Optimal selection of operating parameters in end milling of Al6061 work materials using multiobjective approach
 Jakeer Hussain Shaik^{1}Email author and
 Srinivas J^{1}
DOI: 10.1186/s4075901700206
© The Author(s). 2017
Received: 3 September 2016
Accepted: 17 February 2017
Published: 27 February 2017
Abstract
Background
Machining using vertical CNC end mill is popular in the modern material removal industries because of its ability to remove the material at a fast rate with a reasonably good surface quality.
Methods
In this work, the influence of important common machining process variables like feed, cutting speed and axial depth of cut on the output parameters such as surface roughness and amplitude of tool vibration levels in Al6061 workpieces has been studied. With the use of experimental result analysis and mathematical modelling, correlations between the cutting process conditions and process outputs are studied in detail. The cutting experiments are planned with response surface methodology (RSM) using BoxBehnken design (BBD).
Results
This work proposes a multiobjective optimization approach based on genetic algorithms using experimental data so as to simultaneously minimize the tool vibration amplitudes and workpiece surface roughness. The optimum combination of process variable is further verified by the radial basis neural network model.
Conclusions
Finally, based on the multiobjective optimization approach and neural network models an interactive platform is developed to obtain the correct combination of process parameters.
Keywords
Al6061 workpiece BoxBehnken design Multiobjective optimization Neural network Surface roughness Tool vibration amplitudesBackground
For the metalworking industry, a continuous reduction in manufacturing cost is desirable. An important issue related to reduce overall cost consists of the removal of undesirable or excess work piece material during the machining process. Among different types of material removal operations, endmilling is most important common milling operation due to its capability of producing complex geometric surfaces with reasonable accuracy and surface finish. Over the last two decades, several works focused on the optimum selection of machining parameters based on various criteria such as using basic mathematical models. Some contemporary literature is first presented. Brito et al. (2014) developed a robust parameter design for the process parameters using the multiobjective methods. The numerical results are validated with the experimental cutting tests. Mathivanan et al. (2016) studied the influence of cutting parameters on milling of the composite materials. A CNC end milling was used to machine the composite laminates at various combinations of speeds and depth of cuts. Numan durakbasa et al. (2015) presented the various end milling process parameters as well as the coatings on the surface quality of the machined parts of AISI H13 hot work steel. Some researchers (eg., Hocheng et al. (1997), Arokiadass (2012) and Surinder (2015)) investigated the machining characteristics of an aluminium based composite alloy for the endmilling process. Experiments were conducted based on the central composite design and Analysis of Variance (ANOVA) was used to build the mathematical model. Zhang et al. (2016) implemented a systematic optimization approach to obtain the paretooptimal values of cutting process parameters. Dikshit et al. (2014a, 2014b) studied the cutting process parameters in dry machining of aluminium alloys. Response surface methodology was planned to carry out the experiments and further genetic algorithms were implemented to obtain the optimal parameters such as the cutting speed, feed per tooth, axial and radial depth of cut. Karkalos et al. (2016) focused on the machining of Titanium alloy with the peripheral down milling process and further optimal control studies were implemented to minimize the surface roughness. Ratnam et al. (2016) studied the turnmilling process in tangential and orthogonal directions to minimize the surface roughness of extruded brass material. Several recent works focussed on the optimal machining parameters for multipass milling operations by considering the statistical and artificial intelligent techniques (Wang et al. 2005; Sukumar et al. 2014; Venkata Rao and Pawar 2010; Das et al. 2016; Ren et al. 2016). The efficiency of a neural network model was estimated by conducting the numerical simulations and experiments. Several studies had been focussed on the optimization of important cutting process parameters using intelligent optimization techniques like genetic algorithms and radial basis neural networks (Briceno et al. 2002; Mounayri et al. 2010; Mounayri et al. 2005). Using, different neural network models and optimization algorithms the impact of the surface roughness on the process parameters are extensively studied (Palanisamy et al. 2007; Palanisamy and Kalidass 2014; Zain et al. 2011; Saffar and Razfar 2010). Khorasani et al. (2016) studied the effects of cutting parameters and cutting fluid pressure intensity on the surface roughness of milled parts. The important parameters were modelled and analysed using both the multilayer perceptron and radial basis neural networks.
In spite of above works, very few works are found in literature dealing with the optimal process parameter selection based on simultaneously minimization of tool vibration amplitudes during cutting as well as surface roughness average values of the workpiece. The milling experiments are conducted on the CNC vertical milling machining centre by considering three levels of feed rate, spindle speed and axial depth of cut. Using the response surface methodology with BoxBehnken design, a mathematical model is developed to predict the surface roughness and amplitude of tool vibration levels in terms of the cutting process variables. Using the experimental data, neural network model is created to approximate the relationship between the three process parameters and two output variables. Furthermore, the equations obtained from response surface methodology are employed as functionestimators for GAbased optimization module, which attempts to minimize simultaneously the tool vibration amplitude and average roughness. The resulting optimum process parameters are reported and discussions are made. Thus, data generation, interaction of responses, implementation of multiobjective genetic algorithms, parallel radial basis neural network modelling for comparison of results is explained one after the other.
Methods
Machining parameters and their levels
S. No  Factor  Low  High 

1  Spindle speed (rpm)  1800  3000 
2  Feed rate (mm/min)  20  60 
3  Axial depth of cut(mm)  0.2  0.8 
Experimental layout for the BBD
Std Order  Feed(f)(mm/min)  Speed(s)(rpm)  Axial depth of cut(b)(mm)  Amplitude of vibration level(A)(mv)  Surface roughness (Ra) μm 

1  20  1800  0.5  0.0640  0.800 
2  60  1800  0.5  0.1430  0.333 
3  20  3000  0.5  0.1128  2.200 
4  60  3000  0.5  0.0944  0.333 
5  20  2400  0.2  0.1780  2.860 
6  60  2400  0.2  0.1980  0.530 
7  20  2400  0.8  0.2220  0.800 
8  60  2400  0.8  0.0730  0.330 
9  40  1800  0.2  0.1462  0.200 
10  40  3000  0.2  0.0834  1.130 
11  40  1800  0.8  0.0634  0.200 
12  40  3000  0.8  0.0896  1.730 
13  40  2400  0.5  0.0752  1.200 
14  40  2400  0.5  0.0752  1.200 
15  40  2400  0.5  0.0720  1.200 
Response surface modeling
The coefficients in the above expressions signifies the weightage factorial values on the output responses. The positive and negative signs of the coefficients reflect the respective proportionality.
Multiobjective optimization
In order to obtain the optimal solutions for different design problems with various input data sets optimization methods are needed severely. In single optimization problem, there is only one output criterion and such work has been studied over the past 50 years. When there is more than one objective, a different treatment is required. The multiobjective problems ascend in the complex real world industries like machining, design, transportation industries etc. It is seen that, all the important real world practical problems involving multiple criteria with several constraints are drawing much attention towards the multiobjective optimization. These problems could be effectively solved with less computational effort and high accuracy. In multiobjective optimization problems, genetic algorithms approach is a better technique compared to other methods and has received considerable attention by the researchers. GA is based on the principle of survival for the fittest. In this method, initially a population of strings is selected randomly. These are encoded in binary digits and it is traditionally used to signify the chromosomes using with zeros and ones. Further, the fitness value (maximization or minimization problems) is computed. Further to create a new population, operations like reproduction, crossover and mutation were applied consecutively. Once the new population is generated it is further evaluated and tested for the conformability.
With X = [N, f, b] ^{T} and N, f and b represent the speed, feed and axial depth of cut. The function of f(X) and g(X) represents the amplitude of vibration and surface roughness, which are unknown and to be fitted from the experimental data.
Results and discussions
Interaction plots of responses
Training with radial basis function (RBF) neural netwoks
 (i)
Centre: It is the input domain vector, generally saved in the output layer weights in the hidden layer neuron.
 (ii)
Measurements of distance: It is considered as the distance between the hidden node centre (c) and the input parameter vector (x) called the Euclidian distance of measure and it is given as ‖x(t) − c _{ j(t)}‖.
 (iii)
Transfer function: It describes the functional mapping of the central nodal vector distance and the output of the neuron. When the distance of measure between the two vectors are small, then preferably transfer such as Gaussian function is used which mainly amplifies the values of the output vector. The Gaussian function parameter width for the k^{th} unit of the hidden neuron vector is evaluated by the following expression:
Where the P is the value determined heuristically for the method of the closest neighbors; given a cluster center c _{ k }, let k _{ 1 } , k _{ 2 } ,……,k _{ P } be the indices of the P nearest neighboring cluster centers.
Output results of the trained neural network model
Case  Inputs  Outputs  

f in mm/min  N in rpm  b in mm  Amplitude of vibration(A) in mv  Surface roughness (R_{a}) in μm  
Initial Value  RBF Value  % error  Initial Value  RBF Value  % error  
1  20  1800  0.5  0.064  0.06479  0.005  0.8  0.824  0.0002 
2  20  3000  0.5  0.1128  0.1228  0.001  2.2  1.45  0.07 
3  40  1800  0.2  0.1462  0.1189  0.002  0.2  0.49  0.002 
4  40  3000  0.8  0.0896  0.0912  0.0001  1.73  1.56  0.0017 
5  40  2400  0.5  0.0752  0.074  0.0001  1.2  0.95  0.002 
Using the RBFN, the percentage of error is less than 1% for the central vector of 9. It is confirmed from these above simulations, that the level of error are acceptable. The modeled algorithms in this work could be implemented and it can be further used efficiently in the estimation of correct process parameter studies.
Optimization using multiobjective GA
Pareto optimal solutions obtained from multiobjective GA
Sl. No  Speed (Rpm)  Feed (mm/min)  Axial depth of cut (mm)  Amplitude of vibration level (mv)  Surface roughness (Ra μm) 

1  1800.730  41.525  0.658  0.241  2.825 
2  1800.994  41.751  0.689  0.242  2.783 
3  1800.902  41.623  0.700  0.242  2.767 
4  1801.054  41.675  0.709  0.242  2.754 
5  1801.026  41.822  0.795  0.250  2.622 
6  1800.954  41.826  0.799  0.251  2.615 
7  1800.954  41.828  0.730  0.243  2.723 
8  1800.819  41.813  0.706  0.242  2.757 
9  1801.005  41.818  0.790  0.249  2.631 
10  1801.089  41.808  0.754  0.245  2.687 
11  1800.974  41.628  0.750  0.246  2.691 
12  1801.107  41.782  0.773  0.247  2.657 
13  1801.036  41.711  0.785  0.249  2.638 
14  1800.735  41.553  0.664  0.241  2.817 
15  1800.950  41.629  0.719  0.243  2.739 
16  1800.980  41.578  0.739  0.244  2.708 
17  1800.962  41.792  0.744  0.245  2.702 
18  1801.063  41.633  0.725  0.243  2.731 
Confirmation table of optimal process parameter
S1 No  Optimal input set  Outputs  

f in mm/min  N in rpm  b in mm  Amplitude of vibration (A) in mv  Surface roughness (R_{a}) in μm  
GA Value  RBF Value  Experiment  % error  GA Value  RBF Value  Experiment  % error  
1  41.826  1800.954  0.799  0.251  0.236  0.249  0.796  2.615  2.458  2.598  0.650 
Conclusions

It is evident that the spindle speed and axial depth of cut are having significant influence on the amplitude of vibrations as compared to the surface roughness. However, the interaction effects signify, that low feed rate with high spindle speed minimizes the surface roughness as well as the amplitude tool vibration levels.

The mathematical model developed in the work gives the good corelation between the process parameters and the responses. In addition, the Pareto based multiobjective genetic algorithms model can obtain good quality solutions in short time and are suitable for the multiobjective environment due to its population based nature.

The confirmatory tests are conducted by using both the experiment and trained radial basis neural network model gives an additional validation for the correctness of the process parameter for multiobjective response.

With the use of the GA based multiobjective optimization developed in this work, it would be possible to obtain the conditions for good surface finish with a lesser amplitude of vibrations.
Declarations
Acknowledgements
There are no acknowledgements for this work.
Funding
Not applicable for the current project.
Authors’ contributions
All authors contributed widely to the work presented in this paper. All the numerical simulations and experimental works are carried out in National institute of Technology Rourkela. The paper has been carefully written to avoid the mistakes at all stages of the manuscript. Finally, the manuscript has been formulated according to journal guidelines and authors approve final manuscript.
Competing interest
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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