Journal of Cleaner Production 152 (2017) 474e496
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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
Multi-objective robust optimization of the sustainable helical milling process of the aluminum alloy Al 7075 using the augmentedenhanced normalized normal constraint method Robson Bruno Dutra Pereira a, *, Rodrigo Reis Leite b, Aline Cunha Alvim b, ~o Roberto Ferreira b, J. Paulo Davim c Anderson Paulo de Paiva b, Joa a b c
~o Joa ~o Del-Rei, 170 Frei Orlando Square, Sa ~o Joa ~o del Rei, MG, 36880-000, Brazil Department of Mechanical Engineering, Federal University of Sa , 1303 BPS Avenue, Itajuba , MG, 37500-903, Brazil Institute of Industrial Engineering and Management, Federal University of Itajuba Department of Mechanical Engineering, University of Aveiro, Campus Santiago, 3810-193, Aveiro, Portugal
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 October 2016 Received in revised form 17 March 2017 Accepted 18 March 2017 Available online 21 March 2017
Helical milling is an eco-friendly hole-making process considering energy economy, tool inventory reduction, tool life cycle increase, set-up and non-productive times reduction due to tools changes and better borehole quality. In order to achieve the best results in terms of the sustainable manufacturing aspects energy, quality, and productivity, the present paper proposes to optimize the multi-objective helical milling process of the aluminum alloy Al 7075. With consideration to sustainable objectives, the axial cutting force component, related to energy consumption, the total roundness, related to borehole geometrical quality, and the material removal rate, related to productivity, were taken into account. The process factors axial and tangential feed per tooth and cutting velocity were selected, besides the noise factor tool overhang length, allowing to optimize bias and variance of cutting force and roundness together with the deterministic response material removal rate. In order to achieve a complete exploitation of the Pareto frontier, the new multi-objective optimization method augmentedenhanced normalized normal constraint method was proposed. It was obtained a set of Pareto optimal solutions for the mean square error of the axial cutting force, mean square error of the total roundness, and material removal rate, achieving the trade-off among energy, quality, and productivity. Therefore, different optimization scenarios were obtained, allowing to the experimenter the possibility of choice, guaranteeing a sustainable hole-making process. Furthermore, besides allowing the possibility of choosing different solutions, the TOPSIS decision-making approach was performed so that the best compromise solution was found among the Pareto optimal solutions. The helical milling of the aluminum alloy Al 7075 is presented as a green machining process. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Helical milling Sustainable manufacturing Multi-objective robust optimization Mean square error Augmented-enhanced normalized normal constraint
1. Introduction Sustainable manufacturing accounts environmental, social, and economic aspects, and also the conscious use of natural resources (Mathew and Vijayaraghavan, 2016). In the scope of machining, the research on alternative processes have been important to enhance process performance and reduce damage to the environment (Pusavec et al., 2015). The conventional drilling is one of the most
* Corresponding author. E-mail address:
[email protected] (R.B.D. Pereira). http://dx.doi.org/10.1016/j.jclepro.2017.03.121 0959-6526/© 2017 Elsevier Ltd. All rights reserved.
€ nshoff et al., 1994) and the important hole-making processes (To most performed machining operation for the assembling process (Rey et al., 2016). However, this process has some drawbacks. The cutting velocity in the vicinity of the tool center point is close to zero, leading to an increase of the thrust force due to the fact that the material removal in this region is similar to an extrusion process (Iyer et al., 2007). Others disadvantages are the difficulty of the heat dissipation and chip evacuation, high cutting efforts, and poor surface quality due to friction among tool, chip, and workpiece (Olvera et al., 2012). This process may affect the machining properties of the workpiece, generate burrs on the exit of the holes and poor borehole surface roughness (Besseris and Kremmydas, 2014). As these inconveniences may lead to losses and damage to the environment, it is necessary to apply a more sustainable
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Abbreviations AENNC ANNC CCD DoE ENNC GRG MOP MQL MRR MSE NBI NNC NSGA OLS RPD RSM TOPSIS WLS WS
Augmented-enhanced normalized normal constraint Augmented normalized normal constraint Central composed design Design of experiments Enhanced normalized normal constraint Generalized reduced gradient Multi-objective optimization problem Minimum quantity lubrication Material removal rate Mean square error Normal boundary intersection Normalized normal constraint Non-dominated sorting genetic algorithm Ordinal least squares Robust parameter design Response surface methodology Technique for order preference by similarity to ideal solution Weighted least squares Weighted sum
Nomenclatures Helical milling responses Fz Axial cutting force component [N] MRR Material removal rate [mm3/min] Ront Total roundness [mm] Helical milling variables ae Radial cutting depth [mm] a*p Maximum axial cutting depth per helical rotation [mm] DB Borehole diameter [mm] Dh Helical path diameter [mm] Dt Tool diameter [mm] e Eccentricity fza Axial feed per tooth [mm/tooth] fzt Tangential feed velocity [mm/min] G Ratio between peripheral and frontal cuts lto Tool overhang length [mm] n Number of revolutions per minute of the spindle [rev/min] vc Cutting velocity [m/min] vf Feed velocity of the tool center point [mm/min] vft Tangential feed per tooth [mm/tooth] vfha Axial feed velocity of the helix [mm/min] vfht Tangential feed velocity of the helix [mm/min] z Number of tool teeth a Helix angle [ ] Others variables Di Divergence degree of the i-th objective function Mean equation Ez(y), b y TOPSIS index Edj U EdPN Euclidean distance of a normalized weighted response j , Edj value in relation to the pseudo nadir and utopia points, respectively fi i-th objective function f*i , fi(x*i ) Individual minima of the i-th objective function Normalized objective function vector f fi fPN i fN fPN fU *
fr f*za, f*zt, v*c mr MSE[Fz]
i-th normalized objective function Maximum value of the i-th objective function Nadir point Pseudo nadir point Utopia point Normalized anchor point Optimal value of fza, fzt and vc, respectively Number of solution points Mean square error equation of Fz
MSE[Ront] MSE[F*z] MSE[Ron*t ] MRR* nsub Nr p Qij, Q ij R2 R2adj R2pred T T Vz(y), b s2 wij wlij wuij x xi* x*MSE[Fz] x*MSE[Ront] x*MRR z
gij gPN ij gijU gPN gU D dr xi r ui tsol U
475
Mean square error equation of Ront Optimal value of MSE[Fz] Optimal value of MSE[Ront] Optimal value of MRR Number of MOP sub-problems Utopia line vector Number of objective functions Hyperplane points and normalized hyperplane points Coefficient of determination Adjusted coefficient of determination Coefficient of determination for prediction T matrix Target value for the mean equation Variance equation Weight of the i-th objective function Lower limit for the weight of the i-th objective function Upper limit for the weight of the i-th objective function Vector of control factors Optimal decision vector Optimal decision vector of MSE[Fz] Optimal decision vector of MSE[Ront] Optimal decision vector of MRR Vector of noise factors Normalized weighted response value Pseudo nadir of the normalized weighted response value Utopia of the normalized weighted response value Negative ideal solution Positive ideal solution Uniform spacing Normalized increment Shannon's entropy of the i-th objective function Experimental radius Weight considering Di TOPSIS global solution Experimental space
manufacturing process, guaranteeing a cleaner hole-making process. The helical milling process is a hole-making process which allows to obtain boreholes with varied diameters with the same tool due to the helical trajectory of the tool (Denkena et al., 2008). This process has some other advantages regarding to conventional drilling such as low cutting forces, good chip evacuation, reduction of burr formation, greater dimensional and geometrical quality and, additionally, improved surface finish (Denkena et al., 2008). Besides better borehole quality, the helical milling is an eco-friendly process with consideration to energy economy, tool inventory reduction, tool life cycle increase, set-up and non-productive time reduction due to tool change. These aspects make the helical milling process a sustainable alternative to the conventional drilling process. The helical milling comprises deterministic responses that could be modeled through mechanistic or statistical techniques. One of the advantages of statistical approaches is the possibility of contemplation of noise factors to achieve process robustness. Robust parameter design includes a set of engineering practices and tools that can integrate sustainability considerations throughout the product development processes (Gremyr et al., 2014). In the helical milling quality improvement itinerary, it is important to apply the robust modelling and optimization, aiming to attain better quality and to reduce variability and consequent wastes. In order to achieve quality, productivity, and sustainable manufacturing, non-trivial techniques have been applied (Martins et al., 2016). Several dissimilar and contradictory objectives must be simultaneously optimized to achieve better results in terms of quality, productivity and energy consumption in machining (Yan and Li, 2013). In the case of the helical milling, the current
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literature has not assessed the multi-objective optimization of responses related to energy, quality and productivity, achieving different optimization scenarios considering these sustainable responses for this green hole-making process. The present work aims to optimize the multi-objective helical milling process of the aluminum alloy Al 7075. Experimental results were achieved through a central composite design using a combined array, taking into account process and noise parameters. Then, the axial cutting force component (Fz), related to energy consumption, and the total roundness (Ront), related to geometrical quality, were modeled through robust parameter design to optimize bias and variance of these responses. The deterministic response material removal rate (MRR) was also considered to improve the productivity. As in sustainable manufacturing some environmental and economic aspects should be considered, to take into account responses related to energy, quality and productivity of the green hole-making process helical milling cooperates to a cleaner borehole production. To obtain a set of Pareto optimal solutions, achieving sustainable scenarios for hole-making with helical milling, the new approach augmented-enhanced normalized normal constraint method (AENNC) was proposed, guaranteeing the complete assessment of the Pareto frontier. Then, the trade-off among these objectives was achieved, allowing the experimenter to choose the appropriate Pareto set for guaranteeing a cleaner hole-making process. From the decision maker's view point, a decision-making approach is needed after applying a multi-objective optimization method so that a unique solution can be selected. In this sense, the technique for order of preference by similarity to ideal solution (TOPSIS) was applied in order to find the most desired solution among the Pareto optimal solutions. The novelty of this study, with consideration to the experimental aspects, is the introduction of the helical milling process as a sustainable machining process, allowing to obtain boreholes with a more efficient technique, besides taking into consideration responses related to green aspects of this process. The new AENNC multi-objective optimization method is presented in order to provide the best results for different process responses, allowing obtaining a complete exploitation of the Pareto frontier for cases where p 3 objective functions, enabling the decision maker to choose different practical scenarios, according to his/her goals. Two of the three responses were modelled through RPD allowing the achievement of robustness with regard to the tool overhang length variation and a sustainable hole-making process. The challenges of the present work are related to the achievement of different optimization scenarios and a complete exploitation of the Pareto frontier, besides the compromise in presenting a sustainable holemaking process and the attainment of the best results in terms of energy, quality and productivity responses. The proposed approach was effective to overcome these challenges. This study is in the scope of sustainable manufacturing due to three main aspects: (i) the helical milling process of the aluminum alloy Al 7075, which is a green machining process for hole-making, is studied experimentally; (ii) RPD is used to achieve helical milling robustness to the tool overhang length variation, decreasing the sensibility of the responses with consideration to this uncontrollable factor, process variability and consequent losses; and (iii) the application of the new multi-objective optimization method AENNC considering three responses related to sustainable aspects, i.e., energy, quality and productivity. The obtained Pareto optimal results through AENNC constitute sustainable scenarios for the helical milling process.
different movements: a rotational movement around its own axis; the tool orbits around the borehole axis; and the tool feed along the axial direction. These two last movements generate the helical course of the tool (Li et al., 2014b). The movement around the borehole axis (tangential feed) makes the peripheral-cutting edge generate a discontinuous cut, and the axial feed makes the endcutting edges generate a continuous cut at the same time. The cutting process of the helical milling is divided into peripheral and frontal (axial) cut (Li et al., 2014b). Unlike conventional drilling, in which the borehole diameter (DB) is determined by the tool diameter (Dt), in the helical milling the borehole diameter is determined by the tool diameter and the helical path diameter (Dh) (Denkena et al., 2008). This kinematics, illustrated in Fig. 1, allows for the attainment of boreholes with different diameters using one tool by changing the helical diameter (Qin et al., 2012). The helical milling flexible kinematics supports the attainment of different borehole diameters with only one tool, reducing tool inventory. This soft tool path decreases cutting force levels in the axial direction, fomenting energy economy, besides improving dimensional, geometrical, and microgeometrical quality. According to Denkena et al. (2008), to apply the helical milling process, it is necessary to define the feed velocity of the tool center point (vf) in [mm/min], and the maximum axial cutting depth (a*p) in [mm]. The feed velocity (vf) can be decomposed into two components, the axial feed velocity of the helix (vfha) in [mm/min] and the tangential feed velocity of the helix (vfht) in [mm/min], as in Eq. (1). The axial feed velocity (vfha) is determined through Eq. (2), considering the axial feed per tooth (fza) in [mm/tooth], while the tangential feed velocity of the helix (vfht), related to helical path diameter (Dh), is calculated considering the tangential feed velocity (vft), related to the borehole diameter (DB), according to Eq. (3). Finally, vft is obtained through Eq. (4), considering the tangential feed per tooth (fzt) in [mm/tooth]. In these calculations, z is the number of teeth of the tool, and n in [rev/min] is the number of revolutions per minute of the spindle, which defines the cutting velocity (vc) in [m/min] with consideration to the tool diameter.
1.1. Helical milling kinematics In the helical milling process, the cutting tool performs three
Fig. 1. Helical milling kinematics.
R.B.D. Pereira et al. / Journal of Cleaner Production 152 (2017) 474e496
vf ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v2fha þ v2fht
(1)
vfha ¼ fza $z$n
(2)
vfht ¼ vft $ðDh =DB Þ
(3)
vft ¼ fzt $z$n
(4)
The helix angle (a) in [ ] is calculated according to Eq. (5) while the maximum a*p is obtained through Eq. (6), both related to the components of the helical feed milling velocity.
.
a ¼ arctan vfha vfht
a*p ¼ tanðaÞ$p$Dh
(5) (6)
Since the helical milling process can be separated into two movements, peripheral cut and frontal cut, the ratio (G) between these two movements can be calculated to express the efficiency of the process. This ratio is dependent only on the borehole and tool diameters as G ¼ ðD2B D2t Þ=D2t , and the greater this ratio is, greater is the volume removed by peripheral cut with regard to the volume removed by frontal cut, which is similar to drilling (Brinksmeier et al., 2008). The correct adjustment of the tool diameter in relation to the desired borehole diameter may minimize the problems related to frontal cut. Once the green manufacturing processes are able to lessen the adverse impacts of technology in the environment (Mathew and Vijayaraghavan, 2016), the helical milling, considering its movements and advantages in respect to drilling, is a sustainable manufacturing process.
1.2. Helical milling responses and green aspects Machining forces are related to many factors such as tool wear (Bhattacharyya et al., 2010) and power (Pusavec et al., 2015), and also energy consumption, which has been considered as an attribute of performance for sustainable manufacturing (Franco et al., 2016). Considering helical milling process, the axial machining force component (Fz) in [N], with similar levels of fza and fzt, is the most important cutting force component in amplitude, as recently demonstrated in some researches (Wang et al., 2011). Prediction and optimization of cutting forces is a great way to increase the productivity inherent to the helical milling process (Liu et al., 2012), besides preventing machining damage (Wang et al., 2011). Predicting cutting forces in helical milling has been an important subject studied by many researchers for calculating cutting power, obtaining tight tolerances and low levels of tool wear (Ventura and Hassui, 2013). The modelling of cutting force components in helical milling can be performed by analytical or statistical approaches. The advantage of the statistical approach is that the models may include process and noise factors that are difficult to understand and model mechanically, allowing the attainment of robust decisions on the potential for improving process efficiency and energy savings (Hana et al., 2012). Wang et al. (2011) developed an analytical cutting force model to evaluate the characteristics of discontinuous milling on the titanium alloy (Tie6Ale4V). The authors concluded that the analytical model is an efficient tool to predict force changes with different cutting parameters; the model provides information that will help avoiding tool wear and damage, preserving the workpiece surface quality. The obtained models presented 10% error due to noise
477
interference. The error due to noise could be considered experimentally by using robust parameter design, preventing the process of these interferences. Geometric shape has been considered as a quality index of manufacturing process (Vazquez et al., 2015). Total roundness (Ront) in [mm] is used as an indicator to measure the geometrical accuracy of the boreholes (Li et al., 2014a) or of cylindrical parts. Ront may also be modelled through statistical methods. Sasahara et al. (2008) studied the roundness profile of the helical milling process in the aluminum alloy Al 7075. First, they compared the helical milling with two tool paths, the first for roughing and the second one for finishing the borehole, with the helical milling in just one operation. The results showed that the first strategy obtained better roundness levels. Next, they compared the roundness of the helical milling process with the roundness of drilling process, and the first process obtained better results. The authors also assessed the borehole geometrical quality considering different lubrication strategies, concluding that the minimum quantity lubrication (MQL) technique decreases the shape error. However, they did not provide the obtained values of the roundness and the helical milling parameters effects on roundness were not evaluated. The material removal rate (MRR) in [mm3/min] is a productivity response evaluated through a deterministic model. It has been considered in experimental studies together with other machining responses such as energy consumption (Zhong et al., 2016), surface roughness, flank wear, and cutting forces (Jozi and Celent, 2015), surface roughness, and cutting energy (Yan and Li, 2013). MRR can be studied with other probabilistic response functions as a criterion in the multi-objective optimization of machining processes (Yan and Li, 2013). In the helical milling process, MRR can be evaluated through Eq. (7). Considering the helical milling kinematics, basic arithmetical manipulations can be applied to express MRR in function of the specific cutting parameters fza, fzt and vc of the helical milling, as expressed in Eq. (8). The MRR explained derivation is demonstrated in Appendix A, with the radial cutting depth (ae) [mm] in helical milling in Eq. (A.2).
MRR ¼ a*p $ae $vf sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D3B fza D 2 $vc $ $ f 2za þ fzt $ h MRR ¼ 250$z$ Dh $Dt fft DB
(7)
(8)
2. Robust parameter design and mean square error Robust Parameter Design (RPD) was first advocated by Taguchi and it comprises mathematical and statistical techniques that aim to choose the levels of controllable factors of the process that make it less sensitive to variations transmitted by noise factors, thus making the process more robust to noise factors (Al-Ghamdi, 2013). RPD is a technique which can be used to promote the sustainable product development (Gremyr et al., 2014). There are two types of structures available to use RPD: crossed arrays and combined arrays. On crossed arrays, the interactions between controllable and noise factors are not taken into account. Combined arrays require a lower number of runs compared to crossed arrays (Montgomery, 2013). Response surface methodology (RSM) may be used together with Taguchi's philosophy as an approach to RPD in order to make designs and analysis more effective. Such methodology consists of techniques capable of generating models that accurately represent the region of the optimum of a searched response (Myers et al., 2016). To find this region, one of the designs that may be used is
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the central composed design (CCD) based on a combined array. Such design accurately provides the searched region. RPD-RSM and other design of experiments (DoE) based techniques can be employed for ‘designing for the environment’, making it possible to obtain process and product conditions less sensitive to noise variations, with high-quality and lower production costs (Fratila and Caizar, 2011). In accordance with Paiva et al. (2014), the RPD-RSM approach considers noise and control factors. In this way, it can achieve a response surface model that takes into account interactions between controllable and noise factors through ordinary least squares (OLS) or weighted least squares (WLS), leading to mean equation Ez(y) and variance equation Vz(y) for a unique response. This model is generically represented in Eq. (9), where x ¼ ðxi1 ; xi2 ; …; xip ÞT is the vector of control factors, and z ¼ ðzj1 ; zj2 ; …; zjp ÞT is the vector of noise factors. k and r are the number of control and noise factors, respectively, i ¼ 1, 2, …, k and j ¼ 1, 2, …, r.
yðx; zÞ ¼ b0 þ
k X
b i xi þ
i¼1
þ
k X r X
k X
bii x2i þ
i¼1
XX
bij xi xj þ
i
