Determining the Effect of Cutting Parameters on Surface Roughness in End Milling of Al-356/SiCp MMC using Fuzzy Logic M. Chandrasekaran1, Shubhajit Das2, D.Devarasiddappa3 Department of Mechanical Engineering, North East Regional Institute of Science & Technology, Nirjuli, Arunachal Pradesh, 791 110, India e-mail:
[email protected] Department of Mechanical Engineering, National Institute of Technology, Arunachal Pradesh, 791 110, India Department of Automobile Engineering, Rajiv Gandhi Govt. Polytechnic, Itanagar, Arunachal Pradesh, 791 113, India Emails:
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Abstract: Machining is the most wide spread metal cutting process in the manufacturing industry and milling is most commonly used for rapid removal metal. In this work, an experimental investigation and the effect of cutting parameters on surface quality of the component produced are studied in milling Al-356/SiCp metal matrix composite. The process parameters are spindle speed (N), feed rate (f) and axial depth of cut (d) and CLA value of surface roughness is considered as response variable. Machining experiments are performed based on Taguchi L9 orthogonal array. The novelty of the work is Fuzzy Logic modeling with minimal experimental datasets. Nine set of rules based on Mamdani Fuzzy Inference System are constructed and simulated with MATLAB software. Analysis of variance is showed feed rate and spindle speed have significant effect on surface roughness. The combination of high spindle speed and low feed at low depth of cut produced better surface roughness. The prediction accuracy of the model is verified and it shows 88.44% accuracy. The developed fuzzy model can be used for development of expert system for process control. Keywords: Metal matrix composites, Fuzzy Logic, Surface roughness, Milling, ANOVA
1. INTRODUCTION Machining is the most wide spread metal cutting process in mechanical manufacturing industry. Among various conventional machining processes, ‘milling’ is used as one of the most widely used metal removal processes in industry and milled surfaces are largely used to mate with other parts in die, particularly in aerospace and automotive industries. Due to its wide spread application, milling operation has always been among the main research topics to improve machining accuracy and efficiency. In studying the performance of machining process, the Machinability characteristics of work-piece and tool combination is important and is judged by surface finish, tool wear, tool life, cutting forces and cutting temperature developed [1]. Metal matrix composites has found greater application due to its improved properties like high strength, hardness, wear resistance and strength to weight ratio and it replaces non-reinforced alloys [2]. Among the various types of MMCs, aluminium based composites with SiC as popular reinforcement material has been used in manufacturing industries. A number of studies have been presented in machining Al-SiCp MMC using different cutting tools such as carbide, coated carbide and diamond in turning, drilling,
reaming and threading of MMC materials employing approaches like Taguchi, RSM and ANN and fuzzy logics [3, 4, 5]. A knowledge based system using FL was employed by Abburi and Dixit [6] for surface roughness prediction in turning process. An ANN module was used to produce large amount of machining data sets to form FL model rule base. Sentilkumar et al. [7] applied neural networks to study the tribological behavior of sintered hybrid composites having Cu-SiC-Gr reinforcements in various percentages by conducting abrasive wear tests. The basic machining parameters viz., sliding velocity & distance, load with varied SiC abrasive of grit size (80-400) having particle size 45-192 μm were considered as input design parameters. Better prediction was reported with NN model trained using GA optimized training function. Rajasekaran et al., [8] have modeled surface roughness prediction using fuzzy logic in turning of carbon fiber reinforced polymer (CFRP) composites using cubic boron nitride (CBN) cutting tool. The average percentage error is reported as 6.62% with a maximum and minimum percentage error as 18.30% and 0.32% respectively. Harun Akkus et al., [9] found fuzzy logic surface roughness prediction model found better than regression and neural network model in hard turning of AISI 4140 steel. Pradhan et al.,
[10] used neural network and fuzzy logic to predict various responses (material removal rate, tool rate wear and radial over cut) in electrical discharge machining of AISI D2 steel. With average prediction errors in the range of 4.94% to 16.22% in all the three types of prediction and the model predicts with agreeable accuracy. Issam et al., 11] have developed response surface and fuzzy logic models for cutting force prediction in turning of reinforced poly ether ether ketone (PEEK) plastics. Comparison of the models showed that fuzzy logic based prediction model was superior to RSM. The fuzzy logic surface roughness prediction model found efficient with 92.73 % model accuracy in end milling of Al-SiCp MMCs components [12]. In addition to basic machining parameters (spindle speed, feed rate and depth of cut), reinforcement content (vol. %) was also considered. Further, developed model was used to optimize cutting conditions by integrating with particle swarm optimization technique. Modeling of machining parameters is attempted mainly using neural network, response surface models, regression analysis etc. Very few researchers have employed fuzzy logic technique for machining parameters prediction. Requirement of a large amount of experimental data sets to develop fuzzy logic model, becomes costlier in practice and hence limited research work is reported. The novelty of the present work is an attempt to apply fuzzy logic model with a very few experimental datasets (9 sets) in AlSiCp MMC machining. The analysis of variance of the response variable is also carried out to determine most influential parameter. The parametric variation study of surface roughness is also presented using 3D plots of fuzzy inference system. 2. EXPERIMENTATION In this work, an experimental investigation is carried out and the effect of cutting parameters on surface quality of the component produced is studied in machining Al-356/SiCp metal matrix composite (MMC). In the present work, surface roughness (Ra) of the machined surface is considered as a function of three basic machining parameters viz., spindle speed (N), table feed rate (f) and axial depth of cut (d). The machining parameters along with their levels and corresponding values are shown in Table 1. Table 1 Machining parameters and levels Sr. No. 1 2
Parameters Spindle speed, N (rpm) Feed rate, f (mm/min)
1
Levels 2
3
707
1004
1414
14
20
28
3
Depth of cut, d (mm)
0.5
1.0
1.5
Taguchi design of experiments is employed for conducting the experiments and to evaluate the effect of the machining parameters. The study of the effect of the parameters with a limited number of experiments is carried out with the help of a planned orthogonal array. An orthogonal array determines the number of experiments to be performed ensuring that all levels of all factors are tested in an equal measure. Proper selections of the orthogonal array need to be made which depends on the computation of total degree of freedom. In this study, L9 orthogonal array is selected which requires 9 trials to study the effects of the three input parameters of three levels each. Table 2 shows the 9 set of experiments along with the cutting parameters along with their levels. Table 2 Experimental design matrix Expt. No. 1 2 3 4 5 6 7 8 9
Spindle speed N (rpm) 707 707 707 1004 1004 1004 1414 1414 1414
Feed rate f (mm/min) 14 20 28 14 20 28 14 20 28
Depth of cut d (mm) 0.5 1.0 1.5 1.0 1.5 0.5 1.5 0.5 1.0
Surface roughness is an important measure as it affects wear resistance, ductility, tensile, fatigue strength, etc., for machined parts and cannot be neglected in design. The experimental design must aim to determine the optimal levels of the output factors such that it is robust to the variability caused by the noise factors. For measuring the variation present in the output data, Taguchi defined signal to noise (S/N) ratio. The maximization of the S/N ratio simultaneously optimizes the quality characteristics and minimizes the effect of noise factors. The quality characteristics assigned for surface roughness is ‘smaller is better’. The S/N ratio for ‘smaller the better’ can be computed as follows: (1) Where, y is the ordinate of measured roughness value and n is the total number of experiments conducted. The signal to noise (S/N) ratio is used to measure the quality characteristics deviating from the desired values. The term signal (S) in the S/N ratio represents the desirable value (mean) and the term noise (N) represents the
undesirable value (S.D) for the output characteristic. The S/N ratio is thus the ratio of the mean to the S.D. A greater S/N ratio corresponds to better quality and signifies better parameters. The experimental results for surface roughness and the corresponding S/N ratio are shown in Table 3. Table 3 Experimental results for surface roughness and S/N ratio Expt. No.
N (rpm)
1 2 3 4 5 6 7 8 9
707 707 707 1004 1004 1004 1414 1414 1414
f (mm/ min) 14 20 28 14 20 28 14 20 28
d (mm) 0.5 1.0 1.5 1.0 1.5 0.5 1.5 0.5 1.0
Ra (µm) 2.30 2.96 3.20 2.10 1.77 2.28 1.51 1.04 2.58
S/N ratio (dB)
-7.235 -9.426 -10.103 -6.444 -4.959 -7.158 -3.579 -0.341 -8.232
The average effect of the input parameters and their interactions at different levels is as shown in Fig. 1.
Fig. 1 Average effect of input parameters at different levels To assert the dominance of one parameter over the other parameter in influencing the quality characteristics, Analysis of variance (ANOVA) is an established way. Table 4 shows a summary of the ANOVA results for the 9 set of experiments. Table 4 ANOVA for surface roughness Factors
DO F 2
SS
V
Fratio 63.69
Pure sum 1.91
N (rpm) 1.94 0.97 f (mm/ 2 1.10 0.55 36.05 1.07 min) d (mm) 2 0.69 0.34 22.48 0.65 Error 2 0.03 0.02 Total 8 3.75 DOF: degrees of freedom, SS: sum of squares V: variance, PC: percentage contribution
The depth of cut found to have least influence with 17.43 % contribution. Thus it signifies that spindle speed and feed rate are the two most influential design variables for controlling surface roughness in Al-SiCp MMC machining. 3. DEVELOPMENT MODEL
OF
PREDICTION
For domains in which description of observations have no well defined boundaries of set of observations, the theory of fuzzy logic unit is applied. Fuzzy set theory was first proposed by Lotfi Zadeh [13] as an effective tool to incorporate the linguistic terms in computing. Generally referred as fuzzy rule based model (FLRM), it consists of a set of rules in the form of if-then conditional statements and associated fuzzy subsets. A typical fuzzy logic unit thus comprises of a fuzzifier, a fuzzy rule base, an inference engine and a defuzzifier. In this study, the experimental dataset were modeled using fuzzy logic. Membership functions characterize the fuzziness in a fuzzy set whether the elements in the set are discrete or continuous in graphical form for eventual use in the mathematical formalism of fuzzy set theory. Certain element of the domain is considered as a member of each fuzzy set to a varying degree, known as membership grade. The input variables are fuzzified into three subsets as low (L), medium (M) and high (H) while the output variable (surface roughness) is fuzzified into five subsets as very good (VG), good (G), average (A), bad (B) and very bad (VB). The performance of FLRM is mainly dependent on knowledge base constituted by the type/shape of membership functions. In the present work, Gaussian shape of membership function is employed to describe the input fuzzy sets while for output fuzzy set triangular membership functions is used for simplicity. The graphical representation of the membership functions used is shown in Fig. 2. Gaussian membership function is depicted in Fig. 2 (a). Gaussian function depends upon two parameters mean (μ) and variance (σ). It is mathematically expressed as in Eq. (2).
PC 50.87
(2)
28.44 17.43 3.25 100%
It can be seen from Table 4 that spindle speed is the most dominating factor with 50.87 % contribution followed by feed rate (28.44 %).
Fig. 2 (b) shows the graphical representation of triangular membership function used for fuzzyfying surface roughness. It is defined as a function of vector x which depends upon three parameters a, b and c. It is mathematically expressed as given in Eq. (3).
(a) Gaussian membership function
(b) Triangular membership function Fig. 2 Membership functions used
(a) Fuzzification of Spindle speed
(a) Fuzzification of feed rate
(3)
Where, a & c represent feet of the triangle and b represents peak. The relationship between the inputs and the outputs in a fuzzy model is characterized by a set of linguistic statements called as fuzzy rules. The following 9 set of rules were constructed based on the actual experimental surface roughness of a machined component in end milling process and simulated with MATLAB software. Mamdani type fuzzy inference system is employed in the present study. Rule 1: If (N is low) and (f is low) and (d is low) then (Ra is very good) Rule 2: If (N is low) and (f is medium) and (d is medium) then (Ra is very bad) Rule 3: If (N is low) and (f is high) and (d is high) then (Ra is very bad) Rule 4: If (N is medium) and (f is low) and (d is medium) then (Ra is very good) Rule 5: If (N is medium) and (f is medium) and (d is high) then (Ra is bad) Rule 6: If (N is medium) and (f is high) and (d is low) then (Ra is bad) Rule 7: If (N is high) and (f is low) and (d is high) then (Ra is very good) Rule 8: If (N is high) and (f is medium) and (d is low) then (Ra is very good) Rule 9: If (N is high) and (f is high) and (d is medium) then (Ra is bad) The membership functions used for the three input variables and one output variable are as shown in Fig. 3.
(a) Fuzzification of depth of cut
(a) Fuzzification of surface roughness Fig. 3 Membership functions used The fuzzy output of all the rules is converted into a non-fuzzy value using a de-fuzzifier and is the response value for the given data sets. The centroid of area (COA) method is used in this work. Amongst various defuzzification methods in practice, COA method gives accurate value quickly, based on centroid calculation. 4. RESULTS AND DISCUSSIONS 4.1 Validation of the prediction model The predictive performance of the developed fuzzy logic based surface roughness prediction model is compared with experimental data sets. The validation results are given in Table 5. Table 5 Validation result of FL model
N (rpm)
707 707 707 1004 1004 1004 1414 1414 1414
f (mm/ min) 14 20 28 14 20 28 14 20 28
Exp. FL Ra Pred. (µm) 0.5 2.30 1.91 1.0 2.96 3.01 1.5 3.20 3.16 1.0 2.10 1.75 1.5 1.77 2.69 0.5 2.28 2.81 1.5 1.51 1.50 0.5 1.04 1.19 1.0 2.58 2.55 Minimum error % Maximum error % Average % error
d (mm)
% error
16.95 1.66 1.25 16.67 34.20 18.86 0.66 12.61 1.16 0.66 34.20 11.56
The minimum and maximum error found to be 0.66% and 34.20% respectively. The average percentage error recorded in 11.56% while the model accuracy is 88.44%. The model predictions found have agreeable with experimental values. 4.2 Parametric study of response variable The parametric variation of surface roughness is studied using 3-diemnational plots obtained from fuzzy inference system. The graphical plots given Fig. 4 depict the relationship between input parameters and surface roughness of an end milled Al-SiCp MMC component.
(a) Surface Roughness Vs N & d Fig. 3 Functional variance of surface roughness It can be distinctly observed from Fig. 4 (ac) that feed rate and spindle speed vary surface roughness values significantly. It can also be seen that depth of cut has least influence on surface roughness variation. 5. CONCLUSIONS In this paper, surface roughness prediction model is using fuzzy logic is attempted in end milling of Al-SiCp MMC components. The development of fuzzy logic prediction model using very few experimental data sets is the novelty of the work explored the present paper. The significant factors affecting response variable is also discussed using analysis of variance. The parametric study of surface roughness is also presented using 3-dimensional graphical plots. The following conclusions can be drawn from the current investigation in end milling of Al-SiCp metal matrix components.
(a) Surface Roughness Vs N & f
(b) Surface Roughness Vs d & f
Fuzzy logic technique can be effectively applied to predict surface roughness in MMC machining. The fuzzy logic surface roughness prediction model developed with very few experimental data sets found efficient with 11.56% average percentage error and 88.44% model accuracy. Better surface finish can be obtained at higher spindle speed, low feed and depth of cut, as found in published research work. Spindle speed and feed rate have significant influence on surface roughness variation with 55.87 % and 28.44 % contribution respectively. With 17.43 % contribution, depth of cut found to have least effect on surface roughness variation.
The proposed fuzzy logic modeling can be extended and applied to other processes too. The predictive capability of the model can be
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