Free Bending Process Research Articles

Texture and bendability evolution mechanism of 6063 aluminum alloy tube formed by free-bending technology employing cross-scale numerical modeling

With the improvement of application requirements, the combination of precise shape and high performance of tube components has become a burning issue. This work investigates the free-bending process of 6063 aluminum alloy tubes using cross-scale numerical modeling. The cross-scale framework integrates macroscopic finite element model (FEM) and crystal plasticity finite element model (CPFEM) through strain history. CPFEM exhibits excellent agreement with the macroscopic FEM and experimental results for both the Mises stress and texture evolution. Predictions indicate that as bending deformation increases, the volume fractions of the initial Cube texture decrease, while the Goss texture component increases. The overall texture strength continuously decreases. Meanwhile, slip mode plays a critical role in texture evolution, causing similar trends in the inner and outer bend regions. Additionally, the findings from the cross-scale simulation accurately predict the detailed texture evolution of the 6063 aluminum alloy tube under various feeding speeds. The development of Goss texture in various forming regions and the formation of substructures within Goss-oriented grains are primary factors contributing to reduced tube formability, which could illustrate the primary mechanisms for variation in tube bendability effectively. The proposed cross-scale method lays the foundation for research on complex spatial tube components as well. Moreover, cross-scale simulation facilitates the prediction of macroscopic deformation and microstructural evolution in critical regions of tube components, allowing for the optimization of bending processes based on cross-scale simulation results.

Forming characteristics of thin-walled tubes manufactured by free bending process-based nontangential rotation bending die

The free-bending process of a metal tube involves a geometric relationship between the eccentricity, the rotation angle of the bending die, the deformation zone length, and the bending radius. Ideally, during the forming process, the contact position between the bending die, and the outer bend of the tube remains tangent. However, due to factors such as the clearance of the bending die and material properties, the rotation angle can be adjusted within a specific range while still ensuring smooth tube formation. The tangential state is disrupted when the rotation angle changes, resulting in overbending or underbending. Thus, in this study, a new theoretical analysis of the free bending process, accounting for clearance, was developed to analyze the material flow and changes in the bending radius during the nontangential contact between the bending die and the tube. In addition, the reasons for achieving smooth tube bending even after adjusting the rotation angle were explained, and the deformation mechanism of the tube under the combined effects of additional tangential force from the bending die and axial propulsive force was analysed. Furthermore, the impact of the rotation angle on the bending radius and the displacement of the strain neutral layer (strain NL) was determined. Afterwards, finite element (FE) modeling and forming experiments were conducted to verify the proposed theoretical analysis under different deformation zone lengths and eccentricities conditions. Besides, the distribution of the inner and outer wall thicknesses of the tube under the nontangential rotation of the bending die was further analysed. The simulation and experimental results fit well with that obtained from theoretical analysis.

Theoretical analysis, finite element modeling and experimental investigation of the impact of friction between tube and bending die on the formability of the tube during the free-bending process

In the free-bending process, the tube undergoes bending and deformation due to the action of a guide mechanism and bending die. The plastic deformation zone of the bent tube is less constrained by the die, and the quality of the formed tube is significantly affected by the friction between the tube and the die. To assess the impact of friction between tube and die on the formability of the bent tube, the theoretical modeling that considers the friction coefficient is conducted. Afterward, the free-bending experiments and finite element simulations are performed using Cr12MoV and ceramic bushing. The theoretical and experimental results are compared with those obtained from finite element simulation under different friction conditions to confirm the validity of finite element simulation. The influence of friction on the arc radius, wall thickness variation, and cross-section deformation of the curved tube is explored and discussed. With the increase of friction coefficient, the arc radius decreases gradually, the wall thickness thickens more obviously, and the cross-sectional distortion becomes more serious. Furthermore, the effect of different bushing materials on the surface quality of aluminum alloy and stainless-steel bent tubes is experimentally investigated. Those findings expand our understanding of the influence of tube-die friction on deformation behavior and it is necessary to first determine the friction condition during the actual free-bending forming process.

Effect of bending radius on deformation behavior of H62 brass tubes in a less constrained free bending process

Effect of bending radius on deformation behavior of H62 brass tubes in a less constrained free bending process

Springback Prediction of Free Bending Based on Experimental Method

The springback phenomenon has an impact on tube-processing quality during the free-bending process. For different pipe benders, the forming process is affected by different factors, such as gaps between the tube and the bending die and friction between the tube and the guiding mechanism and the bending die; thus, the theoretical U-R relationship cannot complete the precise processing required. In order to overcome the influence of springback during the free-bending forming process, a U-R experiment was performed first, and the actual U-R relationship was established. The U-R experiment demonstrated that when the bending die offset U increased, the tube-bending radius R decreased. Then, based on the results of the springback experiments, a springback prediction method was presented. The experimental method successfully predicted springback, demonstrating that the springback problem can be effectively solved through compensation of the arc section.

Investigation on variation characteristics of bent tube axis and determination of bending die motion trajectory in free bending process

In free bending process, the axis shape of bent tube is determined by motion trajectory of bending die. The bent tubes with different bending radii and bending directions can be formed by continuously adjusting the position and posture of die. To accurately form the pre-designed bent tube, the formation mechanism of bending arc in free bending process was analyzed. The mathematical model between bending radius and deviation was established and the moving direction of bending die was also determined according to the plane space azimuth where the bending arc segment is located. The formation process of transition segments with variable curvature and variable bending direction is illustrated during the movement of bending die, and the influence of transition segment on the axis shape was also explored. By comparing the axis deviation of experimental and simulated bent tubes, the length of transition segment and the moving path of bending die can be optimized. Finally, the applicability of free bending forming technology in forming bent tubes with different axis features was verified by conducting free bending experiments on bent tubes with three typical shapes. Due to the high flexibility of free bending forming technology, the work in this paper could promote the engineering application of this technology in the precise control of axis shape of bent tube.

Investigation on the influence of weld position on the deformation behavior of welded tube during free bending process

The plastic deformation behavior of welded tube is affected by the non-uniform distribution of the mechanical properties of welded tube during the free bending process. To explore the influence of weld position on the forming quality and axis dimensional accuracy of welded tube, the free bending experiment and numerical simulation of welded tube were conducted in this paper. First, the principle of free bending was theoretically deduced and the stress distribution of bent tube was analyzed. Then, the hardness test and uniaxial tensile test were conducted to obtain the mechanical properties of weld zone and parent zone of welded tube. The material strength in the weld zone of welded tube is significantly higher than that in the parent zone. Finally, the free bending experiment and numerical simulation with different weld positions were carried out, and the influence of weld position on the bending radius, cross-sectional distortion, and wall thickness of bent tube was discussed. All these findings advance the insight into the free bending deformation behavior of welded tube and help to improve the forming quality of welded tubes and facilitate the application of free bending technology in welded tube.

Study on the Iterative Compensation Method for Continuous Varying Curvature Free Bending

The parts formed by the bending process not only have high precision of appearance dimension but also have good performance. In recent years, enterprises have put forward higher requirements for the forming process and product quality. Therefore, a new method for iterative compensation of bending springback with certain generality is proposed for continuous curvature bending. The purpose of this study is to take curvature as an iterative parameter and make the shape size reach the expected value through the finite compensation. On the basis of establishing this iterative compensation mechanism, the convergence of curvature iteration in the general free bending process is proved. The reliability of the proposed iterative compensation method in the bending process engineering application is verified by combining simulation with experiment. The two materials of 304 stainless steel and ST12 cold rolled steel were studied, and the two-dimensional plane stress-strain model Abaqus cantilever beam was established by using finite element software. The bending forming simulation was carried out based on the above iterative compensation mechanism. Finally, through the bending experiments of four models, the feasibility of the iterative compensation mechanism of curvature in the continuous curvature plane bending process is verified, and different models are selected to clarify that the method has the characteristics of generality, that is, it will greatly improve the flexibility of the bending process in industrial applications without the limitation of material types and mechanical models.

Investigation on the influence of mandrel on the forming quality of thin-walled tube during free bending process

The forming defects such as the cross-sectional distortion and axial instability often occur during the free bending process of thin-walled tube. To eliminate or suppress the above-mentioned forming defects, the method of inserting the mandrel inside tube was employed in this paper. First, the principle of free bending with mandrel was theoretically deduced, which was used to explain the mechanism of the supporting force provided by the mandrel on the deformation behavior of tube. Then the influence of the mandrel position, the number of core balls in mandrel and the clearance between the mandrel and tube on the free bending forming quality of thin-walled tube was analyzed and summarized by the numerical simulation method. Finally, the free bending experiment of thin-walled tube with optimized mandrel parameters was conducted to verify the reliability of the numerical simulation method and the rationality of the mandrel parameters. All of these findings advance the insight into the deformation behavior of thin-walled tube influenced by mandrel and help to improve the forming quality of thin-walled tube and facilitate the application of free bending technology in thin-walled tube.

Springback prediction of AL6061 pipe in free bending process based on finite element and analytic methods

The free bending process is a promising process for forming metal pipes. It can be achieved without the frequent replacement of mould. This process has attracted considerable attention of researchers. However, its springback after unloading is a key issue that influences the final formed shapes of the pipe. In this study, finite element (FE) and analytic methods are used to predict the springback phenomena of the AL6061 pipe. The analytic model is enhanced by considering the neutral layer offset. Furthermore, to better investigate the springback process, the FE model of the free bending process is established. The influence of process parameters (e.g. friction, clearance, and mobile die section shape) on bending springback is investigated after the free bending process. The springback angle generally varies in the range of 2–2.5°, and the influence of process parameters on the final springback of the pipe in the free bending process is also discussed. Results showed that the neutral layer offset has a tendency to move towards the material tensile direction in the free bending process, which is different from the traditional rotary bending. Thus, the analytic model of pipe bending springback is optimised with the addition of the neutral layer offset. This study contributes to reinforcing the understanding of the springback mechanism and has a guiding significance for free bending process quality.

Physical and Technical Foundations of the Use of Alternating Free Bending for Producing Long-length Semi-products from Metals and Alloys with Improved Mechanical Properties

In this work, we give a theoretical justification of the non-monotonic character of strain in the process of refinement and formation of a grain-type structure during the deformation processing of low-alloyed copper heat-hardenable alloys. A regularity is revealed, suggesting the alternating behavior of the strain state in the process of the continuous bending of billets. It is found that the continuous free bending process in the conditions of multi-cycle (four cycles) processing increases the strength and produces a gradient-type structure and a gradient of mechanical properties. Using fabrication of the experimental samples of the contact wire as an example, it is shown that the obtained results can serve as a scientific and technical foundation for the development of complex methods for the processing of axis-symmetrical long-length objects from copper heat-hardenable alloys in the form of wires and shaped products with improved mechanical properties, with potential adaptability for manufacturing.

Theoretical modelling and finite element simulation of AA6061 involute components based on 3D free bending process

In this study, theoretical modelling and finite element simulations were performed to reveal the forming mechanics of involute components based on a 3D free bending process. During forming the involute components, as the bending radius increased, the equivalent stress, the tangential strain, and the ellipticity of the cross-section were gradually decreased. Furthermore, the compressive stresses located inside the components were greater than the tensile stresses located outside them; thus, the thickening inside the involute components were greater than the thinning outside them. In addition, under the same bending radius, the equivalent stress and tangential strain of the spatial involute components were larger than those of the plane involute. Therefore, the thickening proportion of the inner wall, and the thinning proportion of the outer wall of the spatial involute components were greater than those of the plane involute. The cross-section ellipticity of the spatial involute components were smaller than that of the plane involute components. The results acquired from the theoretical modelling are in line with those obtained from finite element simulation and experimentation.

Sensitivity analysis of process and tube parameters in free-bending processes

Free-bending processes are used to manufacture highly-complex profile shapes for different kinds of industry sectors. This paper focuses on the enhanced version of the MOS bending technique (6DOF), which is used by BMW to produce semi-finished products for the tube hydroforming process. In order to achieve a better process understanding, the bending process was analyzed with regard to process and tube parameters. In the first experimental bending series, the process precision was measured and evaluated by standard deviation and process capability. In the second bending series, the analysis focuses on the weld seam position and the wrinkling behavior of the tube. The correlations shown between process parameters and the resulting bending geometry are the basis for the validation of a process simulation model developed in LS-Dyna. Therefore, the comparison of experimental data and data measured numerically represents a good agreement. The FEM model was used to perform a numerical based sensitivity analysis of the bending process in relation to process and tube parameters. The result identifies the main factors contributing to the free-bending process.

Finite element modelling and experimental investigation of the impact of filling different materials in copper tubes during 3D free bending process

3D free bending process, an advanced metal forming technology, has attracted much attention due to its unique geometrical flexibility and efficiency. Filling tubes with materials may effectively reduce the distortion in the cross-section area and restrain wrinkling and collapse of tube wall. In the present study, the impacts of filling different materials on the copper tubes during 3D free bending process were investigated. We have found that copper tubes filled with low melting point alloys could induce the most uniform stress distribution, which result in better formability and moderate thickness changing rates when compared to SS304 steel balls and PU rubbers. The lowest ellipticity reached to 1.467%.

Investigation of the effect of relative thickness (t0/d0) on the formability of the AA6061 tubes during free bending process

3D free bending technology is a fabrication technology that has drawn more and more attention all over the world in recent years. During the free bending process, the relative thickness (t0/d0) has a great impact on stress–strain distribution and the movement of the neutral layer, thus further affecting the formability and cross-section distortion of the tube. In this study, relative thickness (t0/d0) were set as 0.033, 0.067, 0.1 and 0.133, respectively. A mechanical analysis model was built to analysis the equivalent stress distribution and the displacement of the strain neutral layer (ξ), and the reliability of the theoretical model was verified. The results showed that the equivalent stress is the lowest and its distribution is the most uniform when the relative thickness (t0/d0) was set as 0.067, which leads to the best formability under all conditions. The peak values of equivalent stress under all conditions appear at the 10° cross-section and the 150° cross-section, respectively, which leads to the thickness of the inner and outer tube changes dramatically. Due to the effect of feeding force which increases the compressive stress of the inner tube and reduces the tensile stress of the outer tube correspondingly, the equivalent stress of the inner tube was higher than the values of the outer tube at the same positions. The displacement of the strain neutral layer (ξ) decreases with the increase of the initial thickness of the tube. The lowest values of ellipticity of 3.48% and 2.85% are reached at the two typical cross-sections when the relative thickness is 0.133.

Wall thickness distribution of Cu–Al bimetallic tube based on free bending process

In this study, we focused on bimetallic tube comprising copper and aluminum (Cu–Al) and proposed a theoretical model of its wall thickness distribution by the free bending technology. Compared to the single metal tube, the minimum thickness of the copper tube is smaller than the minimum thickness of the copper layer in the Cu–Al bimetallic tube, whereas the minimum thickness of the aluminum tube is greater than that of the Cu–Al bimetallic tube under different bending radii; the maximum wall thickness of the copper tube is larger than that of the copper layer in the Cu–Al bimetallic tube, whereas the maximum wall thickness of the aluminum tube is smaller than that of the aluminum layer in the Cu–Al bimetallic tube. Further, the reliability of the proposed theoretical model was verified by finite element simulation and experiments. Both of these results showed that the wall thickness distribution of the bimetallic layer of the metal tube tends to be more uniform. The offset rule of the strain neutral layer of Cu–Al bimetallic tube in the free bending process was also revealed. Moreover, the difference between the U–R curve of the Cu–Al bimetallic tube and the single metal tube was also investigated, and the results indicated that the U–R curve of the Cu–Al bimetallic tube is roughly located between the U–R curves of copper and aluminum.

U-R relationship prediction method for aluminum alloy circular tube free-bending process based on sensitivity analysis of material parameters

The bending radius (R) of the bending component is defined by the deflection (U) of the bending die in the tube free-bending process. The U-R relationship is the key factor to obtain the precise geometry size of the complex bending tubular components. Therefore, this study aims at proposing a new method to predict the U-R relationship for the arbitrary power hardening aluminum alloy (Al alloy) circular tube based on the U-R relationship of the reference material and the sensitivity analysis of material parameters, which may reduce many experimental works. In the current study, AA1100 alloy was set as the reference material, and the effects of each material parameter on the U-R relationship were investigated by carrying out the deformation and sensitivity analysis of the FEA simulation results. The results show that the bending radius increases with the decrease of elastic modulus (E), density (ρ), and strain-hardening exponent (n) and the increase of strength coefficient (K) and initial yield stress (σs), where σs has the greatest influence on the U-R relationship. Moreover, the U-R relationship prediction method for arbitrary power hardening Al alloy circular tube was presented based on the sensitivity analysis of the reference material. Finally, the bending tests of the AA6061-T6 tubes were carried out to prove the accuracy of the U-R relationship prediction method. The bending results show that the experimental U-R relationship of the AA6061-T6 tube was consistent with the predicted value, and the prediction method had good applicability to power hardening Al alloy circular tube.

Free-bending process characteristics and forming process design of copper tubular components

Three-dimensional free-bending is a new and an advanced forming technology to manufacture the complex metal hollow components with continuously varying radius. In this study, the principle, process analysis, and the CNC control of free-bending were introduced in detail. The characteristics of the free-bending process, such as the motion trace scope of bending die and the stress variation in the free-bending process, were numerically investigated through finite element method using ABAQUS finite element code. With the simulation model, the material correction factor (Km) of copper was determined and the correction factor (Kc) for the clearance between the tube and bending die was also proposed. Moreover, the effects of the key process parameters including the clearance between the tube and bending die (Δc), the distance between the center of the bending die and the head of guide sleeve (A), and the axial feeding velocity (v) on the forming quality of the tubular bending components were studied as well. Through the finite element simulation and analysis, the optimum parameters (Km, Kc, Δc, A, and v) used in the free-bending process of the tubular component are summarized and the forming process design of the copper tubular component was also obtained. Based on the forming process design, the simulation and bending test of the copper tubular component were carried out, and the dimensions of the bending components gave a very good agreement with the results obtained from finite element modeling. Furthermore, there was no obvious cross section distortion, excessive thickening, and thinning of wall thickness of the formed tubular components. It is concluded that the three-dimensional free-bending technology is a novel forming process used to manufacture a sound complex three-dimensional hollow component with asymmetric cross sections and continuous varying radii.

Numerical simulation and experimental study on mechanism and characteristics of tube free-bending forming process

Free-bending is a new flexible bending forming technology, which has the great bending potential and can achieve complex bending geometries without changing the die and re-clamping the tube. In our research, the FEA model for tube free-bending was established and the bending ratio of down to R/D0 ≈ 2.5 of brass tube was realized in the finite element simulation. With the simulation model, the motion trace scope of bending die and stress variation in free bending process were identified and it was found that the equivalent stress and the displacement of the strain neutral layer increased with the decrease of bending radius. Meanwhile, the absolute value of the maximum tangential strain in extrados (PE11=1.779) is much less than that in extrados (PE=-2.337) when the bending ratio is about 2.5. The finite element simulation results also confirmed that the axial boosting force during free-bending process led to a displacement of 0.3 mm of the strain neutral layer from the inner side of the bend into the direction of the outer bend and a maximum wall thickness reduction of 6% in the extrados when the bending radius is minimal. From the bending tests, the minimum bending ratio of R/D0 ≈ 2.8 of brass tube were realized, and the bent tube also has very small wall thickness reduction and the resulting bending geometry shows only small cross section deformations and rupture since the bend die holds the required roundness. Both finite element analysis and bending test verify the above-mentioned characteristics of free-bending.

Simulation and experimental research of the free bending process of a spatial tube

The free bending technology is regarded as a promising fabricating technology in the recent years. Due to characteristics of complex product shape and dieless forming, this technology arises more and more attention recently. Firstly, this paper analyzed movement track of bending die based on the principle of free bending technology. Then, distribution characteristics of equivalent stress and strain on tube and bending die during different stages of the free bending process were analyzed. Afterwards, this paper studied the influence law of clearance between tube and bending die, fillet radius of guider, feeding speed on the tube free bending quality. Relationship between eccentricity U of bending die and bending radius R of tube relates to the bending program directly. In this paper, U-R relationship was obtained by finite element simulation to verify the accuracy of the built model. FE simulation and bending experiments were conducted based on the research results. The result revealed that dimension of the bent spatial tube was close to the CAD model and proved the reliability of U-R relationship. Deviation of the bending radius and bending angle is supposed to occur due to springback after forming.