Analysis and optimization of mass percentage of zycoprint polymer and abrasives in achieving stability of suspension mixture in abrasive water jet machining

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Introduction
The challenges in machining several engineering materials, especially difficult-to-cut materials, demand rapid progress in machining technologies. The popularity of Abrasive water jet (AWJ) machining is rising due to its adaptable and flexible manufacturing capabilities [1,2]. In AWJ machining technology, suspension and injection jet methods are possible alternatives. While comparing the two, the first one can function with greater geometric accuracy and less angular error, causing smaller kerf taper ratios [3,4]. Suspension-type AWJ machining has significant advantages in energy management. These machines are extensively in use due to their versatile nature and ability to cut several metallic and non-metallic materials in the manufacturing sector. In the suspension-type AWJ machining technique, a suspension mixture (also called slurry) made of water, abrasives, and a polymer is prepared beforehand and directed through a nozzle at high pressures to form a fine jet. Several studies have been conducted on the suspension-type AWJ machining of different materials, viz., glass fibre-reinforced plastic composites [5,6], discontinuously reinforced Caryota urens fibre polyester composites [7], titanium alloy [8], mild steel [9], etc., as per Taguchi's L 9 orthogonal array (OA) to save the material cost, reduce the number of experiments and to evaluate the effect of respective process parameters on performance. Ramesha et al. [6] compared the effect of process parameters (namely Abrasive size, stand-off distance, abrasive concentration, and traverse rate) on kerf width and surface roughness while using the suspension-type AWJ technique for machining glass fibre-reinforced plastic composites. According to the authors, composite and conventional materials can be machined using a suspension-type AWJ process with reduced surface roughness and improved material removal. The authors suggested that suspension-type AWJ machining can produce better machining capabilities than abrasive water jet machining when a set of suspension parameters are optimized. Shetty and Hegde [7] recently attempted machining a discontinu-ously reinforced Caryota urens fibre polyester composites workpiece using a suspension-type AWJ process. The authors observed the effect of process parameters (water jet pressure, traverse rate, stand-off distance, abrasive flow rate, depth of cut, and abrasive size) on surface roughness using the Taguchi-based fuzzy logic model. The researchers claim that it is possible to machine the workpiece even at low water jet pressure (300 bar), resulting in minimum surface roughness. Dumbhare et al. [9] conducted the experimental test sequences as per Taguchi's L 9 OA to analyze the effect of machining parameters on the performance of ultra-high-pressure abrasive slurry jet machining of mild steel. The authors found that standoff distance and traverse rate positively affect the surface roughness and kerf taper angle more than the abrasive flow rate after multi-objective optimization using the response surface methodology. The author recommended exploring the suspension parameters for machining in modern manufacturing industries. It is observed that most of the studies focused on several parameters such as hydraulic, nozzle, machining, and abrasive except suspension. It is found from the literature that the stability of the suspension mixture critically affects the performance of Suspension-type AWJ machining.
The suspension-type AWJ process is based on the direct-pumping system. In this system, the pre-mixed slurry is charged in a pressure vessel in which high-pressure water is pumped to pressurize the slurry. The directpumping systems are usually mixed with high-viscous additives (polymers) to suspend the storage vessel's abrasive particles and reduce their settling velocity. As per the latest review conducted by Sreekumar et al. [10], the polymers influence the suspension mixture's particles' resistance to sedimentation, which helps in maintaining the stability of the cutting process. The settling of the abrasives and the dispersive behaviour of the mix affect the suspension stability of the suspension mixture. The authors claim that selecting the proper polymer and its required concentration or mass percentage plays a vital role in holding the abrasive particles to avoid their settlement in the suspension mixture. Suspension-type AWJ machining with polymer additives has several benefits that are wellrecognized by researchers, making it a hotspot of research in recent years. Louis et al. [11] claim that the polymer additives stabilize the suspension mixture in suspensiontype AWJs. Due to these additives, the viscosity of the suspension mixture becomes four times higher than water. During the jet generation process in the suspension nozzle, the increased viscosity shifts the Reynolds number of the flow to lower values leading to an intensified abrasive particle acceleration, enhancing the material removal. Improved abrasive particle acceleration and suspension stability positively influence the cutting potential of abrasive suspension jets. The popular method used by previous researchers [12][13][14] to check the suspension stability of the suspension mixture is the "sedimentation method". An increase in polymer concentration at a specified limit enhances the performance of AWJ machining even at an increased distance of the nozzle from the workpiece and low water jet pressure.
The polymers are long-chained molecules that impart a viscoelastic fluid behaviour to the suspension mixture. There are various polymer additives during the Suspension-type AWJ machining of several materials, including SUPER-WATER/polyacrylamide (PAM) [15][16][17], Xanthan [16,18], polyox [19], carboxy methyl cellulose (CMC/ cellulose gum) [16,17] and others. Recently, Wang et al. [20] studied the rheological properties of the suspension mixture with PAM and CMC used in suspension-type AWJs. The authors concluded that the abrasive does not influence the apparent viscosity of the slurry mixture. But the increased suspension stability will be a dominant factor in obtaining good-quality machined surfaces. Hence, the authors recommended studying the suspension stability and optimization of suspension parameters used in the suspension-type AWJ.
As per the recommendation by Sreekumar et al. [10], selecting a suitable polymer to get a stable suspension mixture is better. The polymers mentioned above have better suspension capability but cannot suspend the abrasive particles for an extended period. Therefore, they cannot be pre-mixed and stored. Hence, exploring the suspension stability of the suspension mixture using a polymer is necessary, which overcomes the above-said limitation. In this direction, a stable abrasive water suspension mixture is prepared in the current work using a polymer called 'zycoprint' (used by previous researchers, as mentioned in Tab. 1-serial numbers 1 and 8). There are several benefits of zycoprint polymer over other commercially available polymers [21]. It has a long-lasting ability to suspend abrasive particles and better suspension stability even at low concentrations (about 1%) to create a stable abrasive suspension mixture for experiments. Using the optimal quantity of the mass percentage of polymer (v p ) to prepare the suspension mixture plays a vital role. Previous researchers have used various polymers with different mass percentages during suspension-type AWJ machining of several engineering materials, as summarized in Table 1.
The recent study conducted by Maurya et al. [33] focused on the performance analysis of the suspensiontype AWJ machining of acrylonitrile butadiene rubber under room-temperature and cryogenic conditions. The authors used the zycoprint polymer and garnet abrasives to prepare the suspension mixture during machining, with a mass percentage of 0.8% and 3%, respectively but didn't explore its stability with the specific mass percentages. They used an anchor type agitator with a tangential impeller flow for preparing the suspension mixture. The authors were able to machine acrylonitrile butadiene rubber with good-quality slots using the mass percentages of zycoprint and garnet abrasives (0.8% and 3%, respectively) under cryogenic machining conditions. The experimental work in [33] validates the optimum mass percentages obtained in the present work. Even though relevant studies have been published on suspension-type AWJ machining by considering the several suspension parameters such as mass percentage of polymer and abrasive, type of abrasive, volume fraction of suspension agent, dispersant and particle size of abrasive and many more, none of them focused on the reason behind selecting the prescribed mass percentage of polymer and abrasive.
The study on the optimum suspension parameters analysis to achieve stability of the suspension mixture before using it in the suspension-type AWJ machining process has not been reported in the published scientific literature. Therefore, the current work investigates suspension stability by varying the polymer and abrasive particle mass percentages using the sedimentation method. Achieving the suspension stability can help the custom manufacturing scenario in the Industry 4.0 concept. In custom manufacturing, the industries focus on creating small batches of specialized items made up of glass fibrereinforced composites, elastomers, titanium alloy, nickel alloy, and many more for particular customers. Manufacturing of customized components with small lot sizes takes time and is un-economical to prepare by moulding methods. Hence, several industries and manufacturers are looking for modern manufacturing (green manufacturing) processes, like AWJ machining, to achieve a "lot size of one" in an affordable manner without delay. Hence, knowing the optimum setting of the suspension mixture before using it in AWJ machining of any engineering material, more so in difficult-to-machine material, leads to minimizing the pre-machining time and removing unnecessary hurdles. Providing the machined "lot size of one" at a lower price to the customer at the earliest will become possible and uplift the AWJ machining market in the manufacturing sectors.
The primary objective of the research paper is to prepare different suspension mixtures by varying the zycoprint polymer and abrasive concentrations as per the L 9 OA of the Taguchi method, preferred for the selected number of decision variables (3 2 ). The second objective is to develop the mathematical equations for the percentage of suspension volume (V s ) using linear regression (LR) modelling and validate them with the confirmatory test. The third objective is to use the JAYA algorithm to optimize suspension parameters.

Materials and methods
This section includes the details of polymer, abrasive particles and methodology used in the current work.

Zycoprint polymer
Zycoprint polymer is a copolymer of an ammonium salt and other ingredients like surfactants and paraffin oils. The zycoprint polymer solution at 1% concentration has a higher viscosity than the commercial polymer solution at 1.5% concentration [21]. The physical and chemical properties of the zycoprint polymer are shown in Table 2. The required volume (V polymer ) and mass (mass polymer ) of the zycoprint polymer are calculated using equations (1) and (2).
where v p (%) = mass percentage of the zycoprint polymer, r polymer = density of the zycoprint polymer (1.05 g/ml) and mass water = mass of water (99.98 g).

Abrasive particles
The abrasive particle type, size, and shape significantly influence the suspension mixture [34]. The most commonly used abrasives in AWJ machining are garnet and aluminum oxide (Al 2 O 3 ). Garnets with mesh size #80 (150 to 300 mm) can cut almost all material with a good surface finish [35]. The garnet and Al 2 O 3 with mesh size #80 are selected to prepare the suspension mixture based on the findings from reported literature and the availability of resources. The quantity of the abrasives (garnet and Al 2 O 3 ) required in the suspension mixture is calculated using equation (3) where v a (%) is the mass percentage of abrasive (garnet or Al 2 O 3 ) and mass of the water (mass water ) is 99.98 g.

Slurry (suspension) preparation
The experiments are conducted to investigate the stability of the suspension mixture at different zycoprint concentrations, with sediments being in static conditions. The suspension mixture is prepared in a 100 ml beaker by adding the required amount of zycoprint to 100 ml of water and stirring it at a low speed of 30 rev/min for 10 min using a cylindrical glass tube type of mixer to get a homogeneous mixture. Then, the required amount of the abrasive (garnet or Al 2 O 3 ) is added to the mixture and mixed for 3 min. Further, the prepared mixture is kept aside for 2 h to get maximum sedimentation at the bottom of the beaker. Finally, the suspension ability of the different combinations of the mixtures prepared is compared in terms of the percentage of suspension volume (V s ) to obtain the best combination.

Percentage of suspension volume (V s )
The suspension mixture's stability is evaluated as the suspension volume (V s ) percentage, as shown in equation (4) where V st = 'settlement volume' (volume of abrasive particles settled at the bottom of the beaker in 'ml'), V c = 'clearance volume' (volume of the mixture at the topmost portion, having negligible abrasives in 'ml'). V t = 'total volume' of the suspension mixture (total volume of the beaker) in 'ml.' The settlement and clearance volumes are measured by visual inspection, as shown in Figure 1. In this work, the total volume of the suspension mixture is constant at 100 ml, viz., V t = V c + V s + V st = 100 ml. Larger the V s (%), lesser is the precipitation of the abrasive particles, the better is the dispersion effect and the slurry suspension stability. Therefore, the focus of the present work is to maximize the V s (%) and attaining the preset limit of 100%.

Design of experiments (DoE)
The Full factorial experimental design considers numerous runs, which is expensive. Utilizing Taguchi's approach will reduce costs, time, and resource usage. The dominant suspension parameters were chosen based on the literature  [17,[21][22][23][24][25][26][27][28][29][30][31][32]. The ranges of suspension parameters selected for the experimentation were tested in the preliminary suspension mixture preparation trials. The experimental runs were constructed using Taguchi's L 9 OA, which allows for a smaller number of runs needed than the conventional central composite design used along with response surface methodology. Table 3 details the suspension parameters and levels used for the experimental design to prepare a suspension mixture using garnet and Al 2 O 3 . The percentage of suspension volume (V s ) is considered a response variable.

Linear regression (LR) modelling
The regression equations, for V G s and V A s , are developed using the LR modelling technique, where V G s = percentage of suspension volume with garnet as abrasive, and V A s = percentage of suspension volume with Al 2 O 3 as abrasive [36]. The closeness of the predicted responses to the experimental responses is measured by the 'adjusted R 2 (Adj. R 2 )' and 'predicted R 2 (Pred. R 2 )'. The LR model is considered a good one if the Adj. R 2 is closer to 1, and the difference between the Adj. R 2 and Pred. R 2 is less than 0.2.
The LR model developed for V G s (refer to equation (5)) offers a good fit with Adj. R 2 and Pred. R 2 of 0.7171 and 0.5295, respectively. The value of Adj. R 2 is in reasonable agreement with the Pred. R 2 , as the difference between the two, is less than 0.2. Similarly, the LR model developed for V A s (refer to Eq. (6)) also offers a good fit with high values of Adj. R 2 and Pred. R 2 of 0.9267 and 0.8435, respectively. The value of Adj. R 2 is in reasonable agreement with the Pred. R 2 , as the difference between the two, is less than 0.2.
The main effect plots obtained during the analysis of developed LR models are used to analyze the effect of suspension parameters (v p and v a ) on the mean of V G s and V A s and to determine the optimal levels of the suspension parameters corresponding to the maximum suspension volumes (V G s and V A s ). The effect of the significant interaction term between the v p and v a on the V G s and V A s is explored using contour plots. The software Minitab (2019Minitab ® 19.1.1 (64-bit)) is used to generate Taguchi's L 9 OA and develop the LR model.

Single-objective optimization
In the problem under consideration, each response equation (Eqs. (5) and (6)) is considered the objective function of the optimization problem. The objective is to maximize the percentage of suspension volume. This case is a single-objective optimization problem (SOOP), as each objective function (Eqs. (5) and (6)) is to be optimized individually. The popular 'JAYA algorithm' is used for optimizing V G s and V A s due to its simple concept and better performance than other advanced metaheuristic algorithms [37]. The pseudo-code of the JAYA algorithm is presented below (see page 6). The variables in bold represent matrices.
The JAYA algorithm is implemented through the customized MATLAB (R2020a) programs on an Intel i5 2.11 GHz processor and 8GB RAM laptop. The JAYA algorithm is run for six different combinations of population size (PS) and the number of generations (MaxGen), as shown in Table 4.

Results and discussion
The experiments are conducted as per L 9 OA. Table 5 gives the details of all nine combinations of suspension parameters and the corresponding values of the response variables determined by experimentation.
The analysis of variance (ANOVA) of the LR model is used to check the linear and interaction effects of the polymer and the abrasive concentrations on the percentage of suspension volume (V G s and V A s ). The ANOVA test of the LR model is conducted at a 95% confidence interval. Therefore, the variables with probability value (p-value) 0.05 are considered significant.

LR results for the percentage of suspension volume (V G s ) with Garnet as the abrasive
From the LR results for the percentage of suspension volume (V G s ) with Garnet as abrasive (refer to Tab. 6), it could be observed that 77.98% of the variation in the response variable is caused by the mass percentage of abrasive (garnet) (v a ). Hence, the contribution of v a on the regression model is more than the mass percentage of the polymer (v p ). The p-value of the linear term v a (0.003) is less than 0.05. Hence, the mass percentage of abrasive (Garnet) (v a ) proves significant. Figure 2 shows the main effect plot (a) and contour plot (b) for V G s . The v p is considered in the LR model because it is an Step 3: Initialize gen = 1 while (gen < MaxGen) a.
Find the best and the worst solution Pick the best solution x best = x i corresponding to best fitness f best Pick the worst solution x worst = x i corresponding to worst fitness f worst c.
Update the population x as xx by using the equation Modify the solutions in the updated population such that they satisfy the limits L and U xn = modify (xx) e.
Find the fitness fn of the modified population xn fn = [ fn i ] such that fn i = ' (xn i ) f.
Choose the best solution candidates from x and xn if (fn i > f i ) f i = fn i x i = xn i corresponding to fn i end if g.
Choose the best cost f opt from f f opt = max ( f) x opt = x i of x corresponding to f opt h. gen = gen + 1 end while Step 4: print f opt , x opt N.B. The variables in bold represent matrices.   individual term and main suspension parameter, even though it is insignificant. The individual terms (v p and v a ) are used for the practical usage of the equation [38,39]. From the main effect plot (refer to Fig. 2a), it is observed that the increase in v p from 0.7 to 0.8% increases the average V G s by about 1%. The maximum percentage of suspension volume (V G s ) is observed from the main effect plot and contour plot (refer to Fig. 2b) at 0.80% of v p and 3% of v a .

LR results for the percentage of suspension volume (V A s ) with Al 2 O 3 as the abrasive
From the LR results for the percentage of suspension volume (V A s ) with Al 2 O 3 as abrasive (refer to Tab. 6), it could be observed that the linear terms cause 83.88% of the variation in the response compared to the 11.55% significance exhibited by the squared term. Hence, the contribution of linear terms to the response variable is more. But the p-value of the linear terms v a (0.314) is greater than 0.05. Hence, the mass percentage of abrasive (Al 2 O 3 ) (v a ) proves insignificant. The p-value of the linear terms v p (0.014) is less than 0.05. Hence, the mass percentage of polymer (v p ) proves to be significant. In square terms, the p-value of v p Â v p is 0.016 (significant), even though their percentage of contribution is only 11.55%. Hence, only a large change in the mass percentage of polymer (v p ) brings a difference in the response, which is evident from the medium significance percentage (11.55%) of the square term of v p . Figure 3 shows the main effect plot (a) and contour plot (b) for V A s . The v a is considered in the LR model because it plays a major role in the suspension preparation, even though it is insignificant. It can be seen from the main effect plot (refer to Fig. 3a) and contour plot (refer to Fig. 3b) between the mass percentage of Garnet  The developed LR model for V G s provides a good fit with Adj. R 2 and Pred. R 2 of 0.7171 and 0.5295, respectively. The average percentage error of prediction between 9 experimental and predicted values is 0.046%. It is observed from equation (5) that the positive coefficient of the mass percentage of polymer (v p ) of the developed LR model indicate that as its value increase, the mean of the percentage of suspension volume (V G s ) also tends to increase. But at the same time, the negative coefficient of the mass percentage of abrasive (Garnet) (v a ) indicate that as its value increase, the mean of the percentage of suspension volume (V G s ) tends to decrease. The developed LR model for V A s also offers a good fit with high values of Adj. R 2 and Pred. R 2 of 0.9267 and 0.8435, respectively. The average percentage error of prediction between 9 experimental and predicted values is 0.394%. It is observed from equation (6) that the positive coefficient of the mass percentage of polymer (v p ) of the developed LR model indicate that as its value increase, the mean of the percentage of suspension volume (V A s ) also tends to increase. But at the same time, the negative coefficient of the mass percentage of abrasive (Al 2 O 3 ) (v a ) and square term of mass percentage of polymer (v p ) indicate that as their values increase, the mean of the percentage of suspension volume (V A s ) tends to decrease. The average percentage of errors in both cases, V G s and V A s , are less than 5%. It indicates a close match of experimental and predicted values percentage of suspension volume [40,41]. Hence, it suggests that the developed LR models are acceptable for predicting the response variables (V G s and V A s ).

Confirmation test results
The developed LR models (Eqs. (5) and (6)) are validated with further experiments, as shown in Table 7. The values of suspension parameters selected for the confirmatory test are in the range of levels mentioned in Table 3. The percentage error (% error) for each confirmatory test is calculated using equation (7) [42], and their results are 3.5 Results of single-objective optimization

Conclusions
The suspension mixture's stability is vital in the Suspension-type AWJ machining process. The mass percentage of polymer and abrasives are critical parameters of the suspension mixture. The settling of abrasive particles and the dispersive behaviour of the mix affect the suspension stability of the suspension mixture. The larger the percentage of suspension volume (V s (%)) lesser is the precipitation of the abrasive particles, the better is the dispersion effect and slurry suspension stability. Hence, it is crucial to analyze the suspension stability of the suspension mixture using a zycoprint polymer which has a long-lasting ability to suspend abrasive particles. In this vein, the current research work is attempted. The essential highlights of the novel work include finding the optimal combination of the suspension mixture composition and obtaining the mixture's stability are discussed here. It is found from the experimental runs that in the case of Garnet, the maximum V G s % ð Þ is observed at (3% of v a , 0.70% of v p ) and (3% of v a , 0.80% of v p ). Whereas, in the case of Al 2 O 3 , the maximum V A s % ð Þ is observed at (3% of v a , 0.80% of v p ) and (7% of v a , 0.80% of v p ). The statistical results obtained from the ANOVA of the developed LR models show that the p-values of the models are significant for garnet and Al 2 O 3 . The developed LR models and confirmatory test are in agreement with the experimental results, as the mean % errors for garnet and Al 2 O 3 are 1.293 and 0.019, respectively. The optimum value of the suspension parameter v a is towards the lower level (i.e., Level_1 (3%)), and v p is towards the higher level (i.e., Level_3 (0.80%)) to achieve maximum suspension volumes (V G s = 99.5% and V A s = 100%) obtained from the main effect plots of the LR models. These results are in close agreement with the JAYA algorithm results. The study recommended that achieving the maximum stability of the suspension mixture is possible by considering the suggested settings of the suspension parameters while using it in the Suspension-type AWJ machining process.
In applying the Industry 4.0 features, the manufacturing sectors can benefit from the suggested optimum suspension parameters obtained by the current work in the suspensiontype AWJ process to cut several difficult-to-machine materials (such as glass fibre-reinforced composites, titanium alloy, nickel alloy, polymers, etc.). Further investigation is recommended by considering the process parameters (such as hydraulic, nozzle, machining, abrasive, and work material) along with the stated optimal suspension parameters to study the fluid dynamics of the suspension-type AWJs. Exploring the abrasive particle settlement velocity for different abrasives and their respective concentrations is also recommended for future work so that it can be pre-mixed and stored for an extended duration.