Converting circular tubes into square cross-sectional parts using incremental forming process

Incremental forming process is recently developed to form tubular parts.The fabrication cost and accuracy could be optimized if the effects of process parameters and the optimum values are specified.The aim of this research is using incremental forming of copper tubes to convert a circular tube into a square cross-sectional part.An experimental setup,consisting of a spherical forming punch and a fixture for clamping the tube is designed.The forming punch movement is controlled by a CNC machine.Full factorial design of experiments is carried out in order to determine the effects of process parameters including linear velocity,radial feed,and axial feed of the tool on the thinning ratio and the maximum outer diameter of the square cross-sectional parts.Results show that the radial feed has the major influence on the thinning ratio,while the axial feed plays the major role for the final profile.Increase of radial feed results in higher thinning ratio,and decrease of axial feed results in better shape conformity.Linear velocity does not have a significant effect on thinning ratio.Regression models are also given for predicting the determined responses.

Deformation Calculation of Cross-section Based on Virtual Force in Thin-walled Tube Bending Process

Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation due to the effect of shear load in plastic bending process. When the tube is bent, the extrados-wall bears the tension stress and the intrados-wall bears the compression stress, synchronously the cross-section is affected by the circumferential stress. According to the above, the distribution function and curve of tangential stress can be obtained according to force balance differential equations on circumferential direction and Trasca rule. Subsequently the real state and virtual state moment equations were established, a new method was presented adopting the virtual principle of deformation system to calculate the x-axis and y-axis displacement of arbitrary point on cross-section. So the major and minor axes of deformed cross-section can be calculated according to the displacements of each point, and the variety value of major and minor axes will be obtained further. Finally the theoretical calculating result is compared with NC tube rotary-bending experiment results to verify the rationality of theoretical analysis, and the cross-section deformation rule of thin-walled tube can be received.

Cross-sectional distortion behaviors of thin-walled rectangular tube in rotary-draw bending process

The cross-sectional distortion usually appears during rotary-draw bending process of thin-walled rectangular tube with small bending radius.To study the cross-sectional distortion of the tube,a three-dimensional finite-element model of the process was developed based on ABAQUS/Explicit code and its reliability was validated by experiment.Then,the cross-sectional distortion behaviors of the tube were investigated.The results show that a zone of larger circumferential stress appears on the tube when bending angle reaches 30°.And in the larger circumferential stress zone,the sagging phenomenon is produced obviously.The maximum cross-sectional distortion is located in the larger circumferential stress zone and the angle between the plane of maximum cross-sectional distortion and the bending reference plane is about 50°.The position of the maximum cross-sectional distortion keeps almost unchanged with the variation of the clearances between dies and tube.

Analysis and experiment of cross-section flattening incoreless tube bending

In order to predict the flattening rate of the cross-section accurately during the tube ben- ding, the generation principle, the solution and the influence factor of the cross-section flattening were studied. On the basis of the plane-stress and the assumption that the plastic volume is con- stant, three-dimensionai strain formulas were established in consider of the cross-section flattening. Considering the wail-thickness change, the approximate calculation formulas of short axis flattening rate were deduced, with the outer diameter and the inner diameter as parameters. Because different materials have different cross-section flattening rates, a material correction factor was introduced to modify the formula based on experiments. Finally, the validity of the theoretical formulas was proved according to the calculation and the experiment results, which can provide a reference for the forming quality prediction in tube bending.

HYBRID PERTURBATION-GALERKIN SOLUTION OF THE FLOW IN A CIRCULAR CROSS-SECTION TUBE WITH CONSTRICTION

Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.

Influence of mandrel-cores filling on size effect of cross-section distortion of bimetallic thin-walled composite bending tube

Two new size factors of cross-section hollow coefficient and bending degree are introduced to reveal the size effect of bending forming of bimetallic composite tube.Hollow coefficient and bending degree can limit the commonly used bent tube to the size description range of(0,2.00).The evolution laws of the cross-section distortion forms in the hollow coefficient-bending degree interval are revealed as well as the action of the mandrel-cores on the size effect.Results show the mandrel-cores filling can expand the forming limit of the bent tube,but also bring two other forming defects of wrinkle and rupture.The identification factor(hollow coefficient multiply bending degree)provides a method for querying the cross-section distortion forms of all composite bending tubes.In the identification factor interval(0,1.00),the distribution area of bending forming defects of the composite tube is continuous.The thin-walled composite bending tube collapses when identification factor in(0,0.39),wrinkles when identification factor in[0.39,0.50),and ruptures when identification factor in[0.50,1.00).The mathematical model of size effect is derived,by which the average cross-section distortion rate is found to distribute like a radial leaf in the hollow coefficient-bending degree qualified forming space.The best forming zone is hollow coefficient 0.46-0.68,and bending degree 0.25-0.47.

Experiments on self-excited oscillation in a thin-walled collapsible tube

Self-excited oscillation in a collapsible tube is an important phenomenon in physiology. An experimental approach on self-excited oscillation in a thin-walled collapsi- ble tube is developed by using a high transmittance and low Young＇s modulus silicone rubber tube. The elastic tube is manufactured by the method of centrifugal casting in our laboratory. An optical method for recording the evolution of the cross-sectional areas at a certain position along the longitudinal direction of the tube is developed based on the technology of refractive index matching. With the transparent tube, the tube law is measured under the static no-flow condition. The cross section at the middle position of the tube transfers from a quasi-circular configuration to an ellipse, and then to a dumbell-shape as the chamber pressure is increased. During the self-excited oscillation, two periodic self-excited oscillating states and one transitional oscillating state are identified. They all belong to the LU mode. These different oscillating states are related to the initial cross-sectional shape of the tube caused by the difference of the downstream transmural pressure.

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 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.

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.

PULSATILE BLOOD FLOW THROUGH A VISCOELASTICITY-TETHERED TUBE OF MILD VARYING CROSS-SECTION

In this paper a mathematical model is developed for the description of the pulsatile blood flow through an axisymmetric artery of mild varying cross-section, taking into account the tethering effect of the sorrounding tissues.Based on the linear Navier-Stokes equation and boundary conditions,a set of differential equa- tions for the modulus of phase velocity,blood velocities,pressure and deformation of the vessel wall are deduced and the numerical solutions are found by utilizing the Runge-Kutta method.The axial velocity profiles and the peak wall shear stresses are given for both mild tapering tube and mild stenosed tube.It is shown that the peak wall shear stresses in the tethered tube are higher than those in the free tube.It is also shown that in a series of previously research work on peak wall shear stresses of varying cross-section vessels the free vessel assumption has the tendency of under assessing the peak wall shear stresses and vice versa for the rigid vessel assumption.

Numerical Research on Effect of Sudden Cross-Section Expansion on Detonation Initiation

Numerical simulation has been performed to investigate the DDT(Deflagration-to-Detonation Transition)mechanism by solving fully compressible reactive flow for hydrogen/air mixtures in tube with sudden cross-section expansion.The results reveal the acceleration action of abrupt cross-section on DDT,which is validated by comparing the run up distance and time with corresponding long annular tube and single tube.Detailed discussion of flow field variations finds that the DDT process in cross-section abrupt tube can be divided into three stages(flame acceleration,transition to detonation,and detonation propagation stages respectively)according to different flame modes.Particularly,it is found that formation of vortex could accelerate DDT by promoting turbulent mixing of hot products and cold reactants.Further comparative analysis on DDT characteristics of cross-section abrupt tube with different annular gap lengths shows that different mechanisms dominate in the single tube zone.The conclusions in present study support the cross-section abrupt tube as a means to enhance DDT and provide an alternative potential in practical pre-detonation initiator and pulse detonation engine applications.

Insight into deformation allocation in the multi-pass roll forming of a double-walled brazed tube

Deformation allocation is an important factor that affects 720°curling forming from copper-coated steel strips to double-walled brazed tubes(DWBTs).In this study,four schemes of deformation allocation,considering different weights of the total feed distance,are proposed,and a 3D finite element(FE)model of the multi-pass roll forming process for DWBT is developed and verified to investigate the cross-sectional evolution and deformation features.The results show the following.(i)In the 720°curling forming process from the steel strip into double-walled tubes,the curvature of the formed circular arc initially increases and then remains stable with roll forming,and the inner and outer tubes of the DWBT are formed in the third and fifth forming passes.Size forming can eliminate the gap between the double walls and improve the overall roundness.(ii)For different deformation allocations,the cross-sectional profiles of the roll-formed parts exhibit a discrepancy,and the deformation amount varies with the roll-forming process.The deformation amount in Scheme three is the maximum,and the cross-sectional profile deviates significantly from the ideal shape and fails to form a DWBT,which indicates that the deformation allocation is unsuitable.(iii)The roundness of the outer tube is better than that of the inner tube.Therefore,the roundness of the inner tube is the key to restricting the forming accuracy of the DWBT.Compared with Schemes one and two,Scheme four with a linear allocation of the total feed distance exhibits the best roundness,and the deformation allocation is reasonable;i.e.,when the contact points between the rollers and steel strip are in a straight line,the roundness of the DWBT is in good agreement with the ideal condition.