Double-ridged Rectangular Tube Research Articles

Selection criterion of material filling in ridge grooves for reducing cross-sectional deformation of double-ridged rectangular bent tube

In order to satisfy the further improvement of new communication equipment, filling the ridge grooves on side walls with fillers is the effective method to improve the quality of double-ridged rectangular bent tube in H-typed rotary draw bending. However, how to choose appropriate material filling in ridge grooves to reduce deformation more effectively is a critical issue. Therefore based on the reliable FE models of H-typed rotary draw bending and twice-springback of double-ridged rectangular tube with fillers with different material parameters, a selection criterion of the material of filler to minimize the cross-sectional deformation of bent tube was studied. The selection criterion is that only the height size accuracy of filler should be made sure to be consistent with that of the ridge groove. The strength coefficient K of filler should be considered firstly, and the larger K can reduce the deformation more effectively. The yield strength σs and hardening exponent n can be considered secondly, and filler with higher σs or smaller n can be selected as far as possible. Elastic modulus E may not be taken into account. The reliability of this selection criterion is verified by using 65Mn spring steel filler.

Cross-sectional deformation of H96 brass double-ridged rectangular tube in rotary draw bending process with different yield criteria

Different yield criterion has great difference in predicting the deformation of tube with different material. In order to improve the prediction accuracy of the cross-sectional deformation of the double-ridged rectangular tube (DRRT) during rotary draw bending (RDB) process, Mises isotropic yield criterion, Hill’48 and Barlat/Lian anisotropic yield criteria commonly used in practical engineering are introduced to simulate RDB of DRRT. The inverse method combining uniaxial tensile test of whole tube and response surface methodology was proposed to identify the parameters of Hill’48 and Barlat/Lian yield criteria of small-sized H96 brass extrusion DRRT as well. Then based on ABAQUS/Explicit platform, the FE models of RDB process of DRRT considering Mises, Hill’48 and Barlat/Lian yield criteria were built. The results show that: The variation trend of cross-sectional deformation ratio is same when using different yield criteria. The cross-sectional deformation ratio by using Mises yield criterion is close to that by using Hill’48 yield criterion. However, there is a quite difference between by using Barlat/Lian yield criterion and by using Mises or Hill’48 yield criteria. The prediction values of cross-sectional height deformation by using three yield criteria all underestimate the experiment ones, and the prediction values of cross-sectional width deformation overestimate the experiment ones. By comparing the simulation results of cross-sectional deformation of the DRRT with different yield criteria and experiment ones, Barlat/Lian yield criterion is found to be suitable for describing the RDB process of DRRT.

Cross-sectional deformation behavior of double-ridged rectangular tube with fillers in different stages of H-typed bending

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 twice-springback 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.

A novel method to reduce the distortion of ridged rectangular tube in H-typed rotary draw bending

Ridged rectangular tubes are widely utilized in microwave equipment as waveguides. However, cross-sectional deformation easily occurs when a ridged rectangular tube is bent. Especially for H-typed bending, the deformation of ridge grooves cannot be controlled effectively by using the current bending tools. Therefore, a novel method adding fillers in ridge grooves to reduce the distortion is presented in this paper. According to this method, a three-dimensional finite element model of H-typed rotary draw bending of H96 brass double-ridged rectangular tube with ridge groove fillers was established, and then the reliability of the model and new method was verified by the experiment. It is found that when fillers are used, cross-sectional deformation significantly decreases, especially the height deformation and the spacing deformation of ridge grooves. Moreover, an obvious decrease in the distortion difference between different sections is observed, which means the distribution of deformation ratios along the bending direction is more uniform. Through further validation with a single-ridged rectangular tube, it shows that the novel method is feasible and ridge groove fillers are strongly recommended to be introduced in the bending of different ridged rectangular tubes.

Effect of inner ridge groove filler on deformation of double-ridged rectangular tube in E-typed rotary draw bending

Adding a filler to the inner ridge groove has been considered to reduce the inevitable cross-sectional deformation of double-ridged rectangular bent tube during E-typed rotary draw bending process. Using a numerical simulation method, the three-dimensional finite element models for E-typed rotary draw bending of H96 brass double-ridged rectangular tube without and with inner ridge groove filler under different bending radii were established. Based on the models, it is found that using the filler can obviously reduce the width deformation of inner ridge groove and the good double-ridged rectangular bent tube with small bending radius can be obtained. These results have engineering application worth for improving the forming quality of double-ridged rectangular bent tube.

Influence of mandrel parameters on cross-sectional deformation of H96 double-ridged rectangular tube with ridge groove fillers in H-typed rotary draw bending

Rigid mandrel plays an important role in restricting the cross-sectional deformation of double-ridged rectangular tube in rotary draw bending. So a 3D FE model of H-typed rotary draw bending of the tube was established, and the influence law of rigid mandrel parameters on cross-sectional deformation was obtained. With the increase of core number, the deformation of different parts of tube decreases. When core number exceeds 3, the effect of increasing the core on the improvement of cross sectional deformation is insignificant. A curved mandrel with simple structure was proposed, and the effect of curved mandrel on controlling of cross-sectional deformation is better than that of separated rigid mandrel.

An innovative PVC mandrel for controlling the cross-sectional deformation of double-ridged rectangular tube in rotary draw bending

In order to control the cross-sectional deformation of double-ridged rectangular tube (DRRT) in rotary draw bending (RDB), a PVC mandrel just supporting the back of ridge grooves was introduced. The characteristics of cross-sectional deformation of DRRT and its evolution with the new PVC mandrel were revealed numerically by comparing with that with the mandrel-core die. In order to evaluate the application scope of the new PVC mandrel, the cross-sectional deformation for different specifications of DRRT in RDB were also researched. The results show that: (1) the flange sagging Δh, space deformation between ridges Δd, and width deformation of inner ridge groove Δw by using the new PVC mandrel can be better controlled than that by using the mandrel-core die. But the width deformation of the outer ridge groove ΔW gets a little larger; (2) by using the new PVC mandrel, the maxima of absolute values of Δh and Δw and the maximum of ΔW all increase firstly with the process of bending and then change little when the bending angle is larger than 60°, which are consistent with the variation of the peak value of tangent stress on the flange, while the maximum of absolute value of Δd increases continuously. (3) For small-sized DRRT, its cross-sectional deformation can be well controlled by using the new PVC mandrel. However, with the increase of dimension of DRRT, the cross-sectional deformation of DRRT increases obviously, and its distribution is extremely non-homogeneous.

Multi-Objective Parameter Optimization for Cross-Sectional Deformation of Double-Ridged Rectangular Tube in Rotary Draw Bending by Using Response Surface Methodology and NSGA-II

Cross-sectional deformation of double-ridged rectangular tube (DRRT) inevitably occurs due to the inhomogeneous deformation induced by external boundary conditions in rotary draw bending (RDB). Unreasonable factor combination would aggravate the cross-sectional deformation of DRRT. So, a powerful and efficient method combining Response Surface Methodology (RSM) and Non-Sorted Genetic Algorithm II (NSGA-II) was proposed to optimize the factors to control the cross-sectional deformation of DRRT in RDB. Firstly, an orthogonal experiment was used to screen out the important factors. It was obtained that three factors—clearance between DRRT and mandrel, clearance between DRRT and bending die, and boosting of pressure die—have an important influence on the cross-sectional deformation of DRRT. It can also be observed that the variation trend of flange sagging (FS) is always consistent with that of space deformation between ridges (SDR) with the changing of factors. RSM based on a Box-Behnken design was then used to establish response surface models. The proposed response surface models were used to analyze the relationship of the important parameters to the responses, such as space deformation between ridges, and width deformation of outer and inner ridge grooves (WDO and WDI). Finally, multi-objective parameter optimization for the cross-sectional deformation of DRRT in RDB was performed by using the established model and NSGA-II algorithm. The interaction of responses was revealed and the value range of each response in the space of Pareto optimal solutions was determined. It can be observed that there is always an evident conflict between SDR and WDO in the space of Pareto optimal solutions. By using this optimization method, the absolute values of SDR and WDI were significantly reduced—by 13.17% and 17.97%, respectively—compared with those before optimization, while WDO just increase only a little.

The inverse parameter identification of Hill’48 yield function for small-sized tube combining response surface methodology and three-point bending

Abstract

Influence of different mandrels on cross-sectional deformation of the double-ridge rectangular tube in rotary draw bending process

Cross-sectional deformation of the double-ridged rectangular tube inevitably occurs in the rotary draw bending process. It has serious effect on the characteristic of microwave transmission and restricts the quality and performance of tube. Different mandrels play different roles in the bending process, so the rigid and polyvinyl chloride (PVC) mandrels are applied in the E-typed and H-typed rotary draw bending of double-ridged rectangular tube to study their influence on the cross-sectional deformation. Based on the platform of ABAQUS/Explicit, the three-dimensional finite element models for E-typed and H-typed rotary draw bending of H96 brass double-ridged rectangular tube with rigid and PVC mandrels have been established and validated by experiment. Results show that whether in the E-typed or H-typed bending, the PVC mandrel has better inhibitory effect on the cross-sectional long-side deformation δL, short-side deformation δW, and spacing deformation between the bottom of ridge grooves δw of the tube. And the PVC mandrel can be more helpful to reduce the width deformation of ridge grooves of the tube in H-typed bending. The rigid mandrel can restrain the width expansion deformation of outer ridge groove of the tube more effectively in E-typed bending. However, whether using the rigid or PVC mandrel, the width shrinkage deformation of inner ridge groove of the tube in E-typed bending is less affected by the type of mandrels. And the width of two ridge grooves on sidewalls of the tube in H-typed bending also has the obvious shrinkage deformation.

Impact of springback on the cross-sectional deformation of H96 brass double-ridged rectangular tube in E-typed rotary draw bending

Cross-sectional deformation is one of the critical factors that affect the forming accuracy of double-ridged rectangular tube (DRRT) in E-typed rotary draw bending (RDB). In the forming process, springback is inevitable and it has a direct impact on the cross-sectional deformation. Based on ABAQUS platform, three-dimensional finite element (3D-FE) models for bending and springback of H96 brass DRRT in E-typed RDB were established. With the models, the impact of springback on the cross-sectional deformation was studied. Results show that after springback, the deformation of cross-sectional height and two ridge grooves spacing increase in cores-support zone while decrease in no-cores-support zone. The impact of springback on width deformation is not significant. The maximum values of cross-sectional height deformation and two ridge grooves spacing deformation from 0° to 30° become larger after springback, while the change rules of these two from 30° to 90° are reversed. What’s more, the maximum value of width deformation from 0° to 60° becomes larger after springback while that of outer ridge groove width deformation becomes smaller, and these two from 60° to 90° both have the reversed change rules as well.

Deformation behaviors of double-ridged rectangular H96 tube in rotary draw bending under different mandrel types

Cross-sectional deformation is the most important formability assessment factor in rotary draw bending (RDB) of double-ridged rectangular tube (DRRT). Mandrel type influences the cross-sectional deformation directly. Due to the special cross-sectional shape of DRRT, the selection of right mandrel type becomes the most challenging task. Thus, a disconnect-type rigid mandrel and two kinds of PVC elastic mandrel were proposed. The influence of three mandrels proposed on the cross-sectional deformation of DRRT was investigated. The results show that (1) the type I mandrel can control the height deformation of flange preferably and the type III mandrel can control the deformation of distance between outer and inner ridge groove well. With respect to restraining the width deformation of DRRT, the two mandrels have their own merits. The performance of type II mandrel in preventing height deformation of DRRT is too poor to be used as a mandrel. (2) Only the type III mandrel is feasible when the mandrel support range is larger. Increasing the mandrel support range can decrease the height deformation obviously, but it has little effect on the width deformation. (3) When the size of DRRT is smaller, the type III mandrel can be a better option. However, when the size of DRRT increases, the height deformation of flange will increase evidently and the type I mandrel should be a better choice at this time.

Research on cross-sectional deformation of double-ridged rectangular tube during H-typed rotary draw bending process

Based on the ABAQUS/Explicit, a three-dimensional elastic–plastic finite element model of the H96 brass double-ridged rectangular tube (DRRT) during H-typed rotary draw bending (RDB) was established and its reliability was validated by an experiment. With the model, distribution characteristic of cross-sectional deformation and effects of clearance and friction coefficient between tube and dies and core number on it were studied. The results show that the maximum cross-sectional height distortion ratio appears at the bending angle 60°. And the maximum cross-sectional width distortion ratio between side walls, as well as side walls of the ridge grooves, appears at the bending angle 80° and 60°, respectively. In addition, retracting mandrel has a great effect on the cross-sectional height distortion, but its influence on the cross-sectional width distortion can be ignored. And the maximum cross-sectional distortion ratio initially increases with increasing of clearance between tube and mandrel cm and friction coefficient μb between tube and bending die, and then decreases with their increase, and initially decreases with the increase of core number N, and then increases with increasing of N. Moreover, the reasonable value of N is taken as 4.

Prediction of forming limit based on cross-sectional distortion for rotary draw bending of H96 brass double-ridged rectangular tube

Cross-sectional distortion is one of the main defects severely restricting the improvement of the forming limit in the rotary draw bending of double-ridged rectangular tube. So, how to rapidly and efficiently predict the forming limit (minimum bending radius R min with allowed cross-sectional distortion) and improve it has become an urgent problem to be solved for the development of rotary draw bending of double-ridged rectangular tube. Based on ABAQUS/Explicit, finite element model of rotary draw bending for double-ridged rectangular H96 brass tube has been established and verified by experiment. Using the model combined with the virtual orthogonal experiment, the significance analysis of influence of processing parameters on cross-sectional distortion was carried out. And based on the technique of orthogonal regression analysis, a prediction model of the forming limit with allowed cross-sectional distortion was built. The results show that: (1) processing parameters significantly influencing cross-sectional distortion are tube-mandrel clearance Δc m, tube-bending die friction coefficient μ b, bending radius R, and core number N. (2) Effect laws of significant parameters on R min were obtained: R min gradually decreases with increasing of μ b; when the value of Δc m is smaller than 0.37 mm, R min slightly decreases with increasing of Δc m; and when the value of Δc m is larger than 0.37 mm, R min sharply increases with increasing of Δc m. (3) The 3D forming limit diagrams and the minimum bending radii in different processing conditions were obtained, which can provide a crucial guide for selecting of processing parameters in RDB of the double-ridged rectangular tube.

Optimization of processing parameters for double-ridged rectangular tube rotary draw bending based on grey relational analysis

The rotary draw bending of double-ridged rectangular tube is a complex nonlinear physical process with multifactors coupling effects. Processing parameters, especially clearances and friction coefficients between tube and various dies, have a significant effect on the forming quality of the double-ridged rectangular tube in rotary draw bending. If the values of these processing parameters are inappropriate, some defects including cross-sectional deformation, wall thinning, and wall thickening easily occur in the bending process of double-ridged rectangular tube. So optimization of these processing parameters is of great importance to control these defects. Based on the grey relational analysis method combined with the orthogonal experimental design and finite element simulation, a grey relational analysis model was established for the rotary draw bending process of double-ridged rectangular H96 brass tube. With the model, optimization of clearances and friction coefficients between tube and various dies was implemented with consideration of interactive effects of the above defects. The results show that (1) the main factors influencing cross-sectional deformation, wall thickening, and wall thinning are tube–mandrel clearance Δcm, tube-bending die clearance Δcb, and tube–mandrel clearance Δcm, respectively. (2) The optimal values of clearances Δcm, Δcp, Δcw, and Δcb and friction coefficients μm, μp, μw, and μb of tube–mandrel, tube–pressure die, tube–wiper die, and tube-bending die are 0.15, 0.2, 0.2, 0.2, 0.02, 0.3, 0.06 and 0.17 mm, respectively. Furthermore, the verification for the optimal values of these processing parameters was carried out, and the double-ridged rectangular H96 bent tube obtained by using the optimal values of these processing parameters has the minimum values of cross-sectional deformation, wall thinning, and wall thickening and can satisfy the national aviation industry standards.