Optimization of machining parameters of turning operations based on multi performance criteria

Article history: Received August 2


Introduction
Turning is one of the most basic machining processes in industrial production systems.Turning process can produce various shapes of materials such as straight, conical, curved, or grooved work pieces.In general, turning uses simple single-point cutting tools.Many researchers have studied the effects of optimal selection of machining parameters in turning.Tzeng and Chen (2006) used grey relational analysis to optimize the process parameters in turning of tool steels.They performed Taguchi experiments with eight independent variables including cutting speed, feed, and depth of cut, coating type, type of insert, chip breaker geometry, coolant, and band nose radius.The optimum turning parameters were determined based on grey relational grade, which maximizes the accuracy and minimizes the surface roughness and dimensional precision.
Similarly, the researchers have applied grey relational analysis (GRA) to different machining processes, which include electric discharge machining Lin et al. (2002), determining tool condition in turning (Lo, 2002), chemical mechanical polishing (Lin & Ho, 2003), side milling (Chang & Lu, 2007), and flank milling (Kopac & Krajnik, 2007) to compare the performance of diamond tool carbide inserts in dry turning (Arumugam et al., 2006), and optimization of drilling parameters to minimize surface roughness and burr height (Tosun, 2006).Lin (2004) implemented grey relational analysis to optimize turning operations with multiple performance characteristics.He analyzed tool life, cutting force, and surface roughness in turning operations.Tosun (2006) reported the use of grey relational analysis for optimizing the drilling process parameters for the work piece surface roughness and the burr height is introduced.This study indicated that grey relational analysis approach can be applied successfully to other operations in which performance is determined by many parameters at multiple quality requests.Al-Refaie et al. (2010) used Taguchi method grey analysis (TMGA) to determine the optimal combination of control parameters in milling, the measures of machining performance being the MRR and SR.
Based on the ANOVA; it was found that the feed rate is important control factor for both machining responses.If there are multiple response variables for the same set of independent variables, the methodology provides a different set of optimum operating conditions for each response variable.The grey system theory initiated by Deng (1982) has been proven to be useful for dealing with poor, incomplete, and uncertain information.The grey relational based on the grey system theory can be used to solve the complicated interrelationships among the multiple performance characteristics effectively (Wang et al., 1996).
Therefore, the purpose of the present work is to introduce the use of grey relational analysis in selecting optimum turning conditions on multi-performance characteristics, namely the surface roughness, power consumption and frequency of tool vibration.In addition, the most effective factor and the order of importance of the controllable factors to the multi-performance characteristics in the turning process were determined.

Experimentation procedure and test results
The cutting experiments were carried out on an experimental lathe setup using a HSS MIRANDA S-400 (AISI T -42) cutting tool for the machining of the IS: 2062, Gr.B Mild Steel bar, which is 24 mm in diameter.The percent composition of the work piece material is listed in Table 1.Mar Surf PS1 surface roughness tester was used to measure the Surface roughness R a (µm) of the machined samples and Lathe tool dynamometer was used to measure the cutting forces and measuring cutting tool vibration using Pico Scope 2202 In the present experimental study, spindle speed, feed and depth of cut have been considered as machining parameters.The machining parameters with their units and their levels as considered for experimentation are listed in Table 2.

Grey relational analysis
Original Taguchi method has been designed to optimize a single performance characteristic.The Grey relational analysis based on the Grey system theory can be used to solve complicated multiple performance parameters effectively.As a result, optimization of the complicated outputs can be converted into optimization of a single Grey relational grade.Grey relation analysis is used to find out whether there is consistency between the changing trends of two factors or not, and to find out the possible mathematical relationship among the factors or in the factors themselves.

Data preprocessing
Data preprocessing is normally required since the range and unit in one data sequence may differ from the others.Data preprocessing is also necessary when the sequence scatter range is too large or when the directions of the target in the sequences are different.Data preprocessing is a means of transferring the original sequence to a comparable sequence.Depending on the characteristics of a data sequence, there are various methodologies of data preprocessing available for the gray relational analysis.
If the target value of the original sequence is infinite, then it has a characteristic of the "higher is better."The original sequence can be normalized as follows: When the "lower is better" is a characteristic of the original sequence, then the original sequence should be normalized as follows: However, if there is a definite target value (desired value) to be achieved, the original sequence will be normalized in from: Alternatively, the original sequence can be simply normalized by the most basic methodology, i.e., let the value of the original sequence be divided by the first value of the sequence: where i=1,….,m;k =1,…, n. m is the number of experimental data items, and n is the number of parameters.
x i o (k)denotes the original sequence, x i * (k) the sequence after the data preprocessing, max.and x i o is the desired value of x i o (k).

Gray relational coefficient and gray relational grade
In gray relational analysis, the measure of the relevancy between two systems or two sequences is defined as the gray relational grade.When only one sequence, x o (k), is available as the reference sequence, and all other sequences serve as comparison sequences called a local gray relation measurement.After data preprocessing is carried out, the gray relation coefficient ξ i (k) for the k th performance characteristics in the i th experiment can be expressed as follows, where, ∆ ( ) = | * ( ) − * ( )| and ∆ = 1.00, ∆ = 0.00 and Δ oi (k) is the deviation sequence of the reference sequence x o * (k)and the comparability sequence x i * (k). is the distinguishing or identification coefficient defined in the range 0≤ ξ ≤1 (the value may be adjusted based on the practical needs of the system).A value of is the smaller, and the distinguished ability is the larger.The purpose of defining this coefficient is to show the relational degree between the reference sequence x o * (k) and the comparability sequence x i * (k).= 0.5 is generally used.After the grey relational coefficient is derived, it is usual to take the average value of the grey relational coefficients as the grey relational grade.The grey relational grade is defined as follows: However, in a real engineering system, the relative importance of various factors varies.In the real condition of unequal weight being carried by the various factors, the grey relational grade in Eq. ( 1) was extended and defined as recommended by Deng (1982).
where ∑ = 1 and w k denotes the normalized weight of factor k.
Here, the grey relational grade γ i represents the level of correlation between the reference sequence and the comparability sequence.If the two sequences are identical by coincidence, then the value of grey relational grade is equal to 1.
The grey relational grade also indicates the degree of influence that the comparability sequence could exert over the reference sequence.Therefore, if a particular comparability sequence is more important than the other comparability sequences to the reference sequence, then the grey relational grade for that comparability sequence and reference sequence will be higher than other grey relational grade.Grey relational analysis is actually a measurement of absolute value of data difference between sequences, and it could be used to measure approximation correlation between sequences.

Optimal parameter combination
We know from the analysis of machining process that the lower power consumption and surface roughness as well as lower value of frequency of tool vibration provides better quality of the machined surface.Thus, the data sequences power consumption, surface roughness and frequency of tool vibration both have "smaller-the-better" characteristics.Table 5 lists all of the sequences following data pre-processing of power consumption, surface roughness and frequency of tool vibration by using Eq.
(2).Then, the deviation sequences, ∆ ( ) = | * ( ) − * ( )| has been determined and are shown in Table 6.Grey relational coefficient and Grey relational grade values of each experiment of the full factorial design were calculated by applying equation 5 and 6 and Table 7 and table 8 shows the Grey relational coefficient and grey relational grade for each experiment using full factorial design.The multi-response optimization problem has been transformed into a single equivalent objective function optimization problem using this approach.The higher grey relational grade is said to be close to the optimal.According to performed experiment design, it is clearly observed that experiment no.16 has the highest Grey relation grade.Thus, the sixteenth experiment gives the best multi-performance characteristics of the turning process among the 27 experiments.Table 9 shows the response table and graph of grey relational grade for each turning parameter at different levels, respectively.As shown in Table 9, the important rank in sequence for various turning parameters in machining of mild steel.The order of importance of the controllable factors to the multiperformance characteristics in the turning process, in sequence can be listed as: factor B (Feed rate), A (Spindle speed), C (Depth of cut).Factor B (Feed rate) was the most effective factor to the performance.This indicates that the turning performance was strongly affected by the feed rate  After obtaining the optimal level of the machining parameters, the next step is to verify the improvement of the performance characteristics using this optimal combination.The estimated grey relational grade using the optimum level of the `parameter is the total mean of the grey relational grade is the mean of the grey relational grade at the optimum level and o is the number of machining parameters that significantly affects the multiple performance characteristics.
where is the total mean of the grey relational grade, is the mean of the grey relational grade at the optimum level and o is the number of machining parameters that significantly affects the multiple performance characteristics.Based on equation 8 the estimated grey relational grade using the optimal machining parameters can then be obtained.Table 10 shows the results of the confirmation experiment using the optimal machining parameters The Power consumption P is greatly reduced from 9.65 to 6.63 W, Surface roughness R a is improved from 1.97to 1.88 μm and the frequency of tool vibration f is greatly reduced from 270.7 to 260 Hz.It is clearly shown that multiple performance characteristics in turning process are greatly improved through this study.Improvement in grey relational grade = 0.05 Therefore, a comparison of the predicted values of the power consumption, surface roughness and frequency of tool vibration with that of the actual parameters by using the optimal machining conditions is shown in the above table.An improvement of 5.00% is observed in the grey relational grade.A good agreement between the two has been observed.This ensures the usefulness of grey relational approach in relation to product/process optimization, where multiple quality criteria have to be fulfilled simultaneously.

Conclusion
Experiments are designed and conducted on lathe machine with High speed steel MIRANDA S-400 (AISI T -42) and IS: 2062, Gr.B Mild Steel bar as work material to optimize the turning parameters.Power consumption, surface roughness and frequency of tool vibration are the responses.Full factorial design of experiments and Grey relational analysis is constructive in optimizing the multi responses.
Based on the results of the present study, the following conclusions are drawn: • The optimum combination of turning parameters and their levels for the optimum multiperformance characteristics of turning process are A 1 B 1 C 1 (i.e.Speed-180 RPM, Feed rate-0.08mm/rev and Depth-of-cut-0.1 mm).• Confirmation test results prove that the determined optimum condition of turning parameters satisfy the real requirements.

Fig. 1 .
Fig. 1.Grey relation grades for the power consumption, surface roughness and frequency of tool vibration 4.2 Confirmation Test

Table 4
Experimental design and collected response data

Table
Evaluation of deviation sequence △ oi (k) for each of the responses

Table 7
Grey relational coefficients of each performance characteristics for 27 comparability sequences

Table 8
Evaluated grey relational grades for 27 groups

Table 10
Results of machining performance using initial and optimal machining parameters