A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Springback prediction for incremental sheet forming based on FEM-PSONN technology

In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.

Mechanical properties and microstructure evolution in incremental forming of AA5754 and AA6061 aluminum alloys

This study performs single point incremental forming(SPIF)on two aluminum alloys(i.e.AA5754 and AA6061),and analyzes their post forming mechanical properties and microstructure evolution.The forming parameters namely wall angle(35°-55°),feed rate(1-4 m/min),spindle rotational speed(50-1000 r/min),and lubricant(grease and hydraulic oil)are varied to probe detailed processing effects.The pre-and post-SPIF mechanical properties and microstructures are characterized by conducting tensile tests and optical microscopy,respectively.It is shown that an increase in the wall angle,feed rate and rotational speed causes microscopic variations in the alloys such that the grains of AA5754 and the second phase particles of AA6061 elongate.As a result,the ultimate tensile strength of the formed parts is increased by 10%for AA5754 and by 8%for AA6061.And,the ductility of AA5754 is decreased from 22.9%to 12%and that of AA6061 is decreased from 16%to 10.7%.Regarding the lubricant effect,it is shown that the mechanical properties remain insensitive to the type of lubricant employed.These results indicate that SPIF processing modifies the microstructure of Al alloys in a way to enhance the strength at the cost of ductility.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Finite element and experimental analyses of cylindrical hole flanging in incremental forming

The influence of the size of pre-cut hole of blank on the formability of cylindrical hole flanging in single point incremental forming（SPIF） was studied. The flange is produced in four stages starting from 45° to 90° and employing aluminum as the test material. It is shown that the hole size has significant effects on the stress/strain distribution on the cylindrical flange. The magnitude of hoop strains increases and the flange thickness increases as the hole size increases. Likewise, the von Mises stress reduces with the increasing of hole size. Further, there is a threshold value of hole size（i.e., 80 mm） below which severe stresses occur, which lead to sheet fracturing thus failing the successful forming of cylindrical flange. Moreover, the formability reduces as the hole size is increased above the threshold size. Finally, it is concluded that 80 mm is the threshold size of hole for maximizing the formability of aluminum sheet in incremental hole flanging.

Incremental forming of free surface with magnesium alloy AZ31 sheet at warm temperatures

The formabilityof AZ31 sheet begins to increase drastically at 150℃.The incremental forming technique was thus applied to AZ31 sheet at 150℃to utilize the formability to its fullest capacity at the lowest possible temperature for forming applications.A surface scanning technique was used followed by the tool path generation to incrementally form an egg surface.After thorough examination of various tool paths,the surface was most successfully produced by forming an intermediate shape followed by a series of tool paths.Flexible scale stickers were devised to improve the accuracy in the measurement of grid deformation.

NC INCREMENTAL SHEET METAL FORMING PROCESS AND VERTICAL WALL SQUARE BOX FORMING

The forming principle and deformation analysis of NC incremental sheet metalforming process as well as the process planning, experiment and key process parameters of verticalwall square box forming are presented. Because the deformation of sheet metal only occurs around thetool head and the deformed region is subjected to stretch deformation, the deformed region of sheetmetal thins, and surface area increases. Sheet metal forming stepwise is to lead to the whole sheetmetal deformation. The forming half-apex angle 9 and corner radius R are the main processparameters in NC incremental forming of vertical wall square box. According to sine law, a verticalwall square box can't be formed by NC incremental sheet metal forming process in a single process,rather, it must be formed in multi processes. Thus, the parallel line type tool path process methodis presented to form the vertical wall square box, and the experiment and analysis are made toverify it.

Numerical simulation and experimental investigation of incremental sheet forming process

In order to investigate the process of incremental sheet forming (ISF) through both experimental and numerical approaches, a three-dimensional elasto-plastic finite element model (FEM) was developed to simulate the process and the simulated results were compared with those of experiment. The results of numerical simulations, such as the strain history and distribution, the stress state and distribution, sheet thickness distribution, etc, were discussed in details, and the influences of process parameters on these results were also analyzed. The simulated results of the radial strain and the thickness distribution are in good agreement with experimental results. The simulations reveal that the deformation is localized around the tool and constantly remains close to a plane strain state. With decreasing depth step, increasing tool diameter and wall inclination angle, the axial stress reduces, leading to less thinning and more homogeneous plastic strain and thickness distribution. During ISF, the plastic strain increases stepwise under the action of the tool. Each increase in plastic strain is accompanied by hydrostatic pressure, which explains why obtainable deformation using ISF exceeds the forming limits of conventional sheet forming.

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.

Analysis and optimization of variable depth increments in sheet metal incremental forming

A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.

Bulging in incremental sheet forming of cold bonded multi-layered Cu clad sheet: Influence of forming conditions and bending

Bulge is a defect that causes geometrical inaccuracy and premature failure in the innovative incremental sheet forming (ISF) process. This study has two-fold objectives:(1) knowing the bulging behavior of a Cu clad tri-layered steel sheet as a function of forming conditions, and (2) analyzing the bending effect on bulging in an attempt to identify the associated mechanism. A series of ISF tests and bending analysis are performed to realize these objectives. From the cause-effect analysis, it is found that bulge formation in the layered sheet is sensitive to forming conditions in a way that bulging can be minimized utilizing annealed material and performing ISF with larger tool diameter and step size. The bending under tension analysis reveals that the formation of bulge is an outgrowth of bending moment that the forming tool applies on the sheet during ISF. Furthermore, the magnitude of bending moment depending upon the forming conditions varies from 0.046 to 10.24 N·m/m and causes a corresponding change in the mean bulge height from 0.07 to 0.91 mm. The bending moment governs bulging in layered sheet through a linear law. These findings lead to a conclusion that the bulge defect can be overcome by controlling the bending moment and the formula proposed can be helpful in this regards.

Formability of Materials with Small Tools in Incremental Forming

Single point incremental forming(SPIF)is an innovative sheet forming process with a high economic pay-off.The formability in this process can be maximized by executing forming with a tool of specific small radius,regarded as threshold critical radius.Its value has been reported as 2.2 mm for 1 mm thick sheet materials.However,with a change in the forming conditions specifically in the sheet thickness and step size,the critical radius is likely to alter due to a change in the bending condition.The main aim of the present study is to undertake this point into account and develop a relatively generic condition.The study is composed of experimental and numerical investigations.The maximum wall angle(θmax)without sheet fracturing is regarded as sheet formability.A number of sheet materials are formed to fracture and the trends correlating formability with normalized radius(i.e.,R/To where R is the tool-radius and To is the sheet thickness)are drawn.These trends confirm that there is a critical tool-radius(Rc)that maximizes the formability in SPIF.Furthermore,it is found that the critical radius is not fixed rather it shows dependence on the sheet thickness such that Rc=βTo,whereβvaries from 2.2 to 3.3 as the thickness increases from 1 mm to 3 mm.The critical radius,however,remains insensitive to variation in step size ranging from 0.3 mm to 0.7 mm.This is also observed that the selection of tool with R<Rc narrows down the formability window not only on the higher side but also on the lower side.The higher limit,as revealed by the experimental and FEA results,diminishes due to excessive shearing because of in-plane biaxial compression,and the lower limit reduces due to pillowing in the bottom of part.The new tool-radius condition proposed herein study would be helpful in maximizing the formability of materials in SPIF without performing experimental trials.

Method of closed loop springback compensation for incremental sheet forming process

The closed loop control model was built up for compensating the springback and enhancing the work piece precision.A coupled closed loop algorithm and a finite element method were developed to simulate and correct the springback of incremental sheet forming.A three-dimensional finite element model was established for simulation of springback in incremental sheet forming process.The closed loop algorithm of trajectory profile for the incremental sheet forming based on the wavelet transform combined with fast Fourier transform was constructed.The profile of processing tool path of shallow dishing with spherical surface was designed on the basis of the profile correction algorithm.The result shows that the algorithm can predict an ideal profile of processing track,and the springback error of incremental sheet forming is eliminated effectively.It has good convergence efficiency,and can improve the workpiece dimensional accuracy greatly.

A GENERAL FORM OF THE INCREMENTS OF TWO-PARAMETER FRACTIONAL WIENER PROCESS

A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.

Plasma Surface Cu Alloyed Layer as a Lubricant on Stainless Steel Sheet:Wear Characteristics and On-job Performance in Incremental Forming

To solve the problems of poor forming and easy adhesion of the stainless steel,Cu alloyed layer on the stainless steels was prepared by the double glow plasma surface alloying technique.The experimentalresults indicated that the supersaturated copper dispersedly precipitated in grain interior and crystalboundaries and formed the vermicular structure.The tribologicaltests indicated that the friction coefficient of the Cu alloyed layer was lower than that of the stainless steels.The wear rate of stainless steelin the presence of Cu alloyed layer was approximately 2-fold lower than that in the absence of the alloyed layer.The results of the incrementalforming indicated that the ploughing phenomenon was not observed on the stainless steelin the presence of Cu alloyed layer during the incrementalforming,while the stainless steelpresented the deep ploughing.Therefore,Cu alloyed layer on stainless steelexhibited excellent self-lubrication and forming properties.

Thickness distribution of multi-stage incremental forming with different forming stages and angle intervals

Although multi-stage incremental sheet forming has always been adopted instead of single-stage forming to form parts with a steep wall angle or to achieve a high forming performance, it is largely dependent on empirical designs. In order to research multi-stage forming further, the effect of forming stages(n) and angle interval between the two adjacent stages(Δα) on thickness distribution was investigated. Firstly, a finite element method(FEM) model of multi-stage incremental forming was established and experimentally verified. Then, based on the proposed simulation model, different strategies were adopted to form a frustum of cone with wall angle of 30° to research the thickness distribution of multi-pass forming. It is proved that the minimum thickness increases largely and the variance of sheet thickness decreases significantly as the value of n grows. Further, with the increase of Δα, the minimum thickness increases initially and then decreases, and the optimal thickness distribution is achieved with Δα of 10°.Additionally, a formula is deduced to estimate the sheet thickness after multi-stage forming and proved to be effective. And the simulation results fit well with the experimental results.

Microstructure and M echanical Properties of Magnesium Alloy Sheet by Friction Heating Single Point Incremental Forming

By friction heating single point incremental forming,truncated square pyramid parts with different draw angles of a magnesium alloy AZ31 B were formed at room temperature.Metallurgical,tensile and micro-hardness tests were carried out to obtain the effects of wall angle on microstructure and mechanical properties. The results show that grain in side wall of the formed parts becomes refined significantly. Furthermore,with the increase of draw angle,grain size increases,but strength,hardness and plasticity decrease. In addition, surface roughness tests were performed on the formed surface to determine the influence of speed of forming tool. The results show that surface roughness has a little increase with the increase of tool rotational speed.

Studying Formability Limits By Combining Conventional and Incremental Sheet Forming Process

In this work it is assessed the potential of combining conventional and incremental sheet forming processes in a same sheet of metal.This so-called hybrid forming approach is performed through the manufacture of a pre-forming by conventional forming,followed by incremental sheet forming.The main objective is analyzing strain evolution.The pre-forming induced in the conventional forming stage will determine the strain paths,directly influencing the strains produced by the incremental process.To conduct the study,in the conventional processes,strains were imposed in three different ways with distinct true strains.At the incremental stage,the pyramid strategy was adopted with different wall slopes.From the experiments,the true strains and the final geometries were analyzed.Numerical simulation was also employed for the sake of comparison and correlation with the measured data.It could be observed that single-stretch pre-strain was directly proportional to the maximum incremental strains achieved,whereas samples subjected to biaxial pre-strain influenced the formability according to the degree of pre-strain applied.Pre-strain driven by the prior deep-drawing operation did not result,in this particular geometry,in increased formability.

Experimental Study on Springback of Sheet Metal Single Point Incremental Forming

Sheet metal single point incremental forming （SPIF） is a new technology for flexible process. The springback phenomenon in single point incremental forming has been discussed. Effects of forming angle and shape of the part are analysed using simple experimental method. Tool diameter, sheet thickness, step size, material parameters and the interaction of them are also analysed by using orthogonal test. The results show that the primary factor af- fecting springback is forming angle. In addition, springback is decreased when the specimen has a larger forming angle. The order of the four factors that influence springback is tool diameter, sheet thickness, step size and material parameters. The forming precision will increase if springabck is decreased by optimizing the forming parameters.

Improving Local Temperature Rise in Rotational Incremental Sheet Forming Process by Modifying Forming Parameters Using Response Surface Method

In rotational incremental sheet forming( RISF) process,the friction heating of rotational tool could lead to local temperature rise of the sheet and cause the improvement of sheet's formability.Lightweight metal,such as magnesium alloy,could be deformed by RISF without additional heating. The objective of this study is to investigate the effects of forming parameters,namely,tool rotational speed,feed-rate,step size and wall angle,on the local temperature rise. Using response surface methodology and central composite design( CCD) experimental design,the significance,sequence of parameters and regression models would be analyzed with AZ31 B as the experimental material,and 3D response surface plots would be shown. Combined with actual processing conditions,the measures to improve the local temperature rise by modifying each parameter would be discussed in the end. The results showed that hierarchy of the parameters with respect to the significance of their effects on the local temperature at the side wall was: feed-rate,step size,and rotational speed,while at the bottom it was: feed-rate,step size,wall angle, and rotational speed, and no significant interaction appeared. It was found that the most significant parameter was not rotational speed,but feed-rate,followed by step size,for both test positions. In addition, the local temperature would increase by elevating step size,wall angle,rotating rate,and bringing down of feed-rate.