parametric optimization of water jet machining characteristics of...

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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

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  • 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

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  • 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

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  • 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

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  • 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.

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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

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  • 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.

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  • [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

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    [17] Shanmugam, D.K.; Chen, F.L.; Soirees, E.; Brandt. M. Comparative study of jetting

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  • Figures and Tables

    Figure 1. Water jet Cutting Machine (Model: 1515 Max IEM)

    Figure 2. WJM -work piece after Cutting

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  • 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

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  • 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