International Journal of Lean Thinking Volume 4, Issue 1 (June 2013)
Lean Thinkingjournal homepage: www.thinkinglean.com/ijlt
Optimization Of Pulsed Current Parameters To Minimize Pitting Corrosion In Pulsed Current Micro Plasma Arc Welded AISI 304L Sheets Using Genetic
Algorithm K. Siva Prasad* Department of Mechanical Engineering, Anil
Neerukonda Institute of Technology &
Sciences , Visakhapatnam, INDIA
E-mail: [email protected]
C. Srinivasa Rao Department of Mechanical Engineering, AU
College of Engineering, Andhra University,
Visakhapatnam, INDIA
D. Nageswara Rao Centurion University of Technology &
Management, Odisha, INDIA
A B S T R A C T K E Y W O R D S
A R T I C L E I N F O
AISI 304L, Pulsed current,
Micro Plasma Arc Welding,
Pitting Corrosion,
Genetic Algorithm.
Received 04 January 2013
Accepted 04 June 2013
Available online 30 June 2013
Austenitic stainless steel sheets have gathered wide acceptance in
the fabrication of components, which require high temperature
resistance and corrosion resistance, such as metal bellows used in
expansion joints in aircraft, aerospace and petroleum industry. In
case of single pass welding of thinner sections of this alloy, Pulsed
Current Micro Plasma Arc Welding (PCMPAW) was found beneficial
due to its advantages over the conventional continuous current
process. This paper highlights the development of empirical
mathematical equations using multiple regression analysis,
correlating various process parameters to pitting corrosion rates in
PCMPAW of AISI 304L sheets in 1 Normal HCl. The experiments
were conducted based on a five factor, five level central composite
rotatable design matrix. A Genetic Algorithm (GA) was developed
to optimize the process parameters for minimizing the pitting
corrosion rates.
________________________________
* Corresponding Author
1. Introduction
AISI 304L is a austenitic stainless steel with excellent strength and good ductility at high
temperature. Typical applications include aero-engine hot section components, miscellaneous
hardware, tooling and liquid rocket components involving cryogenic temperature. AISI 304 L
can be joined using variety of welding methods, including Gas Tungsten Arc Welding (GTAW),
Plasma Arc Welding (PAW), Laser Beam Welding (LBW) and Electron Beam Welding (EBW). Of
these methods, low current PAW (Micro PAW) has attracted particular attention and has been
used extensively for the fabrication of metal bellows, diaphragms which require high strength
and toughness. PAW is conveniently carried out using one of two different current modes,
namely a Continuous Current (CC) mode or a Pulsed Current (PC) mode.
Pulsed current MPAW involves cycling the welding current at selected regular
frequency. The maximum current is selected to give adequate penetration and bead
contour, while the minimum is set at a level sufficient to maintain a stable arc [1,2].
This permits arc energy to be used effectively to fuse a spot of controlled
dimensions in a short time producing the weld as a series of overlapping nuggets.
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By contrast, in constant current welding, the heat required to melt the base material is supplied
only during the peak current pulses allowing the heat to dissipate into the base material leading to
narrower Heat Affected Zone (HAZ). Advantages include improved bead contours, greater tolerance to
heat sink variations, lower heat input requirements, reduced residual stresses and distortion, refinement
of fusion zone microstructure and reduced with of HAZ. Based on the worked published [3-8] , four
independent parameters that influence the process are peak current, back current, pulse rate and pulse
width.
In this investigation, experiments conducted using the design of experiments concept were used
for developing mathematical models to predict such variables. Many works were reported in the past for
predicting bead geometry, heat-affected zone, bead volume, etc., using mathematical models for various
welding processes [9-11]. Usually, the desired welding process parameters are determined based on the
experience of skilled workers or from the data available in the handbook. This does not ensure the
formation of optimal or near optimal weld pool geometry [12]. It has been proven by several researchers
that efficient use of statistical design of experiment techniques and other optimization tools can impart
scientific approach in welding procedure [13,14]. These techniques can be used to achieve optimal or
near optimal bead geometry from the selected process parameters.
Kim et.al reviewed that optimization using regression modeling, neural network, and Taguchi
methods could be effective only when the welding process was set near the optimal conditions or at a
stable operating range [15], but, near-optimal conditions cannot be easily determined through full-
factorial experiments when the number of experiments and levels of variables are increased. Also, the
method of steepest ascent based upon derivatives can lead to an incorrect direction of search due to the
non-linear characteristics of the welding process. Genetic algorithm, being a global algorithm, can
overcome the above problems associated with full-factorial experiments and the objective function to be
optimized using GA need not be differentiable [16].
In the present study, a sequential genetic algorithm has been used to optimize the process
parameters and achieve minimum pitting corrosion rate of PCMPAW AISI 304L sheets.
2 EXPERIMENTAL PROCEDURE Austenitic stainless steel (AISI 304L) sheets of 100 x 150 x 0.25mm are welded autogenously with
square butt joint without edge preparation. The chemical composition of SS304L stainless steel sheet is
given in Table 1. High purity argon gas (99.99%) is used as a shielding gas and a trailing gas right after
welding to prevent absorption of oxygen and nitrogen from the atmosphere. The welding has been
carried out under the welding conditions presented in Table 2. From the literature four important factors
of pulsed current MPAW as presented in Table 3 are chosen. A large number of trail experiments were
carried out using 0.25mm thick AISI 304L sheets to find out the feasible working limits of pulsed current
MPAW process parameters. Due to wide range of factors, it has been decided to use four factors, five
levels, rotatable central composite design matrix to perform the number of experiments for investigation.
Table 4 indicates the 31 set of coded conditions used to form the design matrix. The first sixteen
experimental conditions (rows) have been formed for main effects. The next eight experimental
conditions are called as corner points and the last seven experimental conditions are known as center
points. The method of designing such matrix is dealt elsewhere [17,18]. For the convenience of recording
and processing the experimental data, the upper and lower levels of the factors are coded as +2 and -2,
espectively and the coded values of any intermediate levels can be calculated by using the expression
[19].
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Xi = 2[2X-(Xmax + Xmin)] / (Xmax – Xmin) (1)
Where Xi is the required coded value of a parameter X. The X is any value of the parameter from
Xmin to Xmax, where Xmin is the lower limit of the parameter and Xmax is the upper limit of the parameter.
Table 1 Chemical composition of AISI 304L (weight %)
C Si Mn P S Cr Ni Mo Ti N
0.021 0.35 1.27 0.030 0.001 18.10 8.02 -- -- 0.053
Table 2 Welding conditions
Power source Secheron Micro Plasma Arc Machine (Model:
PLASMAFIX 50E)
Polarity DCEN
Mode of operation Pulse mode
Electrode 2% thoriated tungsten electrode
Electrode Diameter 1mm
Plasma gas Argon & Hydrogen
Plasma gas flow rate 6 Lpm
Shielding gas Argon
Shielding gas flow rate 0.4 Lpm
Purging gas Argon
Purging gas flow rate 0.4 Lpm
Copper Nozzle diameter 1mm
Nozzle to plate distance 1mm
Welding speed 260mm/min
Torch Position Vertical
Operation type Automatic
Table 3 Important factors and their levels
Levels
Serial
No
Input Factor Units -2 -1 0 +1 +2
1 Peak Current Amperes 6 6.5 7 7.5 8
2 Back Current Amperes 3 3.5 4 4.5 5
3 Pulse rate Pulses/Second 20 30 40 50 60
4 Pulse width % 30 40 50 60 70
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Table 4 Design matrix and experimental results
Serial
No
Peak
Current
(Amperes)
Back current
(Amperes)
Pulse rate
(Pulses/Second)
Pulse
width
(%)
Pitting
corrosion
rate
(mm/Year)
1 6.5 3.5 30 40 0.54120
2 7.5 3.5 30 40 0.99950
3 6.5 4.5 30 40 0.53390
4 7.5 4.5 30 40 0.82320
5 6.5 3.5 50 40 0.85370
6 7.5 3.5 50 40 0.70170
7 6.5 4.5 50 40 0.79770
8 7.5 4.5 50 40 0.60120
9 6.5 3.5 30 60 0.80370
10 7.5 3.5 30 60 0.99020
11 6.5 4.5 30 60 0.54110
12 7.5 4.5 30 60 0.82740
13 6.5 3.5 50 60 1.12450
14 7.5 3.5 50 60 0.82460
15 6.5 4.5 50 60 0.85000
16 7.5 4.5 50 60 0.67440
17 6.0 4.0 40 50 0.78280
18 8.0 4.0 40 50 0.86260
19 7.0 3.0 40 50 1.23460
20 7.0 5.0 40 50 0.78540
21 7.0 4.0 20 50 0.89920
22 7.0 4.0 60 50 0.81610
23 7.0 4.0 40 30 0.78220
24 7.0 4.0 40 70 0.82250
25 7.0 4.0 40 50 0.66290
26 7.0 4.0 40 50 0.64746
27 7.0 4.0 40 50 0.72800
28 7.0 4.0 40 50 0.71500
29 7.0 4.0 40 50 0.52060
30 7.0 4.0 40 50 0.62900
31 7.0 4.0 40 50 0.61690
3 RECORDING THE RESPONSES
The welded joints were sliced at the mid-section to prepare pitting corrosions test specimens. For
pitting corrosion test, specimens of 50×50 mm (width and length) were prepared to ensure the exposure
of 12 mm diameter circular area in the weld region to the electrolyte. The rest of the area was covered
with an acid resistant lacquer. The specimen size and dimensions are given in Figure 1. The specimen
surface was polished strictly following metallographic procedures. The polarisation studies of the welds
were carried out in 1 Normal HCl solution. Analar grade chemicals and double distilled water were used
Rahul Vylen, N. Rajesh Mathivanan , N. Shashidhar Chandrasekhar / International Journal of Lean Thinking Volume 4, Issue 1(June 2013)
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for the preparation of the electrolyte. The schematic circuit diagram of the potentiodynamic polarization
set up is shown in Figure 2. A potentiostat (Make: AUTOLAB / PGSTAT12) was used for this study in
conjunction with an ASTM standard cell and personal computer. Experiments are performed for 2 hours
duration each at a scan rate of 1 millivolts/mm. The pitting corrosion rate was calculated by polarizing the
specimen anodically and cathodically and by extrapolating the Tafel regions of anodic and cathodic curves
to the corrosion potential. The experimentally evaluated results are presented in Table 4.
12 mm
50mm
50 mm
Figure 1 Dimensions of corrosion test specimen
Figure 2 Block Diagram for Experimental Set up
A- Reference Electrode B- Auxiliary Electrode (Platinum) C-Working Electrode (AISI 304L)
D- Auto lab/PGTAT12 E-Electrolyte (1 N Hcl)
F- D.E. Amplifier
Figure 3a SEM image before corrosion Figure 3b SEM image after corrosion
Corrosion area
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4 DEVELOPING MATHEMATICAL MODELS
The output response of the weld joint (Y) is a function of peak current (A), back current (B),
pulse (C) and pulse width (D). It can be expressed as [20-22].
Y = f (A, B, C,D) (2)
The second order polynomial equation used to represent the response surface ‘Y’ is given by [17]:
Y = bo+bi xi +iixi2 + bijxixj+ (3)
Using MINITAB 14 statistical software package, the significant coefficients were determined and
final model is developed using significant coefficients to estimate pitting corrosion rate values of weld
joint.
The final mathematical model are given by
Pitting corrosion rate (CR)
CR= 0.645694+0.023167X1-0.087025X2+0.008392X3+0.036017X4+0.075631X22-0.127775X1X3
(4)
Where X1, X2, X3 and X4 are the coded values of peak current, back current, pulse rate and pulse
width. 5. CHECKING THE ADEQUACY OF THE DEVELOPED MODELS
The adequacy of the developed models was tested using the analysis of variance technique (ANOVA).
As per this technique, if the calculated value of the Fratio of the developed model is less than the standard
Fratio (from F-table) value at a desired level of confidence (say 99%), then the model is said to be adequate
within the confidence limit. ANOVA test results are presented in Table 5 for all the models. From the table
it is understood that the developed mathematical models are found to be adequate at 99% confidence
level. The value of co-efficient of determination ‘ R2 ’ for the above developed models is found to be
about 0.86 .
Table 5 ANOVA Table
Pitting corrosion rate
Source DF Seq SS Adj SS Adj MS F P
Regression 14 0.72098 0.72098 0.051499 7.11 0.000
Linear 4 0.22746 0.22746 0.056866 7.85 0.001
Square 4 0.20184 0.20184 0.050461 6.97 0.002
Interaction 6 0.29168 0.29168 0.048613 6.71 0.001
Residual Error 16 0.11590 0.11590 0.007244
Lack-of-Fit 10 0.08727 0.08727 0.008727 1.83 0.237
Pure Error 6 0.02863 0.02863 0.004772
Total 30 0.83689
Where DF= Degrees of Freedom, SS=Sum of Squares, MS=Mean Square, F=Fishers ratio
Rahul Vylen, N. Rajesh Mathivanan , N. Shashidhar Chandrasekhar / International Journal of Lean Thinking Volume 4, Issue 1(June 2013)
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6. OPTIMIZATION PROCEDURE
The purpose of optimization is to minimize pitting corrosion rate of AISI 304L welded sheets.
The tool used for optimization is GA. GA is an adaptive search and optimization algorithm that mimics
principles of natural genetics. Due to their simplicity, ease of operation, minimum requirements and
global perspective they have been successfully used in a wide variety of problem domains [23].
6.1 Working Principle of GA
GA simulates the survival of the fittest among individuals over consecutive generation for solving
a problem. Each generation consists of a population of characters. Each individual represent a point in a
search space and a possible solution. The individuals in the population are then made to go through a
process of evolution. The basic concept of GA is to encode a potential solution to a problem as a series of
parameters. A single set of parameter value is termed as the genome of an individual solution. An initial
population of individuals is generated randomly. In every generation the individuals in the current
population are decoded according to a fitness function. The chromosomes with the highest population
fitness are selected for mating. The genes of the parameters are allowed to exchange to produce new
ones. These new ones then replace the earlier ones in the next generation. Thus the old population is
discarded and the new population becomes the current population. The current population is checked
for acceptability or solution. The iteration is stopped after the completion of maximum number of
generations or on the attainment of the best results [23,24].
6.2 Implementation of GA
The GA operates on three main operators namely 1) Reproduction 2) Crossover and 3) Mutation.
Reproduction: It selects the copies of chromosomes proportionate to their fitness value. Here Roulette
wheel was used as reproduction operator to select the chromosomes.
Crossover: After reproduction, the population is enriched with good strings from the previous
generation but does not have any new string. A crossover operator is applied to the population to create
better strings.
Mutation: It is the random modification of chromosomes i.e., changing from 0 to 1 or vice versa on a bit
by bit basis. The need for mutation is to keep diversity in the population.
The GA algorithm for the optimization problem is given below
Step 1: Choose a coding to represent problem parameters, a selection operator, a crossover
operator and a mutation operator.
Step 2: Choose population size (n), crossover probability (Pc) and mutation probability (Pm).
Step 3: Initialize a random population of strings of size L. Choose a maximum allowable
generation number Gmax. Set G = 0. Evaluate each string in population.
Step 4: If G>Gmax or other termination criteria is satisfied, terminate or perform reproduction
on the population.
Step 5: Perform crossover on random pair of strings
Step 6: Perform mutation on every string
Step 7: Evaluate strings in the new population, set G = G+1 and go to step 3.
Rahul Vylen, N. Rajesh Mathivanan , N. Shashidhar Chandrasekhar / International Journal of Lean Thinking Volume 4, Issue 1(June 2013)
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After applying the GA operators, a new set of population is created. Then they are decoded and objective
function values are calculated. This completes one generation of GA. The number of generations is
continued till the termination criterion is achieved. The parameters used in GA are presented in Table 6.
Table 6 Parameters used in GA
Pitting corrosion rate
1 Sample size 40
2 Crossover probability 0.5
3 Mutation probability 0.9
4 Number of generations 100
5 Type of crossover Single
6.3 Objective Function
The optimization of pitting corrosion rate is carried out with the help of its mathematical
equation. The mathematical equation is considered as objective function. The source code was developed
using Turbo C. It is desirable to minimize pitting corrosion rate. The objective function for minimizing
pitting corrosion rate (Equation-4) is taken as the fitness function.
6.4 Results of GA
Figure 5 shows the results obtained by running the C program. The initial variation in the curve is
due to the search for optimum solution. It is evident that the minimum pitting corrosion rate of 0.4931
mm/Year is observed at the 2nd iteration. It then converges to the same value up to 100 generations.
Figure 5 Variation of pitting corrosion rate with number of generations
Co
rro
sio
n
Rat
e
(mm
/Ye
ar)
Number of Generations
Rahul Vylen, N. Rajesh Mathivanan , N. Shashidhar Chandrasekhar / International Journal of Lean Thinking Volume 4, Issue 1(June 2013)
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7 RESULTS & DISCUSSIONS
Based on the results obtained in GA, the optimum values of PCMPAW input parameters and
output response pitting corrosion rate is computed and presented in Table 7. The optimum pitting
corrosion rate of 0.4931 mm/Year is obtained for the welding input parameter combination of Peak
Current 6.5221 Amperes, Back Current 4.2067 Amperes, Pulse rate 30.0292 pulses/second and pulse
width 41.3226 %.
Table 7 Comparison of GA and Experimental values
Welding Parameters Experimental Values GA values
Peak current(Amperes) 7 6.5221
Back current(Amperes) 4 4.2067
Pulse rate (pulses/second) 40 30.0292
Pulse width (%) 50 41.3226
Pitting corrosion rate (mm/Year) 0.5206 0.4391
8 CONCLUSIONS
Empirical models are developed for pitting corrosion rate for PCMPAW AISI 304L austenitic steel
sheets using RSM CCD design matrix. The pitting corrosion rate is optimized using GA. The optimum
value of pitting corrosion rate obtained using GA is 0.4391 mm/Year, where the value obtained
experimentally is 0.5206 mm/Year. The optimum values obtained using GA is in good agreement with
experimental values
9 ACKNOWLEDGEMENTS
The authors would like to thank Shri. R.Gopla Krishnan, Director, M/s Metallic Bellows (I) Pvt
Ltd, Chennai, India and Mr. P V Vinay, Associate Professor, GVP College for PG courses (Technical
Campus), Visakhapatnam for their support to prepare this manuscript.
Rahul Vylen, N. Rajesh Mathivanan , N. Shashidhar Chandrasekhar / International Journal of Lean Thinking Volume 4, Issue 1(June 2013)
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