Application of welding arc to obtain small angular bend in steel plates

Application of Welding Arc to Obtain Small Angular Bend in
Steel Plates

B. Tech Project Report

Submitted in partial fulfillment of the requirements for the degree of

Bachelor of Technology

by

Ashish Khetan Nishant Ranjan Prathyusha.M

05010305 05010329 05010333

Department of Mechanical Engineering

Indian Institute of Technology Guwahati
MAY 2009

Steel Plates




by


05010305 05010329 05010333

Under the supervision of

Dr. U.S. Dixit Dr. S.K. Kakoty

Department of Mechanical Engineering

Indian Institute of Technology Guwahati
MAY 2009

Steel Plates



by


05010305 05010329 05010333

Approved by

Dr. D.Chakraborty Dr. R.G. Narayanan
(Examiner) (Examiner)

Dr. U.S.Dixit Dr. S.K.Kakoty
(Supervisor) (Supervisor)

Acknowledgements

We wish to acknowledge with thanks the continuing guidance and support of our supervisors, Prof.
U.S. Dixit and Prof. S.K. Kakoty. We are also thankful to Mr. D.K. Sharma, workshop In-charge,
and Mr. Chetri, technician at workshop, for their immense help in carrying out the experiments.

05010305 05010329 05010333

Bachelor of Technology,

Department of Mechanical Engineering,

IIT Guwahati.

i

CONTENTS

List of Figures iv

List of Tables v

1. Introduction 1

2. Literature Review 2

2.1 Submerged Arc Welding (SAW)………………………………………………….... 2

2.1.1 Finite Element Modeling……………………………………………………... 2

2.1.2 Neural Network Methods……………………………………………………... 4

2.2 Gas Metal Arc Welding (GMAW)…………………………………………………. 6



2.3 Gas Tungsten Arc Welding (GTAW) …………………………………………….... 10



2.4 Comments on Literature……………………………………………………………. 14

3. Experimental Setup 15

3.1 Manual Torch Holding…………………………………………………………….... 15

3.2 Rack and Pinion System……………………………………………………………. 16

3.3 Simple Two Wheel Vehicle………………………………………………………… 17

3.4 Pug Cutting Machine……………………………………………………………….. 17

ii

4. Experimental Results 19

4.1 Results for 1mm MS plate………………………………………………………….. 19

4.1.1 Neural Network Modeling of 1mm plate data set…………………………….. 24

4.2 Results for 2mm MS plate………………………………………………………….. 27

4.2.1 Neural Network Modeling of 2mm plate data set…………………………….. 33

4.2.2 Results of Double pass welding on 2mm plate……………………………….. 36

5. Conclusion and Future Scope 38

Appendix 1 Background Theory on Probability Distributions 39

Appendix 2 Neural Networks 48

References 58

iii

LIST OF FIGURES

2.1 Weld pool geometry………………………………………………………………… 13

3.1 Circuit diagram of IC 555…………………………………………………………… 16

3.2 Experimental setup………………………………………………………………….. 18

4.1 Bend angle vs. Welding speed for 1mm plate……………………………………… 21

4.2 Variance in bend angle vs. Welding speed for 1mm plate…………………………. 21

4.3 Bend distribution at 40A current for 1mm plate……………………………………. 22



4.6 Experimental values vs. estimated values of scale parameter, λ for 1mm plate……. 26

4.7 Experimental values vs. estimated values of Shape parameter, k for 1 mm plate….. 26

4.8 Bend angle vs. Welding speed for 2 mm plate……………………………………… 29

4.9 Variance in Bend angle vs. Welding speed for 2 mm plate………………………… 29

4.10 Bend distribution at 40A current for 2 mm plate………………………………….. 30



4.13 Bend distribution at 100A current for 2 mm plate………………………………… 33

4.14 Experimental values vs. estimated values of Scale parameter, λ for 2 mm plate…. 35

4.15 Experimental values vs. estimated values of Shape parameter, k for 2 mm plate… 36

4.16 Bend angle in single pass and double pass for 2 mm plate………………………… 37

iv

LIST OF TABLES
Table 3.1 Data set obtained using manual torch holding…………………………….... 15

Table 3.2 Speed mode vs. Speed in cm/s……………………………………………………… 17

Table 4.1 Data set at 40A current for 1mm plate……………………………………………. 19

Table 4.2 Data set at 60A current for 1mm plate………………………………………. 20

Table 4.3 Data set at 80A current for 1mm plate………………………………………. 20

Table 4.4 Training data set for 1 mm plate…………………………………………….. 24

Table 4.5 Testing data set for 1 mm plate……………………………………………… 25

Table 4.6 Data set at 40 A current for 2mm plate…………………………………………… 27

Table 4.7 Data set at 60 A current for 2mm plate…………………………………………… 27

Table 4.8 Data set at 80 A current for 2mm plate……………………………………… 28

Table 4.9 Data set at 100 A current for 2mm plate…………………………………….. 28

Table 4.10 Training data set for 2 mm plate…………………………………………… 34

Table 4.11 Testing data set for 2 mm plate……………………………………………... 34

Table 4.12 Results of double pass welding on 2mm plate………………………………….. 36

v

Chapter 1

Introduction

The use of heat energy at high temperature to melt two pieces of material and joining them
together by material-material adhesion or using some filler has been well known from long
period. This process termed as welding has been extensively used to join the two metal work
pieces. There are many different kinds of welding processes viz., Submerged Arc Welding
(SAW), Gas Tungsten Arc Welding (GTAW) and Gas Metal Arc Welding (GMAW), Laser
Welding, Electron Beam Welding and so on. All of these processes utilize the basic principle
of melting material using arc at high temperature and thereby joining the two pieces.

With the thought of contributing to the research of welding process, a detailed literature
review of the subject has been made. The three major welding processes SAW, GTAW and
GMAW were studied in detail, the associated problems and their suggested solutions focused
by researchers are presented in a categorical way. Most of the research is carried in the
direction of improving the process attributes like weld joint strength, bead geometry, heat
affected zone. Artificial intelligence tools, neural networks and fuzzy algorithms are used by
many researchers to model the process in order to predict these attributes as a function of the
process parameters. Using the physics of the process finite element modeling has also been
done to model the process and to optimize the process parameters. The literature provides an
insight of the process.

The present work explores the possibility of the use of welding arc to obtain small
angular bend in steel plates. The process has many advantages over the mechanical clamping
method. It eliminates any possibility of spring back of the plate. Artifacts having design over
the plate which can not be clamped mechanically can be bent easily using the suggested
process. The process is relatively cheaper also.

A constant current TIG welding machine without feed wire is used in the experiments.
An attempt is made to quantify the angular bend obtained in a flat plate, as a function of the
input parameters of the process, current and welding speed. In lack of literature available, a
number of replicates are performed to analyze the dependence of the bend angle on the
process parameters. Results obtained by performing replicates of the experiment are analyzed
using Weibull probability distribution. In order to establish a functional relationship between
process parameters and the bend obtained data is modeled using neural network. Feasibility
of the process is assessed by performing experiments on two different MS sample plates of
thickness 1mm and 2 mm, and size 3×6 inch.

1

Chapter 2

Literature Review

The literature review is presented in three sections on the basis of the welding process being
dealt with viz., Submerged Arc Welding (SAW), Gas Tungsten Arc Welding (GTAW) and
Gas Metal Arc Welding (GMAW). The welding processes have been modeled using Finite
Element Method (FEM) and Neural Networks (NN). Among various welding processes,
SAW, GTAW and GMAW have been extensively studied. Welding of different materials had
been studied by varying geometries, input parameters and welding conditions.

2.1 Submerged Arc Welding (SAW)

Submerged Arc Welding has been defined by the American Welding Society (AWS) as
follows: “The submerged arc welding process is an arc welding process, which produces
coalescence of metals by heating them with an arc or arcs between a bare metal electrode or
electrodes and the work. The arc and molten metal are shielded by a blanket of granular,
fusible material on the work. Pressure is not used, and filler metal is obtained from the
electrodes and some times from a supplemental source (welding rod, flux or metal granules).”

SAW is normally operated in the automatic or mechanized mode, however, semi-
automatic (hand-held) SAW guns with pressurized or gravity flux feed delivery are available.
The material applications include carbon steels, low alloy steels, stainless steels, nickel-based
alloys and other steels for surfacing applications. The key process variables are wire feed
speed, arc voltage, travel speed, electrode stick-out and polarity and current type (AC or DC).
The other factors that influence the SAW process are flux depth, flux and electrode type,
electrode wire diameter, heat affected zone (HAZ), thermal diffusivity and multiple electrode
configurations.

2.1.1 Finite Element Modeling Techniques

Recently, numerical simulation has been increasingly used as a tool to assist welding process
analysis and optimization, and in particular applied to the prediction of welding induced
residual stress and strain [1]. Wen et al. [1] have modeled a multi-wire SAW process using a
general purpose finite element package ABAQUS. Effects of process parameters and
weldment geometry have been evaluated with and without the consideration of residual
stresses and strains induced from the forming processes prior to welding. The corresponding
2D and 3D finite element models were presented and analyzed to investigate the heat transfer
characteristics in the fusion and heat affected zones during welding. This work also gives the
global distortions caused in a pipe due to welding. The thermal history predicted can be
useful in characterizing welding process parameters such as speed and power input, with
respect to fusion and HAZ geometries and hence weldment integrity.

2

The welding process parameters under investigation depend on the desired output
parameters. Dutta et al. [2] have taken process parameters such as electrode diameter,
electrode travel speed, workpiece thickness, current and voltage that are said to greatly affect
the temperature distribution patterns and hence the residual stresses and distortions. A
coupled transient thermal and structural analysis has been done to study the temperature
distribution and also to minimize the resulting angular distortions through the above said
process parameters in single and multi-pass welded joints using a reusable flux-filled backing
strip. In addition, moving heat source, arc travel speed, current and voltage, temperature-
dependent material properties and deposition of filler material have been given as the
important process characteristics to be taken into consideration for any simulation

Similar work has been done by Michaleris and DeBiccari [3] in which they combined
welding simulations with 3D structural analysis in a decoupled approach to evaluate welding
induced buckling in panel structures. They had used a kinematic work hardening material
model for simulating the plastic behavior of mild steel. The complexities involved in
simulation of welding processes and improved material models for better prediction of
residual stresses and distortions have been discussed by Lindgren [4]. Alberg [5] further
extended these models and developed modeling methodologies using finite element analysis
for predicting deformation, residual stresses and material properties such as microstructure
during and after welding as well as after heat treatment of fabricated aircraft-engine
components.

A large number of models have been reported to predict temperature distributions,
residual stresses and distortions in the welded joints. Most of them have concentrated on a 2D
approximation and have advocated the need for 3D simulation so that they can be better
utilized for simulating the behavior of a complete welded structure. A 3D welding analysis
was given by Runnemalm [6] that made use of an adaptive mesh scheme. A strategy is
presented for coupled thermo-mechanical analysis of welding in order to reduce one of the
major problems arising in finite element analysis of welding i.e., the long computer times
required for complete 3D analysis. In addition to this, other problems like staggered thermo-
mechanical solution process, automatic mesh refinement and coarsening, geometry-based
user input for model definition and analysis of the microstructure evolution for hypoeutectoid
steels, that arise when settling up welding analysis have been dealt using the FE formulation
being implemented in an in-house code.

The influence of submerged arc welding parameters and flux basicity on the weld
chemistry and transfer of different elements have been investigated with varying fluxes and
welding parameters by Pandey et al. [7]. According to this study, during SAW, weld-metal
chemistry is determined mainly by welding consumables and operating variables, other
secondary factors being joint design, heat input of welding and weld thermal history. The
prediction of weld-metal chemistry is rather difficult and complicated due to the reaction
kinetics of submerged arc welding (which is characterized by short reaction time and large
thermal gradient) being altogether different to those of steel-making. This study was aimed at
3

studying the effect of both the parameters, different fluxes and different welding parameters
together on the element transfer and weld composition. The welding speed was kept constant
and the welding current and voltage were varied as welding parameters.

A detailed 3D nonlinear thermal and thermo-mechanical analysis was carried out using
the finite element welding simulation code WELDSIM by Chao and Zhu [8]. Welding of an
aluminium plate using three sets of material properties, viz., properties that are functions of
temperature, room temperature values, and average values over the entire temperature history
in welding were considered in the simulation. The thermal analysis was first performed and
the transient temperature outputs from this analysis were saved for the subsequent thermo-
mechanical analysis. Transient temperature field was taken as a function of time with the heat
flux to the system given as input by a moving source on the boundary. Chao and Zhu [8]
concluded that thermal conductivity has some effect on the distribution of transient
temperature field during welding but material density and specific heat have negligible effect
on the temperature field. In addition, yield stress was found to be the key mechanical
property in welding simulation. Young’s modulus and the thermal expansion coefficient have
found to have small effects on the residual stress and distortion in welding deformation
simulation.

2.1.2 Neural Network Methods

Mathematical models have been developed for SAW of pipes using five level factorial
techniques to predict three critical dimensions of the weld bead geometry and shape
relationships. Murugan and Gunaraj [9] have presented the main and interaction effects of the
process variables on bead geometry and shape factors in graphical form and using which not
only the prediction of important weld bead dimensions and shape relationships but also the
controlling of the weld bead quality by selecting appropriate process parameter values are
possible. The acceptable or appropriate weld shape was said to depend on factors such as line
power which is the heat energy supplied by the arc to the base plate per unit length of weld,
welding speed, joint preparation etc.

Gunaraj and Murugan [10] have also developed a Response Surface Methodology (RSM)
which determines and represents the cause and effect relationship between true mean
responses and input control variables influencing the responses as a two or three dimensional
hyper surface. RSM explores the relationships between several explanatory variables and one
or more response variables with the main idea of using a set of designed experiments to
obtain an optimal response. Reference [10] highlights the use of RSM by designing a four-
factor five-level central composite rotatable design matrix with full replication for planning,
conduction, execution and development of mathematical models. By the development of
mathematical models through effective and strategic planning and the execution of
experiments by RSM, the problem of selection of the optimum combination of input variables
for achieving the required qualities of weld in the manufacturing of pipes by SAW process
can be solved.

4

Yang et al. [11] provide another yet familiar traditional method for modeling the weld
bead geometrical features of SAW process. Curvilinear regression equations were used to
study the relationship between correlation coefficient and the standard deviation of the
deviations between the predicted and measured values with respect to melting rate, total
fusion area, penetration, deposit area, bead height and bead width. Although it was found that
there exists no strong relationship between the correlation coefficient of a correlation
equation and the standard deviation of the deviations between the predicted and measured
values, this statistical analysis shows higher mean deposit area obtained directly from the
melting rate.

Recent investigations have shown that due to low tolerance in some cases, it is not
possible to include all variables in the regression analysis [12]. Yang et al. [12] discuss the
linear regression equations that were found to give correlation coefficients similar to those
obtainable from curvilinear regression equations with the same procedure followed as that of
curvilinear equations. Therefore, linear equations were shown to be equally suitable for
modeling the SAW process.

Neural network modeling has been adopted to model the non-linear relationship between
the five geometric descriptors (height, width, penetration, fused and deposited areas) of a
bead and the welding parameters (current, voltage and welding speed) of SAW process [13].
Ping et al. [13] have shown the advantages of single-output networks by a comparative study
between multi-output networks and single-output networks, each modeling one geometric
descriptor.

Rather than the well-known effects of main process parameters, Karaoglu and Secgin [14]
have focused on the sensitivity analysis of parameters and fine tuning requirements of the
parameters for optimum weld bead geometry. The design variables considered are welding
current, welding voltage and welding speed. An objective function was formed using width,
height and penetration of the weld bead. An experimental study has been done based on the
three-level factorial design of the three process parameters. A mathematical model was
constructed using multiple curvilinear regression analysis. The relative effects of input
parameters on output parameters were obtained from the sensitivity analysis using developed
empirical equations. It has been found that effects of all three design parameters play an
important role in the quality of welding operation. In addition, variations in voltage and speed
do not affect the penetration much.

Sensitivity analysis was also carried out to study distortions in a steel plate [15].
McPherson et al. [15] have established an artificial neural network from a commercially
available system, and the model was fed with data from a series of simple trials using D and
DH 36 steel plates of thicknesses 6 and 8 mm. Along with some already established factors
like plate thickness and heat input, sensitivity analysis of the data showed carbon equivalent
(CEV) of the steel to be a significant factor. In addition, the yield strength to tensile strength
ratio, the steel grade, the edge preparation mode and the rolling treatment were also identified
as being factors which appeared to influence the sensitivity of the plate to welding distortion.
5

2.2 Gas Metal Arc Welding (GMAW)

The GMA welding process is a welding process, which yields coalescence of metals by
heating with a welding arc between a continuous filler metal (consumable) electrode and the
work piece. A continuous wire electrode is drawn from a reel by an automatic wire feeder,
and then fed through the contact tip inside the welding torch and melted by the internal
resistive power and heat transferred from the welding arc. Heat is concentrated by the
welding arc from the end of the melting electrode to molten weld pools and by the molten
metal that is being transferred to weld pools.

The GMA welding parameters are the most important factors affecting the quality,
productivity and cost of welding joint. Weld bead size and shape are important considerations
for design and manufacturing engineers in the fabrication industry. In fact, weld geometry
directly affects the complexity of weld schedules and thereby the construction and
manufacturing costs of steel structures and mechanical devices. Therefore, these parameters
affecting the arc and welding bath should be estimated and their changing conditions during
process must be known before in order to obtain optimum results. These are combined in two
groups as first order adjustable and second order adjustable parameters and defined before
welding process.

The composition of a shielding mixture in arc welding depends mostly on the kind of
material to be welded. To reduce the defects and to have good weldability, argon and helium
are most commonly used as shield gases and they play an important role in reduction of
generation of defects and protection of weld pool. The shielding gas for arc welding must be
easily ionized to ensure that the arc can be sustained at a reasonably low voltage. Helium, one
of the lightest gases, has a higher ionization potential and approximately ten times lighter
than argon. It often promotes higher welding speeds and improves the weld bead penetration
profile. On the other hand, difficulty in initiating the arc and the poor tolerance to cross-
draughts, and the high price of helium, are disadvantages in using Helium. For these reasons,
argon/helium, argon/carbon dioxide, argon/oxygen and argon/carbon dioxide/ oxygen gas
mixtures are more commonly used than pure gases.

2.2.1 Finite Element Modeling

Traditionally, finite element models have been developed to obtain the residual stresses
induced during welding of a specimen and the distortions that the specimen has undergone as
a result of the process. A three-dimensional approach for the finite element formulation
required huge computation time and memory capacity of the computer. Also, to overcome the
inadequacies of two-dimensional models, a laminated plate theory had been proposed [16] for
the analysis of the thermo-elasto-plastic behavior of a thin plate in gas-metal arc bead-on-
plate welding and an FEM formulation was used to solve the governing equations of the
stress and distortion. The knowledge of the mechanism of the transient thermo-mechanical
behavior of a plate under a moving welding heat source is fundamental for the understanding

6

the mechanical aspect of the welding process. The heat conduction model involves heat-
conduction equation solved first in fixed coordinates by considering an instantaneous
Gaussian heat source, which is then integrated with respect to time in a moving coordinate to
provide a quasi-steady-state solution. The effect of the weld deposit as well as of the surface
radiation was neglected.

Considering all mechanical properties to be temperature-dependent, the transient
temperature distributions were obtained and the elliptical shape of the isotherms clearly
showed the great temperature gradient in front of the electrode and the gradual cooling of the
solidified weld. The temperature variations were said to arise from the thermal energy of the
welding arc transferred onto a finite area of the upper surface of the weldment. The effect of
the heat input on the distortion of the weldment, was seen to be an increasing distortion first,
but then a decrease after reaching the maximum value, as the heat input increased. The results
of the plate analysis were obtained by averaging the angular distortions at three different
positions, i.e., at the welding start, at the plate center and at the welding end.

Distortion is a potential problem with all welded fabrications. Shrinkage Volume Method,
a linear elastic finite-element modeling technique has been developed by Bachorski et al. [17]
to predict post-weld distortion. Given the composition of the parent and weld metal, the
parent plate thicknesses, the joint preparation the parent plate constraints, and the welding
parameters, the model is able to predict the post-weld displacement of any point along the
welded plates. The linear elastic shrinkage volume method is a steady state finite-element
approach that assumes that the main driving force for distortion is linear thermal contraction
of the weld metal as it cools from elevated to room temperature. The contraction is resisted
by the surrounding parent metal, resulting in the formation of internal forces. The parent
metal distorts to accommodate these shrinkage forces until equilibrium is achieved. The
shrinkage volume approach is able to predict the magnitude of these distortions reasonably
accurately, and therefore, has the potential to serve as a very useful tool in the prediction of
distortion in large, complex welded structures. For large V-preparation angles, the shrinkage
volume can be assumed to be equivalent to the edge preparation geometry without significant
error. However, for V-angles smaller than 50 degree, where the fusion zone shape becomes
process-dependent, a more accurate means of calculating the shrinkage volume is required.
The magnitude of angular distortion in single-V butt welded joints is influenced by the
included angle of the V preparation. As the included angle increases, so does the resultant
angular distortion.

Numerical models have been developed [18] to analyze the complex thermal cycle in the
weldment caused by a heat input from the moving welding arc due to which the experienced
microstructural changes, thermal stresses and metal movement finally lead to the formation
of residual stresses and distortion in the finished product. Wahab and Painter [18] have
provided a method of obtaining the detailed three-dimensional measurement of a weld pool
form by conducting experimental study of GMAW under various welding conditions and also
determined the relationship between different process variables in addition to exploring the
possibility of using a known weld pool form as the boundary condition representing the
7

welding arc, within a finite element model of GMAW. The important parameters considered
include penetration, pool width, bead height, pool length and the volume and surface area of
the pool below the plate. Most finite element approaches use heat sources defined as
complicated spatial heat flux distributions representing the total energy of the welding
process. The measured weld pool cavity is taken as a temperature boundary fixed at the
melting point of the material. A ‘standard’ plate had been meshed and locally scaled to
duplicate the geometry of a given weld pool cavity and weld bead whose material properties
were temperature dependent allowing radiative and convective heat losses. Increasing
welding speed and current were found to yield longer pool length and thus have the greatest
influence on the length of a weld pool.


A novel technique based on artificial neural networks (ANNs) for prediction of gas metal arc
welding parameters was given by Ates [19]. Input parameters of the model consist of gas
mixtures O2, CO2, Ar, which give the output parameters, tensile strength, impact strength,
elongation and weld metal hardness. ANN controller was trained with the extended delta-bar-
delta learning algorithm. A multi-layer perceptron neural network model with three inputs,
two hidden layer and four outputs was employed. The hyperbolic tangent functions were
selected in the hidden and the output layers. The input and the output values to the multi-
layer perceptron NN were normalized to lie between -1.0 to +1.0. Results showed that, the
neural networks can be used as an alternative way for calculating the gas mixture according
to the presented conventional calculation method. It is sufficient to take gas mixtures to
predict mechanical properties such as tensile and impact strengths, elongation and weld metal
hardness of the joint.

A research was done by Lee and Um [20] on the basis of prediction that there is a
relationship between welding parameters and geometry of the back-bead in arc welding
which is a gap. Through this research, it was found that the error rate predicted by the
artificial neural network was smaller than that predicted by the multiple regression analysis,
in terms of the width and depth of the back-bead. It was also found that between the two
predictions, the prediction of the width of the back-bead was superior to the prediction of the
depth in both methods. A laser vision sensor was used to measure the geometry of the back-
bead. Image processing technique was used to obtain experimental data. Four welding
parameters were established as input variables, and the estimated width and depth of the
back-bead were established as output variables in the artificial neural network. Here, the
hidden layer comprised two layers with six neurons each.

The focus of Kim et al. [21] had been on the development of mathematical models for the
selection of process parameters and the prediction of bead geometry (bead width, bead
height, and penetration) in robotic gas metal arc (GMA) welding. A sensitivity analysis has
also been conducted and compared with the relative impact of three process parameters on
bead geometry in order to verify the measurement errors on the values of the uncertainty in

8

estimated parameters. Sensitivity analysis, a method to identify critical parameters and rank
them by their order of importance, is paramount in model validation where attempts are made
to compare the calculated output to the measured data. The results obtained show that
developed mathematical models can be applied to estimate the effectiveness of process
parameters for a given bead geometry, and a change of process parameters affects the bead
width and bead height more strongly than penetration relatively. The objective of this study is
to find the optimal bead geometry in GMA welding process using mathematical models with
the chosen factors being welding voltage, welding speed and arc current, and the responses
were bead width, bead height and penetration.

Further works of Kim et al. [22] extend to studying the fuzzy linear regression technique
which was developed to study relationships between four process variables (wire diameter,
arc voltage, welding speed and welding current) and four quality characteristics (bead width,
bead height, bead penetration and bead area) and to control the quality of the GMA welding
based on the analysis of the bead geometry. Using the method and experimental results, the
linear programming (LP) models from the fuzzy linear regression approach were developed.
Two validation tests were performed to evaluate the effectiveness of the process models.
Through the models, the prediction of the three quality characteristics (bead width, bead
penetration and bead area) was obtained with the error less than 5%. Also, the center value
calculated from the LP model for the bead width was proved to be the best amongst the bead
geometry.

Kim et al. [23] presented a new algorithm to establish a mathematical model for
predicting top-bead width through a neural network and multiple regression methods to
understand relationships between process parameters and top-bead width, and to predict
process parameters on top-bead width in robotic gas metal arc (GMA) welding process.
Using a series of robotic GMA welding, additional multi-pass butt welds were carried out in
order to verify the performance of the multiple regression and neural network models as well
as to select the most suitable model. The results show that not only the proposed models can
predict the top-bead width with reasonable accuracy and guarantee the uniform weld quality,
but also a neural network model could be better than the empirical models. Process
parameters such as pass number, welding speed, welding current and arc voltage influence
top bead width for GMA welding process. The developed models are able to predict process
parameters required to achieve desired top-bead width, to help the development of automatic
control system as well as expert system, and to establish guidelines and criteria for the most
effective joint design.

Karadeniz et al. [24] had studied the effects of various welding parameters on welding
penetration welded by robotic gas metal arc welding. The welding current, arc voltage and
welding speed were chosen as variable parameters. The depths of penetration were measured
for each specimen after the welding operations and the effects of these parameters on
penetration were researched. As a result of this study, it was obvious that increasing welding
current increased the depth of penetration. In addition, arc voltage was also found to
influence penetration. Enough penetration, high heating rate and right welding profile
9

describe the quality of welding joint. These are affected from welding current, arc voltage,
welding speed and protective gas parameters. Among all, welding current intensity has the
strongest effect on melting capacity, weld seal size and geometry and depth of penetration.

The weld joint strength monitoring in pulsed metal inert gas welding process (PMIGW)
have been addressed by Pal et al. [25] in which RSM (Response Surface Methodology) had
been applied to perform welding experiments. A multilayer neural network model has been
developed to predict the ultimate tensile stress (UTS) of welded plates. Six process
parameters, namely pulse voltage, back-ground voltage, pulse duration, pulse frequency, wire
feed rate and the welding speed, and the two measurements, namely root mean square (RMS)
values of welding current and voltage, are used as input variables of the model and the UTS
of the welded plate is considered as the output variable. The objective was to determine and
represent the cause and effect relationship between the response and input control variables.
Taguchi method relies on the replication each experiment by means of an outer array, itself
an orthogonal array that seeks deliberately to emulate the sources of variation that a product
would encounter in reality. On the other hand, response surface methodology (RSM) explores
the relationships between several explanatory variables and one or more response variables.
The main idea of RSM is to use a set of designed experiments to obtain an optimal response.
Due to the very complicated nature of the welding process, which involves electrical,
thermal, hydraulic, plasma-physics and thermo-metallurgical phenomena, and more
importantly, unavailability of sufficient knowledge about the process dynamics, RSM
methodology was preferred to Taguchi method.

2.3 Gas Tungsten Arc Welding (GTAW)

Gas tungsten arc welding (GTAW), also known as tungsten inert gas (TIG) welding, is an arc
welding process that uses a non-consumable tungsten electrode to produce the weld. The
weld area is protected from atmospheric contamination by a shielding gas (usually an inert
gas such as argon), and a filler metal is normally used, though some welds, known as
autogenous welds, do not require it. A constant-current welding power supply produces
energy which is conducted across the arc through a column of highly ionized gas and metal
vapors known as plasma.

GTAW is most commonly used to weld thin sections of stainless steel and light metals
such as aluminum, magnesium, and copper alloys. The process grants the operator greater
control over the weld than competing procedures such as shielded metal arc welding and gas
metal arc welding, allowing for stronger, higher quality welds. However, GTAW is
comparatively more complex and difficult to master, and furthermore, it is significantly
slower than most other welding techniques.

GTAW can use a positive direct current, negative direct current or an alternating current,
depending on the power supply set up. A negative direct current from the electrode causes a
stream of electrons to collide with the surface, generating large amounts of heat at the weld
region. This creates a deep, narrow weld. In the opposite process where the electrode is

10

connected to the positive power supply terminal, positively charged ions flow from the tip of
the electrode instead, so the heating action of the electrons is mostly on the electrode. This
mode also helps to remove oxide layers from the surface of the region to be welded, which is
good for metals such as Aluminium or Magnesium. A shallow, wide weld is produced from
this mode, with minimum heat input. Alternating current gives a combination of negative and
positive modes, giving a cleaning effect and imparts a lot of heat as well.

2.3.1 Finite Element Modeling

A 3D FE model was developed by Kermanpur et al. [26] in ANSYS to simulate the
multipass GTAW process of Incoloy 800 petrochemical pipes. Incoloy 800 is a fully
austenitic iron-based alloy, which is often selected for sue in high-temperature environments
where a combination of strength and corrosion resistance is required. The birth and death
technique was used to consider mass addition from the ERNiCr3 filler metal into the weld
pool. Movement of the GTAW torch was modeled in a discontinuous manner assuming a
constant welding speed. The transient temperature distribution in the workpiece as well as
the weld pool shapes were predicted under different process conditions. The effect of the
heat source distribution function, heat input and welding speed on temperature distribution
was investigated and computer simulation tools based on FEM were seen to be very useful
to predict welding distortions and residual stresses at the early stage of product design,
formation of defects and weldability and the welding process development.

On the other hand, Fenggui et al. [27] established an integral mathematical model of fluid
flow and heat transfer of GTAW arc and weld pool. The assumption that surface temperature
of weld pool is constant was not made. The behavior of welding arc and weld pool was
symmetrically analyzed including welding arc temperature field, current density distribution,
fluid flow in weld pool and effects of few forces on weld pool shape. Welding arc and weld
pool are two parts of GTAW process. In order to reveal clearly welding process, many
scholars have taken welding arc and weld pool as research objects repeatedly but most
researches were separately concentrated on studying on welding arc behavior or only
simulating on weld pool. The study on the interaction between welding arc and weld pool
was discussed rarely which was illustrated in this work.

Another dimension of GTAW shows analysis of residual stress state in spot welds made
in an HY100 steel disk by an autogenous GTAW process by Talijat et al. [28]. An
uncoupled thermal-mechanical FE model was developed using ABAQUS that took into
account the effects of liquid-to-solid and solid-state transformations. Effects of variations in
mechanical properties due to solid-state phase transformations on residual stresses in the
weld were studied. Extensive experimental testing was carried out to determine the
mechanical properties of HY100 steel. The FE results are in good agreement with Neutron
Diffraction measurements. It was concluded that in thermal analysis one should account for,
(i) conductive and convective heat transfer in the weld pool, (ii) Convective, radiative and
evaporative heat losses at the weld pool surface and (iii) heat conduction into the

11

surrounding solid material, as well as the conductive and convective heat transfer to ambient
temperature.


TIG weld quality is highly characterized by weld pool geometry this is because the weld
pool geometry plays an important role in determining the mechanical properties of weld
[29]. The weld geometry in turn depends on process parameters such as welding speed,
welding current, arc gap etc. Thus, there is a natural quest of researcher to derive input
output relationship between welding parameter and weld quality. It is well known that
modeling the relationships between the input and output variables for non-linear, coupled,
multi-variable systems is very difficult. In recent years, neural networks have demonstrated
great potential in the modeling of the input–output relationships of complicated systems
such as TIG welding [30].

Significant amount of work has been done in this field by Tarng et al. [31]. They
explored the use of neural network to model TIG welding. Both the back-propagation
neural network and counter- propagation neural network [32] were used to associate the
welding process parameters with the features of the weld-pool geometry. A comparison
was made between the two technique and they concluded that both the back-propagation
and counter- propagation networks can model the TIG welding process with reasonable
accuracy. However, the counter- propagation network has better learning ability for the
TIG welding process than the back-propagation network, although the back-
propagation network has better generalization ability for the TIG welding process than
does the counter- propagation network.

To ensure TIG weld quality, several on-line monitoring techniques have been studied and
were developed using vision-based systems directly to estimate weld pool geometry or
indirectly to correlate the weld pool geometry with process parameters such as welding
voltage, welding current, etc. However, there are difficulties involved concerning reliability,
calibration and cost in the use of the monitoring techniques. So apart from on-line
monitoring techniques, modeling, optimization and classification of TIG weld quality are
still extremely important research topics to obtain a high level of weld quality. Tarng and
Juang [33] reported a technique for modelling, optimization and classification of TIG weld
.Thin aluminum plates are joined by using TIG welding. Three features on the weld pool
geometry viz. the front depth, back height and back width of the weld were considered.
These features have a smaller-the-better quality characteristic if the weld has penetrated the
back face of the base metal. Back-propagation network [34] was then used to construct the
relationships between the welding process parameters and the three features on the weld
pool geometry in TIG welding. In addition, simulated annealing algorithm was applied to the
back-propagation network for searching the process parameters with optimal weld pool
geometry (Fig 2.1). Finally, a fuzzy clustering technique called the fuzzy c-means algorithm
[35] was used to classify and verify the aluminum weld quality based on the features on the
weld pool geometry.

12

Fig. 2.1: Weld pool geometry

Moving a step further Juang and Tarng [36] in their later work tried to find the welding
process parameters for obtaining optimal weld pool geometry. Basically, the geometry of the
weld pool has several quality characteristics, for example, the front height, front width, back
height and back width of the weld pool. To consider these quality characteristics together in
the selection of process parameters, the modified Taguchi method [37] is adopted to analyze
the effect of each welding process parameter on the weld pool geometry, and then to
determine the process parameters with the optimal weld pool geometry. Experiments were
performed on 1.5 mm thick stainless steel plates and results were used to illustrate the
proposed approach. It was also emphasized that weld penetration at the back face of the base
metal must be achieved to ensure the weld strength. The front height, front width, beck
height and back width of the weld pool have smaller-the-better quality characteristics.

Back-propagation neural network (BPNN) had been widely used to model the welding
processes. But, the chance of its solutions getting trapped into the local minima is high, as its
working is based on the principle of a steepest descent method. To overcome this difficulty
Pratihar and Dutta [38] utilized a genetic algorithm (GA) [39] (in place of the steepest
descent method), along with the feed forward NN, which may be termed as a genetic-neural
system (GA-NN). Also modeling of TIG welding was done using a conventional linear
regression technique and back propagation neural network. The performance of the three
techniques (regression analysis, BPNN, GA-NN) was compared using some test cases. Both
the NN-based approaches were seen to be more adaptive compared to the conventional
regression analysis. For the test cases Genetic-neural (GA-NN) system outperformed the
BPNN in most of the test cases (but not all). BPNN showed a slightly better performance
compared to the genetic-neural system initially, but after about 60,000 iterations, the latter
started to perform better than the former. It might be due to the fact that the solutions of
BPNN were still lying on the local basin of the deviation (error) function, whereas the GA
continued its search on a wider space, to reach the global optimal solution.

Weld penetration is an important factor to achieve quality weld. Zhao et al. [40]
established a neural network based model for weld penetration control in gas tungsten arc
welding describing the relationship between the front-side geometrical parameters of
weld pool and the back-side weld width with sufficient accuracy. Welding experiments
were conducted to obtain the training data set (including 973 groups of geometrical
parameters of the weld pool and back-side weld width) and the verifying data set (108
13

groups). Two data sets were used for training and verifying the neural network,
respectively. The testing results show that the model has sufficient accuracy and can meet
the requirements of weld penetration control.

2.4 Comments on Literature

It is observed that finite element method and neural network have been extensively applied
for modeling the welding processes. FEM requires the accurate knowledge of material
behavior, physical laws and behavior of the interaction. Once the required information is
available, FEM can be a robust tool to model the processes. Neural network model does not
need any information other than the actual shop floor data. Therefore, if sufficient amount of
data is available, it can be an effective method for modeling the welding processes.
However, it is seen that statistical variation in the process has been paid only scan attention
till now.

14

Chapter 3

Experimental Setup

The welding machine, UNIMACRO 501, a manufacture of ESSETI, is used for carrying out
all the experiments. The machine can be used for TIG and MIG both types of welding. The
MIG welding mode essentially uses feed wire whereas TIG welding allows the optional use
of feed rod. As the purpose is to use welding arc to obtain small angular bend in flat plate
while maintaining its aesthetics, machine is used in TIG welding mode without the use of
feed wire. Machine has different program settings. Program no. 22 is used through out the
experiments. The program sets machine in TIG welding mode. It allows the value of current
to be adjusted with a precision of 1 amp. It sets machine in constant current welding mode.
The current almost remains constant but the value of voltage changes with the small
perturbation in arc length. A tungsten electrode of 4 mm. diameter is used. Argon is used as
the shielding gas at the flow rate of 8-10 std. liter per minute. The sections below brief some
of the unsuccessful and the final successful attempt of fabricating the experimental setup.

3.1 Manual Torch Holding

The work is started with the manual holding of welding torch. A number of experiments are
carried out to examine the welding speed control in manual way. Experiments are carried out
on a sample size of 6×8 inch of MS 1 mm. plate along the 6 inch line through the middle of 8
inch long breadth. Results are tabulated below in Table 3.1.

Table 3.1: Data set obtained using manual torch holding

Sample no. Current (amps) Speed (cm/sec.) Bend (minutes)
1 90 1.33 202
2 90 1.47 285
3 100 1.20 352
4 100 1.27 285
5 110 1.13 236
6 110 1.13 440
7 120 1.13 420
8 120 1.07 374
9 130 1.20 460
10 130 1.07 323
11 140 1.07 457
12 140 1.07 423
13 150 0.80 428
14 150 0.87 537
15 160 0.87 472

15

16 160 0.93 267
17 170 0.73 232
18 170 0.73 400
19 180 0.73 478
20 180 0.73 555

The above results show that manual control of welding speed is difficult to be achieved. It
also shows very high variance in bend obtained with little variation of welding speed at the
constant value of current. In addition, it is also observed that an arc of constant length can not
be achieved in manual welding process. Therefore it was decided to fabricate a set up which
can provide constant welding speed at constant arc length where both the parameters are
adjustable as desired.

3.2 Rack and Pinion system

An attempt is made to design a reciprocating platform with the use of rack and pinion system.
The major difficulties were associated with the drive mechanism as it was required to run the
platform at relatively low speed of 0.25-1.5 cm/sec. A dc motor can not be used to obtain low
speed and at the same time its control is also difficult. Therefore it is required to use a stepper
motor which can be digitally controlled using a computer and can be run at low rpm. A
stepper motor, four phase; 12V; 3A, available in mechatronics lab, is tried to run. As the
control circuit of motor was not available an attempt is made to design the control circuit.A
counter circuit is designed to control the motor. An IC LMC555 is used to generate a square
pulse signal. The 555 timer IC, a standard 8 pin integrated circuit, is used to generate clock
signals. The circuit diagram is shown in the figure 3.1.

Fig. 3.1: Circuit diagram of IC 555

There are three required external parts which determine the timing: two resistors labeled RA
and RB and a capacitor labeled C. The data sheet provides the timing equations as follows:

16

TLOW = ln(2) RB C = 0.693RB C
THIGH = ln(2)( RA + RB )C = 0.693( RA + RB )C
T = Period = TLOW + THIGH = ln(2)( RA + 2 RB )C = 0.693( RA + 2 RB )C

Appropriate values of resistors and capacitors are chosen to run the circuit. As the current
required by motor is 3 A and the IC is able to give only a current of 250 mA, an electro-
mechanical relay, is used to generate the end clock signal to be fed into the motor. But the
relay, could not work at the frequency of 3-5 Hz. Therefore the system could not be used.

3.3 Two wheel’s vehicle

A simple two wheel vehicle is designed to do the welding at constant speed and fixed arc
length. Two stepper motors of rating 12 V, 250 mA, along with the driver IC L293D are used
to run to two wheels. The stepper motors are digitally controlled using computer through
parallel port connection. A simple MATLAB code allows to access the parallel port and to
send the clock signal to the driver IC. The vehicle runs within the speed limits of 0.25-1.5
cm/sec. When finally put into the use to carry the metal plate samples at constant speed it
could not carry heavy earthing wire with it. Therefore the system could not be used.

3.4 Pug Cutting machine

A Leopard pug cutting machine, a manufacture of ESAB, is bought to run the welding torch
at constant speed and having fixed height from the welding surface providing fixed arc
length. The machine is typically made for gas cutting. Therefore a new clamp is fabricated to
hold the welding torch with the slot design to control the arc length. The machine has a speed
controller which provides a continuous variation of speed from mode 0 to 10. The machine is
calibrated to find the numerical values of speed corresponding to different speed modes. The
same is tabulated in the table below.

Table 3.2: Speed mode vs. Speed in cm/sec

Speed mode Speed (cm/sec)
0 0.253
1 0.375
2 0.527
3 0.693
4 0.855
5 1.043
6 1.149
7 1.279
8 1.403

17

9 1.572
10 1.589

The figure 3.2 shows the installed set up on which the final experiments are carried out. Four
samples are kept at one run with a scrap material at the start and end to avoid the end effects.
The samples are supported by two parallel channels at 0.5 inch from the ends. After welding
arc is passed over the samples, they are kept in air for cooling.

Fig.3.2: Experimental setup

Bend in the plates is measured using the co-ordinate measuring machine. The angle between
the planes across the weld line is the angle of bend. Although the machine provides precision
of 1 second in angle measurement, seeing very high variance in replicates, for ease in
calculations it is reported only up to the precision of 1 minute.

18

Chapter 4

Experimental Results

An exhaustive set of experiments are carried out on a sample size of 3×6 inch MS plate of
thickness1 mm and 2 mm along the line of 3 mm length through the middle line of 6 inch
width. Three input parameters are taken into account, welding speed; current; and arc length.
At a fixed value of welding speed and current, arc length can be varied only in a narrow
range to keep the arc stable. Precisely controlling the arc length was not possible. Hence, arc
length is kept constant over all the experiments. Range of other two parameters welding
speed and current is decided under the constraint that the sample should not burn off at any
combination of the parameters. A set of eight replicates is carried out at each value of input
parameters to analyze the variance in output parameter, bend angle. The results are put in two
sections one for thickness 1 mm MS plate and another for 2 mm MS plate.

4.1 Results for 1mm MS plate

Experiments are carried out at 21 different combinations of two input parameters current and
welding speed. Three values of current 40 A, 60 A and 80 A are used. Seven different values
of welding speed are chosen in between 0.69 cm/sec to 1.59 cm/sec. The values chosen are
not at equal intervals but are corresponding to the running modes available in the machine.
Arc length is set fixed at 1.5 mm for all the experiments. Results of the experiment are
tabulated below. Bend angle in eight replicates is denoted by A, B, ….H. Sample mean value
and standard deviation is also reported. Some of the samples did burn at the ends, bend of
these samples are not reported. Table 4.1 shows the results at 40 Amps.

Table 4.1: Data set at 40 A current for 1mm plate

Speed (cm/sec) Bend angle (minutes)

A B C D E F G H Mean Std. Deviation

0.69 117 128 182 182 186 192 249 299 191.88 59.35

0.85 150 194 218 219 235 252 253 310 228.88 46.89

1.15 33 75 121 129 130 138 152 175 119.13 44.95

1.28 13 43 58 133 148 161 183 230 121.13 75.51

1.4 27 47 52 67 88 94 106 152 79.13 39.58

1.57 7 24 58 78 83 101 116 125 74.00 42.15

1.59 79 83 88 88 89 95 113 117 94.00 13.80

19

Table 4.2 shows the results at 60 Amps.




0.69 151 168 174 191 210 217 278 292 210.13 51.13

0.85 92 137 174 186 217 242 248 279 196.88 62.13

1.15 90 125 135 140 152 165 175 191 146.63 31.61

1.28 21 44 72 77 132 152 209 252 119.88 81.28

1.4 73 83 92 98 99 104 106 116 96.38 13.57

1.57 29 66 156 181 182 194 223 262 161.63 77.87

1.59 106 118 139 141 161 168 172 227 154.00 37.59

Table 4.3 shows the results at 80 Amps.




0.69 203 245 255 259 Burnt Burnt Burnt Burnt 240.50 25.68

0.85 82 113 117 139 240 291 342 392 214.50 117.92

1.15 88 137 142 143 161 162 171 179 147.88 28.38

1.28 59 120 123 150 166 263 280 287 181.00 85.29

1.4 29 122 137 138 141 215 257 192 153.88 68.80

1.57 78 96 140 154 156 211 239 243 164.63 61.91

1.59 79 96 109 118 131 149 183 221 135.75 47.10

Figure 4.1 shows the graph of mean bend angle versus welding speed at three different
current values.

20

Fig.4.1: Bend angle vs. Welding speed for 1 mm plate

Fig.4.2: Variance in Bend angle vs. Welding speed for 1 mm plate

Figure 4.2 shows the graph of variance in bend angle versus weld speed at the same three
different values of current. The above results show that for a constant value of current the
bend obtained in plate decreases with the increase in welding speed and at a constant value of
welding speed it increases with the increase in current. But the variance is very high in values
of replicates hence no proper conclusion can be drawn. High variance in replicates can be

21

attributed to inaccuracies in experiment or it may be due to inherent randomness of the
process. The variance curves show that up to some extent variance is small at low value of
current rather than at high value of current.

Assuming the replicates follow Weibull distribution, using Maximum likelihood method
parameters of the probability distribution are calculated. MATLAB package is used for
calculations. The curves of probability distribution at a constant value of current and over the
range of welding speed are plotted together. Figure 4.3 shows the Weibull probability
distribution curves of bend angle obtained at 40 A current and different values of welding
speed. Numbers in boxes are the values of welding speed in cm/sec.

Fig.4.3: Bend distribution at 40 A current for 1 mm plate

22



Fig 4.4 and Fig 4.5 show the same at 60A and 80A respectively. Because of high variance
probability distribution curves overlaps significantly. Narrower is the curve smaller is the

23

variance. Most of the distribution curves are wide which represents very high variance in the
values.

4.1.1 Neural Network modeling of 1 mm plate data set

Neural network modeling of the process is done using MATLAB packages. Current and
welding speed, are taken as input parameters. Weibull distribution parameters, k (shape
parameter) and λ (scale parameter), of the bend angle replicates are taken as the output
parameters. The distribution parameters are estimated using Maximum likelihood method.
Out of the total sample space of 21 data points 12 data sets, covering all the boundaries of 2D
plane and some intermediate values, are used for training the network while rest 9 data sets
are used for testing the network. The numerical values of two input parameters lie in different
range. These values are normalized using the maximum value such that they lie in between 0
to 1. In order for the percentage error in the prediction to be more or less uniform normalized
logarithmic values of the output variables are used.

Levenberg-Marquardt training algorithm is used for training the network. The network
architecture consists one hidden layer with three neurons and one neuron at the output layer.
The transfer function in the first layer is tan-sigmoid and the output layer transfer function is
linear. Learning rate is set as 0.01 and the error goal is set at 0.0001. For the two output
parameters, k and λ, network is trained separately two times. Table 4.4 shows the training
data set.

Table 4.4: Training data set for 1 mm plate

S. No. Current(A) Speed (cm/sec) λ k

1 40 0.69 212.62 3.69

2 40 1.15 132.53 3.34

3 40 1.40 89.61 2.3

4 40 1.59 82.01 7.33

5 60 0.69 229.61 4.65

6 60 1.15 158.47 5.89

7 60 1.40 101.81 9.05

8 60 1.59 181.11 4.52

9 80 0.69 249.69 16.4

10 80 1.15 158.07 7.59

11 80 1.40 172.2 2.54

24

12 80 1.59 184.48 3.29

Table 4.5 shows the testing data set with the estimated values of the output parameters and
the percentage error in prediction.

Table 4.5: Testing data set for 1 mm plate

S. No. Current(A) Speed (cm/sec) λ λ –est. error % k k –est. error %

1 40 0.85 246.93 227.72 7.78 5.72 3.50 38.83

2 40 1.28 134.21 93.36 30.44 1.63 3.71 ‐127.56

3 40 1.57 82.01 85.42 ‐4.16 1.77 4.18 ‐136.05

4 60 0.85 217.92 229.46 ‐5.29 4.01 4.39 ‐9.41

5 60 1.28 133.86 105.05 21.52 1.60 8.49 ‐430.92

6 60 1.57 181.11 163.81 9.55 2.34 5.27 ‐125.38

7 80 0.85 243.61 227.69 6.53 2.10 13.08 ‐522.94

8 80 1.28 204.71 139.44 31.88 2.48 3.83 ‐54.52

9 80 1.57 184.48 195.03 ‐5.72 3.21 2.86 10.91

At the set goal parameter of 0.0001 for training data, maximum error in training data for λ is
8.48% and the root mean square (RMS) is 5.34%. Maximum error in testing data for λ is
31.88 % and RMS error is 17.25 %. Visual depiction of the results is shown in figure 4.6. For
estimation of k, the same goal parameter is set and the maximum error in training data is
67.63% and the RMS error is 28.08%. Maximum error in testing data for k is 522.93% and
the RMS error is 239.05%. Very high error in modeling of k data shows that the values of k
do not follow any pattern. Visual depiction of the results is shown in figure 4.7.

25

Fig.4.6: Experimental values versus Estimated values of Scale parameter, λ for 1 mm plate

Fig.4.7: Experimental values versus estimated values of Shape parameter, k for 1 mm plate

26

4.2 Results for 2 mm MS plate

Experiments are carried out at 20 different combinations of two input parameters current and
welding speed. Four values of current 40 A, 60 A, 80 A and 100 A are used. Five different
values of welding speed are chosen in between 0.53 cm/sec to 1.59 cm/sec. As in the case of
1 mm plates, here also speed values chosen are not at equal intervals but are corresponding to
the running modes available in the machine. Arc length is set fixed at 2.0 mm for all the
experiments. Results of the experiment are tabulated below. Bend angle in eight replicates is
denoted by A, B, ….H. Sample mean value and standard deviation is also reported. Table 4.6,
Table 4.7, Table 4.8 and Table 4.9 show the results at 40 A, 60 A, 80 A and 100 A
respectively.




0.53 80 102 24 27 86 104 92 104 77.38 33.18

0.69 69 84 50 42 79 50 37 77 61.00 18.33

0.85 66 59 35 24 101 104 70 104 70.38 31.05

1.15 43 85 28 21 94 91 26 70 57.25 31.10

1.59 8 57 54 69 39 58 9 17 38.88 24.36




0.53 10 54 31 29 7 6 33 9 22.38 17.19

0.69 43 36 58 7 52 65 83 12 44.50 25.85

0.85 84 73 36 61 48 79 83 92 69.50 19.49

1.15 32 177 40 113 56 104 53 60 79.38 48.81

1.59 33 30 55 62 112 3 22 33 43.75 33.10

27




0.53 9 12 10 8 30 33 33 5 17.50 12.20

0.69 34 48 39 52 45 4 14 10 30.75 18.74

0.85 5 39 55 31 66 14 46 27 35.38 20.42

1.15 44 102 49 52 99 96 98 112 81.50 27.96

1.59 13 38 50 34 59 44 37 101 47.00 25.59




0.53 63 37 63 40 21 75 33 38 46.25 18.49

0.69 73 40 35 35 112 49 30 116 61.25 35.19

0.85 55 4 9 38 77 40 8 48 34.88 26.00

1.15 27 76 22 7 9 71 85 75 46.50 33.19

1.59 31 74 104 30 127 108 104 95 84.13 36.20

Figure 4.8 shows the graph of mean bend angle versus welding speed at four different current
values. Figure 4.9 shows the graph of variance in bend angle versus welding speed at four
different current values.

28

Fig.4.8: Bend angle vs. Welding speed for 2 mm plate

Fig.4.9: Variance in Bend angle vs. Welding speed for 2 mm plate

The data follows almost no pattern. No particular conclusion can be drawn.

As in the earlier section, curves of probability distribution at a constant value of current and
over the range of welding speed are plotted together. Figure 4.10 shows the Weibull
29

probability distribution curves of bend angle obtained at 40 A current and different values of
welding speed. Numbers in boxes are the value of welding speed in cm/sec.


30

Figure 4.11 shows the same at 60 A current.


31



32



Because of high variance probability distribution curves overlaps significantly.

4.2.1 Neural Network modeling of 2 mm plate data set

Neural network modeling of the process is done using MATLAB packages. Out of the total
sample space of 20 data points 12 data sets, covering all the boundaries of 2D plane and some
intermediate values, are used for training the network while rest 8 data sets are used for
testing the network.

Levenberg-Marquardt training algorithm is used for training the network. The network
architecture is same as in the earlier section. Learning rate is set as 0.01 and the error goal is
set at 0.0001. For the two output parameters, k and λ, network is trained separately two times.

Table 4.10 shows the training data set.

33

Table 4.10: Training data set for 2 mm plate

S. No. Current(A) Speed (cm/sec) λ k

1 40 0.53 86.72 2.90

2 40 0.85 79.34 2.71

3 40 1.59 43.36 1.67

4 60 0.53 24.75 1.43

5 60 0.85 76.29 4.78

6 60 1.59 47.69 1.38

7 80 0.53 19.67 1.61

8 80 0.85 39.59 1.85

9 80 1.59 53.19 2.08

10 100 0.53 52.02 2.94

11 100 0.85 37.63 1.31

12 100 1.59 94.53 2.85

Table 4.11 shows the testing data set with the estimated values of the output parameters
and the percentage error in prediction.

Table 4.11: Testing data set for 2 mm plate

S. No. Current(A) Speed (cm/sec) λ λ –est. error % k k –est. error %

1 40 0.69 67.48 80.88 ‐19.86 4.12 2.99 27.52

2 40 1.15 64.95 79.56 ‐22.50 2.12 2.85 ‐34.59

3 60 0.69 49.72 71.66 ‐44.13 1.82 2.67 ‐46.73

4 60 1.15 90.14 80.34 10.88 1.88 3.17 ‐68.49

5 80 0.69 34.20 19.61 42.67 1.69 1.85 ‐9.45

6 80 1.15 90.81 85.63 5.71 3.78 3.45 8.65

7 100 0.69 69.69 44.55 36.07 2.02 1.76 12.73

8 100 1.15 50.85 89.12 ‐75.25 1.40 0.96 31.30

34

At the set goal parameter of 0.0001 for training data, maximum error in training data for λ is
7.75% and the root mean square (RMS) is 3.95%. Maximum error in testing data for λ is
75.25% and RMS error is 38.37%. Visual depiction of the results is shown in figure 4.14. For
estimation of k, the same goal parameter is set and the maximum error in training data is
35.44% and the RMS error is 12.93%. Maximum error in testing data for k is 68.48% and the
RMS error is 35.59%. Visual depiction of the results is shown in figure 4.15.

Fig.4.14: Experimental values versus estimated values of Scale parameter, λ for 2 mm plate

35

Fig.4.15: Experimental values versus estimated values of Shape parameter, k for 2 mm plate

4.2.2 Results of double pass welding on 2 mm plate

Some of the experiments are performed by passing the arc two times over the plate. The
welding torch is run over the plate immediately after the first run completes without allowing
the plate to cool to room temperature. Experiments are performed at two welding speed
values 1.15 cm/sec and 1.59 cm/sec and three values of current 40A, 60A, and 80A. The
results are tabulated below in table 4.12.

Table 4.12: Results of double pass welding on 2mm plate

Current Speed Bend angle
(A) (cm/sec) (minutes)
Std.
A B C D E F G H Mean
Deviation
40 1.15 68 79 80 65 59 76 56 48 66.38 11.60
60 1.15 115 123 129 232 129 163 163 152 150.75 37.60
80 1.15 177 206 202 155 187 118 134 128 163.38 34.43
40 1.59 91 126 133 114 101 108 124 109 113.25 13.94
60 1.59 97 138 110 87 138 81 144 174 121.13 32.45
80 1.59 126 155 188 204 125 147 137 174 157.00 29.15

36

Figure 4.16 shows the increment in bend obtained over the single pass.

Fig.4.16: Bend angle in single pass and double pass for 2 mm plate

37

Chapter 5

Conclusion and Future Scope

The main objective of this study is to asses the dependence of the bend obtained in a flat plate
upon passing welding arc over it, on the process parameters, current and welding speed. It is
observed that the process has very high variance. The two sample plates, MS plates of
thickness 1 mm and 2 mm of size 3×6 inch are used for studying the process.

Results of 1 mm plate show some pattern. With the increase in welding speed at constant
value of current the bend in plate decreases. At a constant value of welding speed with the
increase in current the bend angle increases. Both the observations indicate that with the
increase in heat input the bend obtained increases. However, variance in the process is very
high.

Results of 2 mm plate do not show any pattern. At some constant value of current with
the increase in welding speed the bend obtained increases but at some other current it
decreases. Similarly, at some constant value of welding speed with the increases in current
the bend obtained increases but at some other welding speed it decreases. No regular pattern
indicates that the bend angle is a complex function of the two process parameters, welding
speed and current. Variance in the process is also very high. Results of double pass welding
show that bend in the plate can be increased by passing the welding arc more number of
times.

High values of variance in the process can be attributed to the inaccuracies involved in
experiment or it may be due to inherent randomness of the process. It may be because of very
high sensitivity of the bend with respect to the process parameters, welding speed and current

Future research in this direction can be carried out by performing more number of
replicates to asses variance involved in the process. Experiments can be carried out on
different size of samples with different thickness and different type of materials like stainless
steel and aluminum plates. The process can be formulated as an on-line feedback system by
achieving the bend in successive steps using multi pass welding.

38

Appendix 1

A Background on Probability Distributions

In experiments or trials in which the outcome is numerical, the outcomes are values of what
is known as a random variable. When replicates of the experiment are conducted, different
values of the output variable are outcome of a random variable. If replicates are conducted
theoretically infinite number of times, probability of the outcome of each value of the output
variable can be calculated. But practically performing the replicates infinite number of times
is impossible. Thereby conducting a limited set of replicates and using the data it is tried to
estimate the probability associated with each possible value of the outcome.

A1.1 Probability density function

There are various ways to characterize a probability distribution. The most visual is the
probability density function. A probability density function (PDF) is a function that
represents a probability distribution in terms of integrals. A probability distribution has
density f, if f is a non negative function → such that the probability of the interval [a, b]
a
is given by ∫ f ( x)dx for any two numbers a, and b. This implies that the total integral of f
b

must be 1.
∞

∫
−∞
f ( x)dx = 1

If a probability distribution has density f ( x ) , then the infinitesimal interval [ x, x + dx] has
probability f ( x ) dx .

A1.2 Cumulative distribution function

The cumulative distribution function (CDF) of a real valued random variable X is given by
X → Fx ( x ) = P ( X ≤ x) , where the right hand side represents the probability that the random
variable X takes on a value less than or equal to x . The CDF of X can be defined in terms of
x
the probability distribution function f as : F ( x) = ∫
−∞
f (t )dt

A1.3 Normal distribution

The normal distribution, also called the Gaussian distribution, is an important family of
continuous probability of distributions. It is the simplest and widely used probability
distribution. Each member of this family is defined by two parameters, location and scale: the
mean (average, ) and variance (standard deviation squared σ2) respectively. The standard

39

normal distribution is the normal distribution with a mean of zero and the variance of one. It
is often called the bell curve because the graph of its probability distribution resembles a bell.

Fig A1.1: Probability Density Function of Standard Normal Distribution

The probability distribution function of the normal distribution is the Gaussian function
1
f μ ,σ 2 ( x) = exp( −( x − μ ) 2 / 2σ 2 ), x ∈ R
σ 2π
Where σ > 0 is the standard deviation, the real parameter μ is the expected value. The
density function of the standard normal distribution is:
1
f ( x) = exp( −( x) 2 / 2), x ∈ R
2π
The probability distribution function has notable properties including:
• Symmetry about its mean μ
• The mode and median both equal the mean μ
• The inflection points of the curve occur one standard deviation away from the
mean i.e. at μ − σ , and μ + σ .

The cumulative distribution function F ( x ) , of the normal distribution is expressed in
terms of the density function f ( x ) as follows:
x
Fμ ,σ 2 ( x) = ∫
−∞
f μ ,σ 2 (t )dt

40

x
1
∫ exp(−(t − μ )
2
= 2
/ 2σ )dt , x ∈ R
σ 2π −∞

Where the standard normal CDF is the general CDF is evaluated with μ = 0 and σ = 1 :
x
1
F ( x) = ∫ exp(−(t ) / 2)dt , x ∈ R
2

2π −∞

A1.4 Exponential distribution

The exponential distributions are a class of continuous probability distributions which
describes the times between events in a Poisson process, i.e. a process in which events occur
continuously and independently at a constant average rate. The probability density function
of an exponential distribution has the form

f λ ( x ) = {λ exp( − λ x ), x ≥ 0
0, x < 0
Where λ > 0 is the rate parameter. The distribution is supported on the interval [0, ∞].
The Cumulative distribution function is:

Fλ ( x ) = {1-exp(-λ x), x ≥ 0
0, x<0

Fig A1.2: Probability Density Function of Exponential Distribution with Mean of Unity

41

A1.5 Weibull distribution

The Weibull distribution is a combination of the above mentioned two distributions, as
depending upon the parameter values it may take the form of normal distribution or
exponential distribution. The probability density function of a Weibull random variable x is:
k / λ ( x / λ )k −1 exp( − ( x / λ )k ), x≥0
f λ ,k ( x ) = {
0, x<0
Where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution. A
generalized, 3- parameter Weibull distribution is also used. It has the probability density
function:
k−1
exp(−( x−θ / λ)k ),x≥θ
fλ,k(x) ={0,/xλ<(θx−θ / λ)
k

When θ = 0, it reduces to the 2- parameter distribution.
The cumulative distribution function for the 2-parameter Weibull is
1−exp(−x / λ )k ), x≥0
Fλ,k ( x) = { 0, x<0

Fig. A1.3: Probability Density Function of Weibull Distribution with shape parameter of
value 2 and scale parameter value of 1.

42

Application of welding arc to obtain small angular bend in steel plates

Application of welding arc to obtain small angular bend in steel plates

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