Six-axis free bending and twisting analysis of spiral square tube

Highlights

• Numerical modeling established for six-axis free bending and twisting (6FBT) process.

• A new analytical model for 6FBT of square tube spiral components.

• Wall thickness distribution and section deformation law of square tube during 6FBT process.

Abstract

Six-axis free bending and twisting (6FBT) technology enables the integral forming of square tube components with complex shapes. However, the process analysis method and the deformation behavior of square tube spiral components in the bending and twisting process have not been investigated. In this paper, an analytical model of the bending die trajectory suitable for one-time forming of square tube spiral components is proposed and verified by FE simulations and experiments. In this model, the bending direction of the component axis is changed continuously by adding an additional cross section torsion angle in the bending process of the square tube, and then the spiral member is formed. This paper further reveals the laws of stress, strain, wall thickness distribution and cross section distortion of 304 stainless steel square tube spiral components in the 6FBT process. The results show that during the forming process, the equivalent stress on the edge of the square tube is greater than that on the surface, the wall thickness reduction on each cross section only occurs on the outside of the bent, and the section distortion between the inside and outside of the bent is larger than that between the inside and outside of the twist.

Introduction

Thin-walled stainless steel square tube bending components are widely used in the fuselage load-bearing members of vehicles, ships, construction machinery, environmental control pipeline systems of aerospace equipment, buildings, outdoor sculptures and other facilities because of their advantages of light weight, high strength, large section modulus, good surface decoration and corrosion resistance [1], [2], [3], [4], [5]. However, due to the structural particularity of the hollow and thin wall of the square tube, the stress state of the inner and outer wall of the square tube is complex during bending, and defects such as wrinkling, tension crack, section distortion and springback are prone to occur, which increases the difficulty of manufacturing complex square tube bending components [6], [7], [8], [9], [10].

During the past few decades, many scholars have developed a series of methods and rules to assist in manufacturing high-quality square tube bending components [11], [12], [13], [14]. Zhu et al. proposed a new type of PVC mandrel with 1.5 plastic hardening treatments to reduce the cross section sag of an H96 square bent tube, and the springback angle was reduced by the core-pulling process [15,16]. Through simulations and experiments, Liu and Liu found that the retraction of the mandrel can make the cross section distortion more uniform during the bending of a double-ridged rectangular tube [17]. Liao et al. analyzed the influence of different constitutive models on the torsional springback of asymmetric aluminum square tubes during rotary draw bending, and revealed the law of stress distribution in different forming stages [18]. By analyzing the deformation behavior of square tubes during roll forming, Shim et al. introduced a two-stage forming method, which adjusted the shrinkage load to reduce axial wrinkling and strength, and determined the critical prebending radius to minimize the cross section distortion of square tubes [19]. Ma and Welo designed and manufactured a new flexible rotary stretch bending machine that can manufacture square tube profiles with different curvatures with relatively low die cost, and put forward an analytical framework for springback evaluation in the process of stretching-controlled bending [20,21]. Through orthogonal experiments and range analysis, Shi et al. studied the influence of process parameters on web thickness in the flexible multi-point three-dimensional tensile bending process of rectangular profiles, and obtained the optimal process parameters to minimize the thickness of the inner and outer webs [22]. Cai et al. investigated the influence of different mandrel parameters on the minimum bending radius and forming quality in the local induction heating bending of ultrahigh strength square tubes with variable curvature, and obtained the best forming parameters by deducing the reference formula for the optimization of mandrel parameters [23].

At present, to achieve a reasonable layout of key load-bearing components in the equipment and the requirement of close fitting with other curved sheet metal parts, stainless steel square tube components with spiral axis characteristics and sections twisted along the bending direction have attracted extensive attention [24], [25], [26], [27]. However, the traditional bending processes involved in the above research, such as rotary draw bending, roll bending and stretch bending, are only suitable for the forming of plane square tube bending components, and there are some limitations for the bending of complex spatial square tube components [28], [29], [30]. As a flexible forming technology based on bending die trajectory control, the outstanding advantages in the integral forming of complex bending parts are possessed by 3D free bending technology [31], [32], [33], [34]. The research work of complex spatial bending components is mainly focused on the 3D free bending of circular tubes [35], [36], [37]. Neugebauer et al. developed a "Hexabend" system controlled by six separate hydraulic columns, which is suitable for complex axis tube forming. They also described the specific process of finite element modeling in detail and proved that the shell element used to simulate the process is sufficiently accurate [38]. Based on the three-roll-push free bending process, Groth et al. proposed an algorithm that can determine the typical bending characteristics and quantitatively describe the transition zone along the curvature [39,40]. Merklein-Group and Plettke and Groth introduced a geometry model to describe curvature and alike of freeform-bend tubes [41,42]. Guo et al. established the mathematical model of the U-R relation-ship by analyzing the motion track of the bending die, and the spatial bending components were formed through simulation and experiment [43]. Wang et al. proposed a new theoretical model for the free bending spiral tube, and the accuracy and reliability of the model were verified by finite element simulations and experiments [44]. Zhang et al. proposed a method to obtain the optimal free bending parameters of spatially complex bent tubes by establishing a database of process parameters of stable forming sections and transition sections [45]. A new springback comprehensive control strategy in the process of forming a complex three-dimensional tube was deduced by Wu amd Zhang, which effectively reduces the difficulty of parameter determination [46]. In order to obtain higher forming accuracy, Wang et al. proposed the springback prediction and compenzation method for curved metal tubes with variable curvature considering cross section deformation, which was verified by forming spiral components [47]. Li et al. revealed the 3D free bending mechanism of involute parts through theoretical modeling and finite element simulation [48]. In the research of six-axis free bending of complex circular tube components, a correlation scheme based on hardness was developed by Stebner et al. to predict the residual stress, local strength and strain in the forming process [49].

In addition, a few researchers have recently begun to study the free bending of square tubes. The Tekkaya team designed a new torque superposed spatial (TSS) bending process, and Chatti et al. studied the deformation mechanism and process analysis of square tube forming [50]. A model for judging the validity of bending parameters was established by Hudovernik et al., and the influence of the stress–strain state and bending direction changes of components on bending were investigated by means of finite element simulation and experiment [51,52]. By setting up a comprehensive analytical process model, Staupendahl and Tekkaya revealed the influence of various stresses in the forming zone on the bending moment and springback [53,54]. Cheng et al. discussed the influence of different parameters on the deformation behavior of rectangular tubes by finite element simulation [55,56]. Hashemi and Niknam investigated the influence of key parameters on the forming quality of rectangular copper tubes during free bending [57]. The influence of accumulated plastic strain, hardening and residual stress on the bearing capacity of square tubes during compound free bending was analyzed by Ancellotti et al. [58]. Nevertheless, most of these studies were based on TSS equipment or free bending equipment with passive bending die, while the research on free bending and twisting equipment with six degrees of freedom (6FBT) has not been involved, and the analytical method of process parameters of complex shape components in 6FBT process is not clear. Meanwhile, the deformation behavior of square tubes under the combined action of bending and torsion in the forming process is not explicit, which leads to the lack of effective guidance in the actual production process.

Thus, in this investigation, the forming process of 304 stainless steel thin-walled square tubes with spiral axis characteristics was studied by means of finite element simulation and experiments combined with 6FBT technology. A theoretical model for describing and analyzing the forming process of spiral square tube components was established, and the accuracy of the proposed model was verified by finite element simulation and experiments. Furthermore, the law of stress and strain, cross section distortion and wall thickness distribution in the forming process were also discussed.