Matériaux & Techniques
Volume 107, Number 6, 2019
|Number of page(s)||9|
|Section||Sélection des matériaux et des procédés / Materials and processes selection|
|Published online||24 March 2020|
Modelling and optimization of technological parameters in hot abrasive jet machining of alumina ceramic
Department of Production Engineering, Veer Surendra Sai University of Technology,
Accepted: 20 January 2020
The present work focuses on the experimental investigation of hot abrasive jet machining (HAJM) and precision drilling operation on flat surfaces of K-60 alumina ceramic material using different grades of silicon carbide abrasives. The machining AJM setup is designed based on fluidized bed mixing chamber along with pressurized powder feed chamber. The experiments are performed as per Box-Behnken design of experiments (BBDOEs) with four process parameters (pressure, stand of distance, abrasive temperature and grain size) for parametric optimization in order to control the two technological response characteristics (material removal rate, flaring diameter) of the precision holes on K-60 alumina. Analysis of variance (ANOVA), response surface methodology (RSM) and genetic algorithm (GA) are subsequently proposed for predictive modelling and process optimization. Result shows that application of hot abrasives in AJM process has excellent performance in terms of improved material removal rate, and minimum dimensional deviation of drilled hole. Multi-response optimization GA technique presented the optimal setting of machining variables in HAJM process at air pressure of 6.682 kgf/cm2, abrasive temperature of 60.6 °C, stand-off-distance of 7.1124 mm, abrasive grain size of 275.755 µm, with estimated maximal material removal rate of 0.005 gm/s and minimal flaring diameter of 6.382 mm. The methodology described here is expected to be highly beneficial to manufacturing industries.
Key words: HAJM / K-60 alumina / RSM / ANOVA / genetic algorithm
© SCF, 2020
Science and technology has been advancing to infinite extent in search of newer materials and alloys with high hardness, strength and less weight which are very difficult to be machined with the conventional machining processes for achieving the required accuracy and precision. There is vast demand for the well-finished products of alumina ceramic materials with high accuracy and complex integrated designs. Such features on a component can be achieved only through the advanced manufacturing process. More than twenty different non-traditional manufacturing processes have been invented and successfully implemented in to production engineering during last six decades, among them abrasive jet machining is a constructive non-traditional method for machining hard and brittle materials like glass, ceramics, quartz, GFRP composites and other engineering materials, where the abrasive particles are made to impinge on the work material at a high velocity. The kinetic energy of the high-speed abrasive particles creates brittle fractures on the target material that propagate both in lateral and longitudinal direction to cause material removal. Although number of attempts has been made by the researches in different parts of the globe to search out the machining characteristics and related process parameters to control the requirements of abrasive jet machining, still a further research is required for analysing the effects of various abrasive jet machining parameters to increase the effectiveness of the material.
There are many factors affecting the cutting process behaviour in AJM such as, gas pressure, nozzle diameter, abrasive variables (mass flow rate, grain size), stand-off-distance, etc. The appropriate combination along with proper utilization of pre-cited machining process parameters are of prime importance for acquiring good grade as well as circularity of hole, which generally consumes precious time and effort due to the dynamic behaviour of abrasive jet machining process. Various researchers have been employed methods including statistical as well as computational approaches using RSM [1,2], ANN , for mathematical modelling in order to predict the responses and Taguchi method [4,5], GA [6,7], PSO [8–11], for multi-response optimization in order to control the process parameters during the AJM process. Yet almost no systematic study is reported in hot abrasive jet machining that ensued scope for researchers and also no method currently results in same level of efficiency for all process. Moreover, although number of studies has been executed on abrasive jet machining, (AJM) and abrasive water jet machining (AWJM), research in the field of hot abrasive jet machining process (HAJM) is very limited. Hence, it is necessary to develop an appropriate technological guideline for effective as well as optimum machining of ceramic material by HAJM process. The hot air chamber is the latest extension to the abrasive jet machine which replaces the feeder so that the abrasive particles can be heated to the required temperature. Jagannatha et al.  carried out the experiments on abrasive hot air jet machining and studied the effect of air temperature on the material removal rate of glass etching and grooving along with the roughness to reveal that roughness was reduced by increasing the temperature of carrier media. Thus, the present research is focused on process modelling and multi-response optimization during fluidized bed-hot abrasive jet machining (FB-HAJM) of K-60 alumina ceramic material using statistical approach such as response surface methodology (RSM), followed by computational approach like genetic algorithm (GA). The following technological response characteristics are addressed, material removal rate and flaring diameter of drilled component.
In the present research, K-60 alumina ceramic plate of dimension (25 × 25 × 4 mm) is considered as the workpiece material and silicon carbide (SiC) with three different sizes of 185, 525 and 745 µm are used as the abrasive material for experimentation. For machining experiments, an indigenously designed fluidized bed-hot abrasive jet machining (FB-HAJM) setup is fabricated, which consists of a mono-stage compressor, mixing chamber, heating chamber equipped with thermocouple, high abrasion resistance AISI D2 steel nozzle, and other accessories. In the current investigation air pressure, abrasive temperature, grain size and stand-off-distance are considered as the input process parameters which influence the technological response characteristics in FB-HAJM namely, material removal rate (MRR) and flaring diameter (FD). The identified process parameters with their associated levels are shown in Table 1. The range of process parameters setting have been selected after performing some pilot experiments using fixed stand-off-distance and also by inspecting the workpiece for a through hole of acceptable quality. Also, a detailed literature survey [8,13,14] has been done to select the working range of process parameters. Using the above-mentioned process parameters (4) each with three different levels, a well-designed experimental layout is formulated in conformance with Box-Behnken design of experiments (BBDOEs) which is consisting of twenty seven (27) number of trials . The experimental design layout with its corresponding results are reported in Table 2. Material removal rate (MRR) can be calculated by using the formula (W1−W2)/ΔT i.e. by determining the weight difference of the workpiece material between before and after machining with time span of “ΔT” measured by digital weighing machine (make: Afcoset). Furthermore, the flaring diameter (FD) of the drilled hole on K-60 alumina ceramic is measured by employing coordinate measuring machine (make: ZEISS, model: MC850) with a stylus probe attachment. The schematic view of experimental work and methodology proposed in the current study is presented in Figure 1.
Process parameters and levels.
Design of experimental plan and experimental results.
Schematic layout of experimental setup and methodology proposed.
The results of response characteristics i.e. material removal rate (MRR), and flaring diameter (FD) which were obtained in accordance of BBDOEs were analyzed in Minitab16 through response surface methodology (RSM), developed the mathematical model to find-out the best-fit of correlation between the two responses of the machined component with the input parameters such as air pressure (P), stand-off distance (SOD), abrasive temperature (T) and grain size (GS). Regression equations in the second order (i.e. quadratic model) for the each response (MRR and FD) are presented by: (1) (2)
To avoid the misleading conclusion, statistical analysis is performed for the proposed RSM models (MRR and FD) by employing ANOVA in order to check their adequacy and validity, as shown in Table 3. The estimate F-value of the model for MRR and FD are 12.13 and 7.94, respectively which shows the excellent significance of model because of lower magnitude of F-table value (4.75) at 95% of confidence level. Moreover, it can be clearly seen that the developed quadratic models are statistically significant as the P (probability) value is under 0.05. Particularly, the model developed using RSM for material removal rate and flaring diameter explain the R2 values (i.e. co-efficient of determination) of 0.93 and 0.9 respectively, which are very close to unity (1) ensuring the excellent fit for the model with greater statistical significance. Finally, normal probability plot combined with Anderson-Darling test for MRR and FD are shown in Figure 2, which ensures that the residuals distributed fairly close to a straight line indicating that the errors are dispersed normally and specifying that the terms associated with the model are significant. With p-value (0.35 for MRR and 0.41 in case of FD) received from Anderson-Darling test is greater than significance level value (0.05), which confirms the adequacy of model due to no possible reason was found for the rejection of null-hypothesis. Thus the developed RSM models can be successfully employed as objective function for GA-based optimization.
Results of ANOVA for response model.
Normal probability plot for MRR and FD.
Genetic algorithm (GA) is a population-based search methodology for solving optimization problems stochastically that is based on the mechanism of natural selection that simulates the biological progression process developed from Darwin’s theory of survival of the fittest . The mechanics of GAs is simple, involving copying of binary strings and the swapping of the binary strings. The simplicity of operation and computational efficiency are the two main attractions of the GA approach. In this systematic method, originally a set of possible solutions or chromosomes (normally as a string of genes) are randomly chosen, which serves as the generation (initial population). A basic GA comprises of an encoding mechanism (ranks and signifies the chromosomes by means of a string of bits); a selection mechanism (choosing better fitness function value for minimization or maximization problems); a reproduction mechanism (pairing the chromosomes by probabilistically to reproduce new generation); a crossover mechanism (interchanging the information and genes between chromosomes); and a mutation mechanism (flipping a particular bit of a chromosome to obtain smart convergence). Each of these basic operators works on strings in a population only with simple bit changes. Figure 3 illustrates the flow of the way by which the GA technique operates when optimizing a problem.
The following points give a generic view of how GAs operate : (1) a population of individuals (solutions) is created that consists of random individuals (initialization); (2) a function or a model (objective function) measures individual performance and determines their ability to survive and reproduce; (3) individuals are ranked (ranking) and the best/fittest individuals (according to a fitness function, which is an objective function transformation) are chosen (selection operator) to mate in pairs (crossover operator) and thus create new individuals, hence a whole new population. Every new individual (offspring) carries genetic characteristics from both parents. Slight mutation (mutation operator) occurs from generation to generation with given probability. Other population diversion operators, such as inversion, etc., may be applied to the offspring; (4) in order to satisfy the criteria of the objective function, increasing competition among individuals’ leads to “survival of the fittest.” This way, one generation after the other tends to have better genetic material (or characteristics) that help them survive. Individuals with best characteristics constitute the best solution to the problem; (5) this process continues in a repetitive manner until convergence criteria are met i.e. the chromosomes have the best fitness or potential (optimum) solution for a specific problem is obtained. Immediately after the new generation is created, it is further assessed and checked through experimentation for the conformability and agreement . In this work, Matlab toolbox was utilized for optimization purpose by implementing GA technique with the aim to maximize the material removal rate (MRR) and minimize the flaring diameter (FD). In the present FB-HAJM process, multi-objective optimization problem can be formally defined in following manner: (3) (4) (5)
Here for mathematical descriptions, the objective function f(MRR), and f(FD) are developed by RSM model equations (1)–(2) for material removal rate and flaring diameter, respectively. Figure 4 presents the optimization history, which aims to maximize the material removal rate as well as minimize the flaring diameter, simultaneously in the presence of algorithm-specific parameters of GA. In the present study, the critical (algorithm-specific) parameters are taken concerning population size of 50, reproduction of 0.8, crossover rate of 1.0, number of genes in each population member equal to 20, and maximum number of iterations equal to 221. By solving the optimization problem with GA, the optimized process parameters during hot abrasive jet machining of K-60 alumina ceramic are; air pressure 6.682 kgf/cm2, abrasive temperature 60.6 °C, stand-off-distance 7.1124 mm, abrasive grain size 275.755 μm, with estimated material removal rate (MRR) of 0.005 gm/s and flaring diameter (FD) of 6.382 mm.
Flow chart of GA-based algorithm.
GA based optimization results for material removal rate and flaring diameter.
In Figure 5, it can be found that increase in gas pressure increases MRR, which is attributed to increase in mass flow rate as well as kinetic energy of the abrasives are responsible for material removal by erosion process. From the Figure 5a, it can be found that the MRR is high at high abrasive temperature as compared to low temperature. Here the hot abrasives carried by air are made to strike on the target surface due to which the temperature on the target surface increases, which results in increase in size of radial crack formed on the work material. Due to heat, the abrasive particles get sharper, which helps to remove large amount of chips from the workpiece. The present study reveals that as the temperature of the target surface increases, more plastic deformation can be formed on the target surface due to which erosion rate increases and thus the hot abrasive has a direct impact in increasing the MRR. In Figure 5b, it can be found that as grain size of the abrasives increases, the material removal rate increases. This effect is mainly due to increase in grain size may create larger holes on the work materials which increases wearing away of the work material and thus the material removal rate increases. In agreement with this, the MRR is more for abrasives of larger sizes as compared to smaller sizes of abrasives. Similarly, in Figure 5b, it can be found that as the stand-of-distance increases, MRR also increases. For the reason that, as stand-of-distance increases, the kinetic energy of the abrasive particles become more significant which leads to more number of chips can be removed from the workpiece, which results in increase in MRR.
From the surface plot between the pressure and flaring diameter (Fig. 6a), it is seen that increase in gas pressure increases the flaring diameter. Also, from the surface plot, it is found that increase in abrasive temperature increases the flaring diameter. From the surface plot between grain size and flaring diameter (Fig. 6b), it is seen that increase in grain size increases the flaring diameter.
Machining parameter effect plots for material removal rate (MRR).
Machining parameter effect plots for flaring diameter (FD).
The present study highlighted that application of hot abrasives in AJM process has excellent performance in terms of improved material removal rate, and minimum dimensional deviation of drilled hole. Moreover, increasing grain size as well as SOD, both MRR and FD increase. Empirical models proposed for the technological response characteristics such as material removal rate and flaring diameter have R2 values close to one and P-value less than 0.05, which ensured the greater statistical significance with excellence of fit for the model. The normal probability plot ensures that the residuals distributed fairly near to a straight line indicating that the normality dispersion of errors and implying that the sources associated with the model are significant. Anderson-Darling test for model show adequate, as P-value is over 0.05 at 95% confidence level. Multi-response optimization employing GA technique shows the optimal setting of machining variables in FB-HAJM process at air pressure of 6.682 kgf/cm2, abrasive temperature of 60.6 °C, stand-off-distance of 7.1124 mm, abrasive grain size of 275.755 μm, with estimated maximal material removal rate (MRR) of 0.005 gm/s and minimal flaring diameter (FD) of 6.382 mm. The suggested multiple approaches (experimental, statistical, and computational) are reliable methodologies for improving HAJM process and can be used in model predictive control, real-time process monitoring, and optimization in different machining process.
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Cite this article as: Ranjit Kumar Behera, Sudhansu Ranjan Das, Modelling and optimization of technological parameters in hot abrasive jet machining of alumina ceramic, Matériaux & Techniques 107, 603 (2019)
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