Optimization of cutting parameters considering tool wear conditions in low-carbon manufacturing environment

Journal of Cleaner Production 226 (2019) 706e719

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Optimization of cutting parameters considering tool wear conditions in low-carbon manufacturing environment Changle Tian a, Guanghui Zhou a, b, *, Junjie Zhang a, Chao Zhang a a b

School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710054, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 July 2018 Received in revised form 13 March 2019 Accepted 10 April 2019 Available online 11 April 2019

Carbon emissions have drawn widely attention due to the worsening climate changes. In a machining process, a reasonable selection of cutting parameters can not only save the production cost and time, but also reduce the production carbon emissions. In addition, the wear conditions of different cutting tools also have great influence on cutting parameters selection as they could cause huge difference on carbon emissions. However, in traditional optimization methods of cutting parameters, the tool wear conditions are always ignored. Thus, in order to overcome this limitation, an optimization method of cutting parameters considering the tool wear conditions is developed. Firstly, the quantified relationships among cutting parameters, tool wear and production indexes (production carbon emissions, cost and time) are analysed. Then, a multi-objective cutting parameters optimization model is established based on the above production indexes to determine the optimal cutting parameters and tools. Thirdly, a modified NSGA-II algorithm is used to resolve the proposed model. Finally, a case study is designed to demonstrate the advantages and feasibility of the proposed approach. The results show that (i) the optimal cutting parameters change with the tool wear conditions; (ii) For the same type of cutting tools with different wear conditions, the optimal values of production carbon emissions, cost and time increase along with the raise of the tool wear conditions; (iii) For different available cutting tools with different tool wear conditions, it is necessary to apply a multi-objective optimization method to decide the optimal production carbon emissions, cost and time. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Low-carbon manufacturing Cutting parameters optimization Tool wear condition NSGA-II algorithm Game theory

1. Introduction Nowadays, the environmental concerns, especially the worsening climate changes resulted from the extensive and high carbon emissions, have drawn widely attention. According to the report of the international energy agency (IEA, 2008), manufacturing industry accounts for nearly one-third of the energy consumption and 36 percent of carbon emissions. In order to respond to the environmental deterioration as well as climate changes, a diversity of policies about carbon emissions like carbon tax (Carl and Fedor, 2016) and carbon labelling (Liu et al., 2017) are gradually performed in machining processes. It will undoubtedly impose an extra

* Corresponding author. School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China. E-mail addresses: [email protected] (C. Tian), [email protected]. edu.cn (G. Zhou), [email protected] (J. Zhang), [email protected] (C. Zhang). https://doi.org/10.1016/j.jclepro.2019.04.113 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

economic burden on the manufacturing enterprises. Facing these critical challenges from economy and environment, it is of great importance for manufacturing industry to develop low carbon manufacturing without compromising the production cost and efficiency. In the manufacturing processes, 99% of the environmental impacts are caused by the energy consumption of CNC machine tools (Zhong et al., 2017). However, the carbon emissions modelling mechanisms from energy consumption are very complex (Li et al., 2015a), which is related to the cutting parameters, cutting tools, and so on. It is estimated that through optimizing cutting parameters, carbon emissions could decrease 6e40% (Newman et al., 2012) due to their strong mapping relations (Zhong et al., 2017). Therefore, cutting parameters optimization plays a great role in reducing the carbon emissions in the manufacturing processes. In addition, it has been proved that carbon emissions could suffer about a 44% increase when using a cutting tool with wear conditions, and the cutting parameters could also have a huge difference with various tool wear conditions (Zhou et al., 2018a). Nevertheless,

C. Tian et al. / Journal of Cleaner Production 226 (2019) 706e719

707

Nomenclature

vr, at

Carbon emissions related parameters CE, CEmaterial, CEelec, CEwaste, CEptool, CEpcf, CEwasteptool, CEwastepcf, CEc, CEs, CEr Total carbon emissions, material carbon emissions, energy carbon emissions, waste carbon emissions, carbon emissions produced during tool production, carbon emissions generated in cutting fluid production, the carbon emissions generated during spindle acceleration period, the carbon emissions produced in cutting process, and the carbon emissions generated in the period of fast feed and tool retracting respectively (kg) EFptool, EFpcf, EFwasteptool, EFwastepcf, EFelec The carbon emission factor for the production of cutting tool, the carbon emission factor for the production of cutting fluid, the carbon emission factor for the disposal of cutting tool, the carbon emission factor for the disposal of cutting fluid, and the carbon emission factor for electricity production respectively

Cutting fluid related parameters T0 The replacement cycle of cutting fluid (month) Ma The additional volume of cutting fluid during the life cycle (L) M0 The initial volume in the cutting fluid tank (L) Pd The power of feed drive system(W) Pn The power of spindle rotational(W) P im The material removal power including load loss power(W) Po The basic power(W) vf Feed speed(mm/min) n Spindle rotational speed(r/min) C1, C2, C3, A1, A2, A3, B1, B2, B3, W1, W2, W3, K, v1, w1, x1, y1, z1 Coefficients which need to be investigated by experiments v, f, ap, ae The cutting speed(m/min), feed rate(mm/r), cutting depth(mm), and cutting width(mm) respectively

Cutting tool related parameters Mi The tool mass f tool i (g) T itool The tool life of tool i Ri The sharping times of cutting tool i CT, s, p, q, r, x, y, z, w Related coefficients VBi The flank wear length about tool i (mm) kr ðiÞ The primary side angle in cutting tool i 0 kr ðiÞ The secondary side angle in cutting tool i rε (i) The radius of the tool tip in cutting tool i Production PT tcutting au,tp,tr

t icutting m

U l t ir

time related parameters Production time (s) The cutting time (s) Spindle acceleration and spindle accelerating time and the fast feed as well as tool retracting time respectively One-pass cutting time in each tool path i (s) total passes time The allowance for machining (mm) The feeding distance (mm) One-pass retracting time in each tool path i (s)

the concerned tool wear conditions are seldom considered in current cutting parameters optimization approaches. Thus, it is necessary to introduce the tool wear conditions into the cutting parameters optimization processes to accord with the practical machining conditions and globally reduce the carbon emissions. To realize the above goal, this paper attempts to propose a quantitative multi-objective cutting parameters optimization method, where the cutting tools with different wear conditions are

The steady feed speed and the feed acceleration respectively

Production D PC PCtool PCfluid PCe C1 C itool C2 C3

cost related parameters Hole diameter (mm) Production cost (CNY) Tool cost (CNY) Cutting fluid cost (CNY) Electricity cost (CNY) Manage and manpower cost coefficient (CNY/min) The tool cost (CNY) The cost of cutting fluid per unit volume The cost of electricity (CNY/(KW  h))

Constraints related parameters vmin, vmax The minimum and maximum cutting speed respectively apmin, apmax The minimum and maximum cutting depth respectively fmin, fmax The minimum and maximum feed rate respectively Pmax, Fcmax The maximum power of the machine tool and cutting force allowed respectively l The power effective coefficient Fc The cutting force (N) T min The required minimum tool life tool Ra, Ra0 The prediction value of the surface roughness and the requirement of the surface roughness respectively Algorithm fi S sij S|sij U

related parameters Equilibrium state function An individual in NSGA-II A strategy j of player i A new individual where only the strategy of player i updates by sij The payoff function

regarded as an additional decision variable to obtain the optimal production carbon emissions, cost and time. Firstly, the quantified relationships among cutting parameters, tool wear conditions and production indexes (production carbon emissions, cost and time) are analysed. Then a multi-objective cutting parameters optimization model is established, which is based on the production carbon emissions, cost and time. Thirdly, a modified NSGA-II algorithm is used to resolve the proposed model. Finally, a case is

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provide references to researchers. However, although the tool wear conditions are one of important factors affecting the carbon emissions, the afore-mentioned cutting parameters optimization papers considering tool wear conditions (Shi et al., 2018; Xie et al., 2018; Shoba et al., 2018) are mainly based on the energy consumption and without concerning the carbon emissions. With the lowcarbon manufacturing and carbon policies are becoming more and more attractive, the accurate data of the carbon emissions and globally reducing carbon emissions are very essential to reduce cost and improve competitiveness of products. In the actual manufacturing processes, the cutting tools will inevitably wear. The research on reducing carbon emissions from cutting parameters optimization considering tool wear conditions can not only globally reducing carbon emissions and provide more accurate carbon emission data, but also is more coincident with the actual manufacturing environment. Therefore, it is necessary to analyse the relationships between the carbon emissions and the tool wear conditions. In this paper, the tool wear conditions are introduced as an additional variable to explore the optimal cutting parameters with the objective of carbon emissions.

studied to demonstrate the advantages and feasibility of the proposed approach. The rest of this paper is organized as follows. Related literature are reviewed in Section 2. The detailed description of the multiobjective cutting parameters optimization model considering tool wear conditions is reported in Section 3. The solving algorithm is introduced in Section 4. Section 5 verifies the proposed method by studying the demonstrative case. Finally, the conclusions are drawn and the future work is discussed in Section 6. 2. Literature review In this part, a series of relative researches on cutting parameters optimization related models and solving approaches are summarized to get a deeper understanding of the former achievements. The researches can be divided into two major directions: cutting parameters optimization models and cutting parameters optimization algorithms. 2.1. Cutting parameters optimization models The selection of cutting parameters has an impact on energy consumption and carbon emissions. Many researches related to low energy or low carbon cutting parameters optimization have been actively conducted (Kant and Sangwan, 2014; Li et al., 2016; Zhou et al., 2017; Shi et al., 2018). Some papers focus on the cutting parameters optimization by an experimental design in a given tool (Bilga et al., 2016; Camposeco-Negrete et al., 2016). Apart from the experimental design, some efforts began to move towards establishing the low carbon/energy-oriented cutting parameters optimization models. Much work concentrates on the cutting parameters optimization considering the environment impact from a machining operation in a given tool (Liu et al., 2016; Zhang et al., 2017). Similar to the first one, a great number of papers conducted the cutting parameters optimization models for carbon emissions and energy saving during the multi-pass cutting process (Kant and Sangwan, 2014; Lin et al., 2017; Li et al., 2017). Meanwhile, in order to meet the actual requirements of machining processes, some other factors such as cutting tool selection (Zhou et al., 2017), process routes selection (Li et al., 2017), scheduling (Zhang et al., 2017) and tool wear conditions (Shi et al., 2018; Xie et al., 2018; Shoba et al., 2018) are considered in the cutting parameters optimization for turning, milling and grinding operations. The researchers are summarized in Table 1. It can be firstly seen that cutting parameters optimization considering environmental impacts (i.e. energy consumptions and carbon emissions) is a hot issue and more and more papers are paying close attention to this field. These proposed models play an important role in responding to low carbon manufacturing and can

2.2. Cutting parameters optimization algorithms The solving approaches for cutting parameters optimization models are also a key part of achieving optimal performance indexes including economy, society and environment in the machining process. A large number of literature study the solving approaches to cutting parameters optimization models from various aspects. A handful of researches are made on cutting parameters optimization based on one conventional goals, like minimum processing time or and cost (Gayatri and Baskar, 2015; Wang et al, 2007). Meanwhile, many optimization algorithms, for example, genetic algorithms (GA), particle swarm optimization (PSO) and their evolved algorithms, have been developed to solve the above single objective cutting parameters optimization models. With the development of green manufacturing and to respond to the issues of sustainability, multi-objectives for cutting parameters optimization, such as surface quality, energy consumption, carbon emissions, cost, processing time, etc. (Kant and Sangwan, 2014; Li et al., 2015a, b, 2017), have been paid much more attention. Generally, there are conflicts among the objectives, in which case the improvement of an objective in a machining process would lead to the weakening of another (Yi et al., 2015; Zhang et al., 2017; Li et al., 2017). To identify the trade-off between multiple process responses, Non dominated Sorting Genetic Algorithm II (NSGA-II) (Jiang et al., 2015; Zhang et al., 2017; He et al., 2017), Adaptive Multi-Objective Particle Swarm Optimization (AMOPSO) (Li et al., 2017), back propagation neural network model (Li et al., 2015a, b), Tabu Search (TS) with non-dominated sorting (Li et al., 2016)

Table 1 Cutting parameters optimization models. Authors (years)

Machining process

Energy consumptions

Carbon emissions

Tool wear conditions

Winter et al. (2014) Kant and Sangwan (2014) He et al. (2015) Bilga et al. (2016) Camposeco-Negrete et al. (2016) Zhang et al. (2017b) Li et al. (2017b) Li et al. (2017) Zhou et al. (2017) Shi et al. (2018) Xie et al. (2018) Shoba et al. (2018)

Grinding Multi-pass turning Milling Turning Turning Milling and turning Multi-steps face milling Turning and milling Turning and milling Milling Turning Turning

7

✓

7 7 7 7 7 7 7 7 7

✓ ✓ ✓ ✓ ✓ ✓ ✓

7

✓ ✓ ✓

7 7 7 7 7 7 7

✓ 7 7 7

✓ ✓ ✓

C. Tian et al. / Journal of Cleaner Production 226 (2019) 706e719

and their hybrid algorithms have been developed to solve multiobjective cutting parameters optimization models. Table 2 summarizes the relevant researches. In fact, solutions obtained by the optimization algorithms such as NSGA-II are a set of optimal solutions instead of a single ultimate optimal solution. For the managers or decision-makers, it is difficult to determine an appropriate solution. Weighting approach (Winter et al., 2014; Li et al., 2017; Zhang et al., 2017) and Pareto optimal solutions (He et al., 2017; Zhang et al., 2018; Liu et al., 2018) have been used to address this issue. Weighting approach optimizes the objectives by a weight vector. However, assigning a weight to every objective is difficult. Although Pareto optimal solutions approach can achieve the balance of multiple objectives and offer a group of solutions for planners to choose, it failed to pay enough attention to the improvement of each objective. As a result, the only best solution in the Pareto sets can hardly be generated owing to the lack of enough experienced or knowledgeable to assign a specific weight for every objective. Game theory just studies how individuals draw the most reasonable strategy and profit in complex interactions (Chen et al., 2001). Therefore, game theory is very necessary to be introduced into the solving algorithms to help decision-makers find more appropriate solutions. In summary, compared with the above existing works, little attention has been paid to the tool wear conditions in low carbonoriented cutting parameters optimization. From this point, this paper attempts to bridge this gap and proposes a cutting parameters optimization method considering tool wear conditions to determine the optimal cutting parameters for parts. Moreover, in order to overcome the limits of traditional optimization methods, this paper introduces game theory into the NSGA-II algorithm to improve the Pareto solutions.

3. Multi-objective cutting parameters optimization model considering tool wear conditions

709

3.1. Optimization variables Cutting velocity, feed rate, cutting depth, and tool wear conditions of cutting tools have a significant impact on production cost, time and carbon emissions. Therefore, cutting velocity v, feed rate f, cutting depth ap, and cutting tool (tool wear conditions) are taken as the optimization variables.

3.2. Objective functions Three objectives are considered in this model. The first one is the production carbon emissions CE, the second one is the production time PT, and the third one is the production cost PC.

H ¼ ðminPT; minCE; min PCÞ

(1)

We subsequently build the production carbon emissions, cost and time models with respect to the cutting parameters as well as tool wear conditions in machining processes respectively.

3.2.1. Carbon emission modelling considering tool wear conditions in machining process For a manufacturing operation, many activities such as cutting process, feed process, spindle rotational process, disposal of coolant used, and metal chip post-processing, are associated with carbon emissions. Due to the multiple sources of carbon emissions, the total carbon emissions of an operation can be decomposed into energy carbon emissions, material carbon emissions and waste carbon emissions (Zhou et al., 2018b). Hence, the total carbon emissions of an operation can be calculated by Eq. (2)

CE ¼ CEmaterial þ CEelec þ CEwaste

(2)

1) Material carbon emissions Although carbon emissions in machining process are very important in a low-carbon manufacturing environment, the production cost and time are also not ignored due to economic factors (Gayatri and Baskar, 2015). Therefore, how to identify the optimum cutting parameters and tool wear conditions for simultaneously reducing the production carbon emissions, cost and time is a vital problem. To solve the problem, a multi-objective cutting parameters optimization model considering tool wear conditions will be established in the following sections. The model includes optimization variables, objective functions, and corresponding constraints conditions. The detailed mathematical description of the model is described as follows.

Material carbon emissions are caused by tool and cutting fluid production, which can be decided by Eq. (3).

CEmaterial ¼ CEptool þ CEpcf

(3)

 Carbon emissions produced during tool production Carbon emissions produced by tool production can be obtained by Eqs. (4)e(6) (Zhou et al., 2018b).

Table 2 Related optimization algorithms about cutting parameters optimization models. Authors (years)

Number of optimization objectives

Wang et al. (2007) Winter et al. (2014) Gayatri and Baskar (2015) Jiang et al. (2015) Li et al. (2015b) Li et al. (2016) Zhang et al. (2017) He et al. (2017) Li et al. (2017) Saranya et al. (2018) Ji et al. (2018)

✓

1

✓

2

✓ ✓

✓

Method for optimizing objectives

Improved GA Weighting approach Non-traditional GA, SA, and PSO Hybrid GA Back propagation neural network model TS Improved NSGA-II NSGA-Ⅱ AMOPSO GA GA

Weighting approach Weighting approach / Weighting approach Weighting approach Pareto optimal solutions Weighting approach Pareto optimal solutions Weighting approach Weighting approach /

3

✓ ✓

Optimization algorithm

✓ ✓ ✓ ✓

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tcutting  Mi T itool  ðRi þ 1Þ

CEptool ¼

T itool ¼

 EFptool

8 s >  Pi > > < ap f q vr

Pi ¼ 1 

CT  Pi vx f y azp aw e

P/w

Spindle acceleration Cutting

1

ðfor turningÞ

p

> > > :

(4)

Tool retracting and Fast feed

(5) ðfor milling and drillingÞ

VBi 0:3

3

2 (6)

 Carbon emissions generated in cutting fluid production Carbon emissions generated in cutting fluid production are determined by consumption of cutting fluid, which can be expressed by Eq. (7) (Zhou et al., 2018b).

CEpcf ¼

tcutting ðM0 þ Ma Þ  EFpcf T0

T/s Fig. 1. The power profile of a CNC machine tool in a machining process.

(7)

  CEc ¼ Pd þ Pn þ P im þ Po  tcutting  EFelec 2) Waste carbon emissions Waste carbon emissions mainly consider waste cutting tools and cutting fluids. Because the waste carbon emissions are derived from the waste cutting tools and cutting fluids generated in a machining operation, the waste carbon emissions can be directly calculated by Eqs. 8e10 according to the material carbon emissions (Zhou et al., 2018b).

 EFwasteptool

(8)

tcutting ðM0 þ Ma Þ  EFwastepcf T0

(9)

CEwasteptool ¼

CEwastepcf ¼

tcutting  Mi T itool  ðRi þ 1Þ

CEwaste ¼ CEwasteptool þ CEwastepcf

(10)

In the machining process, energy carbon emissions is produced by energy consumption of machine tools. The power profile of a machine tool is very complex and varies with time, as shown in Fig. 1 (Yi et al., 2015). In order to accurately obtain carbon emissions during a machining process, it is necessary to decompose the energy carbon emissions into three carbon emissions components based on Fig. 1: (1) Carbon emissions produced in the process of spindle acceleration; (2) Carbon emissions generated during the cutting process; (3) Carbon emissions produced in the process of fast feed and tool retracting. Therefore, the energy carbon emissions can be gained by Eq. (11)

CEelec ¼ CEc þ CEs þ CEr

The power of feed drive system is affected by machine performance and feed speed. Feed power of a machine tool can be expressed as a function with respect to feed speed (Zhou et al., 2018b).

Pd ¼ C1  v2f þ C2  vf þ C3

(11)

 Carbon emissions generated during the cutting process Carbon emissions generated during the cutting process are calculated by Eq. (12)

(13)

The spindle rotational power can be expressed as a function of spindle rotational speed (Zhou et al., 2018b), as shown in Eq. (14)

8 ðn < n1 Þ < A1 n2 þ A2 n þ A3 Pn ¼ B1 n2 þ B2 n þ B3 ðn1  n  n2 Þ : ðn > n2 Þ W1 n2 þ W2 n þ W3

(14)

The material removal power considering tool wear related to the specific tool i can be obtained by Eq. (15) (Zhou et al., 2018a).

P im

3) Energy carbon emissions

(12)

8 v1 w1 x1 y1 z1 > < Kð1 þ VBi Þ ae ap f v ðfor millingÞ ¼ Kð1 þ VBi Þw1 f x1 Dy1 vz1 ðfor drillingÞ > : y1 z1 Kð1 þ VBi Þw1 ax1 ðfor turningÞ p f v

 Carbon emissions acceleration

produced

in

the

process

(15)

of

spindle

Carbon emissions produced in the process of spindle acceleration can be expressed as Eq. (16)

CEs ¼ ðPn þ Po Þ  tp  EFelec

(16)

 Carbon emissions produced in the process of fast feed and tool retracting Carbon emissions produced in the process of fast feed and tool retracting can be calculated by Eq. (17)

CEr ¼ ðPd þ Pn þ Po Þ  tr  EFelec

(17)

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3.2.2. Production time A machining process shown in Fig. 2 was defined. The cutting paths could be determined once the cutting tool is given. The cutting process can be depicted as follows: Firstly, the spindle accelerates to stable stage before starting cutting, and we call this period as the prepared period. Secondly, the material is removed from A to B, and this period is named as cutting period. Thirdly, the cutting tool is raised from B to C and retracted from C to D. This period is called as retracting tool period. Finally, the cutting tool moves to the machining tool path 2 and starts a new circle. Therefore, the total processing time is the sum of time of the prepared period, material removing period, and retracting tool period, which can be expressed as Eq. (18)

PT ¼ tp þ tcuting þ tr

(18)

8    > > 2vr 2vr 2vr  > > > < a þ l a þ a vr t t t t ir ¼ ðtrapezoid modelÞ q ffiffiffiffiffiffiffi ffi > > > > ðtriangle modelÞ 2  l > = at :

3.2.3. Production cost The production cost saving has always been one of the core issues of enterprises. During a machining operation, the production cost consists of the following items, i.e., the management cost as well as manpower cost, tool cost, electricity cost and the cutting fluid cost. It can be calculated by Eq. (25)

n v ¼ au pdau

(19)

tcutting  Mi

tcutting ðM0 þ Ma Þ  C2 þ / To h

i þ ðPn þ Po Þ  PT þ P im  tcutting þ Pd  tr þ tcutting  C3 ¼ C1  PT þ

T itool  ðRi þ 1Þ

 C itool þ

The cutting time tcutting can be calculated by Eq. 20e22.

tcutting ¼

m X

(25)

t icutting

(20) 3.3. Constraints

i¼1

m¼

U

(21)

ap

t icutting ¼

pdl

(22)

fv

tr can be obtained by Eq. (23).

tr ¼

m X

(24)

PC ¼ C1  PT þ PCtool þ PCfluid þ PCe

tp can be obtained as shown in Eq. (19).

tp ¼

711

tri

(23)

i¼1

The retracting tool period is decided by feeding process. The feeding time of triangle and trapezoid could be calculated by Eq. (24) (Zhou et al., 2018b).

C B

va

r

In the practical machining processes, the parameters of cutting speed, feed rate, cutting depth, cutting power, and cutting force in a machine tool have their separate acceptable ranges. The data of the cutting velocity, feed rate and cutting depth are going to be within a fair limit. The power needed for the cutting operation shall be controlled under the range of the effective output power. Similarly, the cutting force should be guaranteed within the full range of cutting force. The tool life of the selected tool should be greater than minimum tool life. These related constraints can be expressed in the following Eqs. 26e31.

vmin < v < vmax

(26)

apmin < ap < apmax

(27)

fmin < f < fmax

(28)

C

Machining tool path 1

vrapid

D vf

Machining tool path 2 Machining tool path 3 Machining tool path i

Fig. 2. Diagram of the cutting process.

vd

r

D

A

712

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Start

Pn þ Pd þ P im þ Po < Pmax  l

(29)

Fc < Fcmax

(30)

Generate new population

Initialize parameters of models and algorithm

T itool  T min tool

(31)

Execute crossover and mutation operation

Calculate the fitness function for each individual

Generate new population by improved selecting operation

Calculate equilibrium state function for each individual

Non-dominated sorting and crowding distances calculation

Termination condition?

Moreover, the cutting parameters for the finished machining process have a significant influence on the surface roughness. Therefore, the surface roughness should be constrained within the required surface roughness in the finished machining stage.

Ra  Ra0

(32)

The surface roughness (Li et al., 2014) can be predicted as follows.

8 > > > > <

vf 0

cotkr ðiÞ þ cotkr ðiÞ Ra ¼ . > > 2 > > : ðv  f Þ 8rε ðiÞ

Introducing the game theory

Compare the solutions by equilibrium state function

ðrε /0Þ

Obtain the best solutions

(33) End

others

Fig. 3. The flow chart of the algorithm.

4. An improved NSGA-II for the proposed optimization model Some papers have revealed that there are conflicts among production carbon emissions, time and cost ((Yi et al., 2015; Zhang et al., 2017; Li et al., 2017). Therefore, it is difficult to reduce them simultaneously due to the complex interaction relationship in conflicts. Game theory is a theory to solve the decision-making in conflicts of interest or objective. On that basis, NSGA-II combined with game theory is applied to solve the proposed model to reach the best decision-making of every objective. Firstly, the considered three objectives in this paper are viewed as the players in the game; secondly, a separate strategy set is allocated to every player and the equilibrium state function is designed accordingly to evaluate the equilibrium state among objectives. Finally, by introducing the equilibrium state to the selection operation and non-dominated sorting operation, the improved solutions can be obtained and a balance of multi-objectives is realized. The flow chart of the improved algorithm is shown in Fig. 3 and the core implementation steps are briefly described as follows. Moreover, in the following section, we briefly discuss the basic and improved related operations about algorithm based on game theory. Step 1: Initialize parameters of models and algorithm. Step 2: Calculate the fitness function for each individual: The production time, cost and carbon emissions are then calculated for each individual in the initial population. Step 3: Calculate the equilibrium state function for each individual: The equilibrium state function is then calculated for each individual in the initial population. Step 4: Judge whether the difference of the average fitness of each objective in 50 consecutive generations is less than threshold value? If yes, go to Step 9. Else, go to Step 5. Step 5: Execute Non-dominated sorting and calculate the crowding distance for populations Step 6: Generate the new population by selecting operation based on the non-dominated sorting rank, crowding distance and equilibrium state function. Step 7: Generate the new population by crossover as well as mutation. Step 8: Generate new population and then perform Step 2, Step 3, and Step 4.

Step 9: Compare the solutions by equilibrium state function, and output the best solutions.

4.1. Solution encoding In this paper, the decimal code is selected for solution encoding. A solution consists of four genes: The first gene is the cutting speed, the second is the feed rate, the third gene is the cutting depth, and the fourth is the cutter ID which is an integer, as shown in Fig. 4. 4.2. Equilibrium state function design about the game In the optimization process, strategy allocation for every player is important to ensure the competition among players. The strategy set of processing time are allocated as the selection range of cutting velocity; The carbon emissions’ strategy set are selected as the selection range of cutting depth and cutting tool; and the selection

v

f

ap

ID

Solution 1

a11 a21 a31 a41

Solution 2

a12 a22 a32 a42

… Solution n

a1n a2n a3n a4n

Fig. 4. The representation of a feasible solution.

C. Tian et al. / Journal of Cleaner Production 226 (2019) 706e719

range of feed rate serves as the strategy set of processing costs. The equilibrium state function is calculated by Eq. (34) on the basis of the Nash equilibrium theory (Chen et al., 2001).

fi ¼

3 X

o n   min U S sij  UðSÞ; 0 j ¼ 1; 2; :::n

(34)

i¼1

Theoretically, in the comparison between U(S|sij) - U(S) and 0, if S is Nash equilibrium solution, then U(S|sij)-U(S) generates nonnegative numbers and the minimum value is 0. If S is nonequilibrium solution, then the case that U(S|sij)-U(S) is less than 0 may happen and the minimum value is U(S|sij)-U(S); so if and only if the current chromosome is Nash equilibrium solution of S*, the indicator function fi takes the maximum value 0. When fi gets the value 0, it is considered that the statistical equilibrium solution is obtained. 4.3. The improved selection operation In order to make the next-generation population better than current population, the equilibrium state function is introduced into the selection operation. The specific selection process is as follows: Step 1: Calculate the non-dominated sorting value ri, crowding distance di, and the equilibrium state function fi for each individual in current population. Step 2: Sort out the individuals according to the equilibrium sate function and eliminate the last 10%. Step 3: The next-generation population is formed by the operation shown in Fig. 5. 5. Case study 5.1. Data setting An output shaft shown in Fig. 6 is utilized to verify the proposed approach on the basis of real industrial data from a manufacturing company named Xi'an WINWAY Tools Co., Ltd in China. Some related manufacturing resources including machine tools and cutting tools can support the case study. In order to illustrate the optimization process in the case study, the basic supported data is provided and inputted. Concretely, they include the data of carbon emissions models considering tool wear conditions and the data of the information about the output shaft and related available tools with different tool wear conditions. 1) Data obtainment about carbon emissions models

Chose any chromosome i and j If: rifj Then: Choose i Else:Choose j Fig. 5. The improved selection process.

713

Some related coefficients of carbon emissions models mentioned in Section 2 need to be obtained by experiments to support the case study. Fig. 7 shows the experimental real scene and measurement equipment in WINWAY Tools Co., Ltd. The experiments were carried out on a CNC lathe FTC20. The related parameters of FTC20 can refer to literature (Zhou et al., 2018a). The power demand of the machining process is measured by HIOKI clamp dynamometer PW3360 and SP1001 software. Confocal microscope OLS4000 and digital microscope ISM-PM200 is utilized to measure the flank wear VB of the cutting tool. In order to realize the environmentfriendly machining, the dry turning of ASTM080M46 bar with dimensions of 4100  80 mm is studied in this paper. Coated carbide cutting tool WNMG080412 and APMT1604PDER with different wear levels are applied in experiments. Ten groups of experiments are designed with feed rate in the range from 0.1 to 1 mm/r. Each group of power value is collected from an average of ten measured power values. A change of feed power with respect to feed rate and a fitting function is shown in Fig. 8 (a). Goodness of fit R2 is more than 0.85, which shows the fitting is good. The feed power model is listed in Table 3. In the same time, fifteen groups of experiments are designed with spindle rotational speed in the range from 200 to 2200 r/min. Each group of power value is collected from an average of ten measured power values. Fig. 8 (b) shows a change of spindle rotational power at different spindle rotational speed and the fitting function. Goodness of fit R2 is more than 0.85, which also shows this fitting is good. The spindle rotational power model is also listed in Table 3. The experiments about the material removal power model has been done by our previous paper. We directly give the results in Table 3. Some interested readers can consult our previous paper (Zhou et al., 2018a). 2) Data obtainment about the output shaft The cylindrical surface F1 of the output shaft is applied to illustrate the optimization process. The required processing diameter of the cylindrical surface F1 is 75 mm. In order to reserve a certain allowance for semi-finished or finished machining, the allowance of rough machining is less than 5 mm. In addition, FTC20 is chosen to deal with the cylindrical surface F1. In order to achieve environmental friendly manufacturing, dry cutting is adopted. Moreover, some parameters related to the models and algorithm also need to be inputted. The available cutting tools with different wear conditions in Table 4 are provided for the cylindrical surface F1 machining. These available cutting tools are obtained by the ontology-based method (Zhou et al., 2017) based on the tool sets of the WINWAY Tools Co., Ltd. The related coefficients of constraints and objectives are shown in Table 5. The related carbon emission factors can be referred to the literature (Zhou et al., 2018b). The corresponding parameters of algorithm are listed in Table 6. 5.2. Results and discussions 5.2.1. Optimization results According to the rough machining requirement of the feature F1, carbon emissions models and related algorithm parameters, the optimal wear condition and parameters can be obtained, as shown in Table 7. Compared with the empirical cutting parameters obtained by artificial experiences, the production time and production cost decrease about 80%, and the production carbon emissions reduces about 68%. Following the F1, the optimal cutting parameters and tool with optimal tool wear conditions for other features can also be obtained. Consequently, the proposed method is capable of determining the optimal cutting parameters and cutting tool considering

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197

80

F1

A workshop of Xi’an WINWAY Tools Co., Ltd Fig. 6. The output shaft.

the tool wear conditions under the objectives of production carbon emissions, cost, and time.

(b)

(a)

5.2.2. Performance comparison and discussions

Fixture 38CrMoAl

1) Necessity of multi-objective optimization considering the tool wear conditions Many researches have proved that there is a trade-off among the production carbon emissions, cost, and time when optimizing the cutting parameters. We mainly consider the influences of tool wear conditions on these three objectives.

WNMG080412 SF1001 Network cable

(c)

FTC20

OSL4000

PW3360-30 power analyser

ISM-PM200

Fig. 7. Experimental scene and measurement equipment. (a)FTC20. (b) HIOKI clamp dynamometer PW3360. (c) Confocal microscope OLS4000 and digital microscope ISMPM200.

 The influences of the tool wear on three objectives for the same cutting tools except for wear conditions Different tool wear conditions are studied for the same cutting tools to show the relationship between production carbon emissions, cost, and time with respect to the tool wear conditions. The changes are shown in Table 8. It can be found that the optimal cutting parameters in different tool wear conditions are different, resulting in differences in these three objectives. Production carbon emissions, cost, and time increase with the raise of the tool wear conditions basically. The reason is that the cutting parameters and tool life decrease with the tool wear conditions. Hence, it is necessary to make a multi-objective optimization in achieving a balance among production carbon emissions, cost, and time for the same cutting tools with different wear conditions. To show the necessity of multi-objective cutting parameters optimization considering the tool wear conditions in different cutting tools, Fig. 9 depicts the changes of production carbon

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Fig. 8. A change of power at different parameters and fitting function: a) feed power of feed system b) spindle rotational power.

Table 3 The related carbon emissions considering tool wear conditions. Type

Carbon emissions Model

Feed system power

Pd ¼ 7:6894ðnf Þ2 þ 22:61nf þ 1:495 8 < 6:000  105 n2 þ 1:037n  182:22 ðn < 1100Þ Pn ¼ 0:0006n2 þ 1:784n  396:65 ð1100 < n < 1500Þ : 1:000  104 n2 þ 0:9552n  225:44 ðn > 1500Þ

Spindle rotational power

Material removal power based on tool wear conditions

f 0:724 v0:961 P im ¼ e3:724 ð1 þ VBi Þ1:387 a0:925 p

Table 4 Available cutting tools for the feature F1. Tool ID

VBi(mm)

Name

Radius(mm)

Ri

Mi(g)

C itool (CNY)

T1 T2 T3 T4 T5 T6

0.1 0.15 0.15 0.18 0.2 0.05

TNMG140408-GS MTJNR1616H16 DWLNL1616H08 MCLNR WNMG080404 20X20X300 X1.2

1 0.8 0.9 1.2 0.8 1.2

1 2 3 2 2 1

9.5 10 11 15.5 17.5 22.5

50 30 20 30 98 101

Table 5 Related coefficients of constraints and objectives. s

p

q

r

C1

C3

T min tool

30000

1

0.15

0.2

15.3

0.8651

32

Table 6 Related parameters of algorithm. Algorithm parameters

Value

Size of the population Crossover rate Mutation rate The maximum generations Threshold value

100 0.8 0.2 300 0.001

emissions, cost, and time with respect to different tools with different tool wear conditions. It can be found that T6 and T1 can be used and the solutions of T1 and T6 have the Pareto relationship. The main reason is that different cutting tools also have different

Table 8 The changes of cutting parameters, carbon emissions, cost, and time with respect to VB in the same cutting tools with different wear conditions.  The influences of tool wear conditions on three objectives in different tools VB(mm)

v(m/min)

f(mm/r)

ap(mm)

PT(s)

PC(CNY)

CE(kg)

0.05 0.1 0.15 0.2 0.25 0.28

281.1150 155.9054 102.2241 81.4715 66.2700 47.2319

0.4402 0.9089 1.0000 1.0000 1.0000 1.0000

2.4006 2.4041 2.6739 2.5395 2.4083 2.7149

25.8353 22.9434 30.6451 37.6870 45.6437 62.8324

7.1364 6.2400 8.2934 10.2786 12.8716 19.0426

0.0709 0.0607 0.0712 0.0759 0.0834 0.1120

prices and masses, resulting in the difference in objectives. Hence, for several different available cutting tools with different tool wear conditions, it is necessary to apply a multi-objective optimization method to decide the optimal production carbon emissions, cost, and time. In practical machining processes, the cutting tool will inevitably wear. Therefore, the presented method considering tool wear is more realistic and suitable for practical manufacturing environment. The cutting parameters in the tool with VB ¼ 0.1 are applied to the tool with VB ¼ 0.15, and we find that the cutting power and force violate the constraints of machine tools. It means that the cutting parameters without considering tool wear condition are not enough precise. The same cutting parameters for various wear conditions are unreasonable, which may damage machine tools and workpieces. From the obtained results, the optimal cutting parameters vary with different tool wear conditions. Production carbon emissions, cost, and time vary with the raise of tool wear conditions and show an increasing trend. In order to balance and

Table 7 The optimization result. Method

Tool Wear (mm)

v(m/min)

f(mm/r)

ap(mm)

PT(s)

CE(kg)

PC(CNY)

Empirical parameters Optimized parameters

0.2 0.1

120 158.3683

0.2 0.8968

3 2.4090

120.7500 22.8981

0.1658 0.0596

33.2400 6.0755

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Fig. 11. The changes of production carbon emissions with the increase of the tool wear condition based on fixing cutting parameters (v ¼ 120, f ¼ 0.5, ap ¼ 3). Fig. 9. Pareto relationship between tools with wear conditions.

reduce these economic and environmental performances, it is essential to launch the multi-objective optimization in a given tool with a known and assured tool wear conditions. In addition, for several different available cutting tools with different tool wear conditions, it is necessary to apply a multi-objective optimization method to decide the optimal production carbon emissions, cost, and time. 2) Carbon emission analysis Analysis of tool wear conditions and cutting parameters on

production carbon emissions have been performed using graphs shown in Fig. 10 and Fig. 11 respectively. Fig. 10 pictures the changes of carbon emissions and two parameters by fixing the other two parameters (the four parameters including the tool wear conditions, cutting speed, feed rate, and cutting depth). From Fig. 10, when fixing tool wear conditions, selecting a bigger cutting depth and feed rate are significant for carbon emissions saving when the tool wear conditions change, and selecting a lower tool wear conditions, high cutting depth, high feed rate, and high cutting speed may reduce carbon emissions. From Fig. 11, when the cutting parameters are unchanged, the carbon emissions vary very quickly with the tool wear conditions, especially when the tool wear conditions is near to 0.3 mm. This is because the cutting tool has

(a)VB=0.1, v=80

(b)VB=0.1, f=0.1

(c)VB=0.1, ap=2

(d)f=0.1, v=80

(e)ap=2, v=80

(f)ap=2, f=0.1

Fig. 10. The change of carbon emissions with the different parameters.

C. Tian et al. / Journal of Cleaner Production 226 (2019) 706e719

a) A comparison in objective of production carbon emissions

717

b) A comparison in objective of production cost

c) A comparison in objective of production time Fig. 12. A comparision of proposed solution algorithm with traditional NSGA-II and MOPSO.

reached the limit of the wear conditions so that the tool life is near to zero. 3) Comparison with other optimization methods In order to show the superiority of the improved algorithm, a comparison with traditional NSGA-II and MOPSO method in the same condition is conducted. Fig. 12 shows an average fitness change of the proposed solving algorithm, traditional NSGA-II based solving algorithm and traditional MOPSO algorithm in production time, carbon emissions, and cost. From Fig. 12, it can be seen that the proposed method can achieve the lower results in search capability. In addition, the result of traditional NSGA-II and MOPSO method is respectively obtained by weighting method, namely, 1/3, 1/3, and 1/3 for every objective, as shown in Table 9. It indicates that the proposed solving algorithm is stable and better than traditional NSGA-II and MOPSO method.

In summary, at first, by a comparison with the traditional NSGAII and MOPSO, the search capability of the proposed algorithm is superior to the other two methods, as shown in Fig. 12. Second, another comparison is carried out to demonstrate that the proposed method can overcome the weights setting problem, as shown in Table 9. The main reason is that game theory, especially Nash equilibrium theory is used in the proposed method. Game theory concerns the individual's objective in complex interactions. By introducing the equilibrium state function in the selection operation and Pareto solutions, the population of the algorithm is further improved and relative disequilibrium solutions are gradually eliminated with iterations. Thus, an improved solution can be obtained when algorithm stops.

6. Conclusion In order to response to low-carbon manufacturing, cutting parameters optimization of machining processes considering carbon

Table 9 A comparison with traditional NSGA-II and MOPSO method. Method

Tool wear(mm)

v(m/min)

f(mm/r)

ap(mm)

PT(s)

PC(CNY)

CE(kg)

Traditional NSGA-II Traditional MOPSO Proposed method

0.15 (T3) 0.15 (T3) 0.1 (T1)

178.3375 87.3129 158.3683

0.6981 1.000 0.8968

2.4036 2.4011 2.4090

25.6996 35.3664 22.8981

6.7474 9.1797 6.0755

0.0687 0.0659 0.0596

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emissions has been studied for several years. By optimizing cutting parameters, the carbon emissions of machining process could be tremendously saved. Carbon emissions models in machining process involve many factors. As one of significant factors, the tool wear condition has a significant impact on carbon emissions, The current and urgent need to optimize cutting parameters for carbon emissions reduction in machining processes requires an extension of carbon emissions boundary with a consideration of tool wear conditions. In this way, this paper proposes a quantitative multiobjective cutting parameters optimization method where the tools with different wear conditions are also regarded as an additional decision variable to obtain the optimal production carbon emissions, cost and time. Firstly, the quantified relationships among cutting parameters, the tool wear condition and production indexes (production carbon emissions, cost and time) are analysed. Then a multi-objective cutting parameters optimization model is established with aims to minimize production carbon emissions, cost and time. Thirdly, a modified NSGA-II algorithm is used to resolve the proposed model. Finally, case studies are conducted to verify the advantages and effectiveness of the proposed optimization approach. From the results of the case studies, it is observed that: 1) The optimal cutting parameters vary with the different tool wear conditions. 2) For the same cutting tools except for wear conditions, the optimal processing carbon emissions, cost and time increase with the raise of tool wear conditions. 3) For several different available cutting tools with different tool wear conditions, it is necessary to apply a multi-objective optimization method to decide the optimal production carbon emissions, cost and time. 4) The proposed model is more accordant with practical circumstances. A scientific contribution of this paper is also summarized as follows: A complete and valid cutting parameters optimization approach considering tool wear condition is proposed to save production carbon emissions, cost and time. The manufacturing companies can easily and conveniently apply the proposed method to make an optimization for cutting parameters. Simultaneously considering production carbon emissions, cost and time can help manufacturing companies accommodate sustainable development. As the carbon tax and carbon labelling policy have been carried on many countries or will be extended in more countries in the near future, the proposed method could provide data of carbon emissions and help enterprises enhance competitiveness of products as well as reduce trade barriers. Reasonable selection of cutting parameters, tool paths, and cutting tools plays a significant role in process plan of parts. In the future, we will focus on optimizing tool path and integration optimization of tool paths and cutting parameters considering carbon emissions for mould milling manufacturing. On the other hand, the research on integration optimization of cutting parameters and process routes will be extended to explore the further saving possibility about energy or carbon emissions. Acknowledgments This research is supported by the National Natural Science Foundation of China (grant no. 51575435). References Bilga, P.S., Singh, S., Kumar, R., 2016. Optimization of energy consumption response

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