The presentation deals with using DOE as a tool to analyze angular distortion.

1. Development of Mathematical Model
Using DOE for Analyzing Angular
Distortion of 202 Grade Stainless Steel
GTAW Plates
R. Sudhakaran & Dr. V. VeL Murugan
Dept of Mechanical Engineering
Kumaraguru College of Technology
Coimbatore

2. Angular Distortion
• Angular distortion is a major problem and most
pronounced among different types of distortion in
the butt welded plates.
• In arc welding processes, due to rapid heating and
cooling the work piece undergoes an uneven
expansion and contraction in all the directions.
This leads to distortion in all the directions of the
work piece.

3. To Remove Angular Distortion
• Arrest the work piece in a
base plate
• Pre bend

4. Objectives of the Work
• The extent of angular distortion depend on 1) the
width and depth of the fusion zone relative to plate
thickness, 2) the type of joint 3) the thermo
mechanical properties and 4) the welding process
control parameters
• If an exact magnitude of angular distortion is
predicted, then a weld with no angular distortion
would be the result. It is difficult to obtain
analytical solution to predict angular distortion.
Hence various investigations were made to study
the effects of various parameters on angular
distortion using statistical methods.

5. Objectives of the Work
• In the present work, a mathematical model is
developed to establish a relationship between
important process variables namely, welding
current (I), welding speed (V), gas flow rate (Q),
gun angle (θ), plate length (L) with angular
distortion.
• The design of experiments technique was used to
conduct the experiments. The direct effects of
process variables on angular distortion are studied.

6. Experimental Procedure
o The experiments were
conducted using Lincoln V
350 Pro Electric Digital
Welding Machine.
o A servo motor driven
manipulator was used to
maintain uniform welding
speed.

7. Experimental Procedure
• The welding gun is held
stationary in a frame above the
table and it is provided with an
attachment for setting the
required welding gun angle.
• Argon is used as the shielding
gas and its flow rate is varied
for each experiment as per the
requirements.

8. Plan of Work
Identifying the process variablesIdentifying the process variables
Developing the design matrixDeveloping the design matrix
Conducting the experiments as per the design matrixConducting the experiments as per the design matrix
Development of mathematical modelsDevelopment of mathematical models
Evaluation of coefficients of the modelsEvaluation of coefficients of the models
Checking adequacy of the modelsChecking adequacy of the models
Testing the regression coefficients of the modelsTesting the regression coefficients of the models
Validation of the mathematical modelsValidation of the mathematical models
Analyzing theAnalyzing the
resultsresults

9. Limits of Process Variables
• The angular distortion is
a function of many
independently
controllable process
parameters such as
welding current (I),
welding speed (V), gas
flow rate (Q), gun angle
(θ), plate length (L)
• The design plan was
decided based on the
practical considerations
for the system
Factor Upper
limit
Lower
limit
Welding
current (I) amps
110 70
Welding
speed (V)
mm/min
120 80
Gas flow rate (Q)
liter/min
25 5
Gun
Angle (θ)
Degrees
90 50
Plate Length (L)
mm
200 100

10. Limits of Process Variables
Process
parameters
Limits
-2 -1 0 +1 +2
Welding
current amps
70 80 90 100 110
Welding Speed
mm/min
80 90 100 110 120
Gas flow rate
Liter/min
5 10 15 20 25
Gun angle
Degrees
50 60 70 80 90
Plate Length
mm
100 125 150 175 200

11. Design Matrix
The design matrix chosen to
conduct the experiments was
five factor, five levels central
composite rotatable designs
consisting of 32 sets of coded
conditions .
This design matrix comprises
a full replication factorial
design i.e. 24
= 16 factorial
design plus 7 center points
and 8 star points.

12. Recording of Angular
Distortion
The angular distortion was
determined using
Microscribe G2 coordinate
measuring machine. The
angle β between the two lines
was measured. From the
angle β the angle α was
determined using the
equation
2)180( ÷β−=α

13. Evaluation of Regression
Coefficients
The response
function can be
expressed as α =f (θ,
V, L, I, Q) and the
relationship selected
is a second order
response surface.
The function is as
follows

14. • Quality America – DOE PC –IV software was used
to calculate the coefficients.

15. Development of
Mathematical Model
• Insignificant
coefficients were
dropped along with the
parameters with which
they are associated.
• This was carried out by
conducting backward
elimination analysis
with t- probability
criterion kept at 0.75
• The final mathematical
model is as follows

16. Validity of The Model
• The validity of the
developed model is
tested by drawing
scatter diagram for
the observed and
predicted values of
angular distortion
• The results show
that for the
developed model
the accuracy is 95%.
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
Predicted Values ofAngulardistortion Degrees
ExperimentalValuesofAngular
distortiondegrees

17. Adequacy of The Model
• The adequacy of the model was tested
using the Analysis of Variance Techniques
SS sum of squares, DOF degree of freedom
Mean sum of squares = sum of square terms/DOF
F ratio = MS of lack of fit/ MS of error terms
R ratio = MS of first order term & second order term/ MS of error term
F ratio (6, 5, 0.05) = 4.95
R ratio (20,5, 0.05) = 4.56

18. Results and Discussion
• The mathematical
model given above can
be used to predict the
angular distortion by
substituting the values
of the values of the
respective process
parameters.
• The direct effects of
the process parameters
on angular distortion
are discussed below.
0
1
2
3
4
5
6
7
8
50(-2) 60(-1) 70(0) 80(1) 90(2)
Gun Angles Degrees
AngularDistortionDegrees
V = 100 mm/min
L = 150 mm
I = 90 Amps
Q = 15 Lit/min
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
80(-2) 90(-1) 100(0) 110(1) 120(2)
Welding Speed mm/min
AngularDistortionDegrees
θ =70 °
V = 100 mm/min
L = 150 mm
Q = 15 Lit/min

19. Results and Discussion
0
1
2
3
4
5
6
7
100(-2) 125(-1) 150(0) 175(1) 200(2)
Plate Length mm
AngularDistortionDegrees
θ = 70°
V = 100 mm/min
I = 90 Amps
Q = 15 Lit/min
0
1
2
3
4
5
6
70(-2) 80(-1) 90(0) 100(1) 110(2)
Welding Current Amps
AngularDistortionDegrees
θ = 70°
V = 100 mm/min
L = 150 mm
Q = 15 Lit/min
3.4
3.5
3.6
3.7
3.8
3.9
4
5(-2) 10(-1) 15(0) 20(1) 25(2)
Gas Flow Rate Litre/Min
AngularDistortionDegrees
θ = 70°
V= 100 mm/min
L = 150 mm
I = 90 Amps

20. Conclusions
• The second order quadratic model can be
effectively used to predict angular
distortion in gas tungsten arc welding of
stainless steel 202 grade plates.
• Central composite design can be
conveniently used to analyzing the direct
effects of different combinations of
process parameters within the range of
investigation on the angular distortion of
gas tungsten arc welded stainless steel 202
plates.

21. Conclusions
• The predicted angular distortion is compared
with the experimental one and the deviations
falls within the limit of 95% confidence level.
• The maximum angular distortion is 12° when all
the process parameters are maintained at -1 level
and welding speed is maintained at +1 level.
• Out of the five process parameters selected for
investigation, welding current has strong effect
on angular distortion; plate length and gas flow
rate has a negative effect on angular distortion

22. THANK YOU