Study On The Single Point Incremental Sheet Forming of AISI 321 Variable Wall Angle Geometry


 For rapid prototyping, design validation and small batch productions process with low tooling cost is preferred. Single Point Incremental Forming (SPIF) is a die-less sheet metal forming process which requires only low cost forming tool driven by CNC machine in a toolpath to form required geometry at room temperature from sheet blank clamped in a low cost and low stiffness clamping system. In this study, effect of process parameters such as tool radius, feed rate and lubrication are considered on the formability of the truncated profile of AISI 321 Variable Wall Geometry (VWA). Set parameters conditions with 2 level layers are optimized using numerical and statistical approach. Experimentation on the same setup is carried out by selecting the most, least and mid favorable solutions optimized on the basis of forming forces and stresses in the sheet. Geometrical accuracy, sheet thinning, and forming forces are compared analytically, numerically and experimentally addressing the inadequacy of analytically models for Variable Wall Angle Geometries.


Introduction
Sheet metal work is everywhere from travelling by various transportation means, getting treated in hospitals with medical equipment, using modern gadgets like mobile and laptop, while shopping with currency coins to eating with cutlery. Dies and punches used for most of the sheet metal working are expensive without mass production. Storage of dies is a challenging task speci cally in automobile sector in which components are large with more product life time. With the advancement and increased demand of sheet metal products for various elds, there is a need for advanced and rapid techniques in sheet metal working. Incremental sheet forming is rapid, agile and highly exible process for small batch productions. Designed products can be rapid porotype and tested via this process before rolling out the nal design and product. New tailored design requirements can also be met via Incremental Sheet Forming (ISF). ISF makes variety of 3D shapes using a simple forming tool in low cost, high quality and smaller lead time due to which it has gained the attention of both industry and academia during last two decades.
ISF is the technological advancement of spinning process. During ISF, sheet metal is formed into 3D shape using a simple specialized tool, path guided and force applied by Computer Numeric Controlled (CNC) machining center. Tool is usually in contact with the sheet metal at the point of contact only which generates local area deformation and stresses that allows greater formability limits. ISF is widely adopted for small batch and customized products compared to stamping and deep drawing process [1,2] because with minimum specialized tool forming can be performed by simply importing CAD data into CNC compiler.
In Single Point Incremental Sheet Forming (SPIF), a single tool is in contact with sheet with a de ned toolpath without any die for sheet metal. Tool moves incrementally in set trajectory of toolpath to form the sheet. Only clamping plates and backup supports are used owing to tool forces. Edward Leszak [3] patent the ISF in 1967 by developing the die-less sheet forming axis symmetric products with inexpensive tool attached on turntable in 1964. ISF development history may be grouped into 3 periods [4].Until 1996 researchers mostly worked on the SPIF process which includes major contributions from researchers like Leszak, Berghan and Mason. Mason in 1978 [5] used the rollers progressively in passes to produce desired shape using backing material as a support which later on discovered not to be necessary.
While from 1993 to 2000 major scope of the researchers in Japan was on Two Point Incremental Forming (TPIF) speci cally by Iseki et al. [6] During this era Iseki revolutionized the processes of ISF by starting his experiments with turn table [6] and later on developed 3 dimensional Incremental forming machine in 1996 [7].During this period giant automotive Japanese companies such as Hitachi, Toyota and Honda developed the process of ISF for manufacturing embossed wall panels with different variants of ISF [4].
Later in 2000, researchers expanded their scope of work on ISF from all over the world. Filice et al [8] and Jesweit et al [9] during early 2000's studied the capability of using CNC milling centers for ISF. Most of the patents were from Automotive Industry, Honda in 2002 patented the ISF process in which body is formed incrementally into convex and concave parts using female die. Honda applied ISF in collaboration with Amino [10] to make replacement parts of Honda S800 sports car. Dimensions of original parts is taken with measuring machines and parts is then reproduced using generated coordinates. In 2004, BMW make individual parts from standardized part by using a mandrel type forming tool. Daimler used conventional TPIF to form a full die from interlocked pieces of sheet.
Jesweit et al. [2] concluded that formability of ISF is de ned by four major parameters: sheet thickness, drawing angle, radius of forming tool, feed rate and rotational speed. Mode of deformation is still debatable issue among different researchers. There are two different school of thoughts related to deformation mode of sheet, one of them proposed stretching while other proposed shearing as deformation mode. Allwood et al. [11] purposed combination of stretching and bending deformation mode as formability mechanism. However, Silva et al. [12] concluded that the principal mode of deformation for ISF is in-plane stretching and further they deduced the formability criterion.
Conical frustum cones shapes are being used in diverging and converging cones for throttling purposes having variable wall angle (VWA) pro le. Current study will aim towards the successful forming of conical frustum shown in Fig. 1 using single point incremental forming (SPIF) on AISI 321 sheet.
Geometrical accuracy, sheet thinning, and forming forces will be analytically, numerically and experimentally compared.

Materials And Methods
Material Properties of AISI 321

Numerical Simulation Of Isf
Explicit dynamics module of ANSYS is used for numerical simulation in this study because of nonlinearity and localized nature of plastic deformation of SPIF. Sheet is assumed to have no pre-stress prior to forming. Simulation is performed in a single step and virtual forming speed is 100 times scaled up than the original time taken by the tool to form the sheet which ultimately decreases simulation time and performs effectively. To ensure quasi-static forming simulation, kinetic energy is kept less compared to total internal energy and dynamic effects are not included as simulated by Li et al [13] and Kurra et al [14].
Displacement of tool is approximated by de ning its coordinates in x, y and z directions using damped simple harmonic motion for truncated cone of major diameter 100mm as toolpath from CAD cannot be de ned directly in FEA. Helical tool path is de ned for the tool with respect to time increment. A total end time of 1.8s is divided into 1800 increments de ning the tool path displacement.

Material model de nition & simulation benchmarking
Sheet plasticity is modeled using multilinear isotropic hardening in ANSYS as sheet is under monotonic loading and elastic unloading. For de ning this behavior multilinear true stress values are required against the plastic strain. This model behavior is piece-wise linear stress-total strain curve. Uniaxial tensile test data of true stress and strain obtained from the tensile tests as elaborated Fig. 2 is su cient to de ne the material de nition of AISI321 for sheet.
Forming forces and simulation time are selected as FEA convergence criteria. Experimental results of forming forces obtained by Bagudanch et al [15] are compared with the simulation results of this study for convergence.
Experimental study carried out by Bagudanch et al. [15] in which AISI 304 is numerically simulated and compared with the present study for simulation validation. Results differs slightly by 5.7%, therefore simulation is a good approximation for predict the kinematics of SPIF.

Simulation Trials
Tool radius, feed rate & friction are variable process parameters for simulation. Their levels are de ned and simulation trials are run as per Design of Experiment (DOE).  Table 5.  Prediction of ANOVA approach is compared by performing the actual FE analysis on process parameters of solution 5 in Table 6. Axial forces and stresses obtained through FE analysis are predicted with values obtained by ANOVA.

Forming Forces
Analytical model for the prediction of axial force Eq. (1) is based upon uniform wall angle and does not incorporate feed rate. It fails to give a good approximation of the numerical axial forces of variable wall geometry. Analytical model gives a maximum axial force at wall angle of 50° due to variation of in Eq.
(1) . Experimental forces during the experimentation are estimated directly form the CNC milling machine spindle load as per analytical model purposed by Aggarwal et al. [16] in which cutting forces were directly derived from spindle current and number of revolutions. Analytical, numerical and experimental obtained maximum axial forces are compared as shown in Table 8.

Geometric Pro le Comparison
Formed part shows pillow effect of 0.5mm in height which is due to the fact that base of sheet remains in elastic state while rest of the sheet is in plastic state. Pro le obtained from FE simulation predicts that the elastic recovery of the sheet elastic is more than that of obtained from experimentation. This difference is due to the explicit nature of the solution and the estimation of the tool path analytically.
Maximum spring back occurs near the base-wall interaction of VWA part. Bend/ llet radius is not effected by spring back because tool form the radius after achieving the desired forming depth as shown in Fig. 9 Comparison of spring back is tabulated in Table 9 Table Sheet Thinning Sheet thinning is inevitable during SPIF due to local deformation of clamped sheet that without any die beneath it instead of ow. Excessive wall thinning can lead to the failure of sheet due to tearing. Final thickness of the formed part can be approximated analytically by sine law as indicated in Eq. (2) which is based upon the simple shear forming process. ( Where t 0 is initial thickness of the sheet and α is the angle of wall with respect to horizontal while t is the nal thickness of the sheet. As geometry is variable wall angle, thickness will be different at different depth heights as the wall angle steeply increases with the depth of the sheet.
Thickness is measured experimentally using ultrasonic thickness gauge GE CL5. Comparison of thicknesses obtained analytically, numerically and experimentally are compared and is shown in Fig. 10 Sine law is only an approximation and cannot predict the exact thinning behavior of the sheet. Sine law predicts more thinning in the initial process and less thinning at the nal stage of SPIF as shown in Fig.  11 FE numerical simulation predicted the similar actual pattern of sheet thinning with maximum percentage error of 8.1 %. Hence, numerical solution give better approximation for sheet thinning.

Conclusion
It is concluded from the experimental results that Feed rate is one of the dominating process parameter for SPIF as it increases the forming forces and stresses that causes the excessive thinning of the sheet and may tearing of the sheet. Tool radius has a major contribution in the forming forces however its contribution as compared to feed rate in stress generation is minimal. Although, lubrication has a minor contribution but when compares to axial forces it shows a signi cant in uence in variance of stresses.
Wall thinning is the SPIF process that induces the signi cant effect on the forming part. It is observed that it is varied according to the depth that limits the SPIF for deep drawing. Larger lengths can be drawn by use of die or hydraulic chamber which will control excessive thinning.
Analytical models may better predict the geometries with Uniform Wall Angle (UWA) as compared to Variable Wall Angle (VWA) geometry as SPIF is still to be completely developed analytically. FE model predicts the better results as compared to analytical models for complex geometries like UWA.

Future Recommendations
Forming Forces and thinning analytical models for VWA geometry for AISI 321 is still an area to be explored. Sine law and other force models developed for UWA can only give the approximation. Implicit FE approach is iterative however its computation time is high and requires a system with higher speci cations. Comparison of both explicit and implicit with experimental studies can give better insight of SPIF for VWA.
Optimization algorithm of larger subset using Arti ce Neural Network can be developed for better results.
Work is still going on in the area of SPIF. Literature revealed that analytical models developed by different researchers do not include the frictional effects (nonlinearities). Future research can be done in this aspect.