Integrated optimization of cutting parameters and tool path for cavity milling considering carbon emissions

Journal Pre-proof Integrated optimization of cutting parameters and tool path for cavity milling considering carbon emissions

Guanghui Zhou, Chao Zhang, Fengyi Lu, Junjie Zhang PII:

S0959-6526(19)34324-0

DOI:

https://doi.org/10.1016/j.jclepro.2019.119454

Reference:

JCLP 119454

To appear in:

Journal of Cleaner Production

Received Date:

12 August 2019

Accepted Date:

24 November 2019

Please cite this article as: Guanghui Zhou, Chao Zhang, Fengyi Lu, Junjie Zhang, Integrated optimization of cutting parameters and tool path for cavity milling considering carbon emissions, Journal of Cleaner Production (2019), https://doi.org/10.1016/j.jclepro.2019.119454

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Journal Pre-proof

Integrated optimization of cutting parameters and tool path for cavity milling considering carbon emissions Guanghui Zhouab*, Chao Zhanga, Fengyi Lua, Junjie Zhanga aSchool

of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;

bState

Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710054, China

*Corresponding

author：

Guanghui Zhou, School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China. Email: [email protected] Telephone: +86-29-82668609 Fax: +86-29-82668609 Authors state: Declarations of interest: none.

Journal Pre-proof The number of words: 8720 Integrated optimization of cutting parameters and tool path for cavity milling considering carbon emissions Abstract: Cutting parameters and tool path significantly affect processing time, carbon emissions and processing cost for cavity milling. However, most current researches optimized cutting parameters and tool path independently and ignored their comprehensive effects on carbon emissions. To bridge the gap, this paper proposes a novel multi-objective optimization model to realize low-carbon-oriented integrated optimization of cutting parameters and tool path for cavity milling, which takes processing time, carbon emissions and processing cost as its objectives. A two-layer interactive solution is designed to solve the model, which fist utilizes Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for upper layer optimization of cutting parameters, and then takes its results as the input for under layer optimization of tool path using an improved genetic algorithm (GA), and finally gives feedbacks to the upper layer in each successful iteration. Rough cavity milling of a workpiece made of # 45 steel is taken as an example to illustrate the feasibility and effectiveness of the approach. Experimental results show that the proposed approach could reduce the indicators of low-carbon manufacturing and lead to a 15.38% and 1.92% decrease in average carbon emissions when compared with the traditional approaches and serial optimization approach, respectively. Keywords: Low-carbon manufacturing; Cutting parameters optimization; Tool path optimization; Integrated optimization; Cavity milling 1. Introduction Recent years have witnessed an acceleration of global warming. To cope with the growing greenhouse effect, countries around the world begin to implement carbon tax 1

Journal Pre-proof and carbon labeling policies (Liu et al., 2017; Foumani and Smith-Miles, 2019). According to International Energy Agency (2018), more than 30% of carbon emissions are produced by manufacturing industry. As one of the main sources of carbon emissions, manufacturing industry has nowadays faced double pressures of environment and economy, urging manufacturing enterprises to enforce low-carbon manufacturing strategy (Liang et al., 2018; Giampieri et al., 2019). Specifically, die & mold is known as "the mother of industrial", where cavity milling is a critical process for die & mold manufacturing (Wang et al., 2017). Meanwhile, cutting parameters and tool path jointly affect processing time, carbon emissions and processing cost of cavity milling. Analyzing the linkage mechanisms of cutting parameters and tool path for determining the processing time, carbon emissions and processing cost in cavity milling and then developing an integrated method to optimize cutting parameters and tool path are significant for die & mold manufacturing enterprises in low-carbon manufacturing environment. Nowadays, low-carbon manufacturing (Cai et al., 2019a; Cai et al., 2019b) has received more and more research interests and many literatures have been published in this subject, among which cutting parameters and tool path are two research hot spots but usually optimized independently. For cutting parameters optimization, Lin et al. (2016) built machining parameter optimization models for multi-pass turning operations under dry and wet cut environments to minimize processing time and carbon emissions. Zhang et al. (2017a) constructed a multi-objective cutting parameters optimization model in dry milling to minimize energy consumption, processing time 2

Journal Pre-proof and carbon emissions. Zhang et al. (2017b) proposed an integrated model to optimize cutting parameters and scheduling for reducing carbon emissions in manufacturing process. Sangwan and Kant (2017) established an optimization model to identify the optimal cutting parameters that minimize the energy consumption of machine tools using a response surface methodology and genetic algorithm. Deng et al. (2017) established a multi-objective optimization model of milling process parameters to maximize energy efficiency and material removal rate and minimize carbon emissions. Abbas et al. (2018) established the turning conditions of AZ61 magnesium alloys that could provide the minimum unit-volume machining time, surface roughness and cost of machining one part. Wang et al. (2018) developed a big data enabled intelligent immune system to monitor, analyze and optimize machining processes in order to achieve low carbon manufacturing. Zhou et al. (2019a) introduced a cutting parameters optimization model for machining operations to balance carbon emissions, cutting time and cost in the part machining process. (Tian et al., 2019) analyzed the influence of tool wear conditions on carbon emissions and proposed a cutting parameters optimization method considering tool wear conditions in low-carbon manufacturing. (Mia et al., 2019) utilized cryogenic liquid nitrogen to promotes sustainability and facilitate low carbon emissions for turning Ti-6Al-4V. Wang et al. (2019) established a milling parameter optimization model to minimize carbon emissions and process time. Meanwhile, current works indicate that tool path significantly affects carbon emissions in machining process (Li et al., 2018). Energy consumption (Shi et al., 2019), as the main source of carbon emissions, has become the commonly used objective for 3

Journal Pre-proof tool path selection in low carbon manufacturing. Pavanaskar and McMains (2015) built an analytical energy consumption model for machine tool concerning the effect of tool traces on energy consumption. Pavanaskar et al. (2015) captured the idea of generating tool path for NC milling on the principle of microphotography in favor of energy consumption savings during machining process. Altıntaş et al. (2016) constructed a prediction model for energy consumption of prismatic parts during milling process and also investigated the effect of different tool paths on prismatic parts. Edem and Mativenga (2017) proposed a NC code-based analytical model for energy consumption of tool paths, enabling engineers to predict energy consumption for a given tool path. Edem and Balogun (2018) proposed an analytical method to determine the most energysaving tool path strategy in machining process by evaluating the required energy under the zag, zigzag and rectangular tool path strategies. Xu et al. (2016) put forward an energy potential-field based method for tool path generation, striving for a better tradeoff between the best fitting potential field to minimize the total energy consumption and ideal streamline patterns of the tool path. The above researches demonstrate that both cutting parameters and tool path could significantly affect carbon emissions. However, these researches optimized cutting parameters and tool path independently and ignored their comprehensive effects on carbon emissions. To bridge the gap, this paper aims to establish a multi-objective optimization model to realize low-carbon-oriented integrated optimization of cutting parameters and tool path for cavity milling, which takes processing time, carbon emissions and processing cost as its objectives. A two-layer interactive solution is 4

Journal Pre-proof designed to solve the model, where NSGA-II with an elite strategy is employed for cutting parameters optimization and an improved genetic algorithm (GA) combined with a reasonable tool path point generation algorithm is proposed for tool path optimization. In addition, the solution fist utilizes NSGA-II for upper layer optimization of cutting parameters, and then takes its results as the input for under layer optimization of tool path using an improved GA, and finally gives feedbacks to the upper layer in each successful iteration. Rough cavity milling of a workpiece made of # 45 steel is taken as an example to illustrate the feasibility and effectiveness of the approach. Experimental results show that the proposed approach could reduce the indicators of low-carbon manufacturing and lead to a 15.38% and 1.92% decrease in average carbon emissions when compared with the traditional approaches and serial optimization approach, respectively. The reminder of the paper is organized as follows. In Section 2, we define the problem of integrated optimization of cutting parameters and tool path for cavity milling. Section 3 introduces an integrated optimization model to formalize the problem. Section 4 presents a two-layer interactive solution for solving the model. An application example and two comparison experiments are analyzed in Section 5. The conclusion and future work could be found in Section 6.

2. Problem description For a cavity workpiece with given machine tool, cutting tool and clamp, there are a large number of feasible combinations P= {p1, …, pi, …, pm} of cutting parameters 5

Journal Pre-proof including spindle speed n, feed per tooth fz, cutting depth ap and cutting width ae. Each combination pi corresponds to numbers of feasible tool paths Li= {Li1, …, Lij, …, Lin}, where each tool path Lij consists of void tool path La and cutting path Lc. In addition, as shown in Fig. 1, cutting parameters and tool path affect each other and constitute processing space MF. Then, the problem is defined as: for a given processing space MF of a cavity workpiece, this paper aims to optimize the combination of pi and Lij to achieve coordinative optimization of processing time T, carbon emissions CE and processing cost C, which is expressed as: Foptimal  arg min T ( pi , Lij ), CE ( pi , Lij ), C ( pi , Lij )

(1)

pi , Lij MF

where the cutting conditions are assumed as: 1) The integrated optimization is carried out after the machine tool, cutting tool, workpiece and clamping method being determined; 2) the cavity milling process is a single step with no tool change; 3) if a single step containing multiple cutting layers, the shape and size of each cutting layer are considered to be the same. Tool Spindle speed n Z

Cutting width Feed per tooth fz

Cutting depth

Cutting layers Y

Tool

ae

ap

Actual cutting path Lc per layer X

Air cutting path La X

Fig. 1. Processing space of cavity milling.

6

Journal Pre-proof Nomenclature

mt

Quality of the tool (g)

Optimization variables

fb

reference frequency of machine tool (Hz)

f1

Frequency of the increased lineally power converted from decreasing or increasing slightly situation (Hz)

n

Spindle speed (rpm)

fz

Feed per tooth (mm·r-1)

ap

Cutting depth (mm)

ae

Cutting width (mm)

Lc

Length of cutting path (mm)

La

Length of void tool path (mm)

C1, C2, C3, C1’, C3’, CF, k, A, A1, A2, A3

Coefficients to be fitted

Parameters of objective functions

λ1, λ2, λ3, λ4

Power exponents

T

Processing time (min)

ta

Void cutting time (min)

tc

Cutting time (min)

f

Feeding speed (mm·min-1)

Cme, Cmp, Ccfc, Ccfs, Ct, Celec, Ctc, Ctc’, Ciee

Z

Number of teeth of the cutting tool

CE

Carbon emissions (Kg)

CEmaterial

Material carbon emissions (Kg)

CEelec

Energy carbon emissions (Kg)

CEwaste

Waste carbon emissions (Kg)

CEptool, CEpcfs, CEdtool, CEdcfs

Carbon emissions from manufacturing scrap tools, cutting fluids consumed, postprocessing of scrap tools and cutting fluids wasted, respectively (Kg)

EFptool, EFpcfs, EFelec, EFdtool, EFdcfs, EFrtool

Carbon emission factor for manufacturing scrap tools, cutting fluids consumed, electrical energy (kgCO2·L-1); post-processing of scrap tools, cutting fluids wasted, and tool per grinding (kgCO2·kg-1), respectively

Pidle, Pau, Psp, Pf, Pc

standby power of machine tool, auxiliary power of machine tool, rotary power of spindle, feeding power, cutting power, respectively (W)

Tt

Durability of the tool under specific cutting conditions (min)

The sum of management cost and equipment depreciation cost per unit time, man power cost per unit time (¥·min-1); cutting fluid cost per volume (¥·L-1); cutting fluid cost, total tool cost, industrial electricity consumption cost within processing time, unit tool cost and postprocessing cost, and tool cost per grinding, expense payable to industrial electric energy per kilowatt hour (¥), respectively

Parameters of constrains nmin, nmax

Minimum and maximum permissible rotary speed of machine tool spindles (rpm)

fmin, fmax

Minimum and maximum permissible feeding speed of machine tool spindles. (mm·min-1)

apmin, apmax

Minimum and maximum cutting depth (mm)

aemin, aemax

Minimum and maximum cutting width (mm)

ptotal

Total power of machine tools (W)

η

Power efficiency of machine tool

pmax

Maximum permissible power for operations of machine tool (W)

γε

Tool nose radius

T0

Replacement cycle of cutting fluid in workshop (min)

Fc, Fcmax

Primary and maximum cutting force of machine tool (N)

V0

Initial volume of cutting fluid (L)

Rmax

Va

Added cutting fluid in replacement cycle (L)

Surface roughness requirement for workpiece (μm)

7

Journal Pre-proof 3. Integrated optimization model This section formalizes the above problem via an integrated multi-objective optimization model, which takes geometrical parameters of a workpiece and machining constrains determined by the selected machine tool, cutting tool and clamping method as input, and outputs the optimized cutting parameter set, tool path set, processing time, carbon emissions and processing cost. The optimization variables, objective functions and constraints of the model are defined as follows. 3.1. Optimization variables As mentioned above, this paper aims to select the appropriate cutting parameter set pi and tool path set Lij to achieve coordinative optimization of processing time, carbon emissions and processing cost for cavity milling. To this end, cutting parameters, including spindle speed n, feed per tooth fz, cutting depth ap and cutting width ae, and tool path, including void tool path La and cutting path Lc, are considered as the optimization variables, which are expressed as:

X  ( x1 , x2 , x3 , x4 , x5 , x6 )T  (n, f z , a p , ae , La , Lc )T

(2)

3.2. Objective functions This paper conducts integrated optimization of cutting parameters and tool path under the objectives of minimum processing time, carbon emissions and processing cost. The objective function is expressed as:

8

Journal Pre-proof min f1  X   min T  X   min F  X   min f 2  X   min CE  X   min f3  X   min C  X 

(3)

3.2.1. Processing time In cavity milling, processing time is jointly determined by cutting parameters and tool path. Processing time consists of void cutting time ta and actual cutting time tc in the entire cavity milling process, where fast positioning time is neglected as it is relatively small compared with ta and tc. Cavity milling process is such a process in which the cutting tool begins to engage at the feeding point after completing fast positioning until the end of the corresponding step and returns to non-cutting point. During this process, ta and tc refer to the time taken in no-load operation of machine tool and material removal process, respectively. Based on the above definition, processing time T is calculated as:

T  t a  tc 

La L  c f nZf z

(4)

3.2.2. Carbon emissions According to our previous works (Zhou et al., 2018b), carbon emissions CE resulted from cavity milling process contain material carbon emissions CEmaterial, energy carbon emissions CEelec and waste carbon emissions CEwaste, which are calculated as:

CE  CEmaterial  CEelec  CEwaste

(5)

CEmaterial contains carbon emissions CEptool produced by manufacturing scrap tools and CEpcfs produced by cutting fluids consumed in the cavity milling process, which is 9

Journal Pre-proof calculated as:

CEmaterial  CE ptool  CE pcfs 

L Lc mt L  V  V  EFpcfs EFptool   a  c  0 a nZf zTt  N  1 1000 T0  f nZf z 

(6)

CEelec is produced by energy consumption of the machine tool during cavity milling process, which is defined as:



 Pidle  Pau  Psp  Pf CEelec  

 L

a

f  Lc nZf z   Pc Lc nZf z  EFelec  60000

(7)

where standby power Pidle and auxiliary power Pau of the machine tool are constant, which only depend on the performance of the machine tool. In addition, rotary power Psp of spindles, feeding power Pf and cutting power Pc are calculated by Eqs. (8)-(10) respectively and obtained by the experiments. Rotary power Psp of spindles is calculated as: C1n 2  C2 n  C3  1  Psp  C1 ' n 2  C2 n  C3 ' k ( 2 ) n A  2  C1 ' n  C2 n  C3'

( f  fb ) ( fb  f  f1 )

(8)

( f  f1 )

Feeding power Pf is calculated as:

Pf  A1 f 2  A2 f  A3 f  nZf z

(9)

Cutting power Pc is calculated as: Pc  CF vc1 f 2 a p3 ae4

(10)

CEwaste includes carbon emissions CEdtool produced by postprocessing scrap tools and CEdcfs by post-processing waste cutting fluids consumed in cavity milling process. CEwaste is calculated as: 10

Journal Pre-proof CEwaste  CEdtool  CEdcfs Lc  mt  EFdtool  N  EFrtool    nZf zTt  N  1  1000 



(11)

 La Lc  V0  Va  EFdcfs    T0  f nZf z  Based on Eqs. (5)-(11), the specific function of carbon emissions for cavity milling could be calculated as:

CE 

Lc nZf zTt  N  1

 mt  EFptool  EFdtool  N  EFrtool    1000 









 La L  V0  Va  EFpcfs  EFdcfs  c    f n Zf T  z  0

P

idle

 Pau  Psp  Pf

 L

a

f  Lc nZf z   Pc Lc nZf z

60000

(12)

EFelec

3.2.3. Processing cost The processing cost of cavity milling consists of management and equipment depreciation cost, manpower cost, cutting fluid cost Ccfs, cutting tool cost Ct and industrial electricity consumption cost Celec. It is calculated as:

C  ( Cme + Cmp )T + Ccfs + Ct  Celec

(13)

where Cme is the sum of management cost and equipment depreciation cost per unit time, Cmp is the manpower cost per unit time; Ccfs, Ct and Celec are calculated by Eqs. (14)-(16). Cutting fluid cost Ccfs is calculated as: Ccfs 

T (Vo  Va )Ccfc To

L L  (Vo  Va )Ccfc  a  c  To  f nZf z 

Cutting tool cost Ct is calculated as: 11

(14)

Journal Pre-proof

Ct 



tc Ctc  NCtc Tt( N  1)

 = L C c

tc

 NCtc



(15)

nZf zTt( N  1)

Industrial electricity consumption cost Celec is calculated as:

Celec





 Pidle  Pau  Psp  Pf T  Pc tc  Ciee    60000 (16)  Pidle  Pau  Psp  Pf  La f  Lc nZf z   Pc Lc nZf z  Ciee  =  60000





Thereby, the specific function of processing cost is given by:





  ( V  Va )Ccfc   La Lc  Lc Ctc  NCtc C  Cme + Cmp  o  +    To nZf z  nZf zTt( N  1)    f  Pidle  Pau  Psp  Pf  La f  Lc nZf z   Pc Lc nZf z  Ciee   60000





(17)

3.3. Constraints To make the optimized results coincide with the actual situation in workshop (Ding et al., 2019; Zhou et al., 2019b), constraints of the performance of machine tool, cutting tool and processing quality of workpiece in cavity milling process are considered. Specifically, spindle speed constraints, feeding constraints, cutting depth constraints, cutting width constraints, machine power constraints, cutting force constraints and workpiece surface roughness constraints (Debnath et al., 2016) are considered in this paper and expressed as follows:

12

Journal Pre-proof nmi n  n  nmax   f mi n  f  f max a  p mi n  a p  a p max a  ae  ae max s.t .  e mi n  Ptotal    Pmax  0   Fc  Fc max  0 1000 f 2   Rmax  0  32 

(18)

4. Two-layer interactive solution for the integrated optimization model This section designs a two-layer interactive solution for solving the integrated optimization model. The proposed solution includes three parts, namely NSGA-II for upper layer optimization of cutting parameters, improved GA for under layer optimization of tool path and their interaction mechanism. 4.1. Overview of the solution This paper aims to select an appropriate combination of cutting parameter set pi and tool path set Lij to achieve coordinative optimization of processing time, carbon emissions and processing cost for cavity milling. The combination of cutting parameters and tool path is a typical NP-hard problem with multi-objectives, multiple constraints and decision variables. There are three aspects of works related to this problem, including cutting parameter optimization, tool path optimization and their interaction mechanism to minimize processing time, carbon emissions and processing cost. To this end, we design a two-layer interactive solution (as show in Fig. 2) to explore the optimized solution of the problem that fits with the engineering purpose, 13

Journal Pre-proof where NSGA-II with elite strategy is designed for the upper layer optimization of cutting parameters and an improved GA combined with reasonable tool path point generation algorithm is proposed for under layer optimization of tool path. The reasons for employing NSGA-II and GA in this paper are considered as follows. NSGA-II is a Pareto-based algorithm that could address the limitation existed in many heuristic algorithms like Tabu and Simulated Annealing (Zidi et al., 2019), i.e. subjective weight determination for each objective in multi-objective optimization tasks (three objectives in this paper). It also has relatively low computing complexity but could achieve very high optimization precision (Jauhari et al., 2018). GA is a global optimization algorithm that performs well for optimizing a complex, large and multidimensional problem and provides an optimal result (Chowdhury and Garai, 2017), which could be a good choice for the under-layer optimization of tool path. Cutting parameter optimization and tool path optimization will be introduced at the following sections. As shown in Fig. 2, interaction mechanism and flow of the solution are descripted as follows. Step 1: The relevant algorithm parameters are set. These parameters include population size, maximum number of iterations, crossover probability, mutation probability and prior to the problem solving since there are two optimization algorithms involved: NSGA-II and improved GA. Step 2: The population in cutting parameters optimization module is initialized to generate a set of initial cutting parameters for NSGA-II. Step 3: Information of a set of generated cutting parameters is transmitted to the 14

Journal Pre-proof tool path optimization module via data interface. Step 4: A group of cutting parameters are randomly extracted from the set. Step 5: A coordinate set of tool path points is generated by mesh discretization in processing regions of the cavity based on the cutting width information extracted from the cutting parameters. Step 6: The tool path is generated and optimized using the improved GA with the coordinate set of the generated tool-path points as input. Step 7: Objective function values are calculated and correlated with corresponding cutting parameters and tool path, all of which are further added into the optimum objective set. Step 8: The extracted group of cutting parameters are deleted from the cutting parameters set. Step 9: Determine whether the cutting parameter set is empty or not. Step 10: If not, return to Step 4; otherwise, optimum objective set is transmitted to the cutting parameters optimization module via data interface. Step 11: The cutting parameters optimization module conducts a series of algorithm operations including non-dominated sorting, crowding distance calculation, selection, crossover and mutation to generate a new population of cutting parameters evolved. Step 12: Determine whether the NSGA-II has reached the maximum iterations. Step 13: If not, return to Step 3; otherwise, an optimized combination of cutting parameters and tool path are selected from the optimum objective set and the entire 15

Journal Pre-proof solution comes to an end. Start

Set parameters Mesh discretization in the processing regions

Optimization of tool path

Generate and optimize the tool path using the improved genetic algorithm

Input the optimal tool path and objective informations

Correlate the cutting parameters and tool path as well as the objective function values and add them into the set of optimal objective functions

Initialize populations of cutting parameters based on NSGA-II

N

Transmit set information of cutting parameters

N

Generate new populations of cutting parameters

Reach the maximum iterations？

Algorithm operation including non-dominated sorting using NSGA-II

Y

Transmit set information of optimum objectives

Output optimum combination scheme of cutting parameters and tool path

An empty set of cutting parameters？

Delete this group of cutting parameters Y from the set of cutting parameters

Optimization of cutting parameters

Generate a coordinate set of tool path points

Extract a group of cutting parameters from the set of cutting parameters

End

Fig. 2. Interaction mechanism and flow of the solution.

4.2. Cutting parameters optimization based on NSGA-II NSGA-II with elite strategy (Paul and Shill, 2018) is a commonly used multiobjective optimization algorithm, which achieves selection and evolution through comparison of dominated and non-dominated relationships between individuals within a population and provides a discussion on Pareto optimum solution. Consequently, this paper employs NSGA-II for cutting parameters optimization, which is implemented as follows.

16

Journal Pre-proof 4.2.1. Encoding: decimal floating-point encoding Due to the continuous optimization variables of cutting parameters in optimal ranges, a small value of population pop is vulnerable to local optimum while the excessive value will lead to low computational efficiency of algorithm. To figure out this problem, a decimal floating-point encoding method is utilized in this paper. When conducting optimization of roughing and semi-finishing, chromosomes are made up of four genes: spindle speed n as a floating point in range [nmin, nmax]; feed per tooth fz as a floating point in range [fzmin, fzmax]; cutting depth ap as a floating point in range [apmin, apmax]; and cutting width ae as a floating point in range [aemin, aemax]. Chromosomes are made up of three genes in finishing optimization: spindle speed n, feed per tooth fz and cutting width ae. 4.2.2. Design of crossover mutation operator 1) Crossover operator Arithmetic crossover operator is adopted as the the crossover operator and defined as:

ci   pi  1    pi 1 ci 1   pi 1  1    pi

(19)

where ci and ci+1 are the sub-individuals generated after crossover; pi and pi+1 are the selected parent individuals; α is the coefficient of crossover operator. To enable individuals with better paternity (i.e. lower Rank value) and occupy a larger proportion of offspring genes, this paper designs the following crossover operator coefficient:



pi  Rank pi  Rank  pi 1  Rank 17

(20)

Journal Pre-proof At the early stage of the algorithm, α obtained varies greatly due to the large span of Rank value of population hierarchy and gradually tends to a constant 0.5 as individuals in the population gradually tend to a Pareto frontier with the iterations. 2) Mutation operator Non-uniform step variation is employed as the mutation operator in this paper, provided that the mutation of k-th variable xk in range [xkmin, xkmax] in the selected mutation individual pr is executed. The mutated variable is defined as:

 xk    t , xk max  xk  xk =   xk    t , xk  xk min 

if random(0,1)  0 if random(0,1)  1

(21)

where t is the current iteration number of the algorithm;   t , y  in range [0, y] is calculated by:

  t , y   y  1  r 1t MaxT     

(22)

where r is a random variable in range [0, 1]; MaxT is the maximum number of iterations; λ refers to the attenuation coefficient of mutation step, which is set to 2 according to our previous work (Tian et al., 2019). 4.2.3. Optimum selection of Pareto optimum solution Optimum individuals can be obtained by a comprehensive evaluation of three objectives, namely processing time, carbon emissions and processing cost, from Pareto optimum set derived by extracting non-dominant chromosomes set at the smallest level in the final population. The comprehensive evaluation index PI for these objectives is defined as: 3

O Ij  O Mj

j 1

O Mj

PI  

18

(23)

Journal Pre-proof I M where O j refers to the value of j-th objective function for individual I; O j is the

optimum value of j-th objective function among all individuals in optimal solution set. Based on the description presented above, a specific flowchart of cutting parameters optimization is illustrated in Fig. 3. Start Set parameters including population size, cross/mutation probability , maximum iterations Initialize populations

Non-dominated sorting

N

Generate the first offspring generation ? Y

Selection,crossover and mutation

Iteration number t = 2 Combine parents and offspring Generate a new population?

t=t+1

N

Y Selection, cross- over and mutation Y

t ≤ MaxT ？

Non-dominated sorting Calculate crowded distance Select new individuals to form populations

N Select from Pareto optimum set based on Eq.(23) End

Fig. 3. Flowchart of cutting parameters optimization.

4.3. An improved GA for tool path optimization This section first introduces how to generate reasonable tool path points for given cutting parameters. On that basis, tool path optimization is carried out with an improved GA.

19

Journal Pre-proof 4.3.1. Reasonable tool path point generation There are two steps for reasonable tool path point generation of cavity milling, including processing region determination and tool path point generation, where overcut phenomenon is considered in processing region determination. 1) Determination of the processing region To determine the processing region of the cavity, the contour boundaries is subject to offset with a offset value of the sum of milling cutter radius R and allowance △, and the curve obtained by offsetting the contour is known as the offset loop. The offset process of the contour is illustrated in Fig. 4. The offset loop is classified into inter loop and outer loop, among which the outer loop is deemed as offset loop of outer contour boundary and the inner loop is offset loop of inner contour boundary. For a given cavity workpiece with only one outer loop, the region between inner loop and outer loop represents the processing region of the workpiece. All loops generated within the entire processing region possess the following properties: (1) each loop is not self-intersecting and any two loops are not intersecting either; (2) there is only an outer loop containing inner loops. Outer contour boundary Offset

Loop0 R R

Region

Inner contour boundary

Loop1

Fig. 4. Offset process of a cavity workpiece.

2) Tool path point generation Tool path is an effective connection of discrete tool path points within the 20

Journal Pre-proof processing region with appropriate connection sequence and ways. Therefore, tool path point generation is a critical issue for and serves as the base of tool path generation. As shown in Fig. 5, this paper proposed a specific discretization process for tool path point generation, which involves the following steps. Step 1: A uniform distributed square mesh area Ω on the plane is established with the side length of each square mesh being the cutting width ae. Step 2: Place the region Ω on the processing region R, and calculate the intersection of two regions. Step 3: Retain the meshes within R after intersection calculation as mesh discretization of R and eliminate other redundant meshes. Step 4: Define the vertices within the meshes in R, along with the intersections between inner and outer loops and meshes, as tool path points. y

y

ae 

 Region

x

Step1

x

Step2

y

y

           

 Region

                        Region

Region

                   

   

           

x

Step3

                       

Step4

x

Fig. 5. Flowchart of mesh discretization for the processing region.

Let C= {P1, …, Pi, …, Pm} be a set containing all tool path points generated by discretizing the meshes in the processing region. Then, the tool path can be depicted as the effective connections between all tool path points with appropriate connection sequence and ways. It contains void tool path La and cutting path Lc: 21

Journal Pre-proof L  La  Lc 



Pi , Pj C ,i  j

PP i j

(24)

where PP i j is the direct distance between tool path point Pi and Pj. 4.3.2. Design of an improved genetic algorithm Based on the generated tool path points, this section proposes an improved GA to find an optimized connection sequence and way of tool path points and generate tool path. Notice that traditional GA is easily to fall into local optimum and premature convergence, this paper improves the population initialization and crossover mutation operator of GA to accelerate the evolution speed of populations in large-scale computation and prevent from local optimum and premature convergence. The flowchart of the approach is as shown in Fig. 6 and details of the approach are presented below.

Nearest neighbor algorithm generate half of the population; Randomly generate the other half

Initialize population Start Calculate individual fitness

Set cutting width Mesh discretization of the processing region Generate tool-path points

Duplicate individuals based on fitness

Roulette wheel selection

Execute duplication

Calculate adaptive crossover probability

Generate new offspring population N

fitmax(t+1)-fitmax(t)≤δ? fitavg(t+1)-fitavg(t)≤δ? Y

End

Output the minimum tool path, processing time, carbon emissions and processing cost.

Fig. 6. Flowchart of tool-path optimization. 22

Greedy crossover operator Calculate adaptive mutation probability Heuristic mutation operator

Improved genetic operator

Elite strategy

Generation of reasonable tool path points

Determine processing region

Tool path generation and optimization based on improved genetic algorithm

Gene encoding

Journal Pre-proof 1) Encoding To simplify encoding, this paper adopts an integer encoding scheme and builds an equivalent relationship between tool path points and integers that can be expressed as Pi→i, where i is a constant. Different tool path points correspond to different encoded numbers, and the sequence of integers represents the connection sequence of tool path points. For example, chromosome (9, 5, 1, 3, 7, 4, 2, 10, 8, 6) indicates that tool path starts from tool path point P9 followed by P5, P1, P3, P7, P4, P2, P10, P8, and ends at P6. This encoding scheme ensures the capability of the tool for passing through each tool path point only once, avoiding repetition. The specific encoding scheme is given in Table 1. Table 1 Encoding scheme. Tool path point

P1

P2

···

Pi

···

Pm

Encoding

1

2

···

i

···

m

2) Fitness function The optimization problem in this paper is a multi-objective problem, which involves three objectives differing in orders of magnitude and dimensions. Therefore, it is of great need to normalize the objective function before solving the problem. The normalization method adopted is defined as: f j*  X  

fj X 

f j min  X 

(25)

where f j min  X  is the minimum value of the j-th objective function obtained by the single-objective optimization method. Weight allocation method is adopted, traditionally, to transform multi-objective 23

Journal Pre-proof optimization into a single-object problem, which involves weight allocation with strong subjectivity. To figure out this problem, we multiply the normalized objective functions:

F  X   f1*  X   f 2*  X   f3*  X 

(26)

Therefore, the fitness function is calculated as:

fit 

1 FX 

(27)

3) Population initialization There are two methods for population initialization. The first method is to generate populations randomly, which is applicable for no prior knowledge of solutions to the problem. The second method employs a nearest neighbor algorithm for population initialization. The nearest neighbor algorithm facilitates initial population with good quality but small diversity, leading to the difficulty in convergence to global optimum solution when using such initial population for evolution. To accelerate the convergence speed of the algorithm and ensure the population diversity, this paper uses the random method to generate half of the initial population and nearest neighbor algorithm to generate the other half during population initialization. 4) Improvement of genetic operators (1) Self-adaptive probability of crossover and mutation A self-adaptive adjustment scheme is employed for adaptive selection of the value of crossover and mutation probability. It could not only prevent good genes from being destroyed, but also introduce new genes when the algorithm falls into local optimal solution to accelerate the convergence speed of the algorithm. The self-adaptive adjustment scheme is defined as: 24

Journal Pre-proof Pc max  Pc min  P  fitc  fitavg c max      fit  fit c avg  1  exp  a cos     Pc    fit  fit max avg       P fitc  fitavg  c max

(28)

Pm max  Pm min  fitm  fitavg  Pm max      fit  fit m avg  1  exp  a cos     Pm    fit  fit max avg       P fitm  fitavg  m max

(29)

where Pcmax and Pcmin is the maximum and minimum crossover probability, respectively; fitc represents the larger fitness value in two individuals participating in crossover; fitavg is the average fitness value in population; a is the coefficient that is set to 9.903438 based on the current experience (Tian and Shi, 2018); fitmax represents the maximum fitness of the population; Pmmin and Pmmax represent minimum and maximum mutation probability, respectively; fitm is the fitness value of mutated individuals. (2) Crossover operation A greedy crossover operator is used as the crossover operator, which aims to find the optimum solution via each greedy choice. It also enables the crossed offspring to inherit the parental good genes, which can boosts searching efficiency and global searching ability while shortening the searching time. Let pa1 = (x11, x12, …, x1j, …, x1m) and pa2 = (x21, x22, …, x2k, …, x2m) be two parent individuals to be crossed. Then, the implementation process of greedy crossover operator is as follows: Step 1: Randomly generate a number x, let x1j=x and x2k=x, and add x into the offspring ch1 and ch2. Step 2: If neither of x1j+1 and x2k+1 are in ch1: let x=x2k+1 if d x1 j x1 j1  d x2 k x2 k 1 , 25

Journal Pre-proof x=x1j+1 otherwise, and then x is added into ch1; if x1j+1 is found in ch1 whereas x2k+1 is not: let x=x2k+1 and add into ch1; if x2k+1 is found in ch1 whereas x1j+1 is not: let x=x1j+1 and add into ch1; if both x1j+1 and x2k+1 are in ch1: let x=x2k+1 if d x1 j x1 j1  d x2 k x2 k 1 , x=x1j+1 otherwise, and then x is added into ch1. Step 3: If neither of x1j-1 and x2k-1 are in ch2: let x=x2k-1 if d x1 j x1 j -1  d x2 k x2 k -1 , x=x1j1

otherwise, and then x is added into ch2; if x1j-1 is found in ch1 whereas x2k-1 is not: let

x=x2k-1 and add into ch2; if x2k-1 is found in ch2 whereas x1j-1 is not: let x=x1j-1 and add into ch2; if both x1j-1 and x2k-1 are in ch2: let x=x2k-1 if d x1 j x1 j -1  d x2 k x2 k -1 , x=x1j-1 otherwise, and then x is added into ch2. Step 4: Step 2~3 are iteratively executed until the complete offspring ch1 and ch2 are generated. (3) Mutation operator Heuristic mutation strategy is used for mutation operator and includes the following three steps. Firstly, three different points are randomly generated; then five different chromosomes are obtained by arbitrary interchange positions of three points; finally, the chromosomes with the best fitness value are selected as the offspring. For example, let Pa= (x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) be the parent individuals to be mutated. Let r1=x2, r2=x6 and r3=x8 be three points randomly selected from Pa. Then, five chromosomes, namely P1= (x1, x6, x3, x4, x5, x2, x7, x8, x9, x10), P2= (x1, x8, x3, x4, x5, x6, x7, x2, x9, x10), P3= (x1, x2, x3, x4, x5, x8, x7, x6, x9, x10), P4= (x1, x6, x3, x4, x5, x8, x7, x2, x9, x10) and P5= (x1, x8, x3, x4, x5, x2, x7, x6, x9, x10), are generated by arbitrary interchange positions of x2, x6 and x8. Finally, the chromosome with the best fitness value is selected 26

Journal Pre-proof as the offspring ch (as shown in Fig. 7).

Pa

x12 x2 x3 x4 x5 x6 x7 x8 x9 x10

P1

x12 x6 x3 x4 x5 x2 x7 x8 x9 x10

P2

x12 x8 x3 x4 x5 x6 x7 x2 x9 x10

P3

x12 x2 x3 x4 x5 x8 x7 x6 x9 x10

P4

x12 x6 x3 x4 x5 x8 x7 x2 x9 x10

P5

x12 x8 x3 x4 x5 x2 x7 x6 x9 x10 Best fitness

ch

x12 x6 x3 x4 x5 x8 x7 x2 x9 x10 Fig. 7. Mutation operator.

5) Elite strategy This paper utilizes an elite strategy to reduce the probability of falling into the local optimum caused by the optimum loss of the current population in the next generation. The basic idea of the strategy is as follows: when a population with size N evolves to the t-th generation, top 5% individuals of current generation ranked by their fitness values are used to replace the bottom 5% individuals of the t+1-th generation. 6) Design of the termination criterion The algorithm is terminated if the differences between the average and largest fitness values of the chromosomes over N successive generations are all below a threshold  :

 fitmax  t  1  fitmax  t      fitavg  t  1  fitavg  t   

(30)

where: fitmax(t) and fitmax(t+1) represent the maximum fitness value of the t-th and t+1-th 27

Journal Pre-proof generation, respectively; fitavg(t) and fitavg(t+1) indicate the average fitness value of the population in t-th and t+1-th generation;  is the threshold value. The average fitness is calculated as: N

fitavg   fiti N

(31)

i 1

5 Case study 5.1. Case environment To verify the proposed approach, rough cavity milling of a workpiece made of # 45 steel is taken as an example. As shown in Fig. 8, the processing region of the workpiece is a concave of size 214mm×164mm×5.5mm with two islands inside of the same size 46mm×56mm×5.5mm. The chemical composition of the workpiece is illustrated in Table 2. According to the dimension and material of the workpiece, Dalian VDL-850A (a 3-axis NC machining center) is used as the milling machine and its parameters are illustrated in Table 3. YG EMC54120 4F carbide milling cutter is selected as the cutting tool and its parameters are as shown in Table 4. In addition, as shown in Table 5, carbon emission factors used in the case study is obtained by Narita et al. (2008). 214

56

164

46

126

5.5

Fig. 8. Cavity workpiece.

28

Journal Pre-proof Table 2 Chemical composition of the workpiece made of # 45 steel. Element

Carbon

Chromium

Manganese

Nickel

Phosphorus

Sulfur

Silicon

Mass (%)

0.42-0.50

≤0.25

0.50-0.80

≤0.25

≤0.035

≤0.035

0.17-0.37

Table 3 Parameters of VDL-850A milling machine tool. Machine tool VDL-850A

nmin

nmax

fmin

fmax

pmax

(rpm)

(rpm)

(mm/min)

(mm/min)

(W)

60

8000

1

10000

7.5

Table 4 Parameters of EMC54120 4F carbide milling cutter. Helical Total Cutting tool Z Diameter angle length EMC54120 4F 4 12 mm 75 mm 35°

η

Fcmax (N)

0.8

3000

Length of cutting edge

Equality

Price

32 mm

142 g

¥172

Table 5 Information of carbon emission factors. EFptool

EFdtool

EFrtool

EFpcfs

EFdcfs

EFelec

33.7478

0.01346

0.0184

0.469

3.782

0.7800

In rough cavity milling of the workpiece, we preserve a side processing allowance of 1 mm for semi-finishing and finishing. The operation power of Dalian VDL-850A basic module is 389 W and the power of the spray cutting fluid is 641 W measured by PW3360-30 clamp-on power tester. The initial cutting fluid volume of VDL-850A is 500 L and is replaced every two months afterwards, during which the supplementary cutting fluid volume is 200 L. The service life of the cutter is 180 min, the sum of management cost, equipment depreciation cost and manpower cost per minute is ¥1.3, and the cost of tool and post-treatment is ¥200. The cutting fluid cost is ¥12.5/L and the industrial electricity consumption cost is ¥0.8651/kWh. The proposed approach is implemented by MATLAB R2018 b and all the experiments are conducted on a computer with windows 10 operation system, Core i5 29

Journal Pre-proof CPU and 8G memory. 5.2. Power coefficients fitting To evaluate the carbon emissions of cavity milling process, the power coefficients of Dalian VDL-850A for calculating rotary power Psp of spindles, feeding power Pf and cutting power Pc (namely Eqs. (8)-(10)) should be fitted. To this end, a series of experiments are conducted to obtain the net powers for different kinds of rotary speed, feeding speed and cutting parameters. The experimental scheme for power coefficients fitting is as shown in Fig. 9 and the experimental data could be found in Appendix A. More details about the experiment could refer our previous work (Zhou et al., 2018a). Based on the experimental data, Eqs. (8)-(10) could be calculated by Eqs. (32)-(34). Based on Table A. 1, the spindle rotary power is calculated as:

8.789 107 n 2  0.315n  397.527 (n  1400)  Psp  0.543n  1570.438 (1400  n  1600) 1.379 104 n 2  0.726n  1498.202 (n  1600) 

(32)

Based on Table A. 2, the feeding power is calculated as: Pf  1. 162  105 f 2  0. 021 f  3. 84

(33)

Based on Table A. 3 and A. 4, the cutting power is calculated as: Pc  e 1. 439 vc0. 164 f 0. 683 a 0p. 912 ae0. 885 (b)

(a)

Machine tool

N U1 U2 U3

Experimental Data

I1

I2

I3

(34) Distribution box

Distribution box

Clamp-on power tester

Milling machine

Power tester

Fig. 9. Experiments for coefficients fitting: (a) experimental scheme and (b) process.

30

Journal Pre-proof 5.3. Process of the integrated optimization solution To use NSGA-II and the improved GA for the integrated optimization of cutting parameters and tool path for cavity milling, related hyperparameters are set as follows. The population size of NSGA-II is set to be 100; the maximum number of iterations is 100; the crossover probability is 0.8; the mutation probability is 0.3. The population size of the improved GA is 200; the maximum number of iterations is 500; the maximum crossover probability is 0.9; the minimum crossover probability is 0.5; the maximum mutation probability is 0.2; the minimum mutation probability is 0.01 and the judgment threshold  is set to be 0.00000001. The proposed solution utilizes NSGA-II for upper layer optimization of cutting parameters, and then takes its results as the input for under layer optimization of tool path using an improved GA, and finally gives feedbacks to the upper layer in each successful iteration. The whole solution comes to an end when the upper layer optimization algorithm reaches the predefined iterations, namely 100 iterations in this experiment. The convergence of the solution is as shown in Fig. 10, from which we can see that the processing time, carbon emissions and processing cost in the population have all converged to the minimum over 100 iterations.

31

F(X)

T (min)

Journal Pre-proof

Iterations

Iterations

(b) Convergence diagram of processing time

C (yuan)

CE (kg)

(a) Convergence diagram of F(X)

Iterations

Iterations

(c) Convergence diagram of carbon emissions

(d) Convergence diagram of processing cost

Fig. 10. Convergence diagram of the algorithm.

5.4. Results and discussion 5.4.1 Optimized results The optimized results are as shown in Fig. 11. The pareto set for three objectives (Fig. 11(a)) show that the proposed approach is well converged, which demonstrates the effectiveness of the approach. Based on the feedbacks from process planners, the optimized tool path, feed point and non-cutting point (Fig. 11(b)) are in accordance with the practice and could be used for cavity milling, which demonstrates the feasibility of the approach. According to the results obtained by Fig. 11, the optimized combination scheme of tool path and cutting parameters is as shown in Table 6. In 32

Journal Pre-proof addition, when using this scheme for cavity milling of the workpiece, the processing time, quantity of carbon emissions, processing cost are 18.42586 min, 1.5872 kg and ¥46.523, respectively. Iteration number: 100 Feeding point

Non-cutting point

(a) Pareto set for three objectives

(b) Optimum tool path

Fig. 11. Optimized results. Table 6 Optimized combination scheme of cutting parameters and tool path. n/rpm

fz/mm·r-1

ap/mm

ae/mm

Lc/mm

La/mm

L/mm

2492.34

0.045

1.6

10

8174.43

117.24

8291.67

5.4.2. Discussion To verify the effectiveness and efficiency of the integrated optimization model and two-layer interactive solution, two comparison experiments are discussed in this section. 1) Comparison with the traditional approach We compare the performance of the proposed approach with two traditional approaches commonly used in tool path generation, namely reciprocating mode (RM) and following component mode (FCM) of UG software. We take the cutting parameters optimized by our approach (namely, fz=0.045 mm·r-1, ap=1.6 mm and ae=10 mm) as input for tool path generation using RM and FCM. The results are as shown in Fig. 12 (b) and (c). According to the generated tool paths, the processing time, carbon 33

Journal Pre-proof emissions and processing cost for cavity milling of the workpiece are calculated, as shown in Table 7.

(a) Our method

(b) Reciprocating mode of UG

(c) Following component mode of UG

(d) Serial optimization method

Fig. 12. Comparison with the traditional approach and serial optimization approach.

As shown in Table 7, The results demonstrate that the proposed approach outperforms both RM and FCM approaches in terms of process time, carbon emissions and process cost as well as tool path lengths. Specifically, the length of cutting path is reduced by 122.7 mm compared with the RM approach and by 795.24 mm compared with the FCM approach. The length of void cutting path is reduced by 608.91 mm and 1846.41 mm respectively. The total tool path length is reduced by 8.82% and 31.86%, respectively. Meanwhile, the processing time is shortened by 9.16% and 32.26% respectively; the carbon emission is cut by 6.50% and 24.26% respectively, and the processing cost is saved by 5.96% and 22.59%, respectively. The reasons for the better 34

Journal Pre-proof performance of the proposed approach might be the following two aspects. Firstly, twolayer interactive solution considers synthetically the influence of cutting parameters and tool path for determining processing time, carbon emissions and processing cost. Secondly, NSGA-II could handle multi-objective optimization of cutting parameters with low computing complexity but very high optimization precision. In addition, the improved GA performs well for optimizing a complex, large and multidimensional problem, which is suitable for the under-layer optimization of tool path. Table 7 Comparison with the traditional approaches. Method

Lc/mm

La/mm

L/mm

[T (min), CE (kgCO2), C (¥)]

RM

8297.13

726.15

9023.28

[20.11336, 1.6904, 49.294]

FCM

8969.67

1963.65

10933.32

[24.37094, 1.9722, 57.032]

Proposed

8174.43

117.24

8291.67

[18.42586, 1.5872, 46.523]

2) Comparison with the serial optimization approach

The serial optimization approach optimizes the cutting parameters and tool path independently. In this experiment, NSGA-II and the improved GA used in the proposed integrated approach are used for cutting parameters optimization and tool path optimization, respectively, where the output optimized cutting parameters of NSGA-II are taken as the input of the improved GA for tool path optimization. The hyperparameters of the serial optimization approach are set the same as the integrated approach. The optimized tool path is illustrated in Fig. 12(d) and the optimized results are compared in Table 8, from which we can see that the optimized results obtained by the integrated approach is better than that obtained by the serial approach. More specifically, compared with the serial approach, the total tool path length generated by 35

Journal Pre-proof the proposed approach is reduced by 0.82%. In addition, the processing time is shortened by 2.08%, the carbon emissions are cut by 1.92% and the processing cost is saved by 1.81%. The above results demonstrate that cutting parameters and tool path indeed jointly determine the processing time, carbon emissions and processing cost for cavity milling, where the proposed approach could be a good solution for the integrated optimization of cutting parameters and tool path for cavity milling. Table 8 Comparison with the serial optimization approach (SOA). Method

[n, fz, ap, ae]

Lc/mm

La/mm

L/mm

SOA

[2736.42, 0.041, 1.6, 10]

8190.58

168.79

8359.37

[18.81, 1.6177, 47.367]

Proposed

[2492.34, 0.045, 1.6, 10]

8174.43

117.24

8291.67

[18.42, 1.5872, 46.523]

[T(min), CE(kg), C(¥)]

6. Conclusion and future work This paper proposes a multi-objective optimization model for the integrated optimization of cutting parameters and tool path for cavity milling, where the processing time, carbon emissions and processing cost are considered as the objectives. In addition, a two-layer interactive solution is designed to solve the model, where NSGA-II with an elite strategy is designed for cutting parameters optimization and an improved GA combined with a reasonable tool path point generation algorithm is proposed for tool path optimization. Based on the experimental results, the contributions of this paper could be summarized as follows. Firstly, we analyze the linkage mechanisms of cutting parameters and tool path for determining the processing time, carbon emissions and processing cost for cavity milling, and then propose an integrated model for cutting parameters and tool path optimization. Secondly, we 36

Journal Pre-proof design a two-layer interactive solution to solve the model, which fist utilizes NSGA-II for upper layer optimization of cutting parameters, and then takes its results as the input for under layer optimization of tool path using an improved GA, and finally gives feedbacks to the upper layer in each successful iteration. Lastly, we take the cavity milling of a workpiece made of # 45 steel as an example to illustrate the implementation and feasibility of the approach. Experimental results show that the proposed approach could reduce the indicators of low-carbon manufacturing and lead to a 20.71% decrease of processing time, 15.38% decrease of carbon emissions and 14.28% decrease of processing cost when compared with the traditional approaches, and 2.08%, 1.92% and 1.81% decreases when compared with the serial optimization approach. The potential limitation of the approach might be that the proposed model and solution are for cavity milling of a workpiece whose cavity only has planes, which may not be suitable for the workpiece whose cavity has curved faces. We will figure out this problem in the near future by combing a tool path points generation algorithm (Li et al., 2018) for curved faces with the proposed approach. We plan to solve the integrated optimization model with different heuristic algorithms, such as particle swarm optimization and reinforcement learning, to explore the optimal solution of the integrated optimization problem. We also intend to combine reinforcement learning with deep learning, namely deep reinforcement learning, to support dynamic tool path optimization during cavity milling.

37

Journal Pre-proof Acknowledgement This work was supported by the National Natural Science Foundation of China [grant numbers 51575435].

Appendix A: Table A. 1 Net power obtained by different spindle rotary speed. No. n (rpm) Net power (W) No. 1 200 463.19 17 2 300 491.06 18 3 400 522.71 19 4 500 553.46 20 5 600 585.25 21 6 700 618.02 22 7 800 650.82 23 8 900 683.85 24 9 1000 715.01 25 10 1100 744.46 26 11 1200 777.27 27 12 1300 808.58 28 13 1350 822.81 29 14 1400 808.25 30 15 1425 795.56 31 16 1450 782.66 32

n (rpm) 1475 1500 1525 1550 1575 1600 1650 1700 1800 1900 2000 2200 2400 2600 2800 3000

Net power (W) 772.76 760.15 741.29 725.56 713.83 702.31 687.17 667.81 630.50 610.62 588.85 570.13 556.13 554.02 550.12 555.94

Table A. 2 Net power obtained by different feeding speed. f (mm·min-1)

100

200

300

400

500

600

700

800

900

1000

Net power (W)

5.79

8.05

11.84

14.48

17.40

21.29

23.75

28.73

31.15

37.81

Table A. 3 Level of experimental factors of cutting parameters. Factor* Level 1 Level 2 n (rpm) 600 800 fz (mm·r-1) 0.025 0.035 ap (mm) 0.5 1 ae (mm) 4 6 *Orthogonal experimental table L9(34) is selected to arrange the experiment.

38

Level 3 1000 0.045 1.5 8

Journal Pre-proof

Table A. 4 Net power obtained by different cutting parameters. Test No

N (rpm)

fz (mm·r-1)

ap (mm)

ae (mm)

1 2 3 4 5 6 7 8 9

600 600 600 800 800 800 1000 1000 1000

0.025 0.035 0.045 0.025 0.035 0.045 0.025 0.035 0.045

0.5 1 1.5 1 1.5 0.5 1.5 0.5 1

4 6 8 8 4 6 6 8 4

Net power (W) 11.423 40.988 84.819 56.417 51.522 32.437 67.183 40.738 52.524

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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CRediT author statement: Guanghui Zhou: Conceptualization, Methodology, Funding acquisition, Writing- Reviewing and Editing Chao Zhang: Visualization, Methodology, Formal analysis, WritingOriginal draft preparation Fengyi Lu: Data curation, Writing- Original draft preparation Junjie Zhang: Investigation, Software

Journal Pre-proof Highlights: 

Cutting parameters and tool path jointly affect carbon emissions of cavity milling.

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Proposing a low-carbon-oriented integrated optimization model for cavity milling.

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Designing a two-layer interactive solution for the integrated model.

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Integrated method outperforms traditional method and serial optimization method.