Optimization in CNC end milling of UNS C34000 medium leaded

S¯adhan¯a Vol. 35, Part 5, October 2010, pp. 619–629. © Indian Academy of Sciences

Optimization in CNC end milling of UNS C34000 medium leaded brass with multiple surface roughnesses characteristics BHARAT CHANDRA ROUTARA1 , SAUMYA DARSAN MOHANTY2 , SAURAV DATTA∗,2 , ASISH BANDYOPADHYAY3 and SIBA SANKAR MAHAPATRA2 1

Department of Mechanical Engineering, School of Technology, Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar 751 024 2 Department of Mechanical Engineering, National Institute of Technology (NIT), Rourkela 769 008 3 Department of Mechanical Engineering, Jadavpur University, Raja S. C. Mallik Road, Kolkata 700 032 e-mail: [email protected]; [email protected]; [email protected]; [email protected] MS received 29 August 2009; revised 1 December 2009; accepted 20 January 2010 Abstract. The present study highlights a multi-objective optimization problem by applying utility concept coupled with Taguchi method through a case study in CNC end milling of UNS C34000 medium leaded brass. The study aimed at evaluating the best process environment which could simultaneously satisfy multiple requirements of surface quality. In view of the fact, the traditional Taguchi method cannot solve a multi-objective optimization problem; to overcome this limitation, utility theory has been coupled with Taguchi method. Depending on Taguchi’s Lower-theBetter (LB) response criteria; individual surface quality characteristics has been transformed into corresponding utility values. Individual utility values have been aggregated finally to compute overall utility degree which serves as representative objective function for optimizing using Taguchi method. Utility theory has been adopted to convert a multi-response optimization problem into a single response optimization problem; in which overall utility degree serves as the representative single objective function for optimization. The study of combined utility theory and Taguchi method for predicting optimal setting. Based on Taguchi’s Signal-toNoise ratio (S/N), analysis has been made on the overall utility degree and optimal process environment has been selected finally which corresponds to highest S/N Ratio. Optimal result has been verified through confirmatory test. The case study indicates application feasibility of the aforesaid methodology proposed for multiresponse optimization and off-line control of multiple surface quality characteristics in CNC end milling. Keywords. Multi-objective optimization; utility concept; Taguchi method; CNC end milling. ∗ For

correspondence

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1. Introduction and previous work In recent times, computer numerically controlled (CNC) machine tools have been implemented to realize full automation in machining (Kalpakjian & Stevan 2000; Rao 2001; Bhattacharyya 2006; Groover 2007). CNC machine tools provide greater improvements in productivity, and increase the quality of the machined parts and require less operator input. Out of the various CNC industrial machining processes, milling is one of the vital machining operations. Milling is a common metal removal operation in industry because of its ability to remove material faster with a reasonably good surface quality. It is widely used in a variety of manufacturing industries including aerospace and automotive sectors, where quality is an important factor in the production of slots, pockets, precision moulds and dies. Many researchers have studied the roughness features of the machined surface in end milling process in the past few years. Alauddin et al (1995) established a mathematical model that predicts surface roughness of 190 BHN steel in end milling. The prediction model considered three cutting parameters, viz. depth of cut, spindle speed and feed rate. They used Response Surface Methodology (RSM) to explore the effect of cutting parameters on surface roughness parameter Ra (centre line average roughness). Tsai et al (1999) studied the effect of spindle speed, feed rate and depth of cut on surface roughness in end milling of 6061-T6 aluminum. They used in-process surface roughness recognition and a Neural Network (NN) system to predict the surface roughness. Mansour & Abdalla (2002) developed a mathematical model for surface roughness in terms of cutting speed, feed rate and axial depth of cut. Suresh et al (2002) adopted a twostage approach towards optimization of surface roughness. First, experimental results were used to build mathematical models for surface roughness by RSM. Then, the second order mathematical model was taken as an objective function and was optimized using genetic algorithm (GA) to obtain the machining conditions for a desired surface finish. Oktem et al (2005) developed the mathematical model for Ra in terms of cutting parameters (feed, cutting speed, axial depth of cut, radial depth of cut and machining tolerance). Optimum cutting condition is obtained using GA and the same is verified with experimental measurements. Wang & Chang (2004) developed a mathematical model to analyse the influence of cutting condition (cutting speed, depth of cut, feed) and tool geometry (concavity, axial relief angle) on Ra both in dry and wet cut conditions. Wang et al (2005) studied the influence of cutting parameters (spindle speed, feed rate, depth of cut and tool diameter) on Ra for brass. Ozcelik & Bayramoglu (2006) developed a statistical model for surface roughness in a high speed flat end milling process under wet condition, using machining variables such as spindle speed, feed rate, depth of cut, step over and total machining time for AISI 1040 steel. Ryu et al (2006) investigated the surface texture generated by end milling on SS420J2 steel. Brezocnik et al (2004) proposed a genetic programming to predict Ra considering spindle speed, feed rate, depth of cut and vibration as process parameters on a work piece of 6061 aluminum. (Lou et al 1998; Lou & Chen 1997, 1999) studied the effect of spindle speed, feed rate and depth of cut on surface roughness in end milling process. They used in process surface roughness recognition and neural fuzzy system to predict the work piece surface roughness. Colak et al (2007) predicted surface roughness using evolutionary programming methods. The data for cutting speed, feed and depth of cut of end milling operations are collected for predicting surface roughness and a linear equation is predicted for surface roughness related to experimental study. (Benardos & Vosniakos 2002, 2003) presented a review of different approaches that are used for predicting the surface roughness. A lot of research attention is being given based on Taguchi method, as it is a very efficient optimization tool. Ghani et al (2004) applied Taguchi

Optimization in CNC end milling of UNS C34000 medium leaded brass

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method to optimize the cutting parameters: cutting speed, depth of cut and feed rate in CNC milling machine when machining hardened steel AISI H13 for cutting force and Ra . Good surface finish obtained with high cutting speed, low feed rate and low depth of cut. Taguchi statistical method was used by Yang & Chen (2001) to get optimum milling parameters. Grey relational analysis based on the grey system theory is used for multiple performance characteristics to obtain optimal combinations of the cutting parameters from experimental combinations using orthogonal arrays. Chang & Lu (2007) optimized the cutting parameters combinations on side milling machine using grey relational analysis. Confirmation tests have been conducted with the optimal combination of the cutting parameters and the result shows that the surface quality improves with this approach. Literature depicts that sufficient work has been done for optimizing the process parameters and improving the performance measures of milling process. However, all these studies whether experimental or analytical mostly concentrate on the centre line average roughness Ra value for surface quality. But surface generated by machining is composed of a large number of length scales of superimposed roughness that are generally characterized by three different types of parameters, viz. amplitude parameters, spacing parameters and hybrid parameters (Sahoo 2005). Thus, consideration of centre line average roughness alone is not sufficient to describe surface quality. The other roughness parameters like root mean square roughness (Rq ), kurtosis (Rku ) and mean line peak spacing (Rsm ) need to be addressed. In the present work, multi-objective optimization problem has been addressed to select the best process environment (combination of depth of cut, spindle speed and feed rate) for optimizing multiple surface quality characteristics of UNS C34000 Medium Leaded Brass in CNC end milling. The multiple surface quality characteristics are centre line average roughness (Ra ); root mean square roughness (Rq ); kurtosis (Rku ) and mean line peak spacing (Rsm ) Keeping in mind that traditional Taguchi approach fails to solve a multi-response optimization problem; to overcome this shortcoming utility concept has been coupled with Taguchi method; in the present investigation. Compared to grey relation theory utility concept is simpler without much computational complexity. Moreover, it has been observed that less attempt has been made by previous researchers in application of utility concept. Thus, using utility theory, the multi-objective optimization problem has been converted into an equivalent single objective optimization situation which has been solved by Taguchi method. Detailed methodology of the aforesaid optimization technique has been highlighted in the paper. The study reflects effectiveness of the proposed method in optimizing multiple surface quality features in CNC end milling operation as a case study. 2. Utility concept According to the utility theory (Kumar et al 2000; Walia et al 2006), if Xi is the measure of effectiveness of an attribute (or quality characteristics) i and there are n attributes evaluating the outcome space, then the joint utility function can be expressed as: U (X1 , X2 , . . . , Xn ) = f (U1 (X1 ), U2 (X2 ), . . . , Un (Xn )).

(1)

Here Ui (Xi ) is the utility of the ith attribute. The overall utility function is the sum of individual utilities if the attributes are independent, and is given as follows: U (X1 , X2 , . . . , Xn ) =

n i=1

Ui (Xi ).

(2)

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The attributes may be assigned weights depending upon the relative importance or priorities of the characteristics. The overall utility function after assigning weights to the attributes can be expressed as: U (X1 , X2 , . . . , Xn ) =

n

Wi · Ui (Xi ).

(3)

i=1

Here Wi is the weight assigned to the attribute i. The sum of the weights for all the attributes must be equal to 1. A preference scale for each quality characteristic is constructed for determining its utility value. Two arbitrary numerical values (preference number) 0 and 9 are assigned to the just acceptable and the best value of the quality characteristic respectively. The preference number Pi can be expressed on a logarithmic scale as follows: Xi . (4) Pi = A × log Xi Here Xi is the value of any quality characteristic or attribute i, Xi is just an acceptable value of quality characteristic or attribute iand A is a constant. The value A can be found by the condition that if Xi = X∗ (where X∗ is the optimal or best value), then Pi = 9. Therefore, A=

9 ∗ . log XX

(5)

i

The overall utility can be expressed as follows: U=

n

Wi · Pi .

(6)

i=1

Subject to the condition: n

Wi = 1.

(7)

i=1

Among various quality characteristics types, viz. Lower-the-Better (LB), Higher-the-Better (HB), and Nominal-the-Best (NB) suggested by Taguchi, the utility function would be Higherthe-Better type. Therefore, if the quality function is maximized, the quality characteristics considered for its evaluation will automatically be optimized (maximized or minimized as the case may be). In the proposed approach utility values of individual responses are accumulated to calculate overall utility index. Overall utility index servers as the single objective function for optimization. 3. Taguchi method Taguchi Method was proposed by Genichi Taguchi, a Japanese quality management consultant. The method explores the concept of quadratic quality loss function and uses a statistical measure of performance called signal-to-noise (S/N) ratio, (Antony & Antony 2001).


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It is the ratio of the mean (Signal) to the standard deviation (Noise). The ratio depends on the quality characteristics of the product/process to be optimized (Peace 1993). The optimal setting is the parameter combination, which has the highest S/N ratio. Based on the signal-to-noise (S/N) analysis, the signal-to-noise (S/N) ratio for each level of process parameters are computed. Larger S/N ratio corresponds to better performance characteristics, regardless of their category of performance. It means that the level of process parameters with the highest S/N ratio corresponds to the optimum level of process parameters. Finally, a confirmatory experiment is conducted to verify the optimal processing parameters obtained from the parameter design.

4. Experimentation 4.1 Selection of cutting parameters Surface quality and dimensional accuracy are the two important aspects of a product in any machining operation. Several factors influence the final surface roughness in a CNC milling operation. The theoretical surface roughness is generally dependent on many parameters such as the tool geometry (tool nose radius and flank width, run-out error), tool material, work material, machine-tool rigidity and various cutting conditions including feed rate, depth of cut and cutting speed (Boothroyd & Knight 1989; Alauddin et al 1995). However, factors such as tool wear, chip loads and chip formations, or material properties of both tool and work piece are uncontrollable during actual machining (Huynh & Fan 1992). The presence of chatter or vibration of the machine tool, defects in the surface of work material, wear in the tool or irregularities of chip formation contribute to the surface damage in practice during actual machining operations (Elbestawi & Sagherian 1991; Kline et al 1982). In any experimental study, it is difficult to consider all these factors that affect the surface finish. Available literature reveals that depth of cut, spindle speed and feed rate are the three primary machining parameters and thus these are considered as design factors in the present study. 4.2 Selection of response variables From literature review it is found that, all the studies, whether experimental or analytical, mostly concentrate on the centre line average roughness value for surface quality. But consideration of only centre line average roughness is not sufficient to describe the surface quality of a multi scale rough surface (Sahoo 2005). The present study thus aims at consideration of the following four roughness parameters as the response variables: centre line average roughness (Ra ); root mean square roughness (Rq ); kurtosis (Rku ) and mean line peak spacing (Rsm ). 4.3 Work piece material used The present study was carried out with medium leaded brass UNS C34000. The chemical composition and mechanical properties of the work piece materials are shown in table 1. It is available in material hand book. All the specimens were in the form of 100 mm × 75 mm × 25 mm blocks. 4.4 Cutting tool used Coated carbide tools have been found to perform better than uncoated carbide tools. Thus, commercially available CVD coated carbide tools have been used in this investigation.

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Bharat Chandra Routara et al Table 1. Composition and mechanical properties of work piece materials. Work material

Chemical composition (%Wt)

Mechanical properties

Brass (UNS C34000)

0·095%Fe, 0·9%Pb, 34%Zn and balance Cu

Hardness — 68 HRF, Density — 8·47 g/cc, Tensile strength — 340 MPa

The tools used are flat end mill cutters produced by WIDIA (EM-TiAlN). The tools are coated with TiAlN coating. For each material a new cutter of same specification has been used. The details of the end milling cutters are given below: Cutter diameter, 8 mm; Overall length, 108 mm; Fluted length, 38 mm; Helix angle, 30◦ ; Hardness, 1570 HV; Density, 14·5 g/cc and Transverse rupture strength, 3800 N/mm2 . 4.5 Design of experiment (DOE) The design of experiments technique permits us to carry out the modelling and analysis of the influence of process variables (design factors) on the response variables. In the present study depth of cut (d, mm), spindle speed (N , rpm) and feed rate (f , mm/min) have been selected as design factors while other parameters have been assumed to be constant over the experimental domain. The process variables (design factors) with their values on different levels are listed in table 2. The selection of the values of the variables is limited by the capacity of the machine used in the experimentation as well as the recommended specifications for different work piece and tool material combinations (Oberg et al 2000). Five levels, having nearly equal spacing, within the operating range of the parameters have been selected for each of the factors. In the present investigation, L25 Orthogonal Array (OA) (Peace 1993) design has been considered for experimentation. Interaction effect of process parameters has been assumed negligible. 4.6 Equipments used The machine used for the milling tests is a ‘DYNA V4·5’ CNC end milling machine having the control system SINUMERIK 802 D with a vertical milling head. The compressed coolant servo-cut is used as cutting environment. For generating the milled surfaces, CNC part programs for tool paths have been created with specific commands. Table 2. Process parameters and domain of experiments. Brass Levels

d(mm)

N(rpm)

f(mm/ min)

−1 −0·5 0 +0·5 +1

0·10 0·15 0·20 0·25 0·30

1500 1800 2100 2400 2700

550 600 650 700 750


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Table 3. Experimental results along with design matrix. L25 OA Sl. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Measured roughness parameters

d

N

f

Ra µm

Rq µm

Rku

Rsm mm

−1·0 −1·0 −1·0 −1·0 −1·0 −0·5 −0·5 −0·5 −0·5 −0·5 0·0 0·0 0·0 0·0 0·0 0·5 0·5 0·5 0·5 0·5 1·0 1·0 1·0 1·0 1·0

−1·0 −0·5 0·0 0·5 1·0 −1·0 −0·5 0·0 0·5 1·0 −1·0 −0·5 0·0 0·5 1·0 −1·0 −0·5 0·0 0·5 1·0 −1·0 −0·5 0·0 0·5 1·0

−1·0 −0·5 0·0 0·5 1·0 −0·5 0·0 0·5 1·0 −1·0 0·0 0·5 1·0 −1·0 −0·5 0·5 1·0 −1·0 −0·5 0·0 1·0 −1·0 −0·5 0·0 0·5

1·427 1·257 1·237 1·102 1·185 1·862 1·244 1·167 1·282 1·007 1·210 1·350 1·005 0·837 0·881 1·267 1·125 0·758 0·799 0·985 1·182 0·903 0·761 0·745 0·766

1·650 1·467 1·510 1·332 1·447 2·252 1·477 1·372 1·552 1·220 1·440 1·590 1·252 1·040 1·112 1·542 1·420 0·934 0·987 1·137 1·512 1·104 0·958 0·905 0·942

2·07 2·0 2·47 2·37 2·25 2·88 2·25 2·10 2·20 2·57 2·45 2·33 2·86 2·85 3·35 2·58 2·95 2·60 2·61 2·04 3·14 2·58 3·01 2·48 2·86

0·212 0·212 0·157 0·171 0·182 0·191 0·171 0·175 0·182 0·133 0·199 0·235 0·140 0·138 0·142 0·198 0·136 0·123 0·156 0·152 0·226 0·159 0·145 0·167 0·140

The surface roughness parameters have been measured using the stylus-type profilometer, Talysurf (Taylor Hobson, Surtronic 3+). The measured roughness parameters along with design matrix have been shown in table 3. 5. Data analysis Experimental data regarding features of bead geometry corresponding to L25 Orthogonal Array (OA) design of experiment (table 3) have been explored to calculate utility values of individual quality attributes by using equations (4–5). For all surface roughness parameters a Lower-the-Better (LB) criterion has been used. For all surface roughness parameters, the maximum of entries of table 3 has been considered as just acceptable value; whereas minimum observed value has been treated as the best (desired) value. This is because all surface roughness characteristics follow Lower-the-Better (LB) criteria. The objective is to improve surface finish; which means all types of roughness values should be as lower as possible. Individual utility measures of the responses have been furnished in table 4. The overall utility index has been computed using equation (6); tabulated in table 4 with their corresponding (Signal-to-Noise) S/N ratio. In this computation it has been assumed that all quality features are equally important (same priority weightage). The justification of this assumption is as follows:

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Bharat Chandra Routara et al Table 4. Utility value of individual responses. Measured roughness parameters Sl. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Ra

Rq

Rku

Rsm

Overall utility degree

2·6142 3·8605 4·0181 5·1535 4·4400 0·0000 3·9626 4·5904 3·6670 6·0392 4·2349 3·1592 6·0588 7·8560 7·3526 3·7827 4·9505 8·8300 8·3125 6·2563 4·4649 7·1103 8·7912 9·0000 8·7269

3·0707 4·2313 3·9461 5·1843 4·3668 0·0000 4·1642 4·8922 3·6752 6·0514 4·4147 3·4364 5·7958 7·6273 6·9665 3·7390 4·5527 8·6886 8·1437 6·7470 3·9330 7·0378 8·4381 9·0000 8·6044

8·3998 9·0000 5·3172 6·0383 6·9449 2·6376 6·9449 8·1487 7·3370 4·6247 5·4591 6·3353 2·7592 2·8203 0·0000 4·5570 2·2186 4·4222 4·3552 8·6545 1·1296 4·5570 1·8673 5·2467 5·3111

1·4319 1·4319 5·6071 4·4197 3·5530 2·8820 4·4197 4·0982 3·5530 7·9134 2·3116 0·0000 7·2003 7·4003 7·0031 2·3816 7·6033 9·0000 5·6960 6·0571 0·5429 5·4311 6·7125 4·7487 0·7135

3·8792 4·6309 4·7221 5·1990 4·8262 1·3799 4·8728 5·4324 4·5580 6·1572 4·1051 3·2327 5·4535 6·4260 5·3305 3·6151 4·8313 7·7352 6·6269 6·9287 2·5176 6·0341 6·4523 6·9989 5·8390

Corresponding S/N ratio 11·7748 13·3133 13·4827 14·3184 13·6721 2·7970 13·7556 14·6998 13·1755 15·7877 12·2665 10·1913 14·7335 16·1588 14·5354 11·1624 13·6813 17·7694 16·4262 16·8130 8·0197 15·6123 16·1943 16·9006 15·3268

The common trend in solution of a multi-objective optimization problem is to convert initially these multi-objectives into an equivalent single objective function (overall utility degree in the present case). While deriving this equivalent objective function, different priority weightage are assigned to different responses, according to their relative importance. But, there is no specific guideline available for assigning these response weightage. It entirely depends on the decision maker (individual’s perception or human judgment). That’s why present study assumes equal priority weightage to all the responses. Figure 1 reflect S/N ratio plot for overall utility index. The overall utility index is then optimized (maximized) using Taguchi method. Taguchi’s HB (Higher-the-Better) criterion has been explored to maximize the overall utility index (8). t 1 1 SN (Higher-the-Better) = −10 log . (8) t i=1 yi2 Here t is the number of measurements, and yi the measured ith characteristic value i.e. ith quality indicator. Optimal parameter setting has been evaluated from figure 1. The optimal setting should confirm highest utility index (HB criterion). The predicted optimal setting becomes d0·5 N0·5 f−1 . (superscript represents optimal level of corresponding factors). After evaluating the optimal parameter settings, the next step is to predict and verify the optimal result using the confirmatory test. It has been found that predicted S/N ratio


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Figure 1. Evaluation of optimal setting.

(of overall utility degree) at optimal setting is 18·5815 (highest of entries in table 4) where as in experiment it comes to 21·7531 showing improved quality. That means, after Taguchi analysis once optimal setting is predicted; Taguchi method can provide predicted value of S/N ratio of the objective function at optimal setting. On the other hand, experiment has to be performed at the predicted optimal setting. Experimentally obtained responses are to be aggregated to compute overall utility degree and corresponding S/N ratio. A comparison has to be made between two. Experimentally obtained S/N ratio should be equal or more than that of prediction. Because S/N ratio has always to be maximized which means minimum quality loss (in the present case). 6. Conclusion All studies reported in literature mostly concentrated on the centre line average roughness Ra value for surface quality. It is felt that consideration of centre line average roughness alone is not sufficient to describe surface quality. The other roughness parameters like root mean square roughness (Rq ), kurtosis (Rku ) and mean line peak spacing (Rsm ) should be taken care off and to be included in the analysis. The present study considers aforesaid multiple surface roughness characteristics for simultaneous optimization (minimization) of multiple surface roughness characteristics within experimental domain. The following conclusions may be drawn from the results of the experiments and analysis of the experimental data in connection with multi-response optimization in CNC end milling operation. (i) Utility based Taguchi method has been found fruitful for evaluating the optimum parameter setting. (ii) This approach is efficient enough to solve a multi-response optimization problem. (iii) Confirmatory test has validated the parametric setting determined by utility based Taguchi method. (iv) The said approach can be recommended for continuous quality improvement and off-line quality control of a process/product.

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