parametric optimization of water jet machining characteristics of...
TRANSCRIPT
-
Parametric optimization of Water jet machining characteristics Of blended resin composites
Dr. Athimoolam[1], Rajan[2] & Dr. Thiyagu[3]
1. Associate Professor, Department of Mechanical Engineering, Agni College of Technology
2. Assistant Professor, Department of Mechanical Engineering, Agni College of Technology
3. Associate Professor, Department of Mechanical Engineering, Agni College of Technology
Abstract
Water jet machining(WJM) is basically a suitable process for post-manufacturing fabrication
of polymers and polymer composites as it produces zero or negligible change in thermal
strain in the materials. Polyurethane-Epoxy blended resin composites are widely used in the
shape memory applications. But not much literature available in the machining of these
composites. In the present work Epoxy-polyurethane, blended resin and the particulate
composites prepared with Nanoclay reinforcement are machined using plain WJM and the
optimization of the process is done for less energy consumption. The influence of input
parameters on the cutting time and cycle time are studied and the cutting conditions for
optimum energy consumption are identified. It is observed that if the water pressure is high,
stand-off distance is low and medium finish cut gives less cutting time and cycle time which
in turn reduces energy consumption. The Quality of cut surface is observed by visual
inspection using high- resolution camera and it has been found that the workpiece quality is
maintained for all types of composites prepared. The optimum cutting conditions from the
planned experimental trials are identified by using Grey relational analysis.
Keywords: Nanoclay, composites, machining, WJM, optimization,Grey,blend, resin
Introduction
There are various studies carried out in the field of water jet machining includes the study of
input parameters like water jet pressure, the mass flow rate of water between nozzle and work
piece and traverse and feed rate of the nozzle on the output parameters for instance rate of
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 734
-
material removal (MRR) and roughness. Flow rate of abrasive particles and traverse speed
are identified as the major contributing factor for producing reduced kerfs and increased
metal removal rate in machining of cladded materials. [1] Better hole quality and surface finish
are obtained in addition to low thrust forces compared to conventional process when
machining carbon fiber-reinforced plastics using water jet cutting process. [2] The parameters
such as nozzle diameter, jet velocity ,water pressure and abrasive particle size are optimized
to get better surface roughness, MRR etc. are in Abrasive WJM using a special algorithm. [3]
The surface roughness is optimized by means of RSM technique for the input parameters of
jet speed, standoff distance and traverse speed. [4] It is observed that deformation type of wear
is the cutting mechanism because the jet penetrates into the work piece,. This can be related
to waviness formed in lower portion cut surface, eventhough the response is not fully
investigated. [5, 6] The taper and width of of laminates with thickness less than 5 mm are
minimised using low values of standoff distance. [7, 8] Less heat affected zone makes Water
jet machining a better option for machining composites. It has been observed that the standoff
distance is a major factor in deciding the machined surface quality. [9] Another study using
steel shows that low value of cutting speed yields good machined surface quality on either
side of the work piece. [10] In the fabrication of small and tiny structures, Water jet machining
technologies can be used with low pressures. This gives better surface finish in micro
machined parts if suitable value of standoff distance is selected. [11] The kerf width is
minimized by the optimization of pressure, abrasive flow rate and standoff distance by Anova
and Regression models.The pressure increase leads to increase of kerf width. [12]
K.S.Jai Aultrin et.al.[13]studied the effect of these parameters for machining of Aluminium
silicon carbide materials and obtained the variable bounds for the Abrasive water jet
machining process. Vijayakumar Pal et.al.[14] carried out the similar study including abrasive
size and standoff distance as variables for machining of blind pocket in Ti6Al4 and found that
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 735
-
as the size of the abrasive particles increases, the depth achieved was more because of the
higher energy of the impact . The delamination behaviour on epoxy- graphite composite
materials when it is machined by WJM process is studied and it is observed that the erosion is
due to the collision of the shock wave from the water jet when pure water jet is used for
machining. [15] When the traverse speed of the jet is increased, will result in the increase in
the maximum value of the crack length .If the jet pressure is increased, will lead to decrease
in the maximum value of the crack length. Also if the value of the jet traverse speed is
decreased it leads to increase in the value of the depth of cut which inturn leads to decrease in
crack length as fewer particles penetrate the cracks. It has been identified that Material
removal micro mechanism throughout depth of the kerfs occurred by t he brittle fracture
when Epoxy-graphite laminates are machined. [16] J. Wang [17] studied that the cutting wear
process is analogous thereto within the conventional grinding process, and also the surface
generated is usually of a decent finish.
But,the workdone on the cutting performance parameters and optimizing power consumption
is not given importance in most of study.So,This work focuses on optimizing the cutting
parameters for minimum power consumption within selected range of parameters for these
blended composites machining.
Materials and Methods
The specimens were Nanoclay reinforced Epoxy-Polyurethane blended Polymer Composites
made in the form of sheets by In-situ Polymerization process.
Table 1: Mechanical properties of blended composite material
Table 2: Experimental Parameters
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 736
-
L9 orthogonal array with three parameters at three levels is studied. The range of input
parameter values are identified with the assistance of obtainable literature for the similar
materials and also the water jet machine available in MIT, shown in Figure 1. is employed for
the work.
Figure 1. Water jet Cutting Machine (Model: 1515 Max IEM)
At first, three variables at three levels are considered with an impact angle of jet 90° on the
three mm thick specimens. The range of water pressures in the machine is identified for
cutting, based on the properties of the materials and then it is divided into three levels, i.e. at
247, 254 and 261 MPa. The three levels of traverse speeds 1091, 1130, and 1497 mm/ min
are used for cutting and 2mm, 3mm and 4 mm stand-off distance levels are used between the
workpiece and nozzle. For these experiments, the rate of 0.1 kg/ min is employed. The choice
of the stand-off distance was done to stop delamination of the composites, even though a
smaller value of stand-off distance is preferred for accuracy of cutting. The machine is
configured for “hard” material processing and will not be reconfigured at the time of
experimenting because of the commercial and technical reasons. The performance of cutting
is evaluated by the number of measures in water jet cutting. The standard of the machined
surfaces gives the assesment as the rate of material removal isn't a serious concern within the
scope of the present work.
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 737
-
Results and Discussion
The fabrication of the composite materials is doled out using Water jet because it produces
less damage to the workpieces. The post-manufacturing fabrication is successfully done using
Water jet machining process because it eliminates the issues related to the traditional
machining processes like crack formation because of machine vibration and thermal strain
because of friction between the machine and workpiece. Design of Experiments is completed
to reach the experimental trials. Since three independent variables like Water pressure,
Standoff distance and Quality of cut are considered and every at three levels. The variable
traverse speed is usually recommended by the machine betting on the standard of the cut
chosen. the subsequent Quality of cut options is offered within the machine. i) Q1-Rough cut
ii) Q2-Medium finish iii) Q3-Standard finish iv) Q4-finish cut and v) Q5-Super finish cut
The extremities such as Super finish cut and rough cut are omitted and the
remaining three options are considered for this study. The effect produced by the cutting
conditions on the machining time and total cycle time is studied.
Table 3 Experimental Trials for WJM
Q1-Rough cut; Q2-Medium finish; Q3-Standard finish; Q4-Finish cut; Q5-Super finish cut
With an increase in pressure the velocity of the jet decreases and hence the cutting time for
the composites increases at the given standoff distance. The graph shown in Chart 3 shows
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 738
-
that the cutting time increases when the water pressure decreases. But it remains steady after
the water pressure reaches 254 MPa. It is evident from the graph shown in Chart 3 that the
cutting time remains constant when the standoff distance is maintained very small (2 mm) or
closer to the workpiece. When the standoff distance (SOD) increases cutting time also
increases. This increase is more when the water pressure is more. This is because the velocity
of jet decreases as the pressure of water through the nozzle increases.
Chart 1. Variation of cutting time Vs Traverse speed
The cutting time drastically increases with increase in values of SOD for a given
traverse speed as observed from the graph shown in Chart 1. Hence selection of minimum
standoff distance gives less cutting time with optimum traverse speed.The cycle time is
calculated by the addition of the four-time components such as i) time to approach the
workpiece by the jet travelling through standoff distance, ii) machining time or cutting time,
iii) dwell time and iv) the time for withdrawal of jet. The variation of cycle time also shows a
similar trend as that of the cutting time and they are shown in Chart 2.There is very little
widening at higher values of traverse speed with lower value of flow rate of abrasive particles
at the bottom owing to less interaction. The depth of cut (DOC) increases linearly with
pressure of water but the increase rate declines above a certain level of pressure setting.
Fragmentation of particles at higher pressure level is the cause for decrease in rate of increase
2.5
4.5
6.5
8.5
10.5
12.5
14.5
1470.000 1478.000 1470.000
Cut
ting
tim
e in
sec
Traverse speed in mm/min
Traverse speed Vs Cutting time
SOD 4 mm
SOD 3 mm
SOD 2 mm
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 739
-
of cut depth. For Opening a narrower slot, at higher values of traverse speedswith lower flow
rates, very few particles are participating in erosion.
Chart 2. Variation of Cycle time Vs Traverse speed
Excessive loading exerted because of more water pressure applied on the material
leads to bonding failure or delamination due to factors like workpiece vibration, in the bottom
portion of the workpiece while cutting. Hence,Water pressure is controlled properly in order
to avoid this problem which will reduce mechanical defect. However, through cuts are
obtained at a high water pressure when the traverse speed selected is reasonably high. When
the SOD is increased to 3 mm the cutting time initially increased to 0.070 min at 254 MPa
and maintains at the same value even if the water is pressure increased to 261 MPa. The same
pattern is repeated at the SOD 4mm. This is shown in Chart3 and the variation of cycle time
with water pressure is shown in Chart 4.
8.0
13.0
18.0
23.0
28.0
33.0
1470.000 1478.000 1470.000
Cyc
le t
ime
in s
ec
Traverse speed in mm/min
Traverse speed Vs Cycle time
SOD 4 mm
SOD 3 mm
SOD 2 mm
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 740
-
Chart 3.Variation of cutting time Vs Water pressure
Chart 4. Variation of Cycle time Vs Water pressure
The influence of Water pressure and Standoff distance on another cutting parameter of
Traverse speed is also an important aspect to be studied because the traverse speed value is
generated by the machine at a given water pressure for the Quality of cut chosen. Charts 5
and 6 indicates that there is no change in traverse speed for low water pressure of 247 MPa
and low standoff distance of 2mm. There is slight variation in the traverse speed for 3 mm
SOD and at a pressure of 254 MPa.
0
1
2
3
4
5
6
245 250 255 260 265
Cut
tin
g ti
me
in s
ec
Water pressure in MPa
Pressure Vs Cutting time
SOD 2 mm
SOD 3 mm
SOD 4 mm
0
2
4
6
8
10
12
245 250 255 260 265
Cut
ting
tim
e in
sec
Water pressure in MPa
Pressure Vs Cycle time
SOD 2 mm
SOD 3 mm
SOD 4 mm
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 741
-
Chart 5. Variation of Traverse speed Vs Water pressure
Chart 6. Variation of Traverse speed Vs Standoff Distance
As the composite materials are brittle it generally doesn’t present burrs. It is
observed that if water pressure used is high, smooth exit edge without any burrs are formed in
the machined samples. However, if the water pressure used is low then burrs are visible in
the machined samples especially on the exit side. Also, it is observed that small hairline burrs
are present on the materials when high values of traverse speed is used for cutting. Hence it is
inferred that the burr formation in the specimen or finish of the cut surface depends on the
energy level of the jet on the exit side of the specimen. It is observed in this study that at
0
200
400
600
800
1000
1200
1400
1600
245.00 250.00 255.00 260.00 265.00
Tra
ver
se s
pee
d i
n m
m/m
in
Water pressure in MPa
Pressure Vs Traverse speed
SOD 2 mm
SOD 3 mm
SOD 4 mm
600
800
1000
1200
1400
1600
0 2 4 6
Tra
vers
e sp
eed
in
mm
/min
Standoff distance in mm
SOD Vs Traverse speed
WP 247 MPa
WP 254 MPa
WP 261 MPa
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 742
-
938.5 mm/min traverse speed or 261MPa water pressure are used then there is no burrs
present on the machined surface.
The crack generation process followed the mode I method of fracture. At first, crack
tips are formed followed by the penetration of water into the already developed crack tips
causes a wedge action of water results in the crack propagation. Wedging action occurs
because of particle embedment inside the existing material crack.
When the traverse speed is increased then the value of crack length also reaches maximum
value. But if the jet pressure is increased then the maximum value of crack length will
decrease. This is due to increase in kinectic energy of the jet because of increase in water
pressure. As the jet deflection is reduced, the flow of water into the cracks is also reduced.
This in turn leads to a decrease in maximum value of a crack length. If the the jet traverse
speed value is deccreased then the rate of mass flow increase causes more shearing action.
This results in increased depth of cut, leaving very few particles for penetration of the cracks.
Chart 7. Variation of Cutting time Vs Standoff Distance
Another important aspect of this machining process is that when the water pressure is kept
constant then the cutting time and cycle time are varying linearly for standoff distance. It is
shown in Chart 7 and Chart 8.
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0.000 2.000 4.000 6.000
Cut
ting
tim
e in
sec
Stand off Distance in mm
SOD Vs Cutting time
WP 247 MPa
WP 254 MPa
WP 261 MPa
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 743
-
Chart 8. Variation of Cycle time Vs Standoff Distance
Figure 2. WJM -work piece after Cutting
Figure 3. WJM -Removed material samples after Cutting
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0 2 4 6
Cyc
le t
ime
in s
ec
Stand off Distance in mm
SOD Vs Cycle time
WP 247 MPa
WP 254 MPa
WP 261 MPa
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 744
-
The variation is more pronounced if the standoff distance or water pressure is
increased further. The machined samples for EP/PU, EP/PU/1%NC, EP/PU/2%NC,
EP/PU/3%NC, EP/PU/4%NC and EP/PU/5%NC composites are shown in Figure 2 and the
cut-outs or removed pieces during machining are shown in Figure 3. The machined samples
show good quality cuts as evidenced in the figures with no deviation in dimensions of the
hole. Also, it is observed from the removed materials the burr formation is limited and hence
it can be used for machining of these composites successfully.
Grey Relational Analysis
Optimum process parameters for cutting the composites are identified among the
experiments conducted by using Grey Relational Analysis. Lower the better criterion is used for
the cutting time to identify the optimum process parameters setting. The Maximum and
Minimum entry values are identified for the cutting time and cycle time and the deviation
between them is calculated.
Table 4. Calculation of Rank based on Grey Relational Coefficient
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 745
-
The deviation between the maximum value and the cell value is computed. The actual deviation
divided by the maximum deviation will give the Grey relational coefficient. These values are
given in Table 4.There is Rank deficiency due to the presence of empty cells, unbalanced
nesting, and therefore further analysis is not carried out. The optimum values of Input
parameters are calculated based on the experimental values shown in Table 3.Grey Relational
Analysis is done to find out the optimum values of input parameters to obtain less cutting
time and it is found that the cutting time is minimum (0.05 min) for the pressure of 261 MPa,
SOD 2 mm and with Quality of cut Q2 (medium finish) i.e. traverse speed 1470 mm/min.
Thus the optimum cutting parameters for machining of these composites with less cutting
time and cycle time has been identified.
Conclusion
The property values of the materials and the limitations of the water jet cutting machine are
used as constraints to select input parameter values.The phenomenon of cutting mechanism is
decided by the bond strength and amount of deformation. The mechanism of cutting in the
middle portion of the hole involves the plastic deformation. This phenomenon of erosion
usually occurs in ductile materials. This mechanism is also seen in the erosive process of
brittle materials. The Epoxy-polyurethene blended composites, contains several Nanoclay
particles embedded on the material. It is recommended to use higher levels of water pressure
to reduce the size of the crack but technological constraints are imposed in order to utilize
minimum cutting time and energy. Similarly, the traverse speed of the machine table is
reduced as it is linked with reduction in the number of machined samples or cutting rate.
Water jet machining process machined accuracy and the quality of cut are very good as
observed and it is an advantageous and more suitable cutting process for these types of
composites. The Water jet machining process is optimized by Grey Relational Analysis for
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 746
-
less cutting time and cycle time. Experiments show that Water jet machining may be
successfully employed for machining E/PU/NC composites.
References
[1] Kashif Ishfaq; Nadeem Ahmad Mufti; Naveed Ahmed; Salman Pervaiz. Abrasive
waterjet cutting of cladded material: kerf taper and MRR analysis. Mater. Manuf.
Processes.,2019,34,544-553.
[2] Massimo Durante; Luca Boccarusso; Dario De Fazio;Antonio Langella, Circular
cutting strategy for drilling of carbon fibre-reinforced plastics (CFRPs), Mater.
Manuf. Processes.,2019,34,554-566.
[3] Shankar Chakraborty ;Ankan Mitra. Parametric optimization of abrasive water-jet
machining processes using grey wolf optimizer. Mater. Manuf.
Processes.,2018,33,1471-1482.
[4] Arvind Kumar; Hari Singh; Vinod Kumar. Study the parametric effect of abrasive
water jet machining on surface roughness of Inconel 718 using RSM-BBD
techniques. Mater. Manuf. Processes.,2018,33,1483-1490.
[5] Gnanavelbabu, A.; Kaliyamoorthy Rajkumar; Saravanan, P. Investigation on the
cutting quality characteristics of abrasive water jet machining of AA6061-B4C-hBN
hybrid metal matrix composites. Mater. Manuf. Processes.,2018, 33, 1313-1323.
[6] Bimla Mardi, K. ; Dixit, A. R. ; Mallick, A. ; Alokesh Pramanik; Beata Ballokova;
Pavol Hvizdos; Josef Foldyna; Jiri Sucka; Petr Hlavacek; Michal Zelenak, Surface
integrity of Mg-based nanocomposite produced by Abrasive Water Jet Machining
(AWJM), Mater. Manuf. Processes.,2017,32,1707-1714.
[7] Mustafa Armagan; Armagan Arici, A. Cutting performance of glass-vinyl ester
composite by abrasive water jet, Mater. Manuf. Processes.,2017,32, 1715-1722.
[8] Selvam, R. ; Karunamoorthy, L.; Arunkumar, N. Investigation on performance of
abrasive water jet in machining hybrid composites, Mater. Manuf. Processes.,2017,32,
700 -706.
[9] Vasanth. S.; Muthuramalingam. T.; Vinothkumar, P.; Geethapriyan, T.; Murali, G.
Performance Analysis of Process Parameters on Machining Titanium (Ti-6Al-4V)
Alloy Using Abrasive Water Jet Machining Process. Procedia CIRP.,2016,46,139 –
142.
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 747
-
[10] Piotr Loschnera; Krzysztof Jarosz; Piotr Nieslonya. Investigation of the effect of
cutting speed on surface quality in abrasive water jet cutting of 316L stainless steel.
Procedia Eng.,2016, 149,276 – 282.
[11] Matus Molitoris; Jan Pitel; Alexander Hosovsky; Maria Tothova; Kamil Zidek.
Review of Research on Water Jet with Slurry Injection, Procedia Eng.,2016,149 ,333
– 339.
[12] Deepak Doreswamy; Basavanna Shivamurthy; Devineni Anjaiah; Yagnesh, N. An
Investigation of Abrasive Water Jet Machining on Graphite/Glass/Epoxy Composite.
Int. J.Manuf.Eng., 2015, 10.1155,627218
[13] Jai Aultrin,K.S.; JaiAultrin,M.; DevAnand,P.;Jerald Jose. Modelling the cutting
process and cutting performance in AWJM using Genetic Fuzzy approach, Procedia
Eng.,2012, 38, 4013 – 4020.
[14] Vijaya Kumar Pal.S.K.; Choudhury. Surface characterization and machining of blind
pockets on Ti6Al4V by abrasive water jet machining, Procedia Mater. Sci.,2014,
5,1584-1592.
[15] Shanmugam, D.K.; Nguyen, T.; Wang, J. A study of delamination on graphite/epoxy
composites in abrasive water jet machining. Composites: Part A.,2008, 39 ,923–929
[16] Wang. J. Abrasive Water jet Machining of Polymer Matrix Composites –Cutting
Performance, Erosive Process and Predictive Models. Int. J. Adv. Manuf.
Technol.,1999, 15,757–768.
[17] Shanmugam, D.K.; Chen, F.L.; Soirees, E.; Brandt. M. Comparative study of jetting
machining technologies over laser machining technology for cutting composite
materials. Compos. Struct.,.2002, 57 ,289–296.
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 748
-
Figures and Tables
Figure 1. Water jet Cutting Machine (Model: 1515 Max IEM)
Figure 2. WJM -work piece after Cutting
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 749
-
Figure 3. WJM -Removed material samples after Cutting
Table 1: Major properties of the Test material Mechanical property Test value
1%NC 2%NC 3%NC 4%NC 5%NC Impact strength(J/m) 13.76 13.35 12.94 12.53 12.12 Compressive strength(MPa) 17.81 14.91 12.00 09.10 06.19 Shear strength(kPa) 05.76 04.79 03.82 02.85 01.88 Tensile Strength(MPa) 08.75 10.52 10.55 08.85 05.42 Flexural strength(MPa) 20.01 26.10 28.13 26.09 20.00 Table 2: Experimental Parameters Water pressure(MPa) Traverse speed(mm/min) Standoff distance(mm)
247 1470 2
254 1176 3
261 938 4
Table 3 Experimental Trials for WJM
Expt.No Water pressure (MPa)
Standoff Distance
(mm)
Traverse speed (mm/min)
Machining time
(sec)
Total cycle time
(sec)
1 247 2 Q2(1470) 3.00 9.00
2 247 3 Q3(1130) 3.60 9.60
3 247 4 Q4(1091.8) 4.20 10.20
4 254 2 Q2(1478) 3.00 9.00
5 254 3 Q3(1117.5) 4.20 10.08
6 254 4 Q4(904.96) 5.40 11.22
7 261 2 Q2(1470) 3.00 8.88
8 261 3 Q3(1156) 4.20 9.90
9 261 4 Q4(938.5) 5.40 10.98
Q1-Rough cut; Q2-Medium finish; Q3-Standard finish; Q4-Finish cut; Q5-Super finish cut
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 750
-
Table 4. Calculation of Rank based on Grey Relational Coefficient
Max M/c ing Time -M/c ing time
Max Cycle Time -Cycle time
Lower the better (Machining time)
Lower the better (Total cycle time)
Grey relational coefficient 1
Grey relational coefficient 2
GRC1+ GRC2
Grey relational grade
R a nk
0.04 0.037 1 0.9487 1.0000 0.9070 1.907 0.9535 2
0.03 0.027 0.75 0.6923 0.6667 0.6190 1.287 0.6429 3
0.02 0.017 0.5 0.4359 0.5000 0.4699 0.969 0.4849 6
0.04 0.037 1 0.9487 1.0000 0.9070 1.907 0.9535 2
0.02 0.019 0.5 0.4872 0.5000 0.4937 0.994 0.4968 5
0 0 0 0.0000 0.3333 0.3333 0.667 0.3333 8
0.04 0.039 1 1.0000 1.0000 1.0000 2.000 1.0000 1
0.02 0.022 0.5 0.5641 0.5000 0.5342 1.034 0.5171 4
0 0.004 0 0.1026 0.3333 0.3578 0.691 0.3456 7
AEGAEUM JOURNAL
Volume 8, Issue 6, 2020
ISSN NO: 0776-3808
http://aegaeum.com/ Page No: 751