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To manufacture the large-expansion-ratio double-stepped tube without thinning, a new approach known as multistage axial hydro-forging sequence has been proposed in this study. The whole forming process is divided into five stages. Compared with traditional tube hydroforming, the thickness can be increased by axial compression deformation to reduce the thinning ratio and enhance the forming capacity of the tube in hydro-forging stage and double-stepped hydro-forging stage, respectively. The proposed multistage axial hydro-forging sequence process was implemented by experiments along with the finite element simulation to validate its feasibility. The suitable loading path to prevent defects such as wrinkle and thinning was discussed. The results showed that double-stepped tube with large expansion ratio can be produced successfully with movable dies' design. There is no thinning in the final tube, particularly in all stepped area, and a better thickness distribution could be achieved. As a result, the proposed multistage axial hydro-forging sequence can be a feasible forming approach for the fabrication of large-expansion-ratio double-stepped tubes with high reliability. [ABSTRACT FROM AUTHOR]

In this paper, the advantages of numerical simulation to improve the process of copper electroforming are demonstrated. In this regard, the finite element model of copper electroforming for a rotating cone electrode was first prepared and then, the effect of the key parameters, such as applied current density, solution conductivity, electrode spacing, and anode height, on the uniformity of the thickness was investigated. The model combines tertiary current distribution with Bulter–Volmer electrode kinetics and computational fluid dynamics at the turbulent condition. In order to validate the model, a cone‐shaped shell was produced by electroforming method in the laboratory. The obtained results illustrate that the tertiary current distribution model on the rotating cone cell cathode is accurate and efficient for the electroforming process simulation and it can be used for parametric studies. Moreover, the effect of the current density on the morphology and properties of the electroformed layer was investigated. [ABSTRACT FROM AUTHOR]

Micro deep drawing of metallic cups is a cost effective technique if the parameters are suitably identified, but reducing dimensions increases the difficulties in manufacturing. In this work, formability study of pure copper foils and thickness distribution in micro deep drawing are carried out. The pure copper C1100 foil thickness of 100, 200 and 300 µm is selected and the limit drawing ratio is determined. In order to determine the forming depth in micro scale and force required in formed parts, a micro deep drawing tool assembly is developed. The results shows that 300 μm foil exhibits good formability in tensile test and Ericson cupping test. The excessive reduction in thickness specifically at the cup shoulder corner and the upper part of the side wall is located. The thinning is identified maximum at the side wall of the cup along the transverse direction. The results indicate that copper micro cups with high quality can be efficiently produced with appropriate forming parameters. [ABSTRACT FROM AUTHOR]

This study investigated an influence of the temperature field on thickness distribution of thermoformed products using complex and high-aspect-ratio mold. The optimum temperature field was obtained to achieve a more uniform thickness distribution in the thermoformed products by using finite element simulation. The material properties of acrylonitrile-butadiene-styrene (ABS) polymer sheet were obtained by two rheological measurement tests. The linear viscoelastic properties, such as the storage modulus and loss modulus, were measured by a small amplitude oscillatory shear (SAOS) test for wide ranges of frequency and temperature. The discrete relaxation time and discrete relaxation modulus were obtained by nonlinear regression. The fitting parameters C1 and C2 for the WLF model were obtained by curve fitting. The nonlinear viscoelastic property, such as stress relaxation modulus, was measured by a step strain test. The damping function and fitting parameter α of Wagner-Demarmels (WD) model were determined by curve fitting. Then, the Kaye–Bernstein-Kearsley-Zapas (K-BKZ) constitutive equation was utilized to the thermoforming simulation in order to investigate the material behavior of the polymer sheet. The numerical results showed that a more uniform thickness distribution could be achieved with the optimum temperature field of the sheet. The thinnest part of the products was improved by more than 30%. [ABSTRACT FROM AUTHOR]

In this paper, formability of dissimilar friction stir welded AA 6061 and AA 5083 blanks during single point incremental forming (SPIF) is investigated numerically and experimentally. Sheets from AA6061, AA5083 and FSWed AA6061 to AA5083 are formed by SPIF with different cone angles, and the limiting wall angles are determined. Additionally, the effects of SPIF and FSW processes on the microstructure, mechanical properties and fracture mode are investigated. The empirical results demonstrate that the formability of dissimilar FSWed sheets are not so much different from that of the base metal sheets. Dissimilar FSWed specimen is fractured from the AA 6061 base metal and far from the FSWed region. Although investigation of the fracture surfaces of the tensile tests shows a ductile fracture for AA 5083, AA 6061 and dissimilar FSWed sheets, it is a combination of ductile and brittle fracture after the SPIF. Furthermore, the SPIF of FSWed sheets is simulated numerically using the ABAQUS/Explicit. The results show that the thickness and the major strain have uniform distributions for both FSWed and base metal sheets. On the other hand, minor strain has a non-uniform distribution in the wall of the formed conical part of the FSWed sheet, despite the base metal sheets. [ABSTRACT FROM AUTHOR]

The conventional method cannot explicitly confirm the location and type of the energy loss, therefore this paper employs the entropy production theory to systematically analyze the category, magnitude and location of hydraulic loss under different blade thickness distribution. Based on the analysis, the turbulent entropy and viscosity entropy produced by the separation of boundary layer at the trialing edge are major factors leading to the hydraulic loss. In addition, the separation of the boundary layer can not only cause the energy loss, but also block the passage of the impeller and reduce the expelling coefficient of the blade. Therefore, the hydraulic performance of the blades with increment thickness distribution is obviously better than the decrement one. Further, the flow rate has different influence on the three types of entropy production. Meanwhile, the pressure pulsation on the working surface was investigated. It was concluded that with flow rates increasing, the amplitude of pressure pulsation firstly decreases and then smoothly improves, and reaches the minimum under design flow rate. Finally, the optimal blade was obtained, and the relevant hydraulic performance test was performed to benchmark the simulation result. This research can provide the theoretical reference for designing the reasonable thickness distribution of the blades. [ABSTRACT FROM AUTHOR]

We have derived an analytic form of the thickness redistribution function, Ψ, and compressive strength of sea ice using variational principles. By using the technique of coarse‐graining vertical sea ice deformation, or ridging, in the momentum equation of the pack, we isolate frictional energy loss from potential energy gain in the collision of floes. The method accounts for macroporosity of ridge rubble, ϕR, and by including this in the state space of the pack, we expand the sea ice thickness distribution, g(h), to a bivariate distribution, g(h,ϕR). The effect of macroporosity is for the first time included in the large‐scale mass conservation and momentum equations of frozen oceans. We make assumptions that have simplified the problem, such as treating sea ice as a granular material in ridges, and assuming that bending moments associated with ridging are perturbations around an isostatic state. Regardless of these simplifications, the coarse‐grained ridge model is highly predictive of macroporosity and ridge shape. By ensuring that vertical sea ice deformation observes a variational principle both at the scale of individual ridges and over the pack as a whole, we can predict distributions of ridge shapes using equations that can be solved in Earth system models. Our method also offers the possibility of more accurate derivations of sea ice thickness from ice freeboard measured by space‐borne altimeters over polar oceans. Key Points: We present a framework for sea ice ridging using variational calculusThe new framework accounts for the macroporosity of ice ridges and the nonconservation of energy in ridge formationFrom the statistics of individual ridges, we derive the evolution of the sea ice thickness distribution for the entire pack [ABSTRACT FROM AUTHOR]

A cylindrical deep drawing test was conducted for the purpose of improving the drawability, product accuracy, and quality in warm deep drawing using a superplastic material with large strain rate dependence. Then, the effects of blank holding force (BHF) and punch speed (SPD) on the flange wrinkle behavior and wall thickness distribution were investigated by experiments and theoretical analysis. A Zn-22Al-0.5Cu-0.01Mg alloy superplastic material SPZ2 with a sheet thickness of 1 mm was employed as the experimental material, and a cylindrical deep drawing experiment with the drawing ratio (DR) of 3.1 and 5 was performed at 250 °C. A good agreement was qualitatively obtained between the elementary theory on the flange wrinkle limit, the fracture limit, and the experimental results. In addition, the authors examined each variable BHF and SPD method obtained from the theory and experimentally demonstrated that the variable BHF method has a great effect on uniform wall thickness distribution and that variable SPD has a great effect on shortening the processing time for superplastic materials. Furthermore, the authors demonstrated the effectiveness of the variable BHF/SPD deep drawing method that varies both BHF and SPD simultaneously.

Industry 4.0 aims to digitalize the manufacturing process to increase the productivity and the product quality of plants. A fundamental aspect of the digitalized manufacturing processes is the simulation of the manufacturing process in order to develop its virtual representation, known as digital twin, whose purposes may be monitoring, and control. Algorithms to elaborate the simulated data in order to improve the control of the manufacturing process are very important and they need to be developed. Sheet metal forming is a widely used process to manufacture parts with a high production rate and a low cost. The thinning of the stretched sheet needs to be controlled in detail, because it is strongly connected with the product quality. This work presents a simulation model and a geometric algorithm to evaluate the thickness distribution of a sheet stretched through a forming process. In order to accurately evaluate the thickness trend, a geometric algorithm was proposed which, on the basis of the position of the nodes of the internal and external surface of the sheet, was able to evaluate the thickness value. It enables finding of the minimum value of the stretched sheet thickness. The geometric algorithm was slightly modified, in a second step of the work, to experimentally evaluate the thickness trend of a sheet stretched by a forming process; it was applied to the measurement points obtained through a coordinate measurement machine on the inner and outer surfaces of the sheet. The numerical–experimental comparison of the results shows the appropriateness of the proposed algorithm for numerical data.

In this study, we propose a parameter-free optimization method to control time-dependent responses of a shell structure, where the optimal thickness distribution is determined without design parameterization. The design objective is to minimize the vibration displacements or to control the dynamic responses at arbitrary domains and times for an arbitrary time-dependent loading under the volume constraint. The unsteady optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions with respect to the thickness variation are derived based on the variational method, Lagrange multiplier method and the adjoint variable method. The derived sensitivity function is applied to the H1 gradient method with Poisson's equation, a gradient method in the function space newly proposed in this study to determine the optimal variation of the thickness distribution. With the proposed method, the optimal thickness distribution for time-dependent response problems such as a forced-vibration, a free-vibration or a transient response is obtained while minimizing the objective functional and maintaining the smooth thickness distribution of a shell structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are demonstrated to show the effectiveness of the proposed method, and the results are discussed.

n this paper a finite element model has been proposed for evaluation of primary and secondary current density values on the cathode surface in nickel electroplating operation of a revolving part. In addition, the capability of presented electroplating simulation has been investigated in order to describe the electroplated thickness of the nickel sulfate solution. Nickel electroplating experiments have been carried out. A good agreement between the simulated and experimental results was found. Also the results showed that primary current density can describe the general form of thickness distribution but the relative value of current density using secondary current density can present better description of thickness distribution

Due to the internal flow field is unstable under part-load condition, which has great influence on the structure strength of impeller. Therefore, in order to improve the operation stability, four different thickness distribution blades were proposed, the energy performance, internal flow field and structural dynamic characteristics under 0.2 Q were investigated based on the CFX and Workbench. The results show that the natural frequency is increased by thickening the blade, and the natural frequency of the blade with decrement thickness distribution is larger than the increment one. However, the equivalent stress of the local thickening blade is much lower than uniform thickness blade, that is, the internal flow field and strength of the impeller can be obviously improved by employing the increment thickness distribution. Finally, the test of the blade with increment thickness distribution was conducted to benchmark the accuracy of the simulation. This research could provide reference to the improvement of blade strength characteristics under the part-load condition. [ABSTRACT FROM AUTHOR]

A combination method of beneficial wrinkle and preform shape is proposed to solve the problem of non-uniform thickness distribution during hydroforming of a variable diameter tubular component. The effect of loading path for the hydroform part and the preform shape are simulated by LS-DYNA. At the same time, the wall thickness deviation of the maximum and minimum of the hydroformed part is considered as the optimal target and the loading path for the preform shape is optimized to obtain the beneficial wrinkles by response surface methodology. Simultaneously, hydroforming experiments were conducted to verify the simulation results. Study shows that the loading path plays an important role in the forming of the beneficial wrinkles, which influence the cracking and the wrinkling defects. Only the loading path is appropriate can the beneficial wrinkles be formed and the wrinkles are flattened in the subsequent calibrating process. Response surface methodology is an effective way to obtain the optimal loading path, and the desired loading path can be achieved by controlling the relationship of the axial feeding and the internal pressure. [ABSTRACT FROM AUTHOR]

Abstract Attributes of gypsum vein arrays in the Triassic massive mudstones of SW England were analyzed to infer the process of vein network evolution. Field data demonstrate that there is no clear correlation between vein orientation and thickness; however, sub-horizontal veins have a higher average thickness than the inclined veins. Vein thickness distribution is best characterized by a log-normal distribution. The fractal dimensions ' D ' of vein networks analyzed range from 1.44 to 1.71. Vein networks, which contain abundant bridging veins between neighbouring sub-horizontal veins to form an anastomosing pattern, exhibit a higher D value. The fraction of vein volume derived from image analysis ranges from 6.75 to 17.94%. A positive correlation is revealed by plotting the fractal dimensions of the vein networks versus the number of vein-intersection points, suggesting that an anti-clustering distribution of veins could contribute to more interactions and also intersections of the gypsum veins. The vein attribute data presented indicate that mineralization in the massive mudstones is mainly localized to some of the largest veins as a result of mechanical interaction of neighbouring veins during vein propagation, hindering the nucleation of new veins as a consequence. Accommodation of the bulk rock strain could be facilitated mainly by expansion of the large, backbone veins, which follow a positive feedback mechanism of growth. This study reveals a strong link between the geometric parameters of opening-mode fractures with the history of their formation, propagation and intersection. Highlights • We analyzed multiple attributes of gypsum veins in mudstones to infer vein network evolution. • Vein thickness follows a log-normal distribution. • The anti-clustering vein distribution leads to more vein intersections. • Mineral precipitation is localized to the largest veins due to mechanical interaction. [ABSTRACT FROM AUTHOR]

Abstract A comprehensive performance of formed parts by AA7075-O sheets was studied in friction stir incremental forming (FSIF). Various tool rotation speeds were set to form two typical parts (truncated funnel and pyramid frustum). The formability, surface quality, tensile strength, micro-hardness and thickness distribution of the formed parts were investigated. Results show that the formability generally increases as tool rotation speeds increase. On the contact surface, variation trends of the surface roughness are different in horizontal direction (parallel to tool path) and vertical direction (perpendicular to tool path). However, the surface roughness on the non-contact surface is almost not affected by tool rotation speed. Furthermore, mechanical properties including tensile strength and surface micro-hardness in formed parts are obviously enhanced compared to those of the initial sheet, of which the hardness values begin to fall down gradually after rotation speed reaches 3000 r/min. As for thickness measurement, more uniform thickness distribution of formed parts can be obtained at relative high tool rotation speeds. In general, parts formed at high rotation speed have a better comprehensive performance except the mechanical property. [ABSTRACT FROM AUTHOR]

Sheet metal stretching is one of the most frequently applied sheets forming operation in the industry. Hole flanging is a common sheet forming operation to produce structural sheet metal components. Flanges are used for appearance, rigidity, hidden joints, and strengthening of the edge of sheet metal parts. Trial-end-error is the most common approach for tooling and process design in flanging operations. This paper presents some experimental results of hole-flanging process performed on flat deep drawing steel sheets with circular hole drilled or punched in the centre of blank. Three punches of different geometry i.e. cylindrical, hemispherical and conical were used in this experiment. The effect of both the punch geometry and material mechanical parameters (especially strain hardening and plastic anisotropy) on the limit expansion of the hole, limit strain dependence on hole performing technology as well as sheet thickness distribution along collar formed was determined. [ABSTRACT FROM AUTHOR]

Multi-Point Incremental Forming (MPIF) process is a new hybrid process that combines two common manufacturing methods. These are Multipoint Forming (MPF) and Incremental Sheet Forming (ISF) processes. In this study, an experimental set-up, based on a MP reconfigurable die, was designed and manufactured to explore the flexibility of this innovative process and its potentialities to produce complex parts using the same tools. The obtained results have indicated that this novel technique, that doesn’t require costly equipments, is an effective approach to manufacture multitude of parts with different shapes. Moreover, it has been shown that the parts geometrical accuracy as well as thickness distribution are enhanced compared to the conventional ISF process and that the geometrical defects, called ‘dimples’ and caused by the pins’ ends, are significantly reduced and almost eliminated after the insertion of a rubber piece between the reconfigurable die and the blank sheet. On the other hand, the effect of the size and geometry of the rectangular pins on the geometrical accuracy and the dimpling defect has been studied using a finite element analysis. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering for Thermal Energy & Power / Reneng Dongli Gongcheng is the property of Journal of Engineering for Thermal Energy & Power and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the effects of structural properties distributions on the sound radiation of a thin elastic airfoil. Focusing on flapping-flight in a high-Reynolds and low-Mach regime, we seek optimal conditions to mitigate flapping-sound while maintaining aerodynamic efficiency. The airfoil is immersed in a two-dimensional potential flow field, and is subjected to leading-edge actuation in the form of a small-amplitude periodic heaving motion. The near-field dynamics is governed by Euler-Bernoulli's beam equation of motion and analyzed using thin airfoil theory in conjunction with a discrete-vortex wake model. The near-field results are introduced as an effective dipole-type source term to the right-hand-side of the Powell-Howe acoustic wave equation, and the associated far-field sound is calculated using Green's function formulation. Considering the elastic flapping configuration, we seek optimal material properties and a linear thickness distribution to reduce the sound of an otherwise rigid airfoil while retaining the lift amplitude of the rigid configuration. To this end, the aeroacoustic model is introduced into an optimization scheme, where minimal sound amplitude is sought in the lift direction, subjected to the aforementioned lift force constraint with a 33% assigned tolerance value. The relatively wide tolerance produces in turn an effective Pareto front, reflecting the trade-off between the competing objectives of lower sound levels and aerodynamic efficiency. Compared with the rigid heaving airfoil, over 10 [dB] sound reduction was obtained for the optimal flexible configuration producing the same lift amplitude. The Pareto front also displays a linear relation between sound reduction ratio and lift amplitude ratio, indicating a further substantial sound reduction of up to 30 [dB] for smaller lift ratio values. The effect of optimal structure thickness distribution on the equi-lift sound reduction mechanism is two-fold: The motion and wake dipoles are shifted to an antiphased mode thus reducing the total sound signal, and the motion dipole which represents the unsteady forces, exerted by the airfoil on the fluid while transversing, is fixed in magnitude, thus retaining the lift amplitude value. The system dynamics leading to the opposing sound dipoles is evoked by phase-locking the airfoil motion and circulation, and following Kelvin's theorem, antiphase-locking the airfoil motion and wake circulation. Implications on flapping flags and streamers is briefly discussed as well. [ABSTRACT FROM AUTHOR]

Optimization of thin film uniformity is an important aspect for large-area coatings, particularly for optical coatings where error tolerances can be of the order of nanometers. Physical vapor deposition is a widely used technique for producing thin films. Applications include anti-reflection coatings, photovoltaics etc. This paper reviews the methods and simulations used for improving thin film uniformity in physical vapor deposition (both evaporation and sputtering), covering characteristic aspects of emission from material sources, projection/mask effects on film thickness distribution, as well as geometric and rotational influences from apparatus configurations. Following the review, a new program for modelling and simulating thin film uniformity for physical vapor deposition was developed using MathCAD. Results from the program were then compared with both known theoretical analytical equations of thickness distribution and experimental data, and found to be in good agreement. A mask for optimizing thin film thickness distribution designed using the program was shown to improve thickness uniformity from ±4% to ±0.56%. [ABSTRACT FROM AUTHOR]

The main objective of this study is to investigate the effect of process parameters on maximum formable wall angle in incremental forming of 0.5 mm thickness extra deep drawing steel sheets. For this purpose, four important process parameters namely, tool diameter (A), feed rate (B), part geometry (C) and step depth (D) have been correlated with maximum wall angle. Experiments have been conducted on CNC milling machine in accordance with Taguchi L9 orthogonal array. The statistical methods, signal to noise (S/N) ratio and Pareto ANOVA have been used to find out the optimum process settings and percentage of contribution of different process parameters on maximum wall angle. A linear regression model was also proposed to predict the wall angle as a function of process parameters. Based on the studies, the optimum conditions were found to be A1B2C1D1 (A = 6 mm, B = 1500 mm/min, C = VWACF, and D = 0.7 mm). It was also found that the tool diameter has significant effect on maximum wall angle followed by feed rate, shape and step depth. Furthermore, wall thickness distribution of formed parts under different process conditions has been studied through experiments and finite element simulations using LS-DYNA. A good correlation was found between experimental results and numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the single point incremental forming (SPIF) of friction stir welded (FSWed) 5083 aluminum alloy sheets are investigated experimentally and numerically. The aluminum sheets with 2mm thickness are friction stir welded with the same FSW parameters. In order to obtain the effect of FSW on the formability of SPIF, the base sheets and FSWed sheets are formed to conical shapes with different forming angles and then the limiting wall angles are determined for each condition. The experimental results indicate that the limiting forming angle of FSWed sheet is not so much different than the base sheet and FSW does not have a negative effect on the sheet metal formability in SPIF. To study the effect of SPIF and FSW in mechanical and microstructural properties of the formed parts, the effects of these process on the grain size and micro-hardness is investigated. Furthermore, the incremental forming is numerically simulated using the ABAQUS software and the sheet thickness distribution, obtained from the simulation, is compared with the experimental results. After verification of the numerical simulation model, the effect of FSW on the thickness distribution and strain distribution in SPIF is studied. The results indicate that in weld region and base metal region, the distributions of thickness and major strain are uniform while the distribution of minor strain is nonuniform. [ABSTRACT FROM AUTHOR]

In this research, a new hybrid forming strategy is proposed and investigated numerically and experimentally to improve the formability in single point incremental forming (SPIF). At the first stage, the hydraulic bulging of the sheet metal is performed under a specified fluid pressure to obtain an intermediate shape, then the fluid pressure is removed and the bulged sheet is inverted upside down. Finally, the SPIF of the truncated cone with a certain wall angle is carried out on the pre-bulged sheet. To this end, a die set was designed and manufactured. To study the deformation mechanics and the thickness distribution, finite element modeling using Abaqus/Explicit was employed. The maximum achievable forming depth and the thinning in the hybrid forming strategy were compared with those in the single-stage and the equivalent two-stage SPIF. Results of the 70° wall angle cone show that by implementing the two-stage hybrid forming, the forming depth and the thinning can be improved by 26 and 45% compared to the single-stage SPIF, respectively. On the other hand, the equivalent two-stage SPIF can lead to an improvement of about 10% in the forming depth compared to the single-stage SPIF. [ABSTRACT FROM AUTHOR]

Thin-walled bent tubes are a significant component utilized in the aerospace, shipbuilding, and chemical industries, as well as considering that they are employed as fluid and gas transporters, the quality of their manufacturing and production is critical. In recent years, new technologies for the manufacture of these structures have been developed, the most promising of which is the flexible bending process. Nevertheless, during tube bending, defects like an increase in contact stress and friction force in the bending area, thinning of the bent tube in the extrados zone, ovalization, and spring-back are some of the issues that arise. So, based on the softening and surface effects induced by ultrasonic energy in metal forming, this paper is suggested a novel method to fabricate the bent components by adding ultrasonic vibrations into the static motion of the tube. Therefore, experimental tests and finite element (FE) simulations are employed to assess the impact of ultrasonic vibrations on the forming quality of the bent tubes. Initially, an experimental setup was designed and built to guarantee the transmission of ultrasonic vibrations with a frequency of 20 kHz to the bending area. Afterward, based on the experimental test and its geometrical parameters, a 3D finite element model of the ultrasonic-assisted flexible bending (UAFB) process was developed and validated. According to the findings, forming forces were significantly reduced when the ultrasonic energy was superimposed, and thickness distribution in the extrados zone was significantly enhanced as a result of the acoustoplastic effect. In the meantime, the UV field's application effectively diminishes the contact stress between the bending die and tube, as well as greatly reduces the material flow stress. In the end, it was found that applying UV at the appropriate vibration amplitude can effectively improve ovalization and spring-back. The current study will assist researchers in better understanding the role of ultrasonic vibrations in performing the flexible bending process and achieving improved tube formability. • The influence of ultrasound on the flexible bending process of the thin-walled circular tubes made from aluminium is investigated. • The decrease of the plastic deformation force concomitant with increase the formability is achieved, and the corresponding data was used to verify the established finite element model (FEM). • All three phenomena of acoustic softening, surface effect, and stress superposition were included in the modeling. • Uniaxial tensile test was performed to check material flow stress and calculate strain rate parameter under ultrasonic conditions. • Ultrasonic compression test was developed to calculate the friction coefficient in different vibration amplitude. Therefore, by establishing a relationship between the surface roughness and the amplitude of ultrasonic vibrations, the phenomenon of surface effect was included in the simulations. • Effects of ultrasound on the forming force and thickness distribution is investigated. Based on the simulations, extrados wall thinning and intrados wall thickening can be eliminated and a uniform distribution of bent tube can be created. • UV application under micro-hammer condition significantly reduces the forming force. Also, in the amplitude of 13.5 μ m, the defect of the spring back for the bent tube is effectively reduced. On the other hand, due to the facilitation of material flow into the die cavity, the ovalization after the bending process is also reduced. [ABSTRACT FROM AUTHOR]

This paper focuses on the formability and thickness distribution in incremental sheet forming (ISF) of extra-deep drawing steel (EDD). In ISF, the formability of the material is primarily measured by the maximum formable wall angle and maximum allowable thinning. The maximum wall angle is generally obtained by forming frustum of cones and square pyramids having different wall angles till fracture, which requires a large number of experiments. Therefore in the present study, a continuously varying wall angle conical frustum (VWACF) was used to predict the maximum wall angle to minimize the number of experiments. VWACF is generated using circular, parabolic, elliptical and exponential generatrices. In order to get the maximum allowable thinning, the thickness of the formed geometry has been measured at various points along the depth. In addition, the thickness distribution has been computed theoretically based on the sine law and also using finite element code LS-DYNA. Theoretical and simulated thickness values have been compared with measured thickness values. It was found from the results that the finite element model was more accurate than theoretical model in predicting thickness distribution.