the entire H-typed forming process are obtained and shown in Fig. 11(a) and (b). It can be found that after bending, under the support of mandrel, dBi of section S1 is much smaller than that of section S6. Especially in the outer area of neutral layer, where the deformation is bigger, dBi of each node on section S1 is relatively gentle. But on section S6, the closer to the ridge groove, the larger the dBi, and at the intersection of side wall and ridge groove, that is dBi on node 26(260 ) is the largest. After the mandrel retracting stage, dBi of section S6 is not changed, but dBi of section S1 is significantly increased, due to the support function of mandrel does
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Fig. 10 Position of outer and inner walls of ridge groove, height deformation of ridge groove of section S1 and S6 after bending, mandrel retracting and twice-springback process.
Fig. 11 448 449 450 451 452 453 454 455 456 457
Width deformation of section S1 and S6 after bending, mandrel retracting and twice-springback process.
not exist, and the distribution law of dBi is the same as that of section S6. At this stage, dBi of section S1 is even higher than that of section S6. It is shown that, except for the height deformation of tube, the use and retraction of the rigid mandrel also affect the width deformation of tube in mandrel-support zone more significantly, and the influence on the deformation of side wall in outer area of neutral layer is greater than that in inner area. After the first springback, in the outer area of neutral layer, dBi of these two sections are both reduced and dBi of each node
is basically the same. But in the inner area of neutral layer, dBi is changed from negative to positive, which makes a ‘‘bulk belly” phenomenon appear. After the second springback, dBi in the outer area of neutral layer of section S1 is slightly decreased, while in the inner area is slightly increased. The change of dBi on section S6 is exactly contrary to that on section S1. However, it can also be seen that the changes of dBi on these two sections are both very small and even negligible, that is, there is no need to study dBi during second springback stage emphatically.
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Overall, as same as the height deformation of tube, for the width deformation of tube in mandrel-support zone, the mandrel retracting and first springback stages should both be emphasized and considered. For the non-mandrel-support zone, focusing on the first springback stage is enough.
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3.4. Spacing deformation of ridge grooves
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Like the width deformation of tube, only studying the spacing deformation of ridge grooves dbi of sections S1 and S6 in the entire H-typed forming process, which are shown in Fig. 12. It can be obtained that at any stage of the entire forming process, the bottoms of ridge grooves move to the middle of tube, so that the spacing of ridge grooves is decreased. Along the height direction, from node 27(270 ) to 31(310 ), dbi is gradually decreased, the maximum dbi occurs at the node 27(270 ), so that the bottoms of the ridge grooves have a trapezoidal shape. Similar to the width deformation of tube, after bending, dbi of each node on section S1 is far smaller and more gentle than that of section S6. After mandrel retracting, dbi of section S6 can be considered to remain unchanged, dbi of section S1 is significantly increased to a greater value. After the first springback, dbi of these two sections are both notably reduced, and even the expansion deformation can be found in the inner area of neutral layer. After the second springback, the bottoms of ridge grooves of these two sections move toward the middle, which makes the spacing deformation dbi increased. The change of dbi on section S6 is slightly larger than that on section S1. However, it can also be seen that the variation of dbi during the first springback stage is much greater than that during the second springback. Overall, due to the bottoms of ridge grooves and side walls of tube may move together in the entire H-typed forming process, the law of change of the width deformation of tube and spacing deformation of ridge grooves between each stage is almost identical. Therefore, as the same as the width deformation of tube, for the spacing deformation of ridge grooves in mandrel-support zone, the mandrel retracting and first springback stages should be emphasized and considered. In the nonmandrel-support zone, focusing on the first springback stage is enough.
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Fig. 12
3.5. Cross-sectional deformation of filler
507
During the bending process, the fillers are bent and deformed together with the tube, while in the first springback, they may also have springback synchronously. Therefore, it is necessary to obtain the cross-sectional deformation of bent filler to study whether the springback of filler has an effect on the crosssectional deformation of bent tube during the first springback. At the same time, for comparative research, without the bent tube, the springback of bent filler itself after the mandrel retracting process is also added. According to the previous analysis, it is found that the height deformation of ridge groove in the mandrel-support zone and non-mandrel-support zone is similar, it can be thought that the deformation of different positions of bent filler is almost the same. Therefore, the cross section of filler corresponding to section S6 of tube is selected for research. Fig. 13 shows the height and width deformation of filler on the chosen cross section at bending, mandrel retracting and springback process. It can be drawn that after the bending stage, the height deformation of filler is larger than the width deformation, and the dh’i at node 44(440 ) is the largest. This is because the filler is only squeezed by the ridge groove in the height direction, so the width deformation of filler can be ignored. The deformation of filler does not change after mandrel retracting, so the mandrel retracting process has no effect on the deformation of filler. It can also be seen from Fig. 13(a) that if without the bent tube, only the bent filler itself has springback, the height deformation of filler will decrease, but the change of height deformation in this condition is slightly larger than that in the first springback. This shows that during the first springback process, the springback of filler and ridge groove is interacted, there is still a small interaction between the ridge groove and filler at this time. So that the results are obtained and shown in Fig. 10(d) and Fig. 13(a): after the first springback, the height deformation of ridge groove and filler are slightly reduced. Overall, the distribution law of the height deformation of filler and ridge groove are basically the same at each stage. The deformation of filler is very small, the maximum height deformation and width deformation are only 1.8% and 0.8%, respectively. The springback of deformation can also
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Spacing deformation of ridge grooves of section S1 and S6 after bending, mandrel retracting and twice-springback process.
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Fig. 13
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Height and width deformation of filler at bending, mandrel retracting and first springback process.
Fig. 14 Distribution of maximum cross-sectional deformation of tube along the bending direction after bending, mandrel retracting and twice-springback process. 548 549 550 551
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be negligible. Therefore, the deformation of filler is no longer to be analyzed in the following research. It can also be considered that 3A21 aluminum alloy is a good choice as the ridge groove filler. 4. Distribution of maximum cross-sectional deformation of DRRT in the entire H-typed RDB In order to study the cross-sectional deformation of the whole bent tube more comprehensively, choosing the nodes obtained above where the maximum deformations of dHi, dhi, dBi and dbi
in the cross section occur, dHmax, dhmax, dBmax and dbmax represent the corresponding maximum deformations of each characteristic cross section. The distribution of dHmax, dhmax, dBmax and dbmax along the bending direction in the entire Htyped forming process are shown in Fig. 14. It can be known that, due to the use of filler, dhmax after bending and mandrel retracting process is same and evenly distributed along the bending direction, the difference between each characteristic cross section is very small. However, dHmax, dBmax, and dbmax in mandrel-support zone are significantly smaller than those in the non-mandrel-support zone after
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bending, especially the greater deformations in the width direction, that is, dBmax and dbmax both gradually increase along the bending direction. After mandrel retracting, the distribution of dHmax, dBmax and dbmax along the bending direction tend to be uniform. dHmax in mandrel-support zone increases, that in the sections S2–S5 decreases and that in other sections remains unchanged. Not only in the mandrel-support zone, dBmax and dbmax in sections S0-S6 increase significantly, and that in other sections are slightly decreases. Compared with the cross-sectional deformation after mandrel retracting, during the first springback, dhmax is still approximately constant, but other deformations are all reduced. Especially the deformations in the width direction, the average of dBmax is changed from 13.56% to 4.29%, while the average of dbmax is changed from 40.50% to 11.08%, these deformation are almost reduced by 2/3. After the second springback, dHmax, dBmax and dbmax increase slightly, but the changes of these deformations during the secong springback are much smaller than that during the first springback. Due to the fillers are removed, dhmax begins to be changed and increased at the second springback stage, but the change of dhmax is also very small, which is about 1.58%. This is because most stress of bent tube is released during the first springback stage, but only a small amount of remaining stress is required to be released during the second springback stage. The same results as the analysis of Section 3 can also be obtained from the above research that, for the height and width deformation of tube and spacing deformation of ridge groove, the retraction of mandrel has an obvious effect on these deformations in the mandrel-support zone, which makes the distribution of these deformations more uniform along the bending direction, especially the deformations in the width direction; the first springback makes them reduced significantly, but the second springback makes them increased slightly, the effect of the first springback on these deformations is significantly greater than the second springback. For the height deformation of ridge groove, only the second springback can make it increased slightly, the average of dhmax after the second springback is only 2.56%, which is still far less than dbmax. 5. Conclusions (1) The finite element models including the H-typed rotary draw bending, mandrel retracting and twice-springback stages of double-ridged rectangular tube with 3A21 aluminum alloy ridge groove fillers have been established, and validated by the experiment. (2) For the height and width deformation of tube and spacing deformation of ridge groove, the retraction of mandrel can make the distribution of these deformations more uniform along the bending direction; the first springback makes them reduced significantly, but the second springback only makes them increased slightly. For the smaller height deformation of ridge groove, only the second springback can make it increased slightly. (3) During the first springback process, the springback of cross section of filler and ridge groove is interacted in the height direction, so that the height deformation of
ridge groove and filler are slightly reduced. The distribution law of the height deformation of filler and ridge groove are basically the same at each stage. (4) In the subsequent research of controlling the crosssectional deformation in the entire H-typed forming process with fillers, the smaller height deformation of ridge groove and filler can be neglected. The bending, mandrel retracting and first springback stages, that significantly affect the cross-sectional deformation, should be emphasized and considered at the same time. The second springback stage with less change of cross-sectional deformation can be ignored.
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Acknowledgements
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The authors would like to thank the Science, Technology and Innovation Commission of Shenzhen Municipality of China (Nos. JCYJ20170306160003433 and JCYJ20180306171058717) and 111 Project of China (No. B08040) for the support given to this research.
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References
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1. Qiu D, Klymyshyn DM, Pramanick P. Ridged waveguide structures with improved fundamental mode cutoff wavelength and bandwith characteristics. Int J RF Microw Comput Aided Eng 2002;12:190–7. 2. Yang H, Zhan M, Liu YL. Some advanced plastic processing technologies and their numerical simulation. J Mater Process Technol 2004;151(1–3):63–9. 3. Lu M, Leonard PJ. Design of trapezoidal-ridge waveguide by finite element method. IEE Proc Microwave Antennas Propag 2004;151:205–11. 4. Chen XQ, Zhao X, Lu M, Ren EE. Study on effects of device deformations on the transmission characteristics of trapezoidalridge waveguides. Study Opt Commun 2008(1);54–6 [Chinese]. 5. Xiao YH, Liu YL, Yang H. Research on cross-sectional deformation of double-ridged rectangular tube during H-typed rotary draw bending process. Int J Adv Manuf Tech 2014;73(9– 12):1789–98. 6. Liu CM, Liu YL, Yang H. Influence of different mandrels on cross-sectional deformation of the double-ridge rectangular tube in rotary draw bending process. Int J Adv Manuf Tech 2016;91(1– 4):1243–54. 7. Chen XQ, Ren EE, Lu M, Wang T, Wang L. Analysis of the transmission characteristics of the inverted trapezoidal-ridge waveguide. J Infrared Milli Terahz Waves 2010;31(9):1005–14. 8. Chen Y, Xu YC, Yuan SJ, Du ZF, Xu XY. The influence of the high polymer void filler’s hardness in the I-section tube bending. Mater Sci Technol 2010;18(1):206–9 [Chinese]. 9. Xu XY. Inventor; a machining method of bending waveguide tube. China CN 102361153A; 2012 Feb 22 [Chinese]. 10. Jiang F, Liu YL, Yang H. Study on cross-sectional deformation of H-typed rotary draw bending of H96 brass double-ridged rectangular tube with different ridge groove filler materialsProceedings of the 7th international conference on tube hydroforming. p. 295–301. 11. Zhang K, Liu YL, Yang H. Influence of retracting mandrel on springback of H96 thin-walled rectangular wave-guide tube in rotary draw bending process. Mater Sci Technol 2013;21(1):56–61 [Chinese]. 12. Li H, Yang H, Song FF, Zhan M, Li GJ. Springback characterization and behaviors of high-strength Ti-3AL-2.5V tube in cold
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rotary draw bending. J Mater Process Technol 2012;212 (9):1973–87. 13. Zhu YX, Liu YL, Li HP, Yang H. Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube. Trans Nonferr Metal Soc 2012;22(9):2233–40. 14. Dong WQ, Liu YL, Zhao GY, Yang H. Establishment of springback prediction model for the rotary-draw bending of thin-walled rectangular tube considering variation of Young’s
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modulusThe 10th Asia-Pacific conference on engineering plasticity and its application. p. 182–8. 15. Liu YF, Daxin E. Effects of cross-sectional ovalization on springback and strain distribution of circular tubes under bending. J Mater Eng Perform 2011;20(9):1591–9. 16. Zheng XS, Liu YL, Liu CM, Yang H. Impact of springback on the cross-sectional deformation of H96 brass double-ridged rectangular tube in E-typed rotary draw bending. Int J Adv Manuf Technol 2017;89(9–12):3451–8.
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Please cite this article in press as: LIU C, LIU Y Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.005