Development of Mathematical Model Using DOE for Analyzing Angular

Distortion of 202 Grade Stainless Steel GTAW Plates

R. Sudhakaran & Dr. V. VeL MuruganDept of Mechanical Engineering

Kumaraguru College of Technology

Coimbatore

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.

To Remove Angular Distortion

• Arrest the work piece in a base plate

• Pre bend

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.

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.

Experimental Procedureo 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.

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.

Plan of WorkIdentifying 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 the Analyzing the results results

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

Limits of Process VariablesProcess

parametersLimits

-2 -1 0 +1 +2

Welding current amps

70 80 90 100 110

Welding Speed mm/min

80 90 100

110 120

Gas flow rateLiter/min

5 10 15 20 25

Gun angle Degrees

50 60 70 80 90

Plate Length mm

100 125 150 175 200

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.

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(

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

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

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

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 of Angular distortion Degrees

Expe

rimen

tal V

alues

of A

ngul

ar di

storti

on de

gree

s

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

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

Angula

r D

isto

rtio

n D

egre

es

V = 100 mm/minL = 150 mmI = 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

An

gu

lar D

isto

rti

on

De

gre

es

θ =70 °V = 100 mm/minL = 150 mm

Q = 15 Lit/min

Results and Discussion

0

1

2

3

4

5

6

7

100(-2) 125(-1) 150(0) 175(1) 200(2)

Plate Length mm

An

gu

lar

Dis

tort

ion

De

gre

es

θ = 70°V = 100 mm/minI = 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

An

gu

lar

Dis

tort

ion

De

gre

es

θ = 70°V = 100 mm/minL = 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

Ang

ular

Dis

tort

ion

Deg

rees

θ = 70°V = 100 mm/minL = 150 mmI = 90 Amps

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.

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

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