Design Of Experiment

2.1 Introduction: - Laxmi Oil Pumps & Systems Pvt Ltd is manufacturing organizations, producing lube oil pumps for diesel engine application. Machining of different components of pumps is one of the major activities. Cycle time on high cost machines like VMC, CNC are vital important to monitor the productivity. N14 lop body’s relief valve operation which is done on VMC machining is chosen for study of optimization. The photo of component mounted in the fixture for the operation is given in the fig 2.1 and operation drawing is given in Fig 2.2. A cross-functional team was set to conduct this experiment and target was set to complete the same within month’s period

2.2 Details of the process and its parameters: - relief valve boar machining consist of different operations like rough boring with end mill for axis correction, pre-reamed boring followed by reaming. Mounting hole drilling and tapping are allied operations. The details break up of operations and its timing are given in the table 2.1

N-14 Body Relief Valve Process Details

Present Sec

Sr.No. Tool Speed Feed MM/min

1 Dia.20 SC Endmill 600 60 160

2 Dia.6.5 SC drill 2000 150 25

3 Dia.20 SC Drill 135mm depth 1000 120 100

4 15° Chamfer tool 550 70 30

5 Boring Tool ( 22.00 mm) 135 depth 500 60 /25 200

6 T slot Cutter 400 10 240

7 6.5 Ex. Long drill 700 60 72

8 22.250 C/T reamer 135 depth 300 50 240

9 45 ° Chamfer Tool 600 60 10

10 5/16" X 18 UNC tap 400 564 20

1097

Present Cycle time = 18.50 min. 18.28333

Present cycle time works out to 18.5 min. In order to reduce the cycle time we need to check possibility of optimizing the parameters used (speed and feed) for all the tools. But consequently, change in the parameters of tools will result in changes of following factors also, which we need to monitor.

a) Size consistency of boarb) Change in the Surface finish of the boarc) Change in the Ovality & straightness (geometry) of the

boar.d) Change in the life of the tools.

Considering the operation of the relief valve surface finish is most important, we will monitor this as response (Y) in our experiment and all other factors can be confirmed for effect of changes during the validation process. Specification for surface finish is 1.6 Ra max. And for ovality & tapper it is 20-micron max.

2.3 First trials with Parameter setting: - We used Shainin DOE technique. As suggested in Variable search technique we started experiment with setting all parameters at ‘-‘ as shown in column 3 of Table 2.2 and noted the response as shown n Table 2.3. Now all the parameter setting changed to ‘+’ settings and noted the response. Such a iteration did for obtaining 3 sets of reading of each setting. Test of significance was conducted as shown in Table 2.3. As the ratio D/d is less than 3, there is no significant change in the response. Hence we need to conduct trials further with changing the parameter settings.

Now earlier ‘+’ setting become ‘-‘ setting and new parameters are added at ‘+’ settings. This has shown in Table 2.4

Table 2.2 Parameters setting for First Trial

No Parameter(-) Setting

(+) Setting

A Speed of 22 boring tool 600 750

B Feed of 22 boring tool 70/35 90/40

C Speed of 22.25 Reamer 400 450

D Feed of 22.25 Reamer 70 90

E Depth of cut for reamer 0.1 0.2

F Speed of 20 SC Drill 1100 1200

G Feed of 20 SC Drill 110 120

H Speed of 20.00 End mill 700 800

I Feed of 20.00 End Mill 70 80

Table 2.3 Response for First Trials

Test - Setting + Setting

1st Run 0.8 0.98

2nd Run 0.72 1.15

3rd Run 0.93 0.85

Median 0.8 0.98

Range 0.21 0.3

D ( Difference Between Two Medians ) 0.18

d = Average of Two Ranges 0.255

D/d 0.705

Three runs of each setting with taking readings alternatively response were noted in The Table 2.5.

Table 2.4 Parameters setting for Second Trial

No Parameter(-) Setting

(+) Setting

A Speed of 22 boring tool 500 600

B Feed of 22 boring tool 60/25 70/35

C Speed of 22.25 Reamer 300 400

D Feed of 22.25 Reamer 50 70

E Depth of cut for reamer 0.5 0.1

F Speed of 20 SC Drill 1000 1100

G Feed of 20 SC Drill 100 110

H Speed of 20.00 End mill 600 700

I Feed of 20.00 End Mill 60 70

Table 2.5 Response for Second Trials

Test - Setting + Setting

1st Run 0.85 1.6

2nd Run 0.89 1.42

3rd Run 0.99 1.5

Median 0.89 1.5

Average of median   1.195

Range 0.14 0.18

D (Difference Between Two Medians) 0.61

d = Average of Two Ranges 0.16

D/d 3.8125

After conducting the test of significance the ratio of D/d turns out to 3.812, which indicate that the parameters changed has significant effect on response ‘Y’

2.3.1 Separation of Important and non important factors having effect of response ‘Y”: - In this stage trials were conducted as stated below

a) Number all the factors with alphabets starting from Ab) Run a pair of test with setting A factor at ‘-‘ and remaining

all at ‘+’ (A-R+) Than a mirror image test with A factor at ‘+’ and remaining at ‘-‘ setting. (A+R-)

c) On the graph decision limits are drawn as shown in The Fig 2.3

These decision limits are based on the formula as

Decision limits = median (of all the + setting response or – setting response) ± t0.95 đ /đ 2

Where t is value corresponding to 0.95 or 95% confidence level

& đ / đ2 is an estimate of sigma σ

With three sets of each response for + and – settings we have the two degree of freedom for each of them or four degree of freedom in total. From T table for 4 degree of freedom for two- tailed T test at 95 % confidence level value is 2.776 and statistical constant is 1.91.

Factor thus arrives 2.776/ 1.91 = 1.45 is used for determining the decision limits.

Now after plotting the result of two tests on the graph, possible results are

a) If both the pair of test i.e. A-R+ and A+R- shows the result inside the low side and high side decision limits, factor A, along with all of its associate interaction effect, is unimportant and can be eliminated from further studies

b) If there is complete reversal then A is only important factor and rest of all are unimportant and can be eliminated.

c) If either or both the pairs of the test shows result out side the limits but not complete reversal then factor A along with its associated interaction effect can not be eliminated. A plus some other factor or factors must be considered along with their interaction.

  - Setting + Setting Average UDL (+) LDL(+) UDL (-) LDL(-)

First run 0.85 1.6 1.195 1.73 1.27 1.12 0.66

Second run 0.89 1.42 1.195 1.73 1.27 1.12 0.66

3rd run 0.99 1.5 1.195 1.73 1.27 1.12 0.66

A 0.7 1.38 1.195 1.73 1.27 1.12 0.66

B 0.79 1.4 1.195 1.73 1.27 1.12 0.66

C 0.8 0.95 1.195 1.73 1.27 1.12 0.66

D 0.88 0.97 1.195 1.73 1.27 1.12 0.66

C&D 0.95 1.2 1.195 1.73 1.27 1.12 0.66

E 0.9 0.87 1.195 1.73 1.27 1.12 0.66

C&D&E 1.47 0.92 1.195 1.73 1.27 1.12 0.66

Table 2.6 Response of the entire test with limits.

Fig 2.3 Graph showing decision limits and points plotted.

From the graph we can conclude that parameters C, D & E are only important and having significant effect on the response. All other factors can be eliminated from further study.

2.3.2 Full Factorial for important three factors: - In order to get the optimum setting for factors, we need to concentrate only on three factors as mentioned above and settings for all other factors can be decided, whichever is favorable for us. Hence to reduce the cycle time all these factors can be set at ‘+’ settings.

Full factorial design for three factors along with its interaction is shown in Table 2.7Table 2.6 Full Factorial design

  Speed FeedDepth of

cut Interaction  

Sr no C D E C*D C*E D*E C*D*E Response

1 - - - + + + - 0.85,0.89, 0.99

2 + - - - - + + 0.95

3 - + - - + - + 0.97

4 + + - + - - - 0.9

5 - - + + - - + 0.87

6 + - + - + - - 0.88

7 - + + - - + - 0.8

8 + + + + + + + 1.6, 1.42, 1,5

                 

+ 1.0575 1.0425 1.0125 1.04 1.06 1.035 1.0725 Grand Avg

- 0.8825 0.8975 0.9275 0.9 0.88 0.905 0.8675  

Difference 0.175 0.145 0.085 0.14 0.18 0.13 0.205  

Magnitude 0.0875 0.0725 0.0425 0.07 0.09 0.065 0.1025  

Regression equation works out asY=(Avg of median)+/- ((1/2* C's contribution)*C) +/- ((1/2*D's contribution)*D)…… +/- ((1/2* CDE's contribution)*ABC)

Table 2.7 shows the effect of each factor on ‘Y’ and its coefficient in the regression equationTable 2.7 Effect & Coefficient of each factor

_Term Effect Coef

Constant   0.97

Speed 0.175 0.0875

Feed 0.145 0.0725

Depth of cut 0.085 0.0425

Speed*Feed 0.14 0.07

Speed*Depth of cut 0.18 0.09

Feed*Depth of cut 0.13 0.065

Speed*Feed*Depth of cut 0.205 0.1025

Analysis of variance and residual error are worked out using Minitab software and output is shown in Table 2.8

Table 2.8 Analysis of Variance For response (coded unites)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 3 0.11775 0.11775 0.03925 * *

Speed 1 0.06125 0.06125 0.06125 * *

Feed 1 0.04205 0.04205 0.04205 * *

Depth of cut 1 0.01445 0.01445 0.01445 * *

2-Way Interactions 3 0.1378 0.1378 0.04593 * *

Speed*Feed 1 0.0392 0.0392 0.0392 * *

Speed*Depth of cut 1 0.0648 0.0648 0.0648 * *

Feed*Depth of cut 1 0.0338 0.0338 0.0338 * *

3-Way Interactions 1 0.08405 0.08405 0.08405 * *

Speed*Feed*Depth of cut 1 0.08405 0.08405 0.08405 * *

Residual Error 0 * * *

Total 7 0.3396

2.3.3 Response optimization: - Using the Minitab software response counter is plotted Fig 2.4 As white area is appeared in counter graph optimization is possible.

Fig 2.4 Counter plot from Minitab software

Results of optimizer are as shown in Table 2.10. and graphical representation is shown in Fig 2.5

Table 2.9 Response optimizer

Goal Lower Target Upper Weight Import

Response Target 1.15 1.19 1.23 1 1

Global Solution

Speed 450

Feed 90

Depth of cut 0.148

Predicted Response 1.19

Desirability 1

Composite Desirability 1

Speed

Feed

450440430420410400

90

85

80

75

70

Depth of cut 0.2Hold Values

1.151.23

Responce

Counter plote 2

CurHigh

Low1.0000D

Optimal

d = 1.0000

Targ: 1.1900Responce

y = 1.190

1.0000DesirabilityComposite

0.10

0.20

70.0

90.0

400.0

450.0Feed Depth ofSpeed

[450.0000] [90.0000] [0.1483]

Fig 2.5 Optimized parameter out put from Minitab

2.4 Results & savings:- All three parameter’s sets as per the result obtained in table 2.9 and rest all parameters at ‘+’ settings. Results are validated for 100 components. Responses are well within accepted range. Total cycle time is now reduced to 14.30 min from original of 18.50 min. Reduction of 4.2 min per components resulted in the saving of Rs 38500/- per month ( 1000 components per month with m/c hr rate of Rs 550/-)i.e. Rs 4,62,000 per annum.

2.5 Conclusion:- with the help of DOE we can optimize the parameters without compromising quality and cost per component can be saved to great extend.