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A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network
Materials Today: Proceedings xxx (xxxx) xxx
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A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network M. Chithirai Pon Selvan a,⇑, Divya Midhunchakkaravarthy b, Rohan Senanayake c, Swaroop Ramaswamy Pillai d, Sahith Reddy Madara e a
School of Science and Engineering, Curtin University Dubai, United Arab Emirates Centre of Postgraduate Studies, Lincoln University College, Malaysia Faculty of Engineering, Lincoln University College, Malaysia d Department of Electronics and Telecommunication Engineering, Amity University Dubai, United Arab Emirates e Sharjah Academy for Astronomy, Space Sciences, and Technology, University of Sharjah, United Arab Emirates b c
a r t i c l e
i n f o
Article history: Received 31 August 2019 Received in revised form 7 November 2019 Accepted 23 December 2019 Available online xxxx Keywords: Ti-6Al-4V Abrasive Waterjet Machining (AWJM) Heat affected zone Process parameters Optimization Artificial Neural Network (ANN)
a b s t r a c t Ti-6Al-4V is classified among the most commonly used Ti-alloys and is extensively used in aerospace and medical industries where low-density, high strength and outstanding corrosion resistance are required. This material cannot be processed by conventional machining methods because of its high strength. Abrasive Waterjet Machining, abbreviated as AWJM, is an unconventional machining process suitable for machining Ti-6Al-4V as it generates less heat affected zone. The quality of AWJM is governed by process parameters, the selection of these parameters is critical in this technology to achieve the desirable output measures. This paper provides an experimental investigation for the performance analysis of process parameters on machining Ti-6Al-4V using abrasive waterjet technology. In order to select appropriate parameters, a mathematical equations were developed using Regression Investigation Method (RIM) Artificial Neural Network (ANN) procedures. Based on the input and output data collected from the experiments, modelling is done and tested for the different set of data to ensure the accuracy. These mathematical models can be used to identify the static and dynamic behavior of the process. These models will further help in simulating the process, expanding the design facilities and studying the physical and chemical variation in the process. Models provide understanding the operations, control methods and the possible optimization. The developed models also help in documenting the performance of the existing system. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
1. Introduction Abrasive waterjet machining (AWJM) technology is one of the latest non-conventional approach currently being utilized in the current industries business for material preparing with the asset of absence of thermal mutilation, large flexibility, high machining adaptability and little cutting powers [1]. In comparison to conventional and non-conventional machining advancements, AWJM is utilized progressively with broad appliance for the shape slicing of hard machine materials, for example, titanium compounds, ceramics, composite materials [2]. ⇑ Corresponding author. E-mail address: [email protected] (M. Chithirai Pon Selvan).
Titanium and its amalgams are highly resistant to corrosion, have a large solidarity in comparison to their mass and have excellent thermal characteristics. Titanium alloys such as Ti–6Al-4V are generally utilized in aerospace and flying machine applications, marine applications and high-performance automotive applications. Each of these sectors require materials with high erosion opposition and quality [3]. Titanium and its compounds are hard to process by regular machining procedures inferable from a few inalienable material properties. Ti is a profoundly artificially responsive component with practically all cutting instrument/tool materials, its small modules of flexibility and thermal conductivity additionally hinder machinability [4]. Deciding and streamlining the parameters engaged with a machining procedure is a significant and critical task. Machining
https://doi.org/10.1016/j.matpr.2019.12.215 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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M. Chithirai Pon Selvan et al. / Materials Today: Proceedings xxx (xxxx) xxx
of titanium into completed segments is receiving increasing attention in particularly aviation and defence industries [5]. Ti–6Al–4 V is additionally one of the costliest metals to create, which is another disadvantage to assembling parts utilizing this metal. The procedure of titanium’s machining in the aeronautic trade today is by experimentation. It produces non-productive outcomes since this material is highly chemical responsive with different materials. Ti also has a low thermal conductivity. It is difficult to decide and find the right parameters for machining, since it is a hard to machine material. Today analysts are hoping to grow new models to foresee and upgrade these parameters [6]. Over the most recent two decades, the intelligent frameworks formed by Artificial Neural Network (ANN), have been connected in manufacturing and have been the subject of broad research. This innovation has turned into a significant computing instrument to solve various engineering issues [7]. To adequately control and streamline the abrasive waterjet machining procedures, prescient depth of cut-models (DOC) have already been established for phosphate glass [8], aluminium oxide ceramics [9] and mild steel [10]. However, until now no models have been published for Ti-6Al-4V in literature. Research is needed to completely comprehend the impact of the significant procedure parameters on depth of cut (DOC) of Ti-6Al-4V along with mathematical modelling using RIM and ANN [11]. This paper intents to explore the handled surface profiles by means of experiments to develop a detailed empirical model of DOC. Modelled values are compared with measured values, these performed experiments are designed using taguchi’s approach. Another intent is to use ANN to mathematically model the treated surfaces in terms of DOC in abrasive water-jet machined Ti-6Al-4V alloys. 2. Experimental work 2.1. Material choice Ti-6Al-4V, abbreviated as TC4, is an a/b titanium amalgam, it has a high solidarity to weight proportion and exceptional erosion resistance. Ti-6Al-4V contains about 6% of a a-stabilizer Al and 4% of a b-stabilizer V in its structural composition. The precise composition of Ti-6Al-4V can be found in Table 1. TC4 is one of the most usual utilized titanium combinations and is connected in a wide scope of utilizations where low thickness (density) and good corrosion resistance are vital, for example, aeronautical, space and biomechanical industries. Ti-6Al-4V titanium alloy has various physical and mechanical properties such as density (min – 4.429 g/cm3 to max – 4.512 g/cm3), Youngs Modulus (min – 104 GPa to max – 113 GPa), uniform elongation (min – 5% to max – 18%), ultimate strength (min – 900 MPa to max – 950 MPa), Poisson’s ratio (min – 0.31 to max – 0.37), shear modulus (min – 40 GPa to max – 45 GPa), yield Strength (min – 880 MPa to max 920 MPa).
gravity feed spot which is abrasive. The setup is represented in Fig. 1. The high-pressure water is transformed with a 0.35 mm diameter sapphire orifice and a frequently checked carbide nozzle of 1.05 mm diameter. The checks of the nozzles ensure that the nozzle never gets seriously damaged since worn out nozzles get replaced. Once the high-pressurized water passed the orifice, it arrives at the mixing chamber. Flattened air from a hopper gravity feed spot, which is abrasive, then delivers the garnet 80 mesh abrasives (particles) with a compactness of 4.1 gm/cc and an average width of 0.18 mm to the mixing chamber too. This process gets regulated with a metering disc and results in the AWJ, which is regulated manually with the pressure gauge. There are different parameters that determine the properties of the abrasive flow aside from the pressure and mass flow. The controller can change the standoff distance in the machinist regulator position. The fourth parameter, the traverse speed, is determined by the NC code programming. These parameters have their influence on how deep the cut of the waterjet goes. The slurry and debris of material resulting from this cut are disposed into a catcher container. The variable process parameters (Table 2) are considered as the control factors – ‘‘mass flow rate (g/s), traverse speed (mm/s), water pressure (MPa), and standoff distance (mm)”. Some parameters are kept constant such as (Orifice diameter – 0.34 mm; Nozzle diameter – 1.04 mm; Focusing tube (length – 75 mm, diameter – 1 mm); Impact angle 90°, Abrasive type - Garnet 80 Mesh). The experiments were designed using Taguchi’s method. The choice of orthogonal/symmetrical cluster is the significant factor while planning the tests utilizing Taguchi’s strategy which has been utilized to conduct experiments in the present study. Since four parameters have been picked with number of levels equivalent to 3, L27 orthogonal array has been chosen according to Taguchi’s DOE hypothesis. By utilizing each degree of these parameters, 27 cuts were executed in the titanium composite (Ti-6Al-4V) under the proper ecological conditions (Table 3). The DOC for each experiment was estimated by using a Sigma Scope 500 projector. 3. Empirical model for depth of cut (DOC) Scientific model for the DOC is exactly created dependent on the test information (experimental data) set by utilizing regression investigation method as appeared in Eq. (1). This model relates
2.2. Experimental procedure The AWJ Sweden cutter is fortified with a KMT pressure drive. This pump was used at its design pressure of 4000 bar to make the samples. The instrument consists of a rasping feeder arrangement, a pneumatic controlled regulator, a work section (specimen) table measuring 300 cm length and 150 cm width and a hopper
Table 1 Chemical composition of specimens (Ti-6Al-4V) (wt%). Ti
Al
V
Fe
O
C
N
H
89.546
6.09
4.04
0.24
0.16
0.04
0.02
0.00568
Fig. 1. Schematic of an abrasive waterjet (AWJ) cutting process [9].
Table 2 Three levels of input parameters used in experiment. Parameters
Units
Level 1
Level 2
Level 3
Water Pressure Traverse Speed Standoff Distance Mass Flow Rate
MPa mm/s mm g/s
270 0.5 1.8 8
335 10.25 3.4 11.5
400 20 5 15
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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M. Chithirai Pon Selvan et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 3 Taguchi’s Design of Experiments (DOE). Experiment (Trial) Number
Water Pressure (MPa)
Traverse Speed (mm/s)
Mass Flow Rate (g/s)
Standoff Distance (mm)
Depth of Cut (DOC) (mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400
20 19.25 18.5 17.75 17 16.25 15.5 14.75 14 13.25 12.5 11.75 11 10.25 9.5 8.75 8 7.25 6.5 5.75 5 4.25 3.5 2.75 2 1.25 0.5
8 8.27 8.54 8.81 9.08 9.35 9.62 9.89 10.16 10.43 10.7 10.97 11.24 11.51 11.78 12.05 12.32 12.59 12.86 13.13 13.4 13.67 13.94 14.21 14.48 14.75 15
5 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3 2.3 2.2 2.1 2 1.9 1.8
18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
the DOC to four different input process parameters such as ‘‘p (MPa), u (mm/s), s (mm), ma (g/s)”. !0:14 !0:46 p1:33 s 0:45 qp u2 ma sma Dc ¼ 1:02 3 dp qw d j u E p dp qp u
ð1Þ The units of individual parameters are: (Dc, s, dj, dp – meters), (u – meter per second (m/s)), (qp, qw – kilogram per meter cube (kg/ m3)), (ma – kilogram per second (kg/s)), (p, E – Megapascal (MPa)). This empirical model is legitimate when the following constraints are met: 270 MPa (39160.17 psi) < [water pressure (p)] < 400 MPa (58015.08 psi) 8 g/s (28.8 kg/hour) < [mass flow rate (ma)] < 15 g/s (54 kg/hour) 0.5 mm/s (0.0005 m/s) < [traverse speed (u)] < 20 mm/s (0.02 m/s) 1.8 mm (0.0018 m) < [standoff distance (s)] < 5 mm (0.005 m) Eq. (1) can be rewritten in the following form in order to make the impact of the process parameters more clear as in Eq. (2). 0:93
Dc ¼ 1:02
p1:47 m0:54 dp q0:32 a p
ð2Þ
E1:33 u0:82 s0:01 qw dj
For the material under consideration, it tends to be given by Eq. (3): 0:93
Dc ¼ 2:156 107
p1:47 m0:54 dp q0:32 a p u0:82 s0:01 qw dj
ð3Þ
4. Experimental results and discussions 4.1. Effect of water pressure (p) on depth of cut (DOC) Fig. 2 plots the measurements of the DOC (mm) with respect to p (MPa). An abrasive waterjet machine cuts the specimen keeping
Fig. 2. Effect of water pressure (p) on depth of cut (DOC).
some process parameters constant; (ma) = 15 g/s; (u) = 0.5 mm/s; (s) = 1.85 mm. The results are obtained by incrementing the water pressure on the sample, while still keeping the other process parameters constant. This results in an increase of DOC of the specimen. Fig. 2 shows that DOC (mm) and p (MPa) are almost linearly dependent from each other, increasing water pressure also increases the DOC. Incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.2. Effect of abrasive mass flow rate (ma) on depth of cut (DOC) Fig. 3 plots the measurements of the DOC (mm) with respect to ma (g/s). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (u) = 0.5 mm/s; (s) = 1.85 mm. The results are obtained by incrementing the abrasive mass flow rate on the sample, while still keeping the other process parameters constant. This results in an increase of DOC of the specimen. Fig. 3 shows that DOC (mm) & ma (g/s) are proportional to each other. That means incrementing or
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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Fig. 5. Effect of standoff distance (s) on depth of cut (DOC). Fig. 3. Effect of abrasive mass flow rate (ma) on depth of cut (DOC).
decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.3. Effect of traverse speed (u) on depth of cut (DOC) Fig. 4 plots the measurements of the DOC (mm) with respect to u (mm/s). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (ma) = 15 g/s; (s) = 1.85 mm. The results are obtained by incrementing the traverse speed, while still keeping the other process parameters constant. This results in a decrease of DOC of the specimen. Based on Fig. 4, it can be concluded that DOC (mm) & u (mm/s) are inversely proportional (/) to each other. That means incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.4. Effect of standoff distance (s) on depth of cut (DOC) Fig. 5 plots the measurements of the DOC (mm) with respect to s (mm). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (ma) = 15 g/s; (u) = 0.5 mm/s. The results are obtained by incrementing the standoff distance, while still keeping the other process parameters constant. This results in a decrease of DOC of the specimen. Based on Fig. 5, it can be concluded that DOC (mm) & s (mm) are inversely proportional (/) to each other. That means incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well.
5. Artificial Neural network (ANN) and back propagation algorithm (ANN model Training) Neural network is used in mathematical modelling to approximate the output of various different processes based on its inputs. It is widely used in machine learning for prediction. Neural networks are based on the function of the human brain. Neurons receive inputs through dendrites and based on the inputs it produces outputs that get transferred to the next neuron through axon. This principle is the groundwork for many different algorithms. In this paper there are four inputs and two output. It neural networks it is split in two models. One model with pressure of water, traverse speed an depth of cut as the output. The other is taken as mass flow rate, standoff distance as the input and depth of cut is taken as the output. The reason for taking as two model is to improve the accuracy. More input and output in a single model the output gives less accuracy. In this paper number of hidden layers are chosen as two. As the number of hidden layer has to be between the number of input and the number of output, in this case it is taken as two as the number of input and the output is two respectively for each model. The back-propagation algorithm is commonly used as it gives best results. This algorithm is based on adjusting the weights based on the gradient descent method. The weights are adjusted based on the error, which is the difference between the input and the output. The Fig. 6(a) indicates the overall architecture. Pressure and traverse speed is taken as inputs and the depth of cut is taken as the output. Fig. 6(b) also indicates the overall ANN model with Massflow rate and stand off distance as the input and depth of cut as output. Initially random weights are assumed between the neurons between the values 0 to 1. The input is given to the neural network which propagates through neurons to get the desired output. The error is determined using the formula Error = R1/2(TargetOutput) 2. The weights are now adapted to decrease the error. There is one hidden layer inbetween the input layer and the output layer. The hidden layer can be further increased if more accuracy is required. The error reduction with respect to the weight can be written as dE/dW. By applying chain rule this can be split in to three functions.
dE=dW ¼ dE=dO dO=dN dN=dW:
Fig. 4. Effect of traverse speed (u) on depth of cut (DOC).
ð4Þ
The first one is the rate of change of error with respect to the output, the second function is the change of output with hidden network and the third is the rate of change of network to the weight. Each function is determined by a computation formula. The new weight is are determined in the following way:
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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Fig. 6a. Artificial Neural Network Model.
Fig. 6b. Artificial Neural Network Model.
New Weight ¼ Old Weight g ðdE=dWÞ
ð5Þ
Where g is the learning rate parameter. The learning rate parameter decides the rate of change of weights required to achieve the target. The sensitivity can be written as
@E2 @W AB
ð6Þ
Chain rule states
@E2 @E2 @IB ¼ ¼ OA @W AB @IB @W AB
the DOC based on the water pressure and the traverse speed. The blue line indicates the predicted depth of cut and the red line indicates the actual DOC. Both Figs. 7 and 8 show that the predicted DOC line follows the line of the actual values closely. Fig. 9 shows the learning curve. The backpropagation algorithm is trained for thousand iterations. It can be seen from the diagram that at the end of thousand iterations the error reduced to 0.8. Hence this can be used to mathematically model the system using neural networks. More accuracy can be achieved by increasing the number of data. It can also be done by increasing the number of iterations and by adjusting the initial eights.
ð7Þ
From Eqs. (4) and (2) the final weight for the algorithm can be written as
W ABðnewÞ ¼ W ABðoldÞ g
@E2 OA @IB
ð8Þ
WAB, the weight from neuron A to B depends on the sensitivity of the squared error, E2, to the input, IB, of unit B and on the output signal OA. As mentioned above in this case the inputs Ib are taken as the input. In this paper totally 40 datas are taken and the thirteen datas are taken for testing the data. Remaining 27 datas are used to train in the back propagation algorithm. The matrix obtained was used to determine the output for the new set of data. So it can be said that around 70% data is used for training and the remaining 30% data is used for the testing purposes. It is found that the root mean square error is less than 0.8 Hence this weighted matrix obtaines after the iterations are fed with new set of 27 data which is shown in Figs. 7,8,10,11. The curve for the old and the new data is shown in the figures. The new data taken is also within the same range considered for the training. The Fig. 7 shows the DOC values for various values for water pressures and traverse speeds. Fig. 8 presents the 3D graph for
Fig. 7. Actual DOC vs predicted DOC.
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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Fig. 8. DOC based on Speed and Pressure. Fig. 11. Actual DOC vs Predicted DOC.
Fig. 9. Learning curve.
Fig. 12. Learning curve.
Fig. 10 presents the DOC based on standoff distance and the mass flow rate. Fig. 11 indicates the actual DOC and the predicted DOC. It can be observed in both the diagrams that curves follow almost the same path. Fig. 12 below indicates the learning curve for the backpropagation algorithm. It shows that the error is reduced less than 0.5, the smaller the error, the more accurate the model is. This is also reflected in the previous graph where predicted and the actual depth of cut are almost equal.
6. Conclusions and future prospects
Fig. 10. DOC based on Standoff distance vs Mass flow rate.
Abrasive waterjet cutting has been studied experimentally for Ti-6Al-4V resulting into a regression based empirical model of the depth of cut (DOC). The parameters with a direct consequence on DOC are the mass flow rate (ma), the water pressure (p), the nozzle standoff distance (s) and the traverse speed (u). Pressure and abrasive mass flow rate on the one hand are proportional to the depth of cut. Nozzle standoff distance and traverse speed on the other hand are inversely proportional to DOC. The results of the experiments seem to match the model. The experimental
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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results are used to mathematically model the whole system. ANN is used in modelling the system with back propagation algorithm. As the data is not linear ANN is used instead of the conventional models. It can be observed that the model could predict for the new set of data with more than 90% accuracy. This can be further used in predicting the output for different set of data for various materials. The same data can also be used along with the neuro fuzzy systems, where the fuzzy logic can be used to classify the data and the neural networks can be used to predict the data. Fuzzy classification can be done based on the output depth of cut based on the four parameters. This classification can be used to split the neural network model in to two categories as at present the model is created randomly base on the nature of data. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] A. Gnanavelbabu, P. Saravanan, K. Rajkumar, S. Karthikeyan, Experimental investigations on multiple responses in abrasive waterjet machining of Ti-6Al4V alloy, Mater. Today: Proc. 5 (5) (2018) 13413–13421, Part 2.
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[2] Ahmet Hasçalık, Ulasß Çaydasß, Electrical discharge machining of titanium alloy (Ti-6Al-4V), Appl. Surface Sci. 253 (22) (2007) 9007–9016. [3] Farhad Nabhani, Machining of aerospace titanium alloys, Robot. Comput.Integr. Manuf. 17 (2001) 99–106. [4] Ahmet Hascalik, Ulasß Çaydasß, Hakan Gürün, Effect of traverse speed on abrasive waterjet machining of Ti–6Al–4V alloy, Mater. Design 28 (2007) 953– 1957. [5] E.O. Ezugwu, Z.M. Wang, Titanium alloys their machinablity – a review, J. Mater. Process. Technol. 68 (3) (1997) 262–274. [6] Y.W. Seo, M. Ramulu, D. Kim, Machinability of titanium alloy (Ti– 6Al–4V) by abrasive waterjets, Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf. 217 (2003) 1709–1721. [7] Sahith Reddy Madara, Chithirai Pon Selvan, Swaroop Ramaswamy, Impact of process parameters on surface roughness of hastelloy using abrasive waterjet machining technology, Int. J. Recent Technol. Eng. 7 (5S2) (2019) 419–425. [8] Chithirai Pon Selvan, Sahith Reddy Madara, S.S. Sampath, N.S. Sarath Raj, Effects of process parameters on depth of cut in abrasive waterjet cutting of phosphate glass, in: IEEE Xplore, Advances in Science and Engineering Technology International Conferences (ASET), Abu-Dhabi, 2018, pp. 1–6. [9] Chithirai Pon Selvan, Sahith Reddy Madara, Swaroop Ramaswamy Pillai, Ramesh Vandanapu, In-depth evaluation of process variables in abrasive waterjet cutting of alumina ceramics, in: IEEE Explore, Advances in Science and Engineering Technology International Conferences (ASET), Dubai, United Arab Emirates, 2019, pp. 1–4. [10] Chithirai Pon Selvan, Divya Midhunchakkaravarthy, Swaroop Ramaswamy Pillai, Sahith Reddy Madara, Investigation on abrasive waterjet machining conditions of mild steel using artificial neural network, Mater. Today: Proc. (2019) 1–7. [11] Ghodsiyeh Danial, Davoudinejad Ali, Optimizing finishing process in WEDMing of titanium alloy (Ti6Al4V) by brass wire based on response surface methodology, Res. J. Appl. Sci. Eng. Technol. 5 (4) (2013) 1290–1301.
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network M. Chithirai Pon Selvan a,⇑, Divya Midhunchakkaravarthy b, Rohan Senanayake c, Swaroop Ramaswamy Pillai d, Sahith Reddy Madara e a
School of Science and Engineering, Curtin University Dubai, United Arab Emirates Centre of Postgraduate Studies, Lincoln University College, Malaysia Faculty of Engineering, Lincoln University College, Malaysia d Department of Electronics and Telecommunication Engineering, Amity University Dubai, United Arab Emirates e Sharjah Academy for Astronomy, Space Sciences, and Technology, University of Sharjah, United Arab Emirates b c
a r t i c l e
i n f o
Article history: Received 31 August 2019 Received in revised form 7 November 2019 Accepted 23 December 2019 Available online xxxx Keywords: Ti-6Al-4V Abrasive Waterjet Machining (AWJM) Heat affected zone Process parameters Optimization Artificial Neural Network (ANN)
a b s t r a c t Ti-6Al-4V is classified among the most commonly used Ti-alloys and is extensively used in aerospace and medical industries where low-density, high strength and outstanding corrosion resistance are required. This material cannot be processed by conventional machining methods because of its high strength. Abrasive Waterjet Machining, abbreviated as AWJM, is an unconventional machining process suitable for machining Ti-6Al-4V as it generates less heat affected zone. The quality of AWJM is governed by process parameters, the selection of these parameters is critical in this technology to achieve the desirable output measures. This paper provides an experimental investigation for the performance analysis of process parameters on machining Ti-6Al-4V using abrasive waterjet technology. In order to select appropriate parameters, a mathematical equations were developed using Regression Investigation Method (RIM) Artificial Neural Network (ANN) procedures. Based on the input and output data collected from the experiments, modelling is done and tested for the different set of data to ensure the accuracy. These mathematical models can be used to identify the static and dynamic behavior of the process. These models will further help in simulating the process, expanding the design facilities and studying the physical and chemical variation in the process. Models provide understanding the operations, control methods and the possible optimization. The developed models also help in documenting the performance of the existing system. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
1. Introduction Abrasive waterjet machining (AWJM) technology is one of the latest non-conventional approach currently being utilized in the current industries business for material preparing with the asset of absence of thermal mutilation, large flexibility, high machining adaptability and little cutting powers [1]. In comparison to conventional and non-conventional machining advancements, AWJM is utilized progressively with broad appliance for the shape slicing of hard machine materials, for example, titanium compounds, ceramics, composite materials [2]. ⇑ Corresponding author. E-mail address: [email protected] (M. Chithirai Pon Selvan).
Titanium and its amalgams are highly resistant to corrosion, have a large solidarity in comparison to their mass and have excellent thermal characteristics. Titanium alloys such as Ti–6Al-4V are generally utilized in aerospace and flying machine applications, marine applications and high-performance automotive applications. Each of these sectors require materials with high erosion opposition and quality [3]. Titanium and its compounds are hard to process by regular machining procedures inferable from a few inalienable material properties. Ti is a profoundly artificially responsive component with practically all cutting instrument/tool materials, its small modules of flexibility and thermal conductivity additionally hinder machinability [4]. Deciding and streamlining the parameters engaged with a machining procedure is a significant and critical task. Machining
https://doi.org/10.1016/j.matpr.2019.12.215 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
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of titanium into completed segments is receiving increasing attention in particularly aviation and defence industries [5]. Ti–6Al–4 V is additionally one of the costliest metals to create, which is another disadvantage to assembling parts utilizing this metal. The procedure of titanium’s machining in the aeronautic trade today is by experimentation. It produces non-productive outcomes since this material is highly chemical responsive with different materials. Ti also has a low thermal conductivity. It is difficult to decide and find the right parameters for machining, since it is a hard to machine material. Today analysts are hoping to grow new models to foresee and upgrade these parameters [6]. Over the most recent two decades, the intelligent frameworks formed by Artificial Neural Network (ANN), have been connected in manufacturing and have been the subject of broad research. This innovation has turned into a significant computing instrument to solve various engineering issues [7]. To adequately control and streamline the abrasive waterjet machining procedures, prescient depth of cut-models (DOC) have already been established for phosphate glass [8], aluminium oxide ceramics [9] and mild steel [10]. However, until now no models have been published for Ti-6Al-4V in literature. Research is needed to completely comprehend the impact of the significant procedure parameters on depth of cut (DOC) of Ti-6Al-4V along with mathematical modelling using RIM and ANN [11]. This paper intents to explore the handled surface profiles by means of experiments to develop a detailed empirical model of DOC. Modelled values are compared with measured values, these performed experiments are designed using taguchi’s approach. Another intent is to use ANN to mathematically model the treated surfaces in terms of DOC in abrasive water-jet machined Ti-6Al-4V alloys. 2. Experimental work 2.1. Material choice Ti-6Al-4V, abbreviated as TC4, is an a/b titanium amalgam, it has a high solidarity to weight proportion and exceptional erosion resistance. Ti-6Al-4V contains about 6% of a a-stabilizer Al and 4% of a b-stabilizer V in its structural composition. The precise composition of Ti-6Al-4V can be found in Table 1. TC4 is one of the most usual utilized titanium combinations and is connected in a wide scope of utilizations where low thickness (density) and good corrosion resistance are vital, for example, aeronautical, space and biomechanical industries. Ti-6Al-4V titanium alloy has various physical and mechanical properties such as density (min – 4.429 g/cm3 to max – 4.512 g/cm3), Youngs Modulus (min – 104 GPa to max – 113 GPa), uniform elongation (min – 5% to max – 18%), ultimate strength (min – 900 MPa to max – 950 MPa), Poisson’s ratio (min – 0.31 to max – 0.37), shear modulus (min – 40 GPa to max – 45 GPa), yield Strength (min – 880 MPa to max 920 MPa).
gravity feed spot which is abrasive. The setup is represented in Fig. 1. The high-pressure water is transformed with a 0.35 mm diameter sapphire orifice and a frequently checked carbide nozzle of 1.05 mm diameter. The checks of the nozzles ensure that the nozzle never gets seriously damaged since worn out nozzles get replaced. Once the high-pressurized water passed the orifice, it arrives at the mixing chamber. Flattened air from a hopper gravity feed spot, which is abrasive, then delivers the garnet 80 mesh abrasives (particles) with a compactness of 4.1 gm/cc and an average width of 0.18 mm to the mixing chamber too. This process gets regulated with a metering disc and results in the AWJ, which is regulated manually with the pressure gauge. There are different parameters that determine the properties of the abrasive flow aside from the pressure and mass flow. The controller can change the standoff distance in the machinist regulator position. The fourth parameter, the traverse speed, is determined by the NC code programming. These parameters have their influence on how deep the cut of the waterjet goes. The slurry and debris of material resulting from this cut are disposed into a catcher container. The variable process parameters (Table 2) are considered as the control factors – ‘‘mass flow rate (g/s), traverse speed (mm/s), water pressure (MPa), and standoff distance (mm)”. Some parameters are kept constant such as (Orifice diameter – 0.34 mm; Nozzle diameter – 1.04 mm; Focusing tube (length – 75 mm, diameter – 1 mm); Impact angle 90°, Abrasive type - Garnet 80 Mesh). The experiments were designed using Taguchi’s method. The choice of orthogonal/symmetrical cluster is the significant factor while planning the tests utilizing Taguchi’s strategy which has been utilized to conduct experiments in the present study. Since four parameters have been picked with number of levels equivalent to 3, L27 orthogonal array has been chosen according to Taguchi’s DOE hypothesis. By utilizing each degree of these parameters, 27 cuts were executed in the titanium composite (Ti-6Al-4V) under the proper ecological conditions (Table 3). The DOC for each experiment was estimated by using a Sigma Scope 500 projector. 3. Empirical model for depth of cut (DOC) Scientific model for the DOC is exactly created dependent on the test information (experimental data) set by utilizing regression investigation method as appeared in Eq. (1). This model relates
2.2. Experimental procedure The AWJ Sweden cutter is fortified with a KMT pressure drive. This pump was used at its design pressure of 4000 bar to make the samples. The instrument consists of a rasping feeder arrangement, a pneumatic controlled regulator, a work section (specimen) table measuring 300 cm length and 150 cm width and a hopper
Table 1 Chemical composition of specimens (Ti-6Al-4V) (wt%). Ti
Al
V
Fe
O
C
N
H
89.546
6.09
4.04
0.24
0.16
0.04
0.02
0.00568
Fig. 1. Schematic of an abrasive waterjet (AWJ) cutting process [9].
Table 2 Three levels of input parameters used in experiment. Parameters
Units
Level 1
Level 2
Level 3
Water Pressure Traverse Speed Standoff Distance Mass Flow Rate
MPa mm/s mm g/s
270 0.5 1.8 8
335 10.25 3.4 11.5
400 20 5 15
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M. Chithirai Pon Selvan et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 3 Taguchi’s Design of Experiments (DOE). Experiment (Trial) Number
Water Pressure (MPa)
Traverse Speed (mm/s)
Mass Flow Rate (g/s)
Standoff Distance (mm)
Depth of Cut (DOC) (mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400
20 19.25 18.5 17.75 17 16.25 15.5 14.75 14 13.25 12.5 11.75 11 10.25 9.5 8.75 8 7.25 6.5 5.75 5 4.25 3.5 2.75 2 1.25 0.5
8 8.27 8.54 8.81 9.08 9.35 9.62 9.89 10.16 10.43 10.7 10.97 11.24 11.51 11.78 12.05 12.32 12.59 12.86 13.13 13.4 13.67 13.94 14.21 14.48 14.75 15
5 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3 2.3 2.2 2.1 2 1.9 1.8
18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
the DOC to four different input process parameters such as ‘‘p (MPa), u (mm/s), s (mm), ma (g/s)”. !0:14 !0:46 p1:33 s 0:45 qp u2 ma sma Dc ¼ 1:02 3 dp qw d j u E p dp qp u
ð1Þ The units of individual parameters are: (Dc, s, dj, dp – meters), (u – meter per second (m/s)), (qp, qw – kilogram per meter cube (kg/ m3)), (ma – kilogram per second (kg/s)), (p, E – Megapascal (MPa)). This empirical model is legitimate when the following constraints are met: 270 MPa (39160.17 psi) < [water pressure (p)] < 400 MPa (58015.08 psi) 8 g/s (28.8 kg/hour) < [mass flow rate (ma)] < 15 g/s (54 kg/hour) 0.5 mm/s (0.0005 m/s) < [traverse speed (u)] < 20 mm/s (0.02 m/s) 1.8 mm (0.0018 m) < [standoff distance (s)] < 5 mm (0.005 m) Eq. (1) can be rewritten in the following form in order to make the impact of the process parameters more clear as in Eq. (2). 0:93
Dc ¼ 1:02
p1:47 m0:54 dp q0:32 a p
ð2Þ
E1:33 u0:82 s0:01 qw dj
For the material under consideration, it tends to be given by Eq. (3): 0:93
Dc ¼ 2:156 107
p1:47 m0:54 dp q0:32 a p u0:82 s0:01 qw dj
ð3Þ
4. Experimental results and discussions 4.1. Effect of water pressure (p) on depth of cut (DOC) Fig. 2 plots the measurements of the DOC (mm) with respect to p (MPa). An abrasive waterjet machine cuts the specimen keeping
Fig. 2. Effect of water pressure (p) on depth of cut (DOC).
some process parameters constant; (ma) = 15 g/s; (u) = 0.5 mm/s; (s) = 1.85 mm. The results are obtained by incrementing the water pressure on the sample, while still keeping the other process parameters constant. This results in an increase of DOC of the specimen. Fig. 2 shows that DOC (mm) and p (MPa) are almost linearly dependent from each other, increasing water pressure also increases the DOC. Incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.2. Effect of abrasive mass flow rate (ma) on depth of cut (DOC) Fig. 3 plots the measurements of the DOC (mm) with respect to ma (g/s). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (u) = 0.5 mm/s; (s) = 1.85 mm. The results are obtained by incrementing the abrasive mass flow rate on the sample, while still keeping the other process parameters constant. This results in an increase of DOC of the specimen. Fig. 3 shows that DOC (mm) & ma (g/s) are proportional to each other. That means incrementing or
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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Fig. 5. Effect of standoff distance (s) on depth of cut (DOC). Fig. 3. Effect of abrasive mass flow rate (ma) on depth of cut (DOC).
decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.3. Effect of traverse speed (u) on depth of cut (DOC) Fig. 4 plots the measurements of the DOC (mm) with respect to u (mm/s). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (ma) = 15 g/s; (s) = 1.85 mm. The results are obtained by incrementing the traverse speed, while still keeping the other process parameters constant. This results in a decrease of DOC of the specimen. Based on Fig. 4, it can be concluded that DOC (mm) & u (mm/s) are inversely proportional (/) to each other. That means incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well. 4.4. Effect of standoff distance (s) on depth of cut (DOC) Fig. 5 plots the measurements of the DOC (mm) with respect to s (mm). An abrasive waterjet machine cuts the specimen keeping some process parameters constant again; (p) = 395 MPa; (ma) = 15 g/s; (u) = 0.5 mm/s. The results are obtained by incrementing the standoff distance, while still keeping the other process parameters constant. This results in a decrease of DOC of the specimen. Based on Fig. 5, it can be concluded that DOC (mm) & s (mm) are inversely proportional (/) to each other. That means incrementing or decrementing a parameter value has a significant impact on the value of another parameter and similarly there will be changes (fluctuations) in the jet kinetic energies as well.
5. Artificial Neural network (ANN) and back propagation algorithm (ANN model Training) Neural network is used in mathematical modelling to approximate the output of various different processes based on its inputs. It is widely used in machine learning for prediction. Neural networks are based on the function of the human brain. Neurons receive inputs through dendrites and based on the inputs it produces outputs that get transferred to the next neuron through axon. This principle is the groundwork for many different algorithms. In this paper there are four inputs and two output. It neural networks it is split in two models. One model with pressure of water, traverse speed an depth of cut as the output. The other is taken as mass flow rate, standoff distance as the input and depth of cut is taken as the output. The reason for taking as two model is to improve the accuracy. More input and output in a single model the output gives less accuracy. In this paper number of hidden layers are chosen as two. As the number of hidden layer has to be between the number of input and the number of output, in this case it is taken as two as the number of input and the output is two respectively for each model. The back-propagation algorithm is commonly used as it gives best results. This algorithm is based on adjusting the weights based on the gradient descent method. The weights are adjusted based on the error, which is the difference between the input and the output. The Fig. 6(a) indicates the overall architecture. Pressure and traverse speed is taken as inputs and the depth of cut is taken as the output. Fig. 6(b) also indicates the overall ANN model with Massflow rate and stand off distance as the input and depth of cut as output. Initially random weights are assumed between the neurons between the values 0 to 1. The input is given to the neural network which propagates through neurons to get the desired output. The error is determined using the formula Error = R1/2(TargetOutput) 2. The weights are now adapted to decrease the error. There is one hidden layer inbetween the input layer and the output layer. The hidden layer can be further increased if more accuracy is required. The error reduction with respect to the weight can be written as dE/dW. By applying chain rule this can be split in to three functions.
dE=dW ¼ dE=dO dO=dN dN=dW:
Fig. 4. Effect of traverse speed (u) on depth of cut (DOC).
ð4Þ
The first one is the rate of change of error with respect to the output, the second function is the change of output with hidden network and the third is the rate of change of network to the weight. Each function is determined by a computation formula. The new weight is are determined in the following way:
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Fig. 6a. Artificial Neural Network Model.
Fig. 6b. Artificial Neural Network Model.
New Weight ¼ Old Weight g ðdE=dWÞ
ð5Þ
Where g is the learning rate parameter. The learning rate parameter decides the rate of change of weights required to achieve the target. The sensitivity can be written as
@E2 @W AB
ð6Þ
Chain rule states
@E2 @E2 @IB ¼ ¼ OA @W AB @IB @W AB
the DOC based on the water pressure and the traverse speed. The blue line indicates the predicted depth of cut and the red line indicates the actual DOC. Both Figs. 7 and 8 show that the predicted DOC line follows the line of the actual values closely. Fig. 9 shows the learning curve. The backpropagation algorithm is trained for thousand iterations. It can be seen from the diagram that at the end of thousand iterations the error reduced to 0.8. Hence this can be used to mathematically model the system using neural networks. More accuracy can be achieved by increasing the number of data. It can also be done by increasing the number of iterations and by adjusting the initial eights.
ð7Þ
From Eqs. (4) and (2) the final weight for the algorithm can be written as
W ABðnewÞ ¼ W ABðoldÞ g
@E2 OA @IB
ð8Þ
WAB, the weight from neuron A to B depends on the sensitivity of the squared error, E2, to the input, IB, of unit B and on the output signal OA. As mentioned above in this case the inputs Ib are taken as the input. In this paper totally 40 datas are taken and the thirteen datas are taken for testing the data. Remaining 27 datas are used to train in the back propagation algorithm. The matrix obtained was used to determine the output for the new set of data. So it can be said that around 70% data is used for training and the remaining 30% data is used for the testing purposes. It is found that the root mean square error is less than 0.8 Hence this weighted matrix obtaines after the iterations are fed with new set of 27 data which is shown in Figs. 7,8,10,11. The curve for the old and the new data is shown in the figures. The new data taken is also within the same range considered for the training. The Fig. 7 shows the DOC values for various values for water pressures and traverse speeds. Fig. 8 presents the 3D graph for
Fig. 7. Actual DOC vs predicted DOC.
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Fig. 8. DOC based on Speed and Pressure. Fig. 11. Actual DOC vs Predicted DOC.
Fig. 9. Learning curve.
Fig. 12. Learning curve.
Fig. 10 presents the DOC based on standoff distance and the mass flow rate. Fig. 11 indicates the actual DOC and the predicted DOC. It can be observed in both the diagrams that curves follow almost the same path. Fig. 12 below indicates the learning curve for the backpropagation algorithm. It shows that the error is reduced less than 0.5, the smaller the error, the more accurate the model is. This is also reflected in the previous graph where predicted and the actual depth of cut are almost equal.
6. Conclusions and future prospects
Fig. 10. DOC based on Standoff distance vs Mass flow rate.
Abrasive waterjet cutting has been studied experimentally for Ti-6Al-4V resulting into a regression based empirical model of the depth of cut (DOC). The parameters with a direct consequence on DOC are the mass flow rate (ma), the water pressure (p), the nozzle standoff distance (s) and the traverse speed (u). Pressure and abrasive mass flow rate on the one hand are proportional to the depth of cut. Nozzle standoff distance and traverse speed on the other hand are inversely proportional to DOC. The results of the experiments seem to match the model. The experimental
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215
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results are used to mathematically model the whole system. ANN is used in modelling the system with back propagation algorithm. As the data is not linear ANN is used instead of the conventional models. It can be observed that the model could predict for the new set of data with more than 90% accuracy. This can be further used in predicting the output for different set of data for various materials. The same data can also be used along with the neuro fuzzy systems, where the fuzzy logic can be used to classify the data and the neural networks can be used to predict the data. Fuzzy classification can be done based on the output depth of cut based on the four parameters. This classification can be used to split the neural network model in to two categories as at present the model is created randomly base on the nature of data. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] A. Gnanavelbabu, P. Saravanan, K. Rajkumar, S. Karthikeyan, Experimental investigations on multiple responses in abrasive waterjet machining of Ti-6Al4V alloy, Mater. Today: Proc. 5 (5) (2018) 13413–13421, Part 2.
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[2] Ahmet Hasçalık, Ulasß Çaydasß, Electrical discharge machining of titanium alloy (Ti-6Al-4V), Appl. Surface Sci. 253 (22) (2007) 9007–9016. [3] Farhad Nabhani, Machining of aerospace titanium alloys, Robot. Comput.Integr. Manuf. 17 (2001) 99–106. [4] Ahmet Hascalik, Ulasß Çaydasß, Hakan Gürün, Effect of traverse speed on abrasive waterjet machining of Ti–6Al–4V alloy, Mater. Design 28 (2007) 953– 1957. [5] E.O. Ezugwu, Z.M. Wang, Titanium alloys their machinablity – a review, J. Mater. Process. Technol. 68 (3) (1997) 262–274. [6] Y.W. Seo, M. Ramulu, D. Kim, Machinability of titanium alloy (Ti– 6Al–4V) by abrasive waterjets, Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf. 217 (2003) 1709–1721. [7] Sahith Reddy Madara, Chithirai Pon Selvan, Swaroop Ramaswamy, Impact of process parameters on surface roughness of hastelloy using abrasive waterjet machining technology, Int. J. Recent Technol. Eng. 7 (5S2) (2019) 419–425. [8] Chithirai Pon Selvan, Sahith Reddy Madara, S.S. Sampath, N.S. Sarath Raj, Effects of process parameters on depth of cut in abrasive waterjet cutting of phosphate glass, in: IEEE Xplore, Advances in Science and Engineering Technology International Conferences (ASET), Abu-Dhabi, 2018, pp. 1–6. [9] Chithirai Pon Selvan, Sahith Reddy Madara, Swaroop Ramaswamy Pillai, Ramesh Vandanapu, In-depth evaluation of process variables in abrasive waterjet cutting of alumina ceramics, in: IEEE Explore, Advances in Science and Engineering Technology International Conferences (ASET), Dubai, United Arab Emirates, 2019, pp. 1–4. [10] Chithirai Pon Selvan, Divya Midhunchakkaravarthy, Swaroop Ramaswamy Pillai, Sahith Reddy Madara, Investigation on abrasive waterjet machining conditions of mild steel using artificial neural network, Mater. Today: Proc. (2019) 1–7. [11] Ghodsiyeh Danial, Davoudinejad Ali, Optimizing finishing process in WEDMing of titanium alloy (Ti6Al4V) by brass wire based on response surface methodology, Res. J. Appl. Sci. Eng. Technol. 5 (4) (2013) 1290–1301.
Please cite this article as: M. Chithirai Pon Selvan, D. Midhunchakkaravarthy, R. Senanayake et al., A mathematical modelling of Abrasive Waterjet Machining on Ti-6Al-4V using Artificial Neural Network, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.215