Longitudinal Bending Deformation Research Articles

Bending deformation control in a laser-welded long straight structure by elastic pre-bending technique

Longitudinal bending deformation is the most typical mode of welding deformation in long-straight welded structures with asymmetric cross-sections. It is very critical for manufacturing accuracy to control the longitudinal bending deformation during the welding assembly stage. The objective of this study is to propose an elastic pre-bending technique to control the longitudinal bending deformation induced by welding heat input. Both numerical simulation technology and experimental method are employed to investigate the longitudinal bending deformation in a large-straight structure made of SUS304 stainless steel. In the current study, the effectiveness of the proposed elastic pre-bending method is verified by experiment. Simulation results show that the longitudinal bending deformation caused by welding could be reduced by >90 % by setting an appropriate value of pre-bending deformation. In addition, based on theoretical analysis and simulation results, the control mechanism of longitudinal bending deformation is clarified.

Analytical algorithm of longitudinal bending stiffness of shield tunnel considering longitudinal residual jacking force

Longitudinal bending stiffness is a fundamental parameter of shield tunnels, and its value directly affects the analysis of their longitudinal response. Existing studies have not considered the tensile stiffness of segment ring joints and longitudinal residual jacking force when determining the value of the longitudinal bending stiffness of an existing shield tunnel. Therefore, through theoretical analysis, this study considered the longitudinal bending deformation under an external load action as two parts, namely the longitudinal bending deformation of the homogeneous pipe and the longitudinal bending deformation induced by the opening of the segment ring joints. An analytical algorithm of the longitudinal bending stiffness of the shield tunnel was obtained, considering that this longitudinal bending stiffness was related to various factors such as the elastic modulus of the material of the segment ring, outer diameter of the shield tunnel, width of the segment ring, number of the segment ring joints and tensile stiffness of the connecting bolt. A scaled shield tunnel model that considered tensile stiffness of the segment ring joints and longitudinal residual jacking force was designed, and longitudinal bending stiffness tests of the model were conducted accordingly. The tests were designed to measure the longitudinal bending deformation and opening of the segment ring joints. The validation of the theoretical analysis result based on the test data demonstrates that the longitudinal residual jacking force could only reduce the longitudinal bending deformation and the opening of the segment ring joints at small loads, it had almost no effect under larger loads. The measured longitudinal bending stiffness of the shield tunnel model was generally consistent with that obtained using the theoretical algorithm. Thus, in the longitudinal response analysis of the shield tunnel, the effect of the longitudinal residual jacking force on the enhancement of the longitudinal bending stiffness need not be considered.

An enhanced analytical model for predicting the nonlinear longitudinal equivalent bending stiffness of shield tunnels incorporating combined N-M actions

The longitudinal equivalent bending stiffness (LEBS) is a key parameter of the longitudinal equivalent continuous model (LECM) of shield tunnels. When the incorporating combined actions of axial force and bending moment, i.e., N-M actions, is considered, the LEBS exhibits a significant nonlinearity. In this study, to reflect the actual action range of the circumferential joint and the coupling effect generated by the transverse and longitudinal performance of the shield tunnel, the impact factor of circumferential joint (λ) and the impact factor of transverse bending stiffness of the segmental lining (ψ) are introduced, and an enhanced analytical model for calculating the LBSE is proposed. Four types of longitudinal bending deformation modes of the shield tunnel are divided based on the contact state of circumferential joint and the corresponding neutral axis position. The LEBS of each mode is derived based on the strict elliptical integrals, and the load condition conditions to distinguish the different deformation modes are expressed. Then the performance of the proposed model is verified via the calibrated FEM model, available model tests, and other analytical models. Next, the influences of λ and ψ on the robustness of the proposed model are analyzed. Results show that there is a significant influence of ψ on the LBSE, especially the load combination is compression-bending, and λ also affects the LBSE significantly if λ ≤ 1.

An Investigation into the Effect of Rolling Reduction on 3D Curved Parts Rolling Process

Rolling technology based on arc-shaped rollers is a novel method for rapid manufacturing of 3D curved parts. The method uses a pair of arc-shaped rollers (a convex roller and a concave roller) as forming tools, forming an unevenly distributed roll gap. The sheet metal has both transverse bending and longitudinal uneven extension during rolling, so that surface parts with double curvature are processed. The curvature of the formed surface part can be changed by changing the rolling reduction. Changing the vertical distance between the rollers will cause the overall change of the roll gap height, which will inevitably have a great impact on the forming effect of formed 3D curved parts. In this paper, a finite element model and experiment with different rolling reductions was designed; the influence of rolling reduction on the bending deformation and shape accuracy of formed 3D curved parts was studied. The results show that, with the slight increase of rolling reduction (from 0.04 to 0.12 mm), the longitudinal bending deformation of the formed 3D curved part increases significantly, but its transversal bending is almost not affected. When the maximum rolling reduction is 0.04 and 0.06 mm (the corresponding minimum rolling reduction is less than or equal to zero), the shape accuracy of the formed 3D curved parts is not good enough; when the maximum rolling reduction is greater than 0.06 mm (the corresponding minimum rolling reduction is greater than zero), the shape accuracy of the formed 3D curved parts is significantly better. This indicates that, for the rolling of 3D curved parts based on arc-shaped rollers, ensuring that the minimum rolling reduction is greater than zero is the key to ensuring good shape accuracy of the formed 3D curved parts.

Effect of asymmetry forming technology on longitude curvature radius of 3D curved part in continuous flexible rolling process

Continuous flexible rolling is a novel plastic forming process for 3D curved parts. In this work, asymmetry forming technology was firstly applied in continuous flexible rolling process, which can effectively compensate the lack of longitude bending deformation caused by work hardening. In the process of asymmetry forming technology, by changing the relative longitude elongation between the tensile surface and compressive surface of the sheet metal, the adjusting of longitudinal bending deformation is achieved. In this paper, the finite element model with different friction ratio was designed; the effect of asymmetry forming technology on longitude curvature radius of 3D curved parts was studied. As results demonstrate that: When the friction ratio between the upper (compressive) and lower (tensile) surface are 0.2:0.2, 0.2:0.15, 0.2:0.10, 0.2:0.05 and 0.2:0.2, 0.15:0.2, 0.10:0.2, 0.05:0.2 in turn, the corresponding longitude curvature radiuses of convex curved parts are 226 mm, 236 mm, 254 mm, 272 mm and 226 mm, 219 mm, 207 mm, 199 mm in turn. When the friction ratio between the upper (tensile) and lower (compressive) surface are 0.2:0.2, 0.2:0.16, 0.2:0.12, 0.2:0.08 and 0.2:0.2, 0.16:0.2, 0.12:0.2, 0.08:0.2 in turn, the corresponding longitude curvature radius of saddle curved parts are 330 mm, 321 mm, 315 mm, 306 mm and 330 mm, 339 mm, 345 mm, 350 mm in turn. The longitude bending deformation of sheet metal can be effectively adjusted in the asymmetry forming technology, so the feasibility of this technology is verified.

Laser Welding Deformation Control of STS304 Cylindrical Steel Sheet Structure

Deformation that occurs during girth welding and seam welding of large-diameter STS304 thin plate structure changes the shape of the structure and affects the manufacturing of the next process. In order to control this deformation, the welding deformation generated during girth and seam laser welding was controlled by generating the relationship between the neutral axis and the welding position and initial tensile stress by the tensile force method. The deformation that occurs during girth welding is caused by angular distortion, and the amount of the deformation is affected by the neutral axis and the position of the weld. By changing the position of the welding part, welding deformation by up to 50% has been reduced. Deformation generated during seam welding caused by angular distortion and longitudinal bending deformation created an initial tensile residual stress in the weld, and the deformation was controlled by minimizing the constraint by welding heat stress generated during welding. At this time, when the magnitude of the initial tensile stress due to the external load increased to 50% of the yield stress of the base metal, the final deformation appeared close to zero. Key words: Thermal elastic-plastic analysis, STS304, Laser welding deformation, Initial stress, Elastic pre-straining method

Numerical simulation of bending deformation induced by multi-seam welding of a steel-pipe structure

Longitudinal bending deformation, often induced during gas metal arc welding of long pipe structures, plays a negative role in the accuracy of assembly, external appearance, and various strengths of welded pipe components. In this paper, an experimental and numerical study of pipe welding distortion is presented. A 3D thermo-elastic-plastic finite element model for multi-seam welds (composed of longitudinal (L-seam) and circumferential (C-seam) welds) of pipe components was developed to predict longitudinal bending deformation. The finite element method and experimental results demonstrate good agreement. Therefore, the proposed model can accurately predict welding distortions in multiseam welded pipe structures. Moreover, the results reveal clear distinctions between the longitudinal bending deformations induced by L-seam and C-seam welds due to different selfrestraint strengths. Finally, another characteristic, the bending angle, is analyzed. Linear and nonlinear relationships are observed between the sine of the bending angle and weld length for L-seam and C-seam welds, respectively.

4D pine scale: biomimetic 4D printed autonomous scale and flap structures capable of multi-phase movement.

We developed biomimetic hygro-responsive composite polymer scales inspired by the reversible shape-changes of Bhutan pine (Pinus wallichiana) cone seed scales. The synthetic kinematic response is made possible through novel four-dimensional (4D) printing techniques with anisotropic material use, namely copolymers with embedded cellulose fibrils and ABS polymer. Multi-phase motion like the subsequent transversal and longitudinal bending deformation during desiccation of a natural pinecone scale can be structurally programmed into such printed hygromorphs. Both the natural concept generator (Bhutan pinecone scale) and the biomimetic technical structure (4D printed scale) were comparatively investigated as to their displacement and strain over time via three-dimensional digital image correlation methods. Our bioinspired prototypes can be the basis for tailored autonomous and self-sufficient flap and scale structures performing complex consecutive motions for technical applications, e.g. in architecture and soft robotics. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Influences of welding parameters on axial force and deformations of micro pinless friction stir welding

0.5-mm-thick 7075-T6 aluminum alloy sheets were butt joined successfully by high-speed micro friction stir welding (μFSW) as well as conventional μFSW using a pinless tool. The influences of welding parameters on the axial force, residual stresses, and deformations were studied through experiments. Good surface morphology and defect-free joints were obtained by high-speed μFSW as well as conventional μFSW in a fixed rotational speed/welding speed of 6.67 rad/mm. The axial force during μFSW increased with the increment in welding speed and decreased with the increment in rotational speed. When the ratio of rotational speed/welding speed was 6.67 rad/mm, compared with conventional μFSW (2000/300), the lower axial force of 1460 N was obtained by using high-speed μFSW (10,000/1500). Longitudinal tensile residual stress and transverse compressive residual stress occurred around the weld zone for all μFSW joints. The residual stresses of joint fabricated by a parameter of 10,000/1500 were slightly less than that fabricated by 2000/300. Both longitudinal maximum bending deformation Zmax and transverse angular deformation α increased with the increment in rotational speed and decreased with the increment in welding speed. As a comparison to 2000/300, the welded sheet with a parameter of 10,000/1500 exhibited slightly lower Zmax and α.

Linear Distribution Principle for Sheet Forming Using Continuous Roll Forming Process

Continuous roll forming (CRF) process utilizes two reconfigurable rollers as forming tools to manufacture 3D surface part. In order to investigate the longitudinal deformation of 3D curved surface part, the detailed mathematical methodology using a geometrical relationship is analyzed and described. The results show that the necessary condition for generating longitudinal bending deformation is the linear distribution of the longitudinal fiber. The deformation characteristics of CRF studied by simulation confirm that the ideal longitudinal deformation is generated when the distribution of longitudinal fibers satisfy the linear distribution principle, the maximum length difference of longitudinal fibers is the major factor determining the longitudinal curvature radius of formed part, and increasing maximum length difference of longitudinal fibers incurs an increasing longitudinal curvature. In addition, 3D surface parts with different longitudinal curvature were prepared by CRF process, which had verified the proposed linear distribution principle.

Thermal Cycles and Deformation Characters During High-Speed Micro Friction Stir Welding Process of AA7075-T6 Sheets

Thermal cycles and deformations during high-speed micro friction stir welding (μFSW) under different welding conditions were studied by experimental methods. The results show that the peak temperature and elevated-temperature exposure time (t150) increased with the increasing of rotational speed and decreased with the increasing of welding speed. Increasing rotational speed or welding speed led to an increase in both heating and cooling rates. The joint fabricated by the pinless tool experienced a lower peak temperature, a shorter elevated-temperature exposure time, and a larger temperature gradient than that by the pin tool. The welded sheet presented an anti-saddle deformation character, with convex bending in a longitudinal direction and concave angular bending in a transverse direction. In comparison to the pin tool, the longitudinal maximum bending deformation, Zmax, of the joint fabricated by the pinless tool was reduced by 12.35%, and the transverse angular deformation, α, was reduced by 6.67%. In comparison to the steel backing plate, the Zmax of the joint produced using a copper backing plate was reduced by 40.66%, but the α was increased by 53.27%.

Effect of incremental multi-step technology on longitude bending of 3D curved part in continuous roll process

Continuous roll process based on sheet thickness reduction can effectively form 3D curved parts. In the forming process, work hardening is always an important factor for affecting thickness reduction of a rolled plate. In this paper, incremental multi-step forming technology is proposed for the first time, which is different from the previous multi-step forming technology, which only one set of roll gap is needed in the whole forming process. The forming process of convex and saddle curved parts is simulated, and the effect of incremental multi-step forming technology on longitude bending deformation is studied. The results show that in continuous roll process for a 3D curved part, roll gap distribution is uneven, so thickness reduction of the rolled plate is different along the roll gap. By maximizing the thickness difference between the middle and both sides of the rolled plate, the longitudinal bending deformation of the rolled plate is maximized. When the forming steps are one, two, three, and six, the longitude curvature radiuses of forming a convex curved part is 227 mm, 186 mm, 161 mm, and 154 mm in order, so the longitude bending deformation increase to 18%, 29%, and 32% in order; the longitude curvature radiuses of forming a saddle curved part is 239 mm, 185 mm, 167 mm, and 164 mm in order, so the longitude bending deformation increases to 23%, 30%, and 31% in order. Therefore, this technology is suitable for forming 3D curved parts with large bending deformation.

Research on flexible rolling process of three-dimensional surface part using auxiliary rolls

Flexible rolling is a sheet metal forming process used to rapidly manufacture three-dimensional (3D) surface parts for various industries. In this paper, a flexible rolling method of 3D surface parts using auxiliary rolls is introduced, and a forming mechanism of curved surface parts is described. The generation of instability of a convex surface part in the rolling process was analyzed, and the calculation for longitudinal bending deformation was deduced to obtain an effective design method for the roll gap shape. Numerical simulations and experimentation were performed for two rolling processes, with and without auxiliary rolls, for surface parts, for which the curvature distribution and dimensional accuracy were measured and analyzed. The simulation results show that the flexible rolling process with auxiliary rolls offers a more stable rolling process with smaller curvature fluctuation of the formed parts. The experimental results further verify that the process with auxiliary rolls is better than that without auxiliary rolls, as indicated by the shape error that can be controlled in a narrower range and the smaller error value of fluctuation. Overall, the proposed flexible rolling process with auxiliary rolls offers a feasible method to effectively form 3D surface parts with good forming quality and accuracy.

Preliminary seismic hazard assessment for the proposed Bohai Strait subsea tunnel based on scenario earthquake studies

In this paper we present a preliminary seismic hazard assessment for the proposed Bohai Strait subsea tunnel (BSST) based on scenario earthquakes in a strike-slip stress regime. We studied two scenarios: 1) a right-lateral, strike-slip faulting earthquake event with surface wave magnitude (Ms) 7.4 occurred on the north to northeast (NNE) oriented Tan-Lu fault zone (TLFZ) with a location about 100 km away from BSST (the far field); and 2) a left-lateral strike-slip event with magnitude Ms4.1 occurred in the direct vicinity to BSST (the near field) on the northwest to west (NWW) Zhangjiakou-Penglai fault zone (Zhang-Peng Fault Zone, or ZPFZ). Selections of these two scenario events are based on the characterization of the actual seismo-tectonic settings and representation of earthquake history in the Bohai region. We studied the impacts of these two scenario events on BSST in terms of longitudinal compression, bending, and tunnel cross-section's ovaling deformation. As a preliminary study, we excluded the analysis of formation-structure interaction and focused on the ground motion parameters expressed as the maximum displacement, the peak ground velocity (PGV) and peak ground acceleration (PGA) of the free seismic wave field surrounding the tunnel walls. This simplification is acceptable for the fact that BSST is planned to be constructed in the granite bedrock formation in which the inertial contrast between the formation and the structure is minimal. Seismic hazard assessment for tunnels is completely different from the assessment for above-ground buildings. It is also substantially different from assessment for tunnels built in soil formations, for which the formation (soil)-structure interaction evaluation is critical. We use semi-analytical approach for assessing the seismic impact of the far field, large event to BSST; whereas use the two-dimensional (2D) finite difference time domain (FDTD) numerical simulation technique for assessing the response of BSST to the seismic load of the near field, smaller event. The preliminary results suggest that 1) the impact of the low frequency, far field event has very subtle impact to BSST in terms of longitudinal compression, bending, and cross-section ovaling; and 2) the impact of the high-frequency, near field event has little impact to BSST in terms of longitudinal compression and bending; while has a measurable impact to cross-section ovaling. However, this kind of deformation is within the limit of tolerance under earthquake-resistant design. Over all, the seismic risk posed by regional large earthquakes and local small events to BSST is within allowable risk threshold and manageable with the enforcement of earthquake resistant code.

Influence of a multi-step process on the thickness reduction error of sheet metal in a flexible rolling process

Flexible rolling is a forming process based on thickness reduction, and the precision of thickness reduction is the key factor affecting bending deformation. The major purpose of the present work is to solve the problem of bending deformation error caused by insufficient thickness reduction. Under the condition of different rolling reductions with the same sheet thickness and the same thickness reduction with different sheet thicknesses, the thickness reduction error of sheet metal is analyzed. In addition, the bending deformation of sheet metal under the same conditions is discussed and the influence of the multi-step forming process on the thickness reduction error is studied. The results show that, under the condition of the same sheet thickness, the thickness reduction error increases with increasing rolling reduction because of an increase in work hardening. As rolling reduction increases, the longitudinal bending deformation decreases because of the decrease of the maximum thickness difference. Under the condition with the same thickness reduction, the thickness reduction error increases because of the decrease of the rolling force with increasing sheet thickness. As the sheet thickness increases, the longitudinal bending deformation increases because of the increase in the maximum thickness difference. A larger bending deformation is divided into a number of small bending deformations in a multi-step forming process, avoiding a sharp increase in the degree of work hardening; the thickness reduction error is effectively reduced in the multi-step forming process. Numerical simulation results agree with the results of the forming experiments.

Research on flexible asymmetric rolling process for three-dimensional surface parts

To realize rapid fabrication of three-dimensional surface parts, flexible asymmetric rolling process for continuously forming surface parts is developed. This process employs an auxiliary roll, a pair of upper and lowers bendable rolls as forming tools. By adjusting the height of the auxiliary roll, the sheet metal is inclined before non-uniform rolling, which is conducive to longitudinal bending deformation of the sheet metal after rolling. Meanwhile, the non-uniform thickness reduction of the sheet metal caused by the non-uniform roll gap between the upper and lower rolls makes itself bend in the transverse and longitudinal directions. Owing to small bending behavior of the bendable roll in the experiment, the forming precisions of formed parts are not ideal by the 3D rolling process without the auxiliary roll. In this paper, the flexible asymmetric rolling process is introduced to improve the 3D rolling process for surface parts with well forming precisions. An auxiliary roll is employed in the flexible asymmetric rolling process except a pair of upper and lower rolls. The formation mechanism of the curved surface is set forth, and the parametric equations of the formed surface in flexible asymmetric rolling process are derived. Typically simulations and experiments for forming spherical and saddle surfaces have been performed. The dimensional accuracies of the forming parts are measured, and the differences of the 3D rolling and flexible asymmetric rolling processes are investigated though numerical simulations. The forming results with good dimensional accuracies show that the flexible asymmetric rolling process is feasible for manufacturing three-dimensional surface parts with a broader range.

Analysis of continuous roll forming for manufacturing 3D surface part with lateral bending deformation

Continuous roll forming (CRF) is a novel technology for both single-piece and small-batch manufacturing of 3D surface sheet metal parts. In the CRF process, a pair of flexible rolls is placed to form a non-uniform roll gap. When the flexible rolls rotate in opposite directions with identical angular velocity, the sheet metal is bitten into the roll gap by frictional force, and the sheet metal is non-uniformly thinned in thickness direction and elongated in longitudinal direction. Thus, a 3D surface part with a desired shape is manufactured consecutively. In this paper, CRF is further developed and expanded into LB-CRF, which enables the CRF process to manufacture 3D surface parts not only with transverse and longitudinal bending deformation but also with lateral bending deformation (LB-CRF). The methods to design the curved profiles of flexible rolls and the distribution of the roll gap are provided. Through a series of numerical simulations on the LB-CRF processes, the proposed design methods are verified. The relationship between the distribution of the roll gap and radius of lateral bending curvature is discussed. The LB-CRF processes were presented through experiments, and the results validate the feasibility of adopting the LB-CRF process to manufacture 3D surface part with lateral bending.

수치해석모델을 이용한 강판재의 종굽힘 용접변형 생성기구의 해석

용접변형이란 용접열원에 의해 구조물에 생성되는 불균일 온도분포에 의해서 발생하는 영구적인 변형이다. 용접변형은 용접구조물의 강도와 외관 및 치수 정밀도를 저하시킴으로써 생산성 저하의 주원인이 되기도 하며, 이러한 용접변형을 제어하기 위해 많은 실험과 연구가 수행되었다. 본 논문은 용접시 발생되는 변형 중에 하나인 종굽힘에 대하여 실험과 수치적 해석결과를 통해 비교 및 분석하였으며, 이를 통해 종굽힘 용접변형의 생성기구에 대하여 연구한 것이다. 용접실험은 4, 8.5 mm 두께의 평판에 대해 실시하였으며, 수치적 해석은 MSC.marc 상용프로그램을 사용하였다.

Longitudinal bending deformation analysis of sheet metal in continuous roll forming process

Development of flexible forming is crucial for manufacturing three-dimensional sheet metal parts. In this paper, continuous roll forming (CRF) is investigated to improve the forming results, especially for doubly curved parts. The CRF process employs an upper flexible roll and a lower flexible roll as a forming tool, and the different forming shapes are achieved by controlling and adjusting the distribution of the roll gap between two rolls. This paper is focused on analysis of the longitudinal bending deformation in CRF process, the plane assumption for longitudinal bending analysis is discussed, and the formulation to calculate the longitudinal strain distributed over the cross-section is derived. Through a series of numerical simulation on CRF processes, the validity of the plane assumption and the other theoretical models to analyze the deformation in CRF are confirmed; the relationship between longitudinal elongation distribution and longitudinal bending deformation is discussed and the strain distribution in transverse, longitudinal, and thickness directions is presented. In addition, the CRF experiments on saddle-shaped and torus-shaped parts were carried out, and the theoretical analysis and simulation results are verified by experiments.

Modal Analysis Calculation and Simulation of Ramming Chain

In order to solve a problem that the running of ramming chain is unstable and master each order natural frequency and deformation characteristics of the chain, the method of theoretical calculation and finite element analysis with software ANSYS is used on the natural frequency of the calculation and analysis. By comparing the data obtained from two methods to verify the correctness of the finite element model, the model is used to analyze natural frequencies and corresponding vibration mode of the ramming chain. The results show that under the low order natural frequency, the main deformation of the ramming chain is the lateral bending, longitudinal bending and torsion deformation, so the results provide the basis to master the deformation of the chain.