Development of Mathematical Model to Predict Weld Bead ... · parameters for Metallic inert Gas...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 12 (2018) pp. 10298-10309

© Research India Publications. http://www.ripublication.com

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Development of Mathematical Model to Predict Weld Bead Geometry and

Parameters Optimization for Pulsed MIG Welding Using Statistical Design

of Experiments

Yerriswamy Wooluru1, Swamy D R 2, Jagadish Rangaswamy 3

1JSS Academy of Technical Education, Bangalore-560060, India.

2 JSS Academy of Technical Education, Bangalore-560060, India.

34527 Pitch Pine Lane West, Ypsilanti, Michigan 48197, USA

Abstract

Pulsed MIG welding process offers spray metal transfer at low

average currents, high metal deposition rate and less

distortion. Study the effect of Pulsed MIG welding process

variables on the bead geometry is inevitable to enhance

mechanical properties of weld bead geometry. This can be

achieved by developing mathematical models to predict the

weld bead dimensions in terms of process parameters. Design

of experiments tool was used to develop models for pulsed

MIG welding process. The models so developed can be used

to predict the weld bead geometry.

Keywords: Process parameter optimization, Design of

Experiments, ANOVA, weld bead geometry.

INTRODUCTION

Pulsed MIG welding maintains an arc at low current and

superimposes short periodic pulses (30 – 300 Hz) of high

current in order to detach and transfer single drops of molten

metal from the electrode to the weld pool. The pulsing of the

current at such high and low levels results in mean current.

Parameters in pulsed MIG welding are: Peak current (Ip),

Peak duration (Tp), Base current (Ib), Base current duration

(Tb) and Wire feed speed (Ws).In Pulsed MIG welding

process a square wave current pulses are used as shown in

Figure 1.

Figure 1. Pulsed MIG welding current wave form

It is very important to evaluate the effect of MIG welding

process variables upon weld bead geometry. The weld

quality depends on number of independent variable factors.

Their effects on dependent factors are evaluated through

empirical investigation. In practice, a small number of

controllable variables contribute to a vital share of the effect

of the product quality. These variables do not necessarily

produce a constant effect on the product. The question

would therefore arise as to how efficiently and economically

the contribution of each of these factors can be assessed

individually and also collectively to produce the total effect

on the weld quality. An approach that fulfills these

requirements is available in the statistically designed

experiments.

LITERATURE REVIEW

Christensen [1] formulated no dimensional factors to

relate bead dimensions with the operating parameters.

Chandel [2] demonstrated the theoretical predictions of

the effect of current, electrode polarity, diameter, and

electrode extension on the melting rate, bead height, and

bead width and weld penetration, submerged arc welding

(SAW). Markelj and Tusek [3] modeled the current and

voltage in Tungsten inert Gas welding as quadratic

polynomials of sheet thickness. The results were

presented for algorithmic optimization in the case of T-

joint with fillet weld. Kim [4] distinguished experimental

data obtained for weld bead geometry with those

obtained from empirical formulae in gas metal arc

welding(GMAW).Patel et al. [5], evaluated the welding

parameters for Metallic inert Gas welding and Tungsten

inert Gas welding by Taguchi’s method. It was concluded

that the welding current was most significant parameter for

both the welding operation. Ghazvinloo H.R. et al.[6],

analyzed robotic MIG welding of AA6061’sproperties like

fatigue life, impact and bead penetration properties under

the effect of welding speed, voltage and current. Pradip et

al. [7], have investigate the effects of welding process

parameters of Gas Metal Arc Welding (GMAW) on tensile

strengths of SS 3Cr12 steel material specimen. Duhan et al.

[8], have developed a response surface model to predict



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tensile strength of inert gas metal arc welding of AISI 50110

(EN 31) high carbon steel joint. M. Aghakhani et al. [9],

have done work on optimization of gas metal arc welding

process parameter for increase quality and productivity of

weldment. Kumar [10] studied TIG parameters and pitting

corrosion of Al-alloys using ANOVA, regression analysis

and mathematical models. He found that Peak current (Ip)

and frequency have direct and base current (Ib) and pulse on

time have inverse relation to pitting. Ratnayake and Vik

[11] suggested a methodology to recognize the most

frequently appearing imperfect and defective welds by

grouping based on welding procedure specifications (WPSs)

that contribute to the highest level of quality deterioration.

Joshi [12] studied the MIG and TIG welding. The authors

have used the Design of Experiment method for conducting

the experiments and data analysis. Palani [13] studying TIG

parameters of Al-65032 using Taguchi and mathematical

models found that welding speed impacts weld strength and

percentage elongation more than other parameters.

Statistical design of experiments (DOE) concept has been

successfully applied to many welding situations This may

be achieved by the development of mathematical

expressions, which can be fed into a computer, relating the

bead dimensions to the important welding parameter

affecting these dimensions Also, optimization of the

welding parameters to control and obtain the required shape

and quality of weld beads is possible with these expressions

[14, 15, and 16].

PLAN OF INVESTIGATION

The work was planned to be carried out in the following steps:

1. Identifying important process control variables

2. Finding upper and lower limits of control variables

viz., Pulse current (Ip), Pulse duration (Tp), Wire

feed speed (Ws), Background current (Ib) and

background current duration.

3. Selection of optimization parameter.

4. Development of design matrix.

5. Conducting experiment as per design matrix.

6. Recording responses viz Penetration (P), Width of

the weld bead (W) and Dilution (D).

7. Develop mathematical model to predict weld bead

geometry

8. Determining the co-efficient of the model using

DOE software

9. Check the adequacy of the models

10. Optimize the welding process parameters

IDENTIFYING THE IMPORTANT PROCESS

CONTROL VARIABLES AND FINDING LIMITS

In pulsed MIG welding process, there are many variables

affecting the weld bead geometry .However it was

planned to study the effects of those parameters which

affect definitely the mode of metal transfer and the

amount of heat input to the work piece and thus determine

the bead geometry and shape relationships. Based on their

importance the welding variables have been put in to two

groups as follows.

Primary variables:

Pulse current, Pulse time, Wire feed rate, Welding speed,

feed wire diameter, shielding composition.

Secondary variables:

Background current ,Back ground current duration, mean

current, Volt-ampere ratio ,Shielding gas flow rate ,Torch

angle ,Electrode polarity, Pre heat condition ,burn back,

rise time, Inductance level, short circuit current, Arc

length and electrode stick out. Out of these parameters

only important variables were chosen which has no

dependence on each other .Based on these consideration

pulse current (IP), Pulse time (Tp), Welding speed (Ws),

Background current (Ib), and background current duration

(Tb) were chosen as the control variables. Factors and

their levels are given in Table 1.

WELDING FACTORS AND THEIR LIMITS

Table 1. Factors and their levels

Sl.

No.

Factors Unit Notations Lower

Limit

Basic

Level

Upper

Level

Variation

interval

1 pulse

current

Amps A 300 350 400 50

2 Welding

speed

mm/min B 200 250 300 50

3 Pulse time ms C 2 4 6 2

4 Background

current

Amps D 50 75 100 25

5 Background

current time

period

ms E 5 7.5 10 2.5

The limiting values of the welding parameters and constants

of the experiments were set based on welding knowledge and

experience.

SELECTION OF THE EXPERIMENTAL CONSTANTS

The following welding operational parameters and conditions

were made constant during the experiments.

Plate thickness: 12 mm, V-groove with900 included angle

Feed wire diameter: 1.2 mm

Torch to work angle: 900

Gas flow rate: 20 lit/min



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Nozzle to plate distance: 20 mm

Pre heat: Nil

SELECTION OF OPTIMIZATION PARAMETER

Optimization parameter is the reaction (response) to the action

of the factors (pulse current, Pulse time, Welding speed,

Background current and Background current time period)

determining the behavior of the system being studied. An

optimization parameter should be:

1. Effective from the view point of reaching a goal

2. Universal in nature

3. Quantitative and expressed by a single number

4. Statistically effective

5. With a physical meaning, simple and easy to

calculate.

Based on the above considerations the following parameters

are selected:

Penetration (P):

Penetration is the depth to which the base metal has been

melted. It is normally a function of arc pressure. Arc pressure

is decided from current density. Therefore, welding current is

an important parameter deciding penetration besides the

welding current also decides the deposition rate. Therefore the

heat transferred through the droplets and deposited mass also

has some influence on penetration. Depth of penetration is

also influenced by the nature of the shielding gas .In pulsed

MIG welding although the mean current decides the

deposition rate and penetration the magnitude of the pulse

current also has some influence on the penetration. Generally

higher pulse current gives slightly higher penetration with

larger pulse current can be attributed to the higher arc force

and higher force due to the impinging droplet. The depth of

penetration is also influenced by welding speed.

Width of the weld bead (W):

In consumable arc welding process such as MIG and FCAW

the bead width is controlled by deposition rate welding speed

and also the fluidity of the molten pool. in FCAW processes

the thermo physical property of the molten flux also

contribute to the bead formation. However in pulsed MIG

welding using solid wire the bead width is largely controlled

by the mean current decreased with increasing the welding

speed.

Bead wetting Angle:

It is an important aspect of the deposited weld metal. Bead

wetting angle is particularly important in case of multi pass

welding and surfacing applications as larger bead wetting

angle can lead to inter pass lack of fusion defects and slag

entrapment. In fluxed process like FCAW and SAW the bead

wetting angle can affect the slag detachability .Therefore the

bead wetting angle is an important aspect in V- groove

wetting as well as surfacing .However the effect of current on

bead wetting angle appears to be limited when compare to the

effect of welding speed on wetting angle.

Dilution:

(D) Dilution can be defined as the ratio of the plate fusion

area to the total area. It may also be used as rough measure of

susceptibility to fusion defects and as a mean of comparing

fusion characteristics with other processes. As a direct

measure it is of interest in surfacing applications and also

gives an idea about the inter pass refinement in the multilayer

welding.

FRACTIONAL FACTORIAL DESIGN MATRIX

A five factor, two levels, fractional factorial design with

interaction effect is as shown in Table 2 to conduct the

experiments.

Table 2. Design Matrix

Std

Order

Run

Order

Center

Pt

Blocks A B C D E AB AC AD AE BC BD BE CD CE DE

32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

19 2 1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1

15 3 1 1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1

23 4 1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1

27 5 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 1 -1 -1 1

9 6 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 -1 1 -1 1 -1

4 7 1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 1 -1

3 8 1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1

31 9 1 1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1

11 10 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 1 -1 -1 1

14 11 1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1

25 12 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 -1 1 -1 1 -1

1 13 1 1 -1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 -1 -1



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Std

Order

Run

Order

Center

Pt

Blocks A B C D E AB AC AD AE BC BD BE CD CE DE

10 14 1 1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 1

7 15 1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1

26 16 1 1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 1

12 17 1 1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 -1

24 18 1 1 1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1

8 19 1 1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1

16 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

17 21 1 1 -1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 -1 -1

30 22 1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1

21 23 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1

2 24 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1

13 25 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1

6 26 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1

22 27 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1

18 28 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1

20 29 1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 -1

29 30 1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 1

28 31 1 1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 -1

5 32 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1

EXPERIMENTAL DETAILS

Steel plates of size 150x 75 mm were used for welding trials.

The required number of plates was cut from 12 mm thick

carbon steel (BMC-16) structural steel plate. V- Grooves with

900 included angle were cut into machined on the center of the

specimen and depth of the V- groove was limited to 6mm

only. The specimen was fixed on the carriage in vertical

position. The M450 PS programmable MIG power source was

used in this experiment. The weld beads were deposited using

the welding conditions stipulated by the design matrix as

shown in the Table 2 .The weld runs were made at random to

avoid systematic errors in the result. The experimental setup

with gas flow meter and wire feeder used for bead on plate

experiment in pulsed MIG is shown in figure 3, 4, and 5.It

Consists of a traveling carriage with a table for supporting the

test plate. The carriage speed is continuously varied from 1

mm/sec to 20 mm/sec. A frame held the welding torch above

the table and it was provided with horizontal and vertical

movements for setting the nozzle to job distance. The

experimental set up used for welding in vertical position.

Thought the experiment the test plates were kept stationary

and the welding torch was moved. Vertical and horizontal

movements were provided for the torch. The correct standoff

distance and also for proper centering of the torch with

reference to the V-Groove were made. The welding gun was

allowed to cool to room temperature and spatter was cleaned

from the nozzle after each weld run. Two samples were cut

transverse to the weld bead from each welded plate then

milling, surface grinding, polishing and etching for

examination using 10% nital. Weld bead profiles were

sketched with the help of a profile projector at a magnification

of X10.Areas and dimensions of interest were measured using

a planimeter and scale. The weld bead dimensions and shape

relations were tabulated against their respective welding

conditions in the coded forms as shown in Table 4 .The

tabulated values are averages from two samples from each

specimen. The magnified bead profiles for different welding

trials were made and a sample bead profile is shown in Figure

2.

Figure 2. Weld bead profile

Electrode wire:

The copper coated electrode wire of diameter 1.2 mm and its

nominal composition of the weld metal as supplied by the

manufacturer used in this experiment are as shown in Table 3

Table 3. Chemical composition of electrode material

Carbon 0.05- 0,08%

Silicon 0.4- 0.6%

Manganese 0.03% (Max)

Phosphorus 0.03%



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Gas supply and wire feeder:

The smith’s gas unit used in the study is a pressure flow

device capable of proportionately mixing Argon and

CO2ininfinitely varying proportions. The gas flow rate and gas

mixing ratio were set using separate knobs provided in the

front panel. In this study the gas flow rate was kept at 20

lit/min. The mixing accuracy as reported by the manufacturer

is about + or – 2% of the full scale.

Figure 3. Gas flow meter

Figure 4. Wire feeder

Figure 5. Experimental setup

The wire feeder unit employed is a millermatic four roll drive

feed unit .It provides a continuously variable wire feed speed

from about 1.0 m/mm to 18 m/min.

CONDUCTION OF EXPERIMENT AS PER DESIGN

MATRIX

Sixteen experimental runs were conducted as per the 2 5-1

fractional factorial design matrix at random to avoid any

systematic error creeping into the system. The surface plates

were cross-sectioned at their midpoints to obtain test

specimens. The values of the response are given in Table 4.

Table 4. Design matrix with responses

Std

Order

Run

Order

Center

Pt

Blocks A B C D E Penetration

‘mm’

Weld bead

width in ‘mm’

Dilution

in %

32 1 1 1 1 1 1 1 1 0.75 11.9 43.9

19 2 1 1 -1 1 -1 -1 -1 0.87 8.6 47.9

15 3 1 1 -1 1 1 1 -1 1.09 10 55.53

23 4 1 1 -1 1 1 -1 1 0.88 6.8 45.12

27 5 1 1 -1 1 -1 1 1 0.56 7.5 73.68

9 6 1 1 -1 -1 -1 1 -1 0.81 10 35.11

4 7 1 1 1 1 -1 -1 1 0.83 7.2 45.56

3 8 1 1 -1 1 -1 -1 -1 0.51 8.0 48.0

31 9 1 1 -1 1 1 1 -1 1.13 9.2 56.9

11 10 1 1 -1 1 -1 1 1 0.54 7.0 56.7

14 11 1 1 1 -1 1 1 -1 0.64 6.8 73.4

25 12 1 1 -1 -1 -1 1 -1 0.87 11.0 34.71

1 13 1 1 -1 -1 -1 -1 1 0.64 6.8 65.16

10 14 1 1 1 -1 -1 1 1 0.59 10.3 40.0

7 15 1 1 -1 1 1 -1 1 0.84 6.0 43.85



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Std

Order

Run

Order

Center

Pt

Blocks A B C D E Penetration

‘mm’

Weld bead

width in ‘mm’

Dilution

in %

26 16 1 1 1 -1 -1 1 1 0.67 11.3 38.9

12 17 1 1 1 1 -1 1 -1 0.79 11.5 44.47

24 18 1 1 1 1 1 -1 -1 0.84 6.8 76.56

8 19 1 1 1 1 1 -1 -1 0.88 6.6 76.6

16 20 1 1 1 1 1 1 1 0.79 11.2 45.02

17 21 1 1 -1 -1 -1 -1 1 0.72 6.0 65.0

30 22 1 1 1 -1 1 1 -1 1.02 6.0 73.68

21 23 1 1 -1 -1 1 -1 -1 0.54 9.5 81.58

2 24 1 1 1 -1 -1 -1 -1 0.69 10.0 40.0

13 25 1 1 -1 -1 1 1 1 0.91 11.2 50.0

6 26 1 1 1 -1 1 -1 1 0.73 11.2 39.1

22 27 1 1 1 -1 1 -1 1 0.75 12 41.68

18 28 1 1 1 -1 -1 -1 -1 0.71 10.6 40.1

20 29 1 1 1 1 -1 -1 1 0.85 8.0 47.6

29 30 1 1 -1 -1 1 1 1 0.87 11.9 52.28

28 31 1 1 1 1 -1 1 -1 0.75 11.0 44.8

5 32 1 1 -1 -1 1 -1 -1 0.84 8.9 80.0

MATHEMATICAL MODEL

The study attempts relate the important welding process

parameters to process output characteristics, through

developing empirical regression models for various target

parameters. Linear Regression function is fitted to the data

and the coefficient values are found using regression

analysis with the help of MINITAB statistical software.

The developed mathematical models are accurately

representing the actual pulsed MIG welding process.

NORMAL PROBABILITY PLOT FOR PENETRATION,

WELD BEAD WIDTH AND DILUTION

Validating ANOVA Assumptions It is necessary to check the

assumptions of ANOVA before draw conclusions. There are

three assumptions in ANOVA analysis: normality, constant

variance, and independence. Normality assumptions have

been checked.

Figure 6. Normality plot for Penetration, weld bead width and Dilution



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The normality plot of the residuals above shows that the

residuals follow a normal distribution in all the three cases. It

indicates significant and insignificant factors and residuals

follow a straight line. According to the above normal plots C

and DE are significant for penetration, C, E, BC, CD, are

insignificant for weld bead width and B, BE, CD are

insignificant for Dilution case.

PARETO PLOT FOR PENETRATION, WELD BEAD

WIDTH AND DILUTION MODEL

Pareto chart shows the same results. Since some of the terms

are insignificant, we can drop these terms in the model.

Figure 7. Pareto chart for Penetration, weld bead width and Dilution

Table 5. ANOVA for penetration

Source DF Adj SS Adj MS F-Value P-Value

Model 15 0.506487 0.033766 2.76 0.026

Linear 5 0.215462 0.043092 3.52 0.025

A 1 0.003613 0.003613 0.30 0.594

B 1 0.025312 0.025312 2.07 0.170

C 1 0.137812 0.137812 11.26 0.004

D 1 0.013613 0.013613 1.11 0.307

E 1 0.035113 0.035113 2.87 0.110

2-Way

Interactions

10 0.291025 0.029102 2.38 0.059

A*B 1 0.006613 0.006613 0.54 0.473

A*C 1 0.035113 0.035113 2.87 0.110

A*D 1 0.046513 0.046513 3.80 0.069

A*E 1 0.003612 0.003612 0.30 0.594

B*C 1 0.025313 0.025313 2.07 0.170

B*D 1 0.023113 0.023113 1.89 0.188

B*E 1 0.010512 0.010512 0.86 0.368

C*D 1 0.040612 0.040612 3.32 0.087

C*E 1 0.000613 0.000613 0.05 0.826

D*E 1 0.099012 0.099012 8.09 0.012

Error 16 0.195800 0.012238

Total 31 0.702287

Table 6. Regression coefficients with P-values

Term Effect Coef SE Coef T-Value P-Value VIF

Constant 0.7781 0.0196 39.79 0.000

A -0.0213 -0.0106 0.0196 -0.54 0.594 1.00

B 0.0563 0.0281 0.0196 1.44 0.170 1.00

C 0.1312 0.0656 0.0196 3.36 0.004 1.00

D 0.0413 0.0206 0.0196 1.05 0.307 1.00

E -0.0662 -0.0331 0.0196 -1.69 0.110 1.00

A*B 0.0288 0.0144 0.0196 0.74 0.473 1.00

A*C -0.0662 -0.0331 0.0196 -1.69 0.110 1.00

A*D -0.0762 -0.0381 0.0196 -1.95 0.069 1.00

A*E 0.0212 0.0106 0.0196 0.54 0.594 1.00

B*C 0.0562 0.0281 0.0196 1.44 0.170 1.00

B*D -0.0537 -0.0269 0.0196 -1.37 0.188 1.00

B*E -0.0362 -0.0181 0.0196 -0.93 0.368 1.00

C*D 0.0713 0.0356 0.0196 1.82 0.087 1.00

C*E 0.0088 0.0044 0.0196 0.22 0.826 1.00

D*E -0.1112 -0.0556 0.0196 -2.84 0.012 1.00

Table 7. Model summary –Penetration

S R-sq R-sq(adj) R-sq(pred)

0.110623 72.12% 45.98% 0.00%

Discussion: Table 6 shows the estimation coefficient

(Coef.) of each variable term in a regression model for

penetration along with the corresponding standard deviation

(SD coef), t-statistics (t-Stat) and probability (P) values

determined at 5% significance level. Variable terms with P <

0.05, are C, and DE which are considered statistically

significant for penetration of weld bead geometry. Therefore,



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a second-order model was built to describe the behavior of

each response, followed by the optimization stage to find the

best setting for each factor. The second-order models for

penetration of weld bead geometry in terms of coded variables

with all significant terms are given in Equation (1).The value

of R2 was 72.12%. This means that regression model provided

an explanation of the relationship between independent factors

and the response. The associated p-value for the model was

lower than 0.05 (i.e. α = 0.05, or 95% confidence) which

indicated that the model was considered to be moderately

statistically significant.

Table 8. ANOVA for weld bead width


Model 15 126.735 8.4490 32.03 0.000

Linear 5 33.692 6.7385 25.55 0.000

A 1 6.125 6.1250 23.22 0.000

B 1 8.201 8.2013 31.09 0.000

C 1 0.045 0.0450 0.17 0.685

D 1 19.220 19.2200 72.87 0.000

E 1 0.101 0.1013 0.38 0.544

2-Way

Interactions

10 93.042 9.3042 35.28 0.000

A*B 1 2.101 2.1012 7.97 0.012

A*C 1 8.000 8.0000 30.33 0.000

A*D 1 2.880 2.8800 10.92 0.004

A*E 1 20.801 20.8013 78.87 0.000

B*C 1 0.101 0.1013 0.38 0.544

B*D 1 9.901 9.9012 37.54 0.000

B*E 1 6.125 6.1250 23.22 0.000

C*D 1 0.500 0.5000 1.90 0.188

C*E 1 38.281 38.2812 145.14 0.000

D*E 1 4.351 4.3513 16.50 0.001

Error 16 4.220 0.2638

Total 31 130.955

Table 9. Regression coefficients with P-values

(Weld bead width)


Constant 9.0875 0.0908 100.10 0.000

A 0.8750 0.4375 0.0908 4.82 0.000 1.00

B -1.0125 -0.5063 0.0908 -5.58 0.000 1.00

C 0.0750 0.0375 0.0908 0.41 0.685 1.00

D 1.5500 0.7750 0.0908 8.54 0.000 1.00

E 0.1125 0.0563 0.0908 0.62 0.544 1.00

A*B 0.5125 0.2563 0.0908 2.82 0.012 1.00

A*C -1.0000 -0.5000 0.0908 -5.51 0.000 1.00

A*D -0.6000 -0.3000 0.0908 -3.30 0.004 1.00

A*E 1.6125 0.8063 0.0908 8.88 0.000 1.00

B*C -0.1125 -0.0563 0.0908 -0.62 0.544 1.00

B*D 1.1125 0.5562 0.0908 6.13 0.000 1.00

B*E -0.8750 -0.4375 0.0908 -4.82 0.000 1.00

C*D -0.2500 -0.1250 0.0908 -1.38 0.188 1.00

C*E 2.1875 1.0937 0.0908 12.05 0.000 1.00

D*E 0.7375 0.3688 0.0908 4.06 0.001 1.00

Table 10. Model summary – weld bead width

S R-sq R-sq(adj) R-sq (pred)

0.513566 96.78% 93.76% 87.11%

Discussion: Table 9 shows the estimation coefficient

(Coef) of each variable term in a regression model for weld

bead width along with the corresponding standard deviation

(SD coef), t-statistics (t-Stat) and probability (P) values

determined at 5% significance level. Variable terms with P

< 0.05, A, B, D, AB, AC, AD, AE, BD, BE, CE, DE are

considered statistically significant for weld bead width of

weld bead geometry. The second-order models for weld bead

width of weld bead geometry in terms of coded variables

with all significant terms are given in Equation (2).The

value of R2 was 93.76%. This means that regression model

provided an explanation of the relationship between

independent factors and the response. The associated p-value

for the model was lower than 0.05 (i.e. α = 0.05, or 95%

confidence) which indicated that the model was considered to

be statistically significant.



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Table 11. ANOVA for Dilution


Model 15 6354.93 423.66 43.29 0.000

Linear 5 1627.60 325.52 33.26 0.000

A 1 200.75 200.75 20.51 0.000

B 1 0.07 0.07 0.01 0.934

C 1 876.86 876.86 89.60 0.000

D 1 130.94 130.94 13.38 0.002

E 1 418.98 418.98 42.81 0.000

2-Way

Interactions

10 4727.33 472.73 48.30 0.000

A*B 1 170.25 170.25 17.40 0.001

A*C 1 250.38 250.38 25.58 0.000

A*D 1 107.57 107.57 10.99 0.004

A*E 1 611.71 611.71 62.50 0.000

B*C 1 299.94 299.94 30.65 0.000

B*D 1 61.47 61.47 6.28 0.023

B*E 1 9.17 9.17 0.94 0.347

C*D 1 0.25 0.25 0.03 0.875

C*E 1 3018.84 3018.84 308.46 0.000

D*E 1 197.76 197.76 20.21 0.000

Error 16 156.59 9.79

Total 31 6511.52

Table 12. Regression coefficients with P-values (Dilution)


Constant 9.0875 0.0908 100.10 0.000

A 0.8750 0.4375 0.0908 4.82 0.000 1.00

B -1.0125 -

0.5063

0.0908 -5.58 0.000 1.00

C 0.0750 0.0375 0.0908 0.41 0.685 1.00

D 1.5500 0.7750 0.0908 8.54 0.000 1.00

E 0.1125 0.0563 0.0908 0.62 0.544 1.00

A*B 0.5125 0.2563 0.0908 2.82 0.012 1.00

A*C -1.0000 -

0.5000

0.0908 -5.51 0.000 1.00

A*D -0.6000 -

0.3000

0.0908 -3.30 0.004 1.00

A*E 1.6125 0.8063 0.0908 8.88 0.000 1.00

B*C -0.1125 -

0.0563

0.0908 -0.62 0.544 1.00

B*D 1.1125 0.5562 0.0908 6.13 0.000 1.00

B*E -0.8750 -

0.4375

0.0908 -4.82 0.000 1.00

C*D -0.2500 -

0.1250

0.0908 -1.38 0.188 1.00

C*E 2.1875 1.0937 0.0908 12.05 0.000 1.00

D*E 0.7375 0.3688 0.0908 4.06 0.001 1.00

Table 13. Model summary – Dilution

S R-sq R-sq(adj) R-sq(pred)

0.513566 96.78% 93.76% 87.11%

Discussion :Table 12 shows the estimation coefficient

(Coef) of each variable term in are regression model for

weld bead width along with the corresponding standard

deviation (SD coef), t-statistics (t-Stat) and probability (P)

values determined at 5% significance level. Variable terms

with P < 0.05, A, C,D, E,AB, AC, AD, AE, BC,BD,CE,

DE are considered statistically significant for dilution for

weld bead geometry. The second-order models for weld bead

width of weld bead geometry in terms of coded variables

with all significant terms are given in Equation (3).The

value of R2 was 96.78%. This means that regression model

provided an explanation of the relationship between

independent factors and the response. The associated p-value

for the model was lower than 0.05 (i.e. α = 0.05, or 95%

confidence) which indicated that the model was considered to

be statistically significant.

EFFECTS AND INTERACTION OF PROCESS

VARIABLES:

MAIN EFFECTS AND INTERACTION OF PROCESS

VARIABLES ON DEPTH OF PENETRATION :

Figure 8. Illustration of main and interaction effect on

Penetration



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VARIABLES ON PENETRATION

From Figure 8, it is evident that Penetration (P) increases with

an increase in pulse time (C) and as the Back ground current

(D) increases, penetration (P) decreases considerably. Factors

A, B and C will not enhance the penetration much as they are

insignificant. There is an interaction effect between

background current (D) and background current time period

(E), as the background current (D) increases ,penetration (P)

decreases.

Figure 9. Illustration of main and interaction effect on weld

bead width


VARIABLES ON WELD BEAD WIDTH (W)

From Figure 9, it is evident that weld bead width (W)

increases with an increase in pulse current (A ) and back

ground current (D) and as the Welding speed (B) increases,

weld bead width (W) decreases considerably. Increase the

Factors Pulse time (C)and background current (D) will not

enhance the weld bead width at all. There is an interaction

effect between factors Pulse current and pulse time (AC),

Pulse current and background current time period (AE),

Welding speed and background current period (BE), Pulse

time and background current period (CE),background current

and background current period(DE).


VARIABLES ON DILUTION

Figure 10. Illustration of main and interaction effect on

Dilution

From Figure 10, it is evident that Dilution (D) increases with

an increase in pulse time (C).As Pulse time (A),background

current (D) background current time period (E) increases, the

dilution decreases. There is no effect of welding speed (B) on

Dilution when welding speed varies from lower level to

higher level. There is an interaction effect between factors

Pulse current and background current time period (AE), Pulse

time and background current period (CE).

MATHEMATICAL MODELS IN CODED FORM

After testing adequacy and significance of each coefficient of

the regression equations we obtained the linear mathematical

models for penetration, weld bead width and dilution in the

coaded form as follows.



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Penetration = 0.7781 - 0.0106 A + 0.0281 B + 0.0656 C + 0.0206 D - 0.0331 E + 0.0144 A*B -

0.0331 A*C - 0.0381 A*D + 0.0106 A*E + 0.0281 B*C - 0.0269 B*D - 0.0181 B*E

+ 0.0356 C*D + 0.0044 C*E - 0.0556 D*E (1)

Weld bead width = 9.0875 + 0.4375 A - 0.5063 B + 0.0375 C + 0.7750 D + 0.0563 E + 0.2563 A*B -

0.5000 A*C - 0.3000 A*D + 0.8063 A*E - 0.0563 B*C + 0.5562 B*D - 0.4375 B*E -

0.1250 C*D + 1.0937 C*E + 0.3688 D*E (2)

Dilution = 53.215 - 2.505 A + 0.047 B + 5.235 C - 2.023 D - 3.618 E + 2.307 A*B + 2.797 A*C

+ 1.833 A*D - 4.372 A*E - 3.062 B*C + 1.386 B*D + 0.535 B*E - 0.088 C*D - 9.713 C*E

+ 2.486 D*E (3)

In calculating the predicted value of the optimization

parameters, the coaded values of the factors are inserted in to

the mathematical model.

Rule 1.If an interaction effect has a positive sign, then for

increasing the optimization parameter, what is required is a

simultaneous increase or decrease of the value of the factors,

for example the combination X1= +1 and X2 = +1 or X1= -1

and X2 = -1.

Rule 2.If the interaction effect has a negative sign, then to

increase the optimization parameter the factors should

simultaneously change in different directions for example the

combination X1= +1 and X2 = -1 or X1= -1 and X2 = +1.

Table 14. Prediction of weld bead geometry for a treatment

using the above model

Sl.

no.

A B C D E Dilution

in %

Weld bead

width in

‘mm’

Penetration

in’ mm’

1 -1 -1 1 1 -1 65.15 9.25 1.04

CONCLUSION

Fractional factorial technique can be effectively utilized to

design the experiments for pulsed MIG welding.

Mathematical models based on regression and analysis of

variance technique can be an effective tool for prediction of

weld bead geometry and shape relations. The developed

models can also be utilized for predicting the values of

controlled variables for achieving desired weld bead profile.

These equations can be usefully employed for control of weld

bead contours in mechanized and robotic welding system. The

models can provide a picture of interaction between control

factors and response factors. The suitable ranges of pulse

current, pulse time, welding speed ,background current and

back ground current time period used for the experiment

provide a useful data ,which can be utilized for making bead

in V- groove plate of medium thickness(10-15 mm).The

established welding parameters for 12 mm thick plate with 6

mm depth V- groove (90 0 included angle) can be employed to

get good quality of weld bead.

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