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

A Visagan, P Ganesh

(Department of Production Technology, Madras Institute of Technology, Chennai-600044, India)

Abstract: 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.

Key words: single point incremental forming; AISI 316L; taguchi grey relation analysis; principal component analysis; surface roughness; scanning electron microscopy

1 Introduction

Sheet forming work is a process, used for making required shape using metal sheets such as aluminium,magnesium, stainless steel and carbon steelsetc[1].Generally, sheet metal forming industries use punch and dies for fabrication the product, but production of punch and die is highly expensive[2].Eventhough,traditional punch and die methods would not be economically viable to the small production and batch production[3].To overcome this issue, incremental forming is considered as the potential process.In last few decades, some investigations on this forming of various metal sheets have been tried.Hence, it would be the appropriate technique for fabricating the components used in the application of automotive,aerospace and bio medical[4].Single point incremental forming (SPIF) is an effective forming process used to manufacture desired structure without die.SPIF has lower force, higher formability and low production cost compared with conventional methods[5].SPIF mainly reduces the weight of the required product.Numerous investigations on metal forming have been carried using SPIF in order to improve the response characteristics[6].But optimizing process parameters is very essential in SPIF process to attain the responses.Pratheeshet al[7]studied the process factors in SPIF of inconel 718 by RSM.Process factors such as lubrication viscosity and step depth on wall thickness, roughness and profile accuracy are studied.As increasing step depth, the wall thickness decreased due to increasing scratches during deformation of materials.Optimized parameters on maximum surface roughness, wall thickness and profile accuracy were 3 000 mm/min, 0.2 mm and 105 mm2/s.Dabwanet alstudied the influence of SPIF parameters on roughness of formed aluminum alloy.It was found that the SPIF with greater tool diameter and thin sheet enhanced surface quality of AA1050-H14[8].Mulayet alhave investigated the SPIF of high strength AA5052-H32 alloy sheet.Sheet thickness (ST), step depth, feed rate and diameter of the tool were controlled during the process and the responses measured in the study were roughness and forming angle.RSM with box behnken was proposed to plan the experiment and develop the empirical model[9].Nasulea and Oancea manufactured frustum cone shape from DC05 steel sheet with thickness of 1 mm using SPIF technique.Dimensional configurations such as feed rate, spindle speed are chosen to attain the minimum roughness.Circumferential hammering tool is used to prove the part accuracy of the desired product[10].Baruahet alhave proposed grey relation analysis to optimize the parameters in incremental forming of AA5052-H32 alloy.TaguchiL9was used to conduct the experiments.Vertical step down, feed rate, lubrication and speed on formability and roughness were studied.Optimized parameters in the study were 0.5 mm, 200 mm/min,150 rpm and grease.It was found that the combination of grey analysis-taguchi is appropriate method for ISF process[11].Kumar and Kumar used taguchi technique for optimizing the roughness in SPIF of AA2014.Tool path, sheet thickness, spindle speed and TD on SR are studied.Thickness of sheet and tool speed were found significant for minimum surface roughness[12].

From the observation of past investigation, several researches concentrated on the incremental forming of different sheet materials such as aluminium and steeletc.Commonly, controlling factors such running tool diameters, step depth, thickness of sheet and tool speed are selected to perform the forming process.Roughness has been considered as important characteristics for all investigation, which offered the appearance for the final developed product.Different techniques such as RSM,Taguchi and ANOVA have been applied to determine the optimal parametric conditions on responses.But investigation on combined optimization technique in incremental forming is very limited.Hence, an investigation has been made to form double wall angle pyramid using Single Point Incremental Forming(SPIF) technique.AISI 316L stainless steel is used as the sheet metal to form the product and tools made of tungsten carbide has been used for forming the sheet metal.Independent factors such as tool diameter, step depth, bottom wall angle, feed rate and spindle speed are considered for conducting investigation.Responses measured in the study are Top Wall Angle and Top Wall Angle Surface Roughness.TaguchiL18orthogonal array is used to formulate the experimental combinations.To predict the responses of the process, Grey Relational Analysis coupled with Principal Component Analysis is used.Influence of process parameters on measured responses are studied with aid of mean effect graph.Scanning Electrode Microscope assessment has been utilized for carrying out microstructural study.

2 Experimental

In this investigation, double wall angle pyramid is prepared by SPIF process.The schematic illustration of the SPIF is illustrated in Fig.1.

Fig.1 Illustration of SPIF

For fabrication the product, AISI316L stainless steel is used as base metal sheet and its element composition is presented in Table 1.Dimensions of the base metal sheet breadth, width and thickness are 250 mm × 250 mm × 0.8 mm.Hemispherical shaped tungsten carbide with length of 100 mm and diameter of 8 and 10 mm were used as the forming tool during the forming process.

Table 1 Elemental composition of AISI316L

SPIF parameters are important in order to manufacture the quality product.In this present investigation, five input factors were selected to perform process.Among five parameters, one factor has two levels, other four parameters have three levels.An Orthogonal Array (OA) is a statistical design technique often applied in various industries to investigate the influence control factors.As per the standard, total degrees of freedom (DOF) should be larger than total DOF required for the experiments.Hence, mixed level L18OA was selected and five factors were fixed.

Before selecting the parameter levels, pilot experiments were conducted.By conducting trial experiments, the ranges of levels are fixed.Three levels were identified namely low (L-1), medium (L-2) and high (L-3).Tool diameter, step depth, bottom wall angle, feed rate and spindle speed are selected as the process factors.Factors and their levels are presented in Table 2.TaguchiL18is used to plan the design matrix for SPIF experiments.Totally 18 experiments are conducted (Table 3).

Table 2 Factors and ranges for SPIF

Table 3 Experimental results recoded

Generally, sheet metal products have been manufactured with aid of rolling process, in which microstructure orientation is formed based on the rolling direction.Fig.2 shows the CAD model of the components to be formed.Based on the experimental condition, the double wall angle pyramid was manufactured using milling machine.Responses measured in the study are top wall angle and top wall angle roughness.Roughness of the final object is measured using TR100 surface profile instruments.Three values are taken for each formed product and average value was used as the roughness value.Experimental values recorded after SPIF has been given in Table 3.

Fig.2 CAD model of the components

3 Grey relation analysis—Taguchi approach

Optimization is an important tool in every field for solving the complex problem.Research engineers and scientists show great interest in using optimization technique to reduce the raw materials wastage and processing time[13].Various types of algorithm have been created for verities of problem.An objective of the GRA is to find the correlation between the known and unknown matters of the different parameters.GRA is one among the optimization tool, which is employed for determining the optimal parameters in order to attain the better response characteristics[14].In GRA,when the ranges of output responses are large, the function variable will be neglected.Therefore, range of normalization should be between zero and one[15].

3.1 S/N ratio and normalization

The response such as wall angle and roughness are required to be maximized and minimized respectively.Large response is chosen for wall angle.Similarly,smaller response is selected for surface roughness.Signal noise rate (S/N) for wall angle and roughness can be calculated by Eqs.(1) and (2).This expression is used for the problem where maximum and minimum output responses are needed.

where,nis the number of replication,yijis the response observed.

The normalization was completed for the output variables by using Eqs.(1) and (2).For the higher is the better and the smaller is the better response characteristic, the normalized experimentZijcan be given by Eqs.(3) and (4) respectively.

whereZijis the SPIF results of theithrun of thejthoutput variables.The higher normalized measures correspond to the better response.The best normalized values should be equal to one.The determinedS/Nratio values of the each response and its normalization values are presented in Table 4.

Table 4 Calculated S/N ratio and normalized values

3.2 Grey relation coefficient (GRC)

GRC for each individual response can be measured from the normalized values.To determine optimal and actual normalized results, grey relational coefficient (GRC) is used.GRC can be derived as Eq.(5).

Table 5 Calculated GRC, grade and order

where, εjis grade of grey coefficient forjthexperiment,nmeans no of output response andwjis weight value obtained from PCA.Hence, it is necessary to study the impact of individual factor and levels on grey relation grade.Grade value determined for each level and gradeaverage has been given in Table 6.

Table 6 GRG response

Generally, if the value of GRG is higher, the output characteristics can be considered as better.Accordingly, the optimal parameter condition can be found from the GRG (Table 6).The optimized parameters in the study were tool diameter of 10 mm, step depth of 0.4 mm, bottom wall angle of 73o,feed rate of 1 000 mm/min and spindle speed of 300 rpm.By using single objective optimization method,individual factors cannot be investigated.However, it is important to study the combined effect.Hence, ANOVA is proposed to study the impact of factor on multi objective responses.In this investigation, parameter contribution on better response is given in Table 7.Spindle speed (42%) has given more contribution on the responses followed by tool diameter (35.99%),bottom wall angle (3.79%), step depth (1.68%) and feed rate (1.12%).

Table 7 ANOVA results

3.3 Confirmation test

The confirmation test is carried out in order to verify the optimized parameters and their levels and to determine the enhancement in the GRG.From Table 8, an enhancement in the response is identified when using the optimal conditions in the SPIF process.

Table 8 Confirmation test results

In this investigation, the enhancement of weighted GRG for the SPIF process is 0.196 9, which is attained within the range.Hence, it was observed from this optimization, good agreement was obtained between the predicted and experimental weighted grey relation grade.It is ensured that the Taguchi based GRA combined with PCA is great optimization to provide maximum wall angle and better roughness.

4 Surface roughness and microstructure study

Surface roughness plays an important role in preparing any component or product.Generally,roughness of the product is affected by the excessive wear and friction involved during fabrication[16].Surface roughness is an important criterion, which gives appearance for the final product.In this study,unit of the surface roughness (SR) is denoted asRa(µm)[17].

Three values were measured in each product, the average value was considered as the roughness values.Effect of controlling parameters on SR is shown in Fig.3.The SR increased with increasing tool diameter.At 8 mm tool diameter, SR values were high because excessive wear during the forming process than 10 mm tool diameter.Greater wear has been obtained in smaller tool because of the contacting forces in small area resulted in higher stress.As increasing step depth, SR increased linearly.As step depth increases,hydrostatic stress would be high and form the cracks in the developed product[18].Due to hydrostatic stress during process, rapid void coalescence is formed that causing severe crack(Fig.4).The greater step depth increased the stress that reduced the forming angle.

Fig.3 Effect of roughness

Fig.4 SEM microstructure of cracks and voids at 0.4 mm

Initially, SR increased with increasing bottom wall angle and step depth.At higher bottom wall angle and step depth, the formability of the product would be poor that caused poor SR.Feed rate is one of the important factors.As feed rate increases, SR increases slightly.Then it decreases when further increasing feed rate.At feed rate of 1 000 mm/min, higher friction heat is produced due to the relative contact between metal sheet and hammering tool.Due to friction heating,the surface would be hard, hence surface roughness is high in this condition[19].At higher level of feed rate,hammering tool spends less time, which develops ridges formation in this region.During higher feed rate, forming forces may generate greater vibration that leads to poor surface roughness.Due to the heating friction, scratches were formed in the product as confirmed by Fig.5.

Fig.5 SEM microstructure of scratches and voids at 1 500 mm/min

As studied in the optimization section, spindle speed is the dominant parameter on the responses.Hence, as speed of the tool increases, the SR also increases.This could be due to the tensional stress imposed during the SPIF.The SS of 300 rpm may be potential factor that highly influence the responses.

5 Conclusions

Taguchi GRA coupled PCA was successfully applied for optimizing the process parameters on SPIF of double wall angle pyramid.The results indicated that the tool diameter of 10 mm, step depth of 0.4 mm, bottom wall angle of 73o, feed rate of 1 000 mm/min and spindle speed of 300 rpm were found as optimized parametric condition in the SPIF process.According to the ANOVA test results, spindle speed was the most significant parameter with contribution of 42% followed by tool diameter (35.99%), bottom wall angle (3.79%), step depth (1.68%) and feed rate(1.12%).Enhancement of weighted GRG for the SPIF process is 0.196 9, which is attained within the working range.Hence, good agreement was found between the predicted and experimental weighted grey relation grade.SR increased with increasing step depth, bottom wall angle, feed rate and spindle speed.SR decreased with increasing of tool diameter.SEM characterization revealed that the cracks and voids were formed at higher step depth (0.4 mm) and feed rate (1 500 mm/min) that affected roughness of the deformed product.

Conflict of interest

All authors declare that there are no competing interests.