In this paper, Fuzzy-Taguchi Method has been used to identify the optimal combination of influential factors by analyzing the multi responses in the face milling. Milling experiment has been performed on AMMC (Aluminium Metal Matrix Composite), according to Taguchi orthogonal array (L27) for various combinations of influential parameters: speed, feed, depth of cut and coolant. Fuzzy logic is applied for the analysis of experimental response data of vibrations, temperature, surface roughness and resultant forces. The Fuzzy grade is calculated from this data and Fuzzy grade is optimized using Taguchi method in order to get the optimal parameter values, and also influence of parameters on individual responses is studied using Taguchi S/N ratio analysis. This work is useful for analysis of machining parameters in face milling.
Conventional materials have the limitations in achieving good combination of strength, stiffness, toughness, density, etc. To overcome these limitations and to meet the ever increasing demand of modern day technology, composites are most promising materials in recent days. Metal matrix composites (MMCs) possess high strength, hardness, toughness, and good thermal resistance properties as compared to unreinforced alloys.
Milling is the process of machining flat, curved or irregular surfaces by feeding the work piece against a rotating cutter containing a number of cutting edges. The literature review related to machining of AMMC is presented in the following.
Shivanand et al. (2004) [
To address the lack of research in this issue, the present work has been done on face milling of AMMC with the following objectives:
1) To study the influence of machining parameters on multi responses;
2) To identify the optimal setting of milling process parameters (coolant, cutting speed, feed rate and depth of cut) for optimal responses: vibrations, temperature, surface roughness and resultant forces.
In this experiment four process parameters at three levels have been considered are shown in
L27 orthogonal array as shown in
Step by Step procedure used in the experimental work.
1) Keep the milling machine ready for performing the machining operation;
2) Connect the DAQ system to milling machine;
3) Connect the milling tool dynamometer to the milling machine;
4) Prepare the AMMC work piece sample and fix in machine vice;
5) Fix the milling cutter to an arbor and make machine ready for experiment;
6) Perform milling experiments as per Taguchi design on work piece for various combinations of process control parameters like coolant, spindle speed, feed and depth of cut;
7) Measure surface roughness with the help of a portable stylus-type Talysurf (Taylor Hobson, mitutyo);
8) Measure forces such as thrust force, feed force, cross feed force by using milling tool dynamometer;
9) Measure vibrations by using accelerometer sensor (PCB Accelerometer having Sensitivity 100.5 mV/g) and temperature by using temperature sensor (NI-9211Temperature Module) of LabVIEW based DAQ system.
Experimental responses: surface roughness, vibrations, temperature and resultant forces are measured for different combinations of influential parameters. The measuring instruments and procedure is presented in the following.
Sl. No. | Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|
1 | Coolant | Dry | Kerosene | Soluble oil |
2 | Speed, rpm | 900 | 1120 | 1400 |
3 | Feed, mm/rev | 315 | 500 | 800 |
4 | Depth of cut, mm | 0.8 | 1.0 | 1.2 |
Exp. No. | Process parameters | |||
---|---|---|---|---|
Coolant | Speed (rpm) | Feed (mm/min) | Depth of cut (mm) | |
1 | Dry | 900 | 315 | 0.8 |
2 | Dry | 900 | 500 | 1 |
3 | Dry | 900 | 800 | 1.2 |
4 | Dry | 1120 | 315 | 0.8 |
5 | Dry | 1120 | 500 | 1 |
6 | Dry | 1120 | 800 | 1.2 |
7 | Dry | 1400 | 315 | 1 |
8 | Dry | 1400 | 500 | 1.2 |
9 | Dry | 1400 | 800 | 0.8 |
10 | Kerosene | 900 | 315 | 1.2 |
11 | Kerosene | 900 | 500 | 0.8 |
12 | Kerosene | 900 | 800 | 1 |
13 | Kerosene | 1120 | 315 | 1 |
14 | Kerosene | 1120 | 500 | 1.2 |
15 | Kerosene | 1120 | 800 | 0.8 |
16 | Kerosene | 1400 | 315 | 1.2 |
17 | Kerosene | 1400 | 500 | 0.8 |
18 | Kerosene | 1400 | 800 | 1 |
19 | Soluble oil | 900 | 315 | 1 |
20 | Soluble oil | 900 | 500 | 1.2 |
21 | Soluble oil | 900 | 800 | 0.8 |
22 | Soluble oil | 1120 | 315 | 1.2 |
23 | Soluble oil | 1120 | 500 | 0.8 |
24 | Soluble oil | 1120 | 800 | 1 |
25 | Soluble oil | 1400 | 315 | 0.8 |
26 | Soluble oil | 1400 | 500 | 1 |
27 | Soluble oil | 1400 | 800 | 1.2 |
Exp. No. | Responses | Normalized responses | ||||||
---|---|---|---|---|---|---|---|---|
Resultant force (Kgf) | Vibrations (m/sec2) | Temperature (˚C) | Surface roughness (µm) | Resultant force (Kgf) | Vibrations (m/sec2) | Temperature (˚C) | Surface roughness (µm) | |
1 | 7.28 | 8.29 | 35.1 | 0.26 | 0.84860 | 0.77143 | 0.8537 | 0.93631 |
2 | 9.27 | 8.77 | 35.3 | 0.27 | 0.77821 | 0.63429 | 0.8469 | 0.92994 |
3 | 10.82 | 8.94 | 37.1 | 0.53 | 0.72338 | 0.58571 | 0.7857 | 0.76433 |
4 | 3.00 | 9.24 | 41.7 | 0.69 | 1.00000 | 0.50000 | 0.6293 | 0.66242 |
5 | 7.87 | 9.48 | 43.9 | 1.15 | 0.82773 | 0.43143 | 0.5544 | 0.36943 |
6 | 8.06 | 9.68 | 50.7 | 0.84 | 0.82101 | 0.374 29 | 0.3231 | 0.56688 |
7 | 12.88 | 10.35 | 56.4 | 0.59 | 0.65051 | 0.18286 | 0.1293 | 0.72611 |
8 | 16.40 | 10.57 | 58.4 | 0.60 | 0.52600 | 0.120 00 | 0.0612 | 0.71975 |
9 | 8.66 | 10.69 | 60.2 | 0.58 | 0.79979 | 0.08571 | 0.0000 | 0.73248 |
10 | 7.87 | 8.12 | 30.8 | 0.66 | 0.82773 | 0.82000 | 1.0000 | 0.68153 |
11 | 8.77 | 8.43 | 31.5 | 0.52 | 0.79590 | 0.73143 | 0.9762 | 0.77070 |
12 | 11.70 | 8.62 | 31.8 | 0.43 | 0.69225 | 0.67714 | 0.9660 | 0.82803 |
13 | 23.02 | 8.97 | 39.2 | 0.16 | 0.29183 | 0.57714 | 0.7143 | 1.00000 |
14 | 26.70 | 10.93 | 41.3 | 0.36 | 0.16166 | 0.01714 | 0.6429 | 0.87261 |
15 | 24.35 | 9.67 | 41.7 | 0.65 | 0.24478 | 0.37714 | 0.6293 | 0.68790 |
16 | 29.09 | 10.99 | 43 | 0.55 | 0.07711 | 0.00000 | 0.5850 | 0.75159 |
17 | 27.29 | 9.69 | 43.7 | 0.51 | 0.14079 | 0.37143 | 0.5612 | 0.77707 |
18 | 31.27 | 10.89 | 44.9 | 0.24 | 0.00000 | 0.02857 | 0.5204 | 0.94904 |
19 | 4.90 | 7.87 | 33.6 | 1.20 | 0.93279 | 0.89143 | 0.9048 | 0.33758 |
20 | 4.90 | 8.57 | 33.9 | 1.41 | 0.93279 | 0.69143 | 0.8946 | 0.20382 |
21 | 4.90 | 7.49 | 35 | 0.81 | 0.93279 | 1.00000 | 0.8571 | 0.58599 |
22 | 8.49 | 8.89 | 34.7 | 1.34 | 0.80580 | 0.60000 | 0.8673 | 0.24841 |
23 | 7.55 | 7.65 | 37 | 1.09 | 0.83905 | 0.95429 | 0.7891 | 0.40764 |
24 | 8.12 | 8.27 | 38.4 | 1.32 | 0.81889 | 0.77714 | 0.7415 | 0.26115 |
25 | 16.55 | 9.87 | 37.5 | 1.73 | 0.52069 | 0.32000 | 0.7721 | 0.00000 |
26 | 16.03 | 10.43 | 39.9 | 0.36 | 0.53909 | 0.16000 | 0.6905 | 0.87261 |
27 | 16.58 | 10.99 | 41.6 | 0.50 | 0.51963 | 0.00000 | 0.6327 | 0.78344 |
The surface roughness values of the machined surface are measured in order to analyze the surface finish quality. Surface Roughness is measured with the help of Talysurf (
Spindle vibrations are measured using LabVIEW based DAQ. To measure the vibrations of the spindle, PCB Accelerometer (sensitivity 100.5 mv/g) is placed on spindle as shown in
The temperature at the contact of tool and work piece is measured using LabVIEW software based NI-9211 temperature thermocouple. According to the design of experiments at various conditions Dry, Kerosene and soluble oil (
In order to measure the forces of thrust, feed and cross feed force, milling tool dynamometer (
Data Normalization is done on data which has different range and unit in one data sequence may differ from the others. Data preprocessing is also necessary when the directions of the target in the sequences are different.
If the target data value characteristic is “smaller the better”. The original sequence can be normalized using the Equation (1) as follows:
where
Deals with analysis of multi responses data shown in
The experimental data is analyzed using Fuzzy logic to determine optimum process parameters as in the following.
Figures 5-8 shows the membership function for vibrations, Temperatures, Surface roughness input values in the process parameter.
Using more than three fuzzy sets would cause an explosion in the number of possible expressions. For the current case study 3 fuzzy sets and 4 inputs are considered. This results in a possible 34 = 81 expressions. The five fuzzy sets used in the performance membership function are “very low”, “low”, “medium”, “high”, and “very high”. Again, the trimf shape is employed to map the fuzzy sets. The use of the centroid defuzzification method
is recommended as it results in a more smoothly shaped rule surface. In other words, the output performance index is less sensitive to slight variations in input values which occur near the fuzzy set overlaps. After the input and output membership functions are all defined and their fuzzy sets properly configured, the next step is to write the simplifying rules used to transform the input into output. As shown in the next section, this is the most crucial step in creating a fuzzy logic process parameter system.
Fuzzy grade values are determined from Fuzzy logic using Fuzzy rules (
The evaluation function is: b = [experimental data]; a = readfis (“File name”), t = evalfis (b, a).
After executing above code, the output of FIS editor is obtained as shown in
S. No. | Resultant force | Vibrations | Temperature | Surface roughness | Performance | |||||
---|---|---|---|---|---|---|---|---|---|---|
1 | If | Low | And | Low | And | Low | And | Low | Then | Very high |
2 | If | Low | And | Low | And | Low | And | Medium | Then | High |
3 | If | Low | And | Low | And | Low | And | High | Then | Medium |
4 | If | Low | And | Low | And | Medium | And | Low | Then | Very high |
5 | If | Low | And | Low | And | Medium | And | Medium | Then | High |
6 | If | Low | And | Low | And | Medium | And | High | Then | Medium |
7 | If | Low | And | Low | And | High | And | Low | Then | High |
8 | If | Low | And | Low | And | High | And | Medium | Then | Medium |
9 | If | Low | And | Low | And | High | And | High | Then | Low |
10 | If | Low | And | Medium | And | Low | And | Low | Then | Very high |
- | - | - | - | - | - | - | - | - | - | - |
- | - | - | - | - | - | - | - | - | - | - |
- | - | - | - | - | - | - | - | - | - | - |
78 | If | High | And | High | And | Medium | And | High | Then | Very low |
79 | If | High | And | High | And | High | And | Low | Then | Medium |
80 | If | High | And | High | And | High | And | Medium | Then | Low |
81 | If | High | And | High | And | High | And | High | Then | Very low |
Exp. No. | Input parameters | Fuzzy grade | |||
---|---|---|---|---|---|
Resultant force (Kgf) | Vibrations (m/sec2) | Temperature (˚C) | Surface roughness (µm) | ||
1 | 0.84860 | 0.77143 | 0.8537 | 0.93631 | 0.312 |
2 | 0.77821 | 0.63429 | 0.8469 | 0.92994 | 0.3091 |
3 | 0.72338 | 0.58571 | 0.7857 | 0.76433 | 0.3424 |
4 | 1.00000 | 0.50000 | 0.6293 | 0.66242 | 0.3988 |
5 | 0.82773 | 0.43143 | 0.5544 | 0.36943 | 0.541 |
6 | 0.82101 | 0.37429 | 0.3231 | 0.56688 | 0.4524 |
7 | 0.65051 | 0.18286 | 0.1293 | 0.72611 | 0.416 |
8 | 0.52600 | 0.12000 | 0.0612 | 0.71975 | 0.4777 |
9 | 0.79979 | 0.08571 | 0.0000 | 0.73248 | 0.5 |
10 | 0.82773 | 0.82000 | 1.0000 | 0.68153 | 0.3263 |
11 | 0.79590 | 0.73143 | 0.9762 | 0.77070 | 0.3286 |
12 | 0.69225 | 0.67714 | 0.9660 | 0.82803 | 0.3252 |
13 | 0.29183 | 0.57714 | 0.7143 | 1.00000 | 0.3893 |
14 | 0.16166 | 0.01714 | 0.6429 | 0.87261 | 0.4943 |
15 | 0.24478 | 0.37714 | 0.6293 | 0.68790 | 0.473 |
16 | 0.07711 | 0.00000 | 0.5850 | 0.75159 | 0.5686 |
17 | 0.14079 | 0.37143 | 0.5612 | 0.77707 | 0.447 |
18 | 0.00000 | 0.02857 | 0.5204 | 0.94904 | 0.5144 |
19 | 0.93279 | 0.89143 | 0.9048 | 0.33758 | 0.4091 |
20 | 0.93279 | 0.69143 | 0.8946 | 0.20382 | 0.4605 |
21 | 0.93279 | 1.00000 | 0.8571 | 0.58599 | 0.2908 |
22 | 0.80580 | 0.60000 | 0.8673 | 0.24841 | 0.4837 |
23 | 0.83905 | 0.95429 | 0.7891 | 0.40764 | 0.4157 |
24 | 0.81889 | 0.77714 | 0.7415 | 0.26115 | 0.4906 |
25 | 0.52069 | 0.32000 | 0.7721 | 0.00000 | 0.734 |
26 | 0.53909 | 0.16000 | 0.6905 | 0.87261 | 0.3976 |
27 | 0.51963 | 0.00000 | 0.6327 | 0.78344 | 0.4159 |
Taguchi S/N ratio analysis is performed on Fuzzy grade data shown in
From the results (
Speed 3-Coolant 3-Depth of cut 3-Feed 1
Which means
Speed at level 3 (1400 rpm)
S. No. | Coolant | Speed (rpm) | Feed (mm/min) | Depth of cut (mm) | Fuzzy grade |
---|---|---|---|---|---|
1 | Dry | 900 | 315 | 0.8 | 0.312 |
2 | Dry | 900 | 500 | 1 | 0.3091 |
3 | Dry | 900 | 800 | 1.2 | 0.3424 |
4 | Dry | 1120 | 315 | 0.8 | 0.3988 |
5 | Dry | 1120 | 500 | 1 | 0.541 |
6 | Dry | 1120 | 800 | 1.2 | 0.4524 |
7 | Dry | 1400 | 315 | 1 | 0.416 |
8 | Dry | 1400 | 500 | 1.2 | 0.4777 |
9 | Dry | 1400 | 800 | 0.8 | 0.5 |
10 | Kerosene | 900 | 315 | 1.2 | 0.3263 |
11 | Kerosene | 900 | 500 | 0.8 | 0.3286 |
12 | Kerosene | 900 | 800 | 1 | 0.3252 |
13 | Kerosene | 1120 | 315 | 1 | 0.3893 |
14 | Kerosene | 1120 | 500 | 1.2 | 0.4943 |
15 | Kerosene | 1120 | 800 | 0.8 | 0.473 |
16 | Kerosene | 1400 | 315 | 1.2 | 0.5686 |
17 | Kerosene | 1400 | 500 | 0.8 | 0.447 |
18 | Kerosene | 1400 | 800 | 1 | 0.5144 |
19 | Soluble oil | 900 | 315 | 1 | 0.4091 |
20 | Soluble oil | 900 | 500 | 1.2 | 0.4605 |
21 | Soluble oil | 900 | 800 | 0.8 | 0.2908 |
22 | Soluble oil | 1120 | 315 | 1.2 | 0.4837 |
23 | Soluble oil | 1120 | 500 | 0.8 | 0.4157 |
24 | Soluble oil | 1120 | 800 | 1 | 0.4906 |
25 | Soluble oil | 1400 | 315 | 0.8 | 0.734 |
26 | Soluble oil | 1400 | 500 | 1 | 0.3976 |
27 | Soluble oil | 1400 | 800 | 1.2 | 0.4159 |
Level | Coolant | Speed | Feed | Depth of cut |
---|---|---|---|---|
1 | 7.766 | 9.334 | 7.256 | 7.592 |
2 | 7.516 | 6.794 | 7.456 | 7.649 |
3 | 7.074 | 6.227 | 7.643 | 7.115 |
Delta | 0.692 | 3.106 | 0.387 | 0.534 |
Rank | 2 | 1 | 4 | 3 |
Coolant at level 3 (Soluble oil)
Depth of cut at level 3 (1.2 mm)
Feed at level 1 (315 mm/rev)
Taguchi S/N ratio analysis is applied for data shown in
From
Speed 3-Depth of cut 3-Coolant1, 2 -Feed 3
Which means
Speed at level 3 (1400 rpm)
Depth of cut at level 3 (1.2 mm)
Coolant at level 1, 2 (Dry, Kerosene)
Feed at level 3 (800 mm/rev)
Level | Coolant | Speed | Feed | Depth of cut |
---|---|---|---|---|
1 | −19.58 | −18.42 | −19.20 | −19.03 |
2 | −19.58 | −19.23 | −19.40 | −19.32 |
3 | −18.90 | −20.41 | −19.46 | −19.72 |
Delta | 0.68 | 2.00 | 0.26 | 0.69 |
Rank | 3 | 1 | 4 | 2 |
Level | Coolant | Speed | Feed | Depth of cut |
---|---|---|---|---|
1 | −33.17 | −30.56 | −31.72 | −31.98 |
2 | −31.66 | −32.20 | −32.02 | −32.00 |
3 | −31.31 | −33.37 | −32.39 | −32.15 |
Delta | 1.87 | 2.81 | 0.67 | 0.17 |
Rank | 2 | 1 | 3 | 4 |
Level | Coolant | Speed | Feed | Depth of cut |
---|---|---|---|---|
1 | −18.68 | −17.42 | −20.02 | −19.62 |
2 | −25.50 | −20.38 | −21.46 | −21.56 |
3 | −18.73 | −25.11 | −21.44 | −21.73 |
Delta | 6.83 | 7.69 | 1.44 | 2.11 |
Rank | 2 | 1 | 4 | 3 |
Level | Coolant | Speed | Feed | Depth of cut |
---|---|---|---|---|
1 | 5.0958 | 7.7189 | 3.9266 | 3.4718 |
2 | 7.6211 | 2.9283 | 4.4599 | 6.1405 |
3 | 0.1882 | 5.2580 | 4.5187 | 3.2929 |
Delta | 7.4329 | 2.3297 | 0.5921 | 2.8476 |
Rank | 1 | 3 | 4 | 2 |
From
Speed3-Coolant1-Feed3 -Depth of cut3
Which means
Speed at level 3 (1400 rpm)
Coolant at level 1 (Dry)
Feed at level 3 (800 mm/rev)
Depth of cut at level 3 (1.2 mm)
From
Speed3- Coolant2-- Feed2-Depth of cut3
Which means
Speed at level 3 (1400 rpm)
Coolant at level 2 (Kerosene)
Feed at level 2 (500 mm/rev)
Depth of cut at level 3 (1.2 mm)
From
Coolant3- Depth of cut3 -Speed2- Feed1
Which means
Coolant at level 3 (Soluble oil)
Depth of cut at level 3 (1.2 mm)
Speed at level 2 (1120 rpm)
Feed at level 1 (315 mm/rev)
Conformation experiment is conducted for optimum parameter combination and the values of Vibrations (shown in
According to Fuzzy based Taguchi S/N ratio analysis, the optimal combination of input parameters is Coolant = Soluble oil
Speed = 1400 rpm
Depth of cut = 1.2 mm
Feed = 315 mm/rev
Coolant | Speed (rpm) | Feed (mm/min) | Depth of cut (mm) | Resultant force (Kgf) | Vibrations (m/sec2) | Temperature (˚C) | Surface roughness (µm) |
---|---|---|---|---|---|---|---|
Soluble oil | 1400 | 315 | 1.2 | 19.28 | 10.95 | 38.6 | 0.52 |
The influence of machining parameters on the multi responses is studied and the following conclusions are drawn from the results.
1) The order of influenced parameters found from Fuzzy-Taguchi analysis is as follows:
・ Speed (most influential);
・ Coolant (moderately influential);
・ Depth of cut (least influential);
・ Feed (very least influential).
2) Taguchi analysis shows that speed has more influence on vibrations, forces and temperature and that coolant has more influence on surface roughness.
3) Confirmation test has been conducted and results are satisfactory.
However, this work can be extended further by considering the followings:
・ Accuracy of predictions will be enhanced by generating more experimental data for training;
・ Tools with coated materials like Titanium, diamond, etc., are to be used in order to get the best results.
・ Use of CNC machines is for automatic adjustments of parameter values.