Chapter 2 Design and Development of HPC Nozzle
2.3 Full Factorial Analysis for HPC Nozzle
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There are many methods of design of experiment (DOE) like Multi-vari chart, Variable search, Full factorials, Taguchi methods etc. Out of several methods of DOE, Full factorial analysis is a powerful and popular homing in technique and hence frequently used DOE method. Fig.2.1 shows the commonly used DOE method. Almost all the methods follow some basic methodologies which are appended below:
Identify the important variables or parameters that effect quality through extensive brainstorming with different expert opinion/participation
Separates those variables into different categories, generally not more than 4 important and most severe variables which are known as Red X (most serious variable that effects quality) and pink X (Moderately serious which has moderate impact on quality)
Reduce variations of Red X and pink X through redesign and process improvement
Other than Red X and Pink X there may be lot many variable that do not effects quality should not take into consideration for controlling for minimizing the cost.
Fig.2.1 Commonly used DOE methods
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Normally not more than 4 factors/variables at a time are taken to segregate the critical variables effect on the experimental setup. Full factorial DOE method is one of the powerful and popular tools for identifications of the most severe variables which may cause or affect the performance of the product. Basic principle of the analysis is that every variable can be tested with all levels (generally two) of every other variable. Experimental testing of all possible combinations of pre-selected variables and levels allows for the systematic separation and quantification of all main and interaction effects, thereby giving the chance of narrowing down the number of variables to one or two which are comparatively more severe. The complete full factorial analysis involves two main steps such as preparation of combinatorial matrix which identifies the impact of all individual variables having two levels for each variables and preparation of ANOVA table to identify main effect and interaction effect.
First of all visualize the components of the HPC nozzle and identify the variables that affect the performance of the nozzle functionality. Identify also the response variable i.e. independent variable and dependent variable and some other factors which are not that important but have some impact on the overall performance after interacting with each other’s. These variables are:
Diameter of the nozzle holes
Number of nozzle holes
Pressure of the cutting fluid
Flow rate of cutting fluid
Angle of spry of cutting fluid
Insert type and material
Volume of the nozzle container
Depth of cut
Cutting velocity
Feed
Machining Time
After several brain storming session with concern technical staff and all levels of experts, it has been provisionally identified that out of the above mentioned variables, depending on the severity following 4 variables as shown in Table 2.1. are seem to be vulnerable for the optimized performance of the specialized designed HPC nozzle.
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Table 2.1 Most severe variables that effects performance of the HPC nozzle
Symbol Factors or variables Level (- or +)
Present Value (-) Experimental(+)
A Diameter of the nozzle 0.5 mm 1 mm
B Pressure inside nozzle 80 bar 100 bar
C Angle of the spray pattern 15° 20°
D Flow rate of cutting fluid 120 l/hr 150 l/hr Table 2.2 Combinatorial matrix
A- A+ Total
B- B+ B- B+
D-
5.06
D+ 5.66
D- 5.40
D+ 5.31
Total 4.61 5.56 5.73 5.56
Several experiments with the above 4 variables each with 2 levels are performed and roughness is recorded. A total of 24 or 16 groups were to be tested and among the different combinations, the ones with the best response outcome (surface roughness) in this
3 1 2
4
Random number (Cell no) in the sequence of experimental run
Average roughness of the 2 experiments Roughness in the 1st experiment run
Roughness in the 2nd experiment run
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case are selected.Due to the time and resource constrained only few runs were taken and the test results are shown in the combinatorial matrix in Table 2.2.
Table 2.3 Contribution of individual variables
Factor Total Score/Roughness Difference
A- 4.58+5.56=10.14
A+ is worse than A- by 1.15
A+ 5.73+5.56=11.29
B- 4.58+5.73=10.31
B+ is worse than B- by 0.81
B+ 5.56+5.56=11.12
C- 5.06+5.66=10.72
C- is worse than C+ by 0.01
C+ 5.40+5.31=10.71
D- 5.06+5.40=10.46
D+ is worse than D+ by 0.47
D+ 5.66+5.31=10.93
Based on the above results, an ANOVA table has developed as shown Table-2.4.
Table 2.4 ANOVA for specialized HPC nozzle
Sl.
No.
Individual 2 Variables 3 Variables 4 Variables
Total
A B C D AB AC BC AD BD CD ABC ABD ACD BCD ABCD
1 - - - - + + + + + + - - - - + 1.10
2 + - - - - - + - + + + + + - - 1.25
3 - + - - - + - + - + + + - + - 1.25
4 + + - - + - - - - + - - + + + 1.46
5 - - + - + - - + + - + - + + - 1.54
6 + - + - - + - - + - - + - + + 1.34
7 - + + - - - + + - - - + + - + 1.49
8 + + + - + + + - - - + - - - - 1.03
9 - - - + + + + - - - - + + + - 0.83
10 + - - + - - + + - - + - - + + 1.64
11 - + - + - + - - + - + - + - + 1.53
12 + + - + + - - + + - - + - - - 1.65
13 - - + + + - - - - + + + - - + 1.10
14 + - + + - + - + - + - - + - - 1.50
15 - + + + - - + - + + - - - + - 1.29
16 + + + + + + + + + + + + + + + 1.42
+1.1 6
- 0.82
+0.8 7
- 0.50
- 1.16
+1.4 2
+1.3 2 Pink
X +1.0
6
+.82 -3.68 Red X
+0.10 +0.76 -0.62 +0.12 - 0.12
Table 2.3 shows that contributions of individual variables are not significant in most of the cases except varaiable-1(A).The difference between A- and A+ (it is 1.15) is due to variable -1 alone. Same explanations apply to all other variables as well. From the above table it is clear that variables-1, variable-2, and varable-4’s level+ that is experimental assumed value not performing better than level – (minus) whereas variable-3 perform better when experimental value is taken into consideration.Table 2.4 shows that contributions of individual factor are not significant. 2 factor interactions are responsible
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for the roughness.More specifically if 2 factors are selected for elimination in the 1st attempt, the rightchoice are variable-3 and variable -4 that is CD interaction. Similarly BC interaction has also due importance on the overall performance of the applicator .ThusAB interaction can be considered the Red X, while BC considered as PinkX. The interaction effects can further be analyzed by constructing following Figure (Fig.2.2):
(a) Variable2 and 3 (b) Variable 3and 4 Fig. 2.2Factor interaction effect
Convergence of two lines in both graphs show that they have high level of interaction effects, Fig 2.2 (a),thus need to be eliminated at the first step. Additionally the BC graph (graph 2.2a) shows that the interaction effects is minimum (roughness is -4.83) when both B and C are minus (-). Thus in order to eliminate the interaction between B and C both the value should be present value that is pressure to be maintain 20 bar and angle of spray pattern to be kept 15°. Similarly interaction between CD shows that the value of D is minimum at D- (roughness 5.06) thus we may conclude that the present value of D to be maintained that is flow rate 120 liter per hour.