priority order recognition method of module redesign for

Draft

Priority order recognition method of module redesign for the CNC machine tool product family to improve green

performance

Journal: Transactions of the Canadian Society for Mechanical Engineering

Manuscript ID TCSME-2020-0190.R2

Manuscript Type: Article

Date Submitted by the Author: 07-Jan-2021

Complete List of Authors: Liu, Shihao; Hainan University, Zheng, Wei; Hainan University

Keywords: CNC machine tools, life cycle design, product family, module redesign, green performance

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

© The Author(s) or their Institution(s)

Transactions of the Canadian Society for Mechanical Engineering

Draft

Priority order recognition method of module redesign for the CNC

machine tool product family to improve green performanceShihao Liu1,2, and Wei Zheng1

S. Liu1,2. 1.College of Mechanical and Electrical Engineering, Hainan University, Haikou 570228, China. 2.

Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology, Nanjing University of Aeronautics

and Astronautics, Nanjing 210016, China

W. Zheng1. 1.College of Mechanical and Electrical Engineering, Hainan University, Haikou 570228, China.

Corresponding author: Shihao Liu (e-mail: [email protected])

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Abstract: In order to solve the sequencing problem of module redesign in the greening process of the CNC

machine tool product family, a priority order recognition method based on fuzzy analytic hierarchy process (FAHP)

and grey relational analysis (GRA) was put forward. A hierarchical model of functional modules of the CNC

machine tool product family was constructed, and the types of functional modules were divided. The generality

coefficient of the functional modules was proposed to reflect the influence of the module types on the redesign

priority order. A green performance evaluation indicator system for module instances of CNC machine tool

product family was built, based on which a life cycle-oriented green performance priority order recognition

method was established. FAHP and GRA was utilized to evaluate the green performance of module instances, and

then the priority order of module redesign can be determined by the ratio of green performance evaluation value

and generality coefficient. The feasibility and effectiveness of the proposed priority order recognition method was

verified by a applied case of module green redesign sequencing of gantry machine tool product family. The

application case showed that the proposed priority order recognition method based on FAHP and GRA provides a

scientific basis for companies to carry out the greening improvement project of the gantry machine tool product

family.

Keywords: CNC machine tools, life cycle design, product family, module redesign, green performance

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1 Introduction

Because the issues of global resources decrease, energy consumption and environmental

degradation have been becoming increasingly prominent, environmental protection awareness and

sustainable development concepts are gaining popularity. Modern manufacturing companies must

not only meet diverse and personalized customer needs, but also need to comply with increasingly

stringent environmental protection laws and regulations (Du et al. 2013). As the main

manufacturing equipment of the current manufacturing industry, CNC machine tools have been in

great demand in the machinery market(Li et al. 2019). At present, the mass customization of CNC

machine tools has meet the need of customers with highly personalized products by approaching

the cost, quality and efficiency of mass production. The design of platform-based CNC machine

tool product family is one of the key enabling means to achieve mass customization, and has been

widely used in manufacturing companies (Liu et al. 2019). The design research of the existing

CNC machine tool product family mainly focuses on platform construction, product family

modeling, versatility and diversity trade-offs, etc (Chen et al. 2013), but the environmental factors

of the CNC machine tool product family life cycle are insufficiently considered. If modern

machine tools’ manufacturing companies want to establish and maintain their competitive

advantages, the green design concepts should be integrated into mass customized production

models to improve the comprehensive performance of CNC machine tool product family.

Some progress has been made on the green design and the mass customization technology of

CNC machine tools. Li et al. (2009a) put forward a green design and manufacturing technology

framework for gear processing machine tools based on the analysis of the technical characteristics

of traditional gear processing machine tools and their environmental impact, which provides a

scientific basis for the development of green gear processing machine tools. Wang et al. (2018)

comprehensively evaluated the remanufacturing green degree of CNC machine tools based on the

remanufacturability of each part of the waste CNC machine tools and the multi-level fuzzy

comprehensive evaluation mathematical model, and established an evaluation system of

remanufacturing green degree of CNC machine tool. Wang et al. (2019) established an

optimization model with the greatest user's satisfaction of green machine tool products as the goal

through the green quality function configuration, which was verified by taking a gear hobbing

machine tool as an example. Li et al. (2009b) established a green operation mode of the machine

tool industry based on the main line of product design and the main line of life cycle, and the

green design of machine tools, green production, and remanufacturing design of waste machine

tools were discussed. Zhu et al. (2003) discussed the mass customization basic methods and

modular design methods in machine tool industry, and pointed out that modular design,

configuration design, digital design platform and modular enterprise are the distinctive features

among the mass customization methods. Gu et al. (2001) proposed an idea of developing

reconfigurable automation equipment for mass customization, including research on the design

methodology of reconfigurable machine tools for mass customization. Sheng et al. (2017) applied

the modular design method in the development of CNC product-service system and studied the

module division and configuration modeling method oriented to configuration design process, and

an economical CNC turning center was selected as an example to implement the module division

and configuration modeling of CNC product-service system and to verify the feasibility of

proposed methods. Mourtzis and Doukas (2015) used the Simulated Annealing and Tabu Search

methods to develop into a web-based software platform, which was validated through real

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applications to case studies from the CNC laser welding machines.

The above research results have provided theoretical and methodological support for

companies to carry out the planning of green CNC machine tool product family, but due to the

lack of mandatory standards for green performance and/or insufficient consumer attention to

product environmental performance, some companies rarely or even did not take green

performance constraints into consideration when planning the CNC machine tool product family

previously. Therefore, in the current situation, it is urgent to carry out the greening project for the

CNC machine tool product family. However, due to resource and economic constraints, many

companies can't simultaneously conduct optimization design for all modules of the CNC machine

tool product family to improve their green performance. In order to solve the above problem, the

priority order of the module redesign for the CNC machine tool product family should be

identified firstly.

On basis of establishing a hierarchical model for the CNC machine tool product family, the

relative importance of functional modules is discriminated from the perspective of versatility, and

a green performance evaluation indicator system for module instances was constructed in this

paper. The fuzzy analytic hierarchy process (FAHP) /9E ��F� and Kahraman 2020) and grey

relational analysis (GRA) (Aydemir and G�� 2019) are applied to calculate the green

performance evaluation value of module instances, and the redesign priority order is determined

through combining the relative importance of functional modules with the green performance

evaluation value of module instances, which provides a scientific basis for companies to carry out

the module redesign priority order decision for the CNC machine tool product family.

2 Module classification of CNC machine tool product family

In order to realize the modular design of products facing customers' diverse needs, it is

necessary to study the creation and division of CNC machine tools product family modules (Sheng

et al. 2017). When dividing the CNC machine tool product family modules, it can be done

according to users' needs or according to machine tools' structure, but the decomposition

according to function is the condition and basis for the division of the CNC machine tool product

family modules. The division process of the CNC machine tool product family modules is mainly

to analyze the overall function of the CNC machine tools, and the function decomposition is

carried out from the top to the bottom layer by layer to obtain several independent function

elements until the customer demand functions are divided into sub-functional modules.

According to the strong coupling within a functional module of CNC machine tools and the

weak coupling between the modules, companies usually organize the R&D team to design,

develop, upgrade or redesign with the functional modules as the object. In order to determine the

relative importance of the functional modules, a hierarchical model of the CNC machine product

family functional modules is constructed and the types of functional modules are defined, which is

shown in Figure 1. The mathematical description of the above hierarchical model is as follows.

The CNC machine tool product family P={P1, P2, …, PN} consists of N product variants,

which contains a total of s functions fk(k=1, 2, …, p, …, q,…, s). Each given function fk is realized

by a functional module, and there are nk module instances that can realize the function Fk.

Mk(d)(d=1, 2, …, nk) represents the d-th module instance of the functional module Fk, and �k(k=1,

2, …, N) denotes the number of product variants that contains the functional module Fk.

If �k=N and nk=1, it means that each product variant includes the functional module Fk, the

functional module Fk can be realized by a module instance; and then this kind of functional

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module Fk is defined as a generalized module.

If 1<�k<N and nk>1, it means that the functional module Fk is utilized in at least two product

variants but not in all variants, the functional module Fk can be realized by at least two module

instances; and then this kind of functional module is defined as a incomplete variant module.

If �k=N and nk>1, it means that each product variant includes the functional module Fk, the

functional module Fk can be realized by at least two instances; and then this kind of functional

module is defined as a required variant module.

If �k=1 and nk=1, it means that only one product variant uses the functional module Fk, and

then this kind of functional module is defined as a personalized module.

If 1<�k<N and nk=1, it indicates that the functional module Fk is utilized in only one kind of

module instance and is used in some product variants; and this kind of functional module is

defined as an incomplete generalized module.

Fig. 1 hierarchical model of CNC machine tool product family

As a shared element of all modified products, the redesign of the generalized module or

required variant module can improve the green performance of the entire CNC machine tool

product family, but it must take into account the impact of the redesign of the generalized module

and required variant module on all product variants and related modules, which will increase the

redesign difficulty significantly. Therefore, the generalized module and required variant module

should have the maximum weight.

The redesign of the personalized module only affects the green performance of a certain

product variant, so it should have the minimum weight. For variant modules and incomplete

generalized modules, their weights should be between those of personalized modules and

generalized modules. Therefore, Lk is defined as the generality coefficient of the functional

module Fk, which is used to reflect the influence of the functional module type on the redesign

priority order.

(1)� �NN

L kk

k ,,2,1 ��

3 Green evaluation indicator system of CNC machine tool product family

Based on the core concept of the green design, the goal of green redesign of the CNC

machine tool product family is to reduce the resource consumption, energy consumption and

harmful substance emissions throughout its life cycle, so that the products are easy to recycle and

reuse. Reasonable green performance evaluation of the module instances of the CNC machine tool

product family is the basis for the successful implementation of green improvement.

Wang et al. (2010) conducted quantitative analysis and evaluation on the green performance

of CNC machine tool products from five aspects of environmental attributes, resource attributes,

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energy attributes, economic attributes and human-machine attributes. Li et al. (2019) established a

green evaluation system for CNC machine tools in view of five aspects of processing time,

production cost, processing quality, resource consumption and environmental impact, which was

applied with analysis through factory examples. Liu and Yin (2014) built an evaluation system for

machine tool green remanufacturing processes based on the five decision-making attributes of

green remanufacturing technology feasibility, quality, economy, time and environmental

performance, which can provide a reference for the evaluation of machine tool green

remanufacturing design schemes.

Based on the above research results, combining with the green degree evaluation principle of

product life-cycle technology advancement, environmental coordination and economic rationality,

a hierarchical architecture indicator system for module instances’ green performance evaluation of

CNC machine tool product family is built, which includes target layer A, criterion Layer B and

indicator layer C as shown in Figure 2. The connotation and main functions of the green

performance evaluation system are detailed below.

Gre

en

perfo

rmance e

valu

atio

n o

f mo

dule

instan

ces o

f CN

C m

ach

ine to

ol p

rod

uct fa

milyA

Green design

performance B1

Design reliability C11

Environmental

performance B3

Resource

performance B2

Recycling

performance B4

Structural rationality C12

Process feasibility C13

Material resources C21

Equipment resources C22

Human resources C23

R & D cost C61

Manufacturing cost C62

Maintenance cost C63

Air pollution C31

Oil pollution C32

Solid waste pollution C33

Noise pollution C34

Economic

performance B6

Energy

performance B5

Recycling possibility C41

Recycling method C42

Recycling value C43

Recyclability C44

Energy type C51

Energy consumption C52

Energy efficiency C53

Indicator layer CCriterion layer B

Targ

et la

yerA

Fig. 2 Green performance evaluation system

The design reliability indicator in the green design performance criterion mainly considers

the design time, robustness, integration and coordination of design information, etc; the structural

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rationality indicator mainly considers the manufacturability, assembly function, and openness of

the module instance; the process feasibility indicator mainly considers the production type of the

module instance, the feasibility of the processing, the rationality of the selection of materials and

blanks, etc.

The resource performance criterion mainly considers the material resources, equipment

resources and human resources consumed in the entire life cycle of the module instance from

design, manufacturing, utilization, maintenance to recycling, which has a great impact on

companies' resource allocation efficiency.

The environmental performance criterion mainly considers the destructive effects of air

pollution, oil pollution, and solid waste pollution produced by modules on workshops, factories,

and even the ecological environment during the entire life cycle, as well as the impact of noise

pollution produced on workers' physical and mental health.

The recycling possibility indicator in the recycling performance criterion mainly considers

the impact of the material resource type of the module instances (such as renewable resources or

non-renewable resources, etc.) on recycling; the recycling method indicator mainly considers the

reuse of the entire module instance after recycling, materials recycling ways such as reprocessing,

incineration or landfill; the recycling value indicator mainly examine the balance between benefits

and costs caused by recycling; the recyclability indicator mainly reflect the difficulty of achieving

recycling and the rationality of the recycling process.

The energy performance criterion mainly examines the energy consumed by the module

instances in the entire life cycle and its impact on the green performance of the ecological

environment, including the type of energy (such as traditional energy or clean energy), energy

consumption and energy efficiency, which can provide a useful reference for the development of

energy conservation and consumption reduction.

The economic performance criterion mainly considers the R & D cost, manufacturing cost

and maintenance cost of the module instances in the entire life cycle, which has a great impact on

the market share of the product.

Through in-depth analysis and fuzzy quantification of various indicators (using the level of

excellent, better, medium, poor, and very poor of fuzzy mathematics evaluation theory to describe,

the relative value measurement is 9-7-5-3-1 respectively) (Dinçer et al. 2019), the expert scores

method is applied to establish the green performance evaluation table of the module instances of

CNC machine tool product family. When the score of a certain indicator is large, it means that the

module instance has better green performance in this respect. In order to facilitate the expression

of the calculation formula, the 20 indicators in indicator layer are expressed as f1, f2,…, f20 from top

to bottom.

4 Priority order recognition method based on FAHP and GRA

It can be seen from Figures 1 and 2 that the recognition of module redesign priority order in

the greening process of CNC machine tool product family is a multi-level, multi-criterion,

multi-indicator decision-making problem. The weight of each criterion or indicator will affect the

result of priority order recognition, and this effect is fuzzy. The indicators are not relatively

independent, and there is a large or small correlation between them.

Among many evaluation methods, the Analytic Hierarchy Process (AHP) proposed by the

famous American scientist T.L. Saaty in early 1970 is a systematic method that combines

qualitative analysis and quantitative analysis (Ma et al. 2020). AHP makes the decision-maker's

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subjective judgment process mathematical and logical, so that the decision-making is easy to be

accepted. The basic steps of the application of AHP (Singh et al. 2020) are as follows: (1)

Building a ladder hierarchy structure of the evaluation problem; (2) Constructing a pairwise

comparison judgment matrix; (3) Using Mathematical software to calculate the eigenvalues and

eigenvectors of each judgment matrix and making them pass the consistency test; (4) Calculating

the total weight of the measure layer to the target layer, so as to obtain the optimal solution.

Through analysis, it can be seen that the judgment matrix in the analytic hierarchy process

continuously adjusts the elements in the matrix until the judgment matrix meets the consistency

test standard, however, this standard is a empirical data usually. In addition, in the process of

determining the weight of the evaluation index, the factors that affect the weight of the evaluation

index include subjective factors such as judgment level, personal preference and experts’

knowledge structure. The subjective factors themselves are vague and unobjective, and it is

unlikely to measure them on a precise scale. In this case, the Fuzzy Analytic Hierarchy Process

(FAHP) (Wang 2020), which combines the advantages of the fuzzy method and the analytic

hierarchy process, will be able to solve the problem well. Therefore, in order to more accurately

identify the priority order of green redesign of each module of CNC machine tools, fuzzy analytic

hierarchy process was chosen to determine the weight coefficient of each module.

Among the current various system analysis methods, Grey Relational Analysis (GRA) is an

important part of the theory of grey systems. The grey system refers to systems with incomplete or

uncertain information, and the unique advantages of modeling with poor information and small

sample make the grey system theory widely used. GRA measures the closeness between factors

according to the degree of similarity or difference between the development trends of grey system

factors, and there is no requirement on the number of experimental samples, and the samples do

not need to have a typical distribution law (Parthiban et al. 2019). Through sequence modeling

with GRA, realistic laws are generated, and the amount of calculation is small (Wang et al. 2020).

Since the green evaluation indicators of each module of CNC machine tools contain quantitative

or qualitative information, and often lack of large enough data samples for mathematical modeling;

the relationship between the indicators is not clear; and the degree of impact of each indicator on

the overall green performance of the machine tool are often fuzzy numbers, which are in line with

the characteristics of grey information system, it is often difficult to research with traditional

mathematical statistics. In order to solve the above problem, GRA was applied to evaluate and

analyze the green performance indicators of each module of CNC machine tools in this paper.

In order to solve the sequencing problem of module redesign in the greening process of the

CNC machine tools, the fuzzy analytic hierarchy process(FAHP) and the grey relational

analysis(GRA) were introduced to construct the priority order recognition method of module

redesign for the CNC machine tool product family, and the implementation process of the method

is shown in Figure 3.

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Module division and selection of

the CNC machine tool product

family according to Figure 1

Green performance

evaluation for each

indicator of module

instances

Determining the evaluation

criterions and indicators of each

module according to Figure 2

Priority order of module

redesign for the CNC machine

tool product family

Calculating the weight

coefficient of each

criterion and indicator

through FAHP

Calculating the comprehensive

green evaluation value of each

module instance through GRA

Figure. 3 Implementation process

4.1 FAHP-based weight calculation method of module green performance

Fuzzy analytic hierarchy process (FAHP) is a multi-criterion decision-making method, which

quantitatively analyzes qualitative problems, expresses the degree of human cognition on things in

the form of fuzzy numbers (Wang and Lin 2020). Fuzzy analytic hierarchy process (FAHP)

overcomes the shortcomings of the difficulty of consistency check of the judgment matrix of the

analytic hierarchy process (AHP), and expands the scope of application of AHP. The steps of

using FAHP to calculate the weight of each criterion and the weight of the indicator corresponding

to each criterion are as follows.

(1) Establishing fuzzy complementary judgment matrix. By judging the comparison among

the factors, the quantitative expression is carried out in the way of "the relative importance of the

two factors to their upper level indicators (or criterion or target)". If the scale method of 0.1 ~ 0.9

as shown in Table 1 is used for quantitative scaling, a fuzzy complementary judgment matrix

R=(rij)n×n(i,j=1, 2, …, n) is obtained. In the above matrix R, rij=0.5 represents the factor ri is as

important as itself; if rij�[0.1, 0.5), it means that the factor rj is more important than the factor ri; if

it is, it means that the factor ri is more important than the factor rj; if rij=0.5, it means that the

factor ri is as important as the factor rj.

Tab. 1 0.1~ 0.9 scale method and its meaning

Scale Definition Explanation

0.5 Equally important The two factors are equally important

0.6 Slightly important Comparing the two factors, one factor is slightly more important than the other

0.7 Obviously

important

Comparing the two factors, one factor is significantly more important than the

other

0.8 Much more

important

Comparing the two factors, one factor is much more important than the other

0.9 Extremely

important

Comparing the two factors, one factor is extremely important than the other

0.1, 0.2

0.3, 0.4

Reverse

comparisonIf the judgment rij obtained from comparing the factor ri with the factor rj, then

the judgment obtained by comparing the factor rj with the factor ri is rji=1-rij

(2) Weight coefficient calculation. If R=(rij)n×n is a fuzzy complementary judgment matrix,

and W=(W1, W2, …,Wi, …, Wn ) is a weight vector, then the general formula proposed by Xu

(2001) is used to solve the weight of the fuzzy complementary judgment matrix. The expression of

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the general formula is as follows:

(2)� �1

121,

�

��

nn

nr

W

n

ji ij

i

In the formula, Wi is the weight coefficient of factor ri.

(3) Consistency test. In order to judge whether the weight value calculated according to

formula (2) is reasonable, it is necessary to conduct a consistency test on the comparative

judgment process. Based on the definition of the compatibility index I(A, B) and feature matrix

W* of the judgment matrix described by Chen and Zhao (2004), the compatibility index and

feature matrix of the judgment matrix can be calculated, and their expressions are as follows:

(3)� � ��

n

ji jiij ban

BAI1,2

11

,

(4)� �nnijaA

�

(5)� �nnjibB

�

(6)� �nnijWW

� �

(7)njiWW

WW

ji

iij ,,2,1, ��

��

Among them, A and B are fuzzy complementary judgment matrices. If the compatibility

index value is less than a specific threshold � (generally �=0.1 is taken), the judgment matrix can

be considered as a satisfactory consistency matrix. The smaller the � is, the higher the decision

maker's requirement on the consistency of the fuzzy judgment matrix is.

For the case of multiple experts’ evaluation, each expert gives the fuzzy complementary

judgment matrix of the same factor set according to Table 2, and the corresponding weight set can

be calculated according to equation (2). If the compatibility index between each judgment matrix

and its corresponding feature matrix, and the compatibility index between any two judgment

matrices are less than a certain threshold �, it can be confirmed that it is reasonable and reliable to

use the mean value of the weight set as the weight distribution vector of the factor set.

4.2 GAR-based priority order recognition method for green performance of modules

Grey relational analysis(GRA) is a method to judge the correlation degree between factors

according to the similarity of the geometric shape of each factor's change curve (Hu 2020). The

main purpose of GRA is to simplify the multi-attribute decision-making problem into a

single-attribute decision-making problem, that is, integrating multiple performance indicator value

to a number in the range of [0, 1] to achieve comprehensive comparison. The realization process

of the GAR-based priority order recognition method of module redesign for the CNC machine tool

product family is as follows.

For all the module instances, the expert scoring method is used to give the scores of their 20

indicators (T = 20), and the decision matrix Y is constructed whose expression is as follows.

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(8)

�

�

��

�

�

�

TVTvTT

tVtvtt

Vv

Vv

yyyy

yyyy

yyyy

yyyy

Y

��

��

��

��

��

��

21

21

222221

111211

In the decision matrix Y, ytv is the green evaluation score of the indicator t(t=1, 2, …, t …, T)

corresponding to the module instance v(t=1, 2, …, v …, V) .

According to the scoring rules, all the indicators belong to benefit-type attributes (that is, the

larger the attribute value is, the better the indicator is), and the decision matrix Y is processed

through using the following formulas.

(9)

tt

ttvtv

yy

yyx

minmax

min

��

�

(10)},,,{ 21 tVttt yyyy ��

In the above formulas, minyt, maxyt are the minimum and maximum values of all elements in

vector yt respectively.

The normalized matrix X after processing decision matrix Y is obtained according to equation

(9), whose expression is as follows:

(11)

�

�

��

�

�

�

TVTvTT

tVtvtt

Vv

Vv

xxxx

xxxx

xxxx

xxxx

X

��

��

��

��

��

��

21

21

222221

111211

The reference sequence x0={x1(0), x2(0),…,xt(0),…, xT(0)}T is composed of the optimal

values of the indicators in the normalization matrix X, where xt(0)=max{xt1, xt1,…, xtV}. The grey

correlation coefficient ctv between each indicator xtv in the indicator sequence xt(v)=max{x1v, x2v,…,

xtv,…xtV} of each module instance v and the corresponding indicator xt(0) in the reference

sequence is calculated by the following equation.

(12)

tvtvt

tvt

tvtvt

tvtvt

tvxxxx

xxxxc

��

��

)0()0(

)0()0(

maxmax

maxmaxminmin

�

�

In the above equation, ( is the resolution coefficient, and its value is in the range of [0,1]. The

smaller the ( is , the greater the difference between the correlation coefficients is, and the stronger

the discriminating ability is /��Y!� � and Güllü 2015). (=0.5 is taken usually, and then the grey

correlation coefficient matrix C can be constructed according to equation (12).

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(13)

�

�

��

�

�

�

TVTvTT

tVtvtt

Vv

Vv

cccc

cccc

cccc

cccc

C

��

��

��

��

��

��

21

21

222221

111211

FAHP is used to calculate the weight coefficient vector {W1,W2,…,Wt,…,WT} of all

evaluation indicators relative to the target layer as described in above section, and then the grey

correlation vector of all module instances can be calculated according to the following formula.

(14)

},,,,,{

},,,{

21

21

21

222221

111211

21

Vv

TVTvTT

tVtvtt

Vv

Vv

T

gggg

cccc

cccc

cccc

cccc

WWWG

��

��

��

��

��

��

��

�

�

�

�

��

�

�

�

Among them, gv is used to express the grey correlation degree between the evaluation object

v (module instance) and the reference sequence. The smaller the grey correlation degree of a

module instance is, the worse the green performance of the module instance in multiple product

variants is. Dividing the above-mentioned grey correlation degree gv by the corresponding

functional module generality coefficient, the smaller the obtained quotient value is, the more

necessary to take this module instance as a priority option for green redesign it is.

5 Case application and analysis

Changzhou hanwei CNC Technology Co., Ltd. of China is a modern CNC equipment

manufacturing enterprise that integrates product development, design, production and sales, and

the gantry machine tool product family is one of its main products. In order to comply with the

trend of the green manufacturing industry, the company plans to launch a green redesign pilot

project for the gantry machine tool product family, and the module green performance evaluation

and redesign priority order recognition is an important part of the green redesign project. Gantry

machine tool product family adopts a modular structure, mainly including functional modules

such as Bed, Column, Screw, Spindle, Motor, Crossbeam, Guide, Rotary table, etc., as shown in

Figure 4.

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as shown in Figure 4. Different scoring ways were adopted for different green performance

criterions according to actual conditions. According to the fuzzy quantification approach presented

in section 3, green performance indicators’ data of green design performance criterion, resource

performance criterion, recycling performance criterion, energy performance criterion and

economic performance criterion was determined by each sub-group with a consensus after

in-depth discussion and analysis. Many researchers have worked out CO2 emissions from the

manufacture of subassemblies of machine tools (Deng et al. 2017; Cao et al. 2012; and Zhang et al.

2018), which provides a useful reference for the calculation and analysis of green performance

indicators’ data of the environmental performance criterion in this paper. Therefore, on basis of

research results of the impact of CO2 emissions on the environment (Chen et al. 2020), experts of

each sub-group analyzed and calculated environmental performance’s data of the 8 modules of the

gantry machine tool from their own job roles, and scored green performance indicators of

environmental performance through combining the quantification evaluation scale as described at

the end of section 3. Finally, all the green performance indicators were scored as shown in Tables

3-8.

Tab. 3 Data of green design performance

Green performance

indicators

Sub-gro

upsBed Column Screw Spindle Motor Crossbeam Guide

Rotary

table

S1 7 7 5 9 5 5 9 5

S2 9 5 7 9 9 3 5 9

S3 5 3 3 9 7 9 5 7

S4 5 7 5 9 9 5 7 5

Design

reliability f1

S5 9 3 5 9 5 3 9 9

S1 7 5 9 5 7 7 9 5

S2 5 3 7 9 7 5 9 7

S3 7 5 5 7 3 9 9 9

S4 9 7 7 9 5 9 9 7

Structural

rationality f2

S5 7 5 7 5 3 5 9 7

S1 5 3 3 5 7 1 9 3

S2 3 5 1 3 5 3 7 5

S3 5 1 3 5 3 5 5 7

S4 5 3 5 7 5 1 5 3

Process

feasibility f3

S5 7 3 3 5 5 5 9 7

Tab. 4 Data of resource performance

Green performance

indicators

Sub-gro


Rotary

table

S1 1 5 7 3 3 5 5 3

S2 3 3 5 5 5 7 9 5

S3 5 7 3 3 7 5 7 3

S4 3 5 3 1 5 3 9 1

Material

resources f4

S5 3 5 7 3 5 5 5 3

S1 5 7 9 5 9 3 5 7

S2 3 5 7 7 5 5 5 5

S3 3 9 5 5 7 7 7 3

S4 7 9 5 3 5 3 5 5

Equipment

resources f5

S5 7 5 9 5 9 7 3 5

S1 7 5 9 3 9 3 5 1

S2 9 5 7 3 9 1 9 3

S3 7 5 5 7 9 5 7 3

S4 7 3 9 7 9 3 7 3

Human

resources f6

S5 5 7 5 5 9 3 7 5

Tab. 5 Data of environmental performance

Green performance

indicators

Sub-gro


Rotary

table

S1 3 5 7 5 9 7 9 3Air pollution f7 S2 9 3 9 9 7 9 5 7

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S3 5 1 7 7 5 3 3 5

S4 3 5 5 9 7 9 5 3

S5 5 1 7 5 7 7 3 7

S1 3 3 7 5 3 5 5 1

S2 1 5 1 3 7 7 5 7

S3 3 3 3 9 5 5 7 1

S4 1 9 3 3 3 3 3 3

Oil pollution f8

S5 7 5 1 5 7 5 5 3

S1 3 7 3 9 3 5 3 1

S2 1 3 9 7 7 3 5 7

S3 3 1 5 5 3 1 5 3

S4 5 3 3 5 5 3 9 1

Solid waste

pollution f9

S5 3 1 5 9 7 3 3 3

S1 5 1 7 3 7 3 3 3

S2 9 5 1 5 5 5 1 5

S3 3 1 3 7 7 5 3 7

S4 5 3 1 5 9 7 5 7

Noise pollution f10

S5 3 5 3 5 7 5 3 3

Tab. 6 Data of recycling performance

Green performance

indicators

Sub-gro


Rotary

table

S1 3 5 7 5 7 3 5 7

S2 1 3 9 7 9 9 9 5

S3 3 1 3 9 5 7 3 3

S4 1 5 7 7 5 9 5 3

Recycling

possibility f11

S5 7 1 9 7 9 7 3 7

S1 5 1 3 7 9 3 5 9

S2 3 3 9 9 5 7 7 7

S3 5 3 5 3 3 5 9 5

S4 7 5 3 9 5 7 7 5

Recycling

method f12

S5 5 3 5 7 3 3 7 9

S1 3 5 3 3 7 5 1 3

S2 1 3 5 5 3 7 5 7

S3 3 1 9 7 1 5 3 5

S4 3 5 3 3 3 3 1 7

Recycling

value f13

S5 5 1 1 7 1 5 5 3

S1 9 5 5 3 3 7 5 3

S2 5 5 1 5 5 5 7 7

S3 3 3 3 5 3 3 5 3

S4 3 9 5 7 9 5 3 5

Recyclability f14

S5 5 3 1 5 5 5 5 7

Tab. 7 Data of energy performance

IndicatorsSub-grou

psBed Column Screw Spindle Motor Crossbeam Guide

Rotary

table

S1 5 3 9 3 5 3 7 5

S2 3 9 3 5 7 5 1 3

S3 9 3 5 7 3 5 3 1

S4 3 3 5 5 3 7 1 3

Energy type f15

S5 5 7 3 5 7 5 3 3

S1 1 5 3 3 9 7 3 5

S2 3 7 5 1 5 7 7 3

S3 5 5 7 7 3 9 5 1

S4 5 3 5 1 3 5 7 1

Energy consumption

f16

S5 1 5 5 3 5 7 3 5

S1 9 1 7 5 7 3 1 3

S2 5 3 3 7 5 5 3 5

S3 3 5 5 7 9 7 7 9

S4 5 3 3 9 9 5 1 3

Energy

efficiency f17

S5 3 3 7 7 5 5 3 5

Tab. 8 Data of economic performance

Green performance

indicators

Sub-gro


Rotary

table

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S1 3 9 3 3 5 5 9 1

S2 5 5 9 1 3 7 3 7

S3 9 7 3 3 1 5 7 3

S4 5 5 5 5 1 3 7 1

R & D cost f18

S5 3 9 5 3 5 5 9 3

S1 3 5 1 7 9 5 7 1

S2 3 7 1 5 3 3 3 3

S3 9 3 7 3 9 1 3 3

S4 5 5 3 7 7 1 9 5

Mmanufacturing cost

f19

S5 5 5 3 3 7 5 3 3

S1 3 1 5 9 9 3 3 5

S2 9 3 7 9 9 7 7 5

S3 3 7 9 9 9 9 5 3

S4 7 1 7 9 9 7 7 7

Maintenance

cost f20

S5 3 3 7 9 9 9 3 5

After all the five sub-groups had finished scoring the green performance indicators, the

arithmetic mean of each indicator’s data was employed as its green performance value, for

example, the data of design reliability indicator of the bed was calculated according to table 3 as

follows: (7+9+5+5+9)/5=7. Finally, on basis of Tables 3-8, a green performance evaluation table

for the functional modules of the gantry machine tool product family was established in the above

way as shown in Table 9.

Tab. 9 Evaluation value of green performance for modules of gantry machine tools

5.2 Indicators' weight calculation based on FAHP

The expert scoring method was applied to establish the fuzzy complementary judgment

matrix of the criterion layer relative to the target layer, and the fuzzy complementary judgment

matrix of each indicator relative to its corresponding criterion. The fuzzy complementary

judgment matrix RA[B of the criterion layer relative to the target layer constructed is as follows.

�

�

��

�

�

��

5.04.03.03.05.04.0

6.05.04.04.05.05.0

7.06.05.04.06.06.0

7.06.06.05.07.07.0

6.05.04.03.05.05.0

6.05.04.03.05.05.0

BAR

Indicators Bed Column Screw Spindle Motor Crossbeam Guide Rotary table

Design reliability f1 7 5 5 9 7 5 7 7

Structural rationality f2 7 5 7 7 5 7 9 7

Process feasibility f3 5 3 3 5 5 3 7 5

Material resources f4 3 5 5 3 5 5 7 3

Equipment resources f5 5 7 7 5 7 5 5 5

Human resources f6 7 5 7 5 9 3 7 3

Air pollution f7 5 3 7 7 7 7 5 5

Oil pollution f8 3 5 3 5 5 5 5 3

Solid waste pollution f9 3 3 5 7 5 3 5 3

Noise pollution f10 5 3 3 5 7 5 3 5

Recycling possibility f11 3 3 7 7 7 7 5 5

Recycling method f12 5 3 5 7 5 5 7 7

Recycling value f13 3 3 5 5 3 5 3 5

Recyclability f14 5 5 3 5 5 5 5 5

Energy type f15 5 5 5 5 5 5 3 3

Energy consumption f16 3 5 5 3 5 7 5 3

Energy efficiency f17 5 3 5 7 7 5 3 5

R & D cost f18 5 7 5 3 3 5 7 3

Manufacturing cost f19 5 5 3 5 7 3 5 3

Maintenance cost f20 5 3 7 9 9 7 5 5

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According to equation (2), the weight vector of the criterion layer was obtained, which is

WA[B={0.16, 0.1567, 0.1933, 0.18, 0.1633, 0.1467}. According to equation (6) and (7), the

feature matrix W*A[B of the fuzzy complementary judgment matrix RA[B was constructed.

�

�

��

�

�

��

500.0473.0449.0431.0484.0478.0

527.0500.0476.0458.0510.0505.0

551.0524.0500.0482.0535.0529.0

569.0542.0518.0500.0552.0547.0

517.0490.0465.0448.0500.0495.0

522.0495.0471.0453.0505.0500.0

*

BAW

According to equation (3), the compatibility between the judgment matrix and the feature

matrix was calculated to be 0.062 <0.1, so it can be confirmed that taking the weight vector WA[B

as the weight distribution of the criterion layer is reliable. Similarly, the weight vectors of the

indicator layer relative to the corresponding criterion layer can be calculated, and the results

obtained are as follows.

WB[C1={0.267, 0.333, 0.4}

WB�[C2={0.311, 0.311, 0.378}

WB>[C3={0.25, 0.25, 0.25, 0.25}

WBP[C4={0.237, 0.213, 0.263, 0.287}

WB"[C5={0.289, 0.422, 0.289}

WB.[C6={0.334, 0.333, 0.333}

Combining the weight of the criterion layer relative to the target layer with the weight of the

indicator layer relative to the criterion layer, the weight vector WA[C of each indicator relative to

the target layer was obtained as follows.

�

�

��

�

�

�

�

�

�

�

�

�

��

66

55

44

33

22

11

CB

CB

CB

CB

CB

CB

BACA

W

W

W

W

W

W

WW

={0.0427, 0.0533, 0.064, 0.0487, 0.0487, 0.0592, 0.0483, 0.0483, 0.0483, 0.0483, 0.0427,

0.0383, 0.0473, 0.0517, 0.0472, 0.0689, 0.0472, 0.0490, 0.0489, 0.0489}

5.3 Priority order recognition based on GRA

Based on the expert's scoring of different indicators for each functional module as shown in

Table 3, the grey correlation coefficient matrix of the indicators of the 8 functional modules of the

gantry machine tool product family was obtained according to equations (9) to (13), which is as

follows.

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�

�

��

�

�

�

4286.04286.06.0116.03333.04286.0

3333.05.03333.015.03333.05.05.0

3333.015.03333.03333.05.015.0

5.03333.05.0115.03333.05.0

3333.05.015.03333.05.05.03333.0

3333.03333.0111111

111113333.011

13333.013333.0113333.03333.0

115.05.015.03333.05.0

5.05.011113333.03333.0

5.03333.05.015.03333.03333.05.0

3333.05.03333.05.015.03333.03333.0

3333.011113333.013333.0

5.05.011113333.05.0

3333.06.03333.014286.06.04286.06.0

3333.03333.03333.013333.0113333.0

3333.015.05.03333.05.05.03333.0

5.013333.05.05.03333.03333.05.0

5.015.03333.05.05.03333.05.0

5.05.03333.05.013333.03333.05.0

C

In matrix C, the elements from the first row to the third row constitute the grey correlation

coefficient matrix of the green design performance of the 8 functional modules, denoted as C1; the

elements from the fourth row to the sixth row constitute the grey correlation coefficient matrix of

the resource performance of the 8 functional modules, denoted as C2; the elements in the seventh

row to the tenth row constitute the grey correlation coefficient matrix of the environmental

performance of the 8 functional modules, denoted as C3; the elements from the eleventh row to

the fourteenth row constitute the grey correlation coefficient matrix of recycling performance of

the 8 functional modules, denoted as C4; the elements in the fifteenth row to the seventeenth row

constitute the grey correlation coefficient matrix of the energy performance of the 8 functional

modules, denoted as C5; the elements from the eighteenth row to twentieth row constitute the grey

correlation coefficient matrix of the 8 functional modules, denoted as C6. Therefore, the

expressions of C1, C2, C3, C4, C5, and C6 are as follows.

0.5 0.3333 0.3333 1 0.5 0.3333 0.5 0.5

1 0.5 0.3333 0.5 0.5 0.3333 0.5 1 0.5

0.5 0.3333 0.3333 0.5 0.5 0.3333 1 0.5

C

� ��

0.3333 0.5 0.5 0.3333 0.5 0.5 1 0.3333

2 0.3333 1 1 0.3333 1 0.3333 0.3333 0.3333

0.6 0.4286 0.6 0.4286 1 0.3333 0.6 0.3333

C

� ��

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0.5 0.3333 1 1 1 1 0.5 0.5

0.3333 1 0.3333 1 1 1 1 0.33333

0.3333 0.3333 0.5 1 0.5 0.3333 0.5 0.3333

0.5 0.3333 0.3333 0.5 1 0.5 0.3333 0.5

C

� ��

0.3333 0.3333 1 1 1 1 0.5 0.5

0.5 0.3333 0.5 1 1 0.5 1 14

0.3333 0.3333 1 1 0.3333 1 0.3333 1

1 1 0.3333 1 1 1 1 1

C

� ��

1 1 1 1 1 1 0.3333 0.3333

5 0.333 0.5 0.5 0.3333 0.5 1 0.5 0.3333

0.5 0.3333 0.5 1 1 0.5 0.3333 0.5

C

� ��

0.5 1 0.5 0.3333 0.3333 0.5 1 0.3333

6 0.5 0.5 0.3333 0.5 1 0.3333 0.5 0.3333

0.4286 0.3333 0.6 1 1 0.6 0.4286 0.4286

C

� ��

On basis of the formula (14), grey correlation vectors (G1, G2, G3, G4, G5, G6) of the 6

evaluation criterions of the 8 functional modules of the gantry machine tool product family were

obtained, which are as follows.

G1= WB[C1×C1={0.5000, 0.3333, 0.3888, 0.6335, 0.4445, 0.3888, 0.8665, 0.5000}

G2= WB�[C2×C2={0.4341, 0.6285, 0.6933, 0.3693, 0.8445, 0.3851, 0.6415, 0.3333}

G3= WB>[C3×C3={0.4166, 0.5000, 0.5416, 0.8750, 0.8750, 0.7083, 0.5833, 0.4166}

G4= WBP[C4×C4={0.5601, 0.5246, 0.7022, 1.0000, 0.7182, 0.8935, 0.7062, 0.8815}

G5= WB"[C5×C5={0.5742, 0.5963, 0.6445, 0.7187, 0.7890, 0.8555, 0.4036, 0.3815}

G6= WB.[C6×C6={0.4762, 0.6115, 0.4778, 0.6108, 0.7773, 0.4778, 0.6432, 0.3650}

According to the above calculation results, the comparisons of the 6 evaluation criterions of

the 8 functional modules of the gantry machine tool product family are displayed as Figures 5-10.

Fig.5 Green design performance comparison

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Fig.6 Resource performance comparison

Fig.7 Environmental performance comparison

Fig.8 Recycling performance comparison

Fig.9 Energy performance comparison

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Fig.10 Economic performance comparison

Then, drawing on the formula (14), the grey correlation vector G of the 8 functional module

instances relative to the reference sequence was obtained as follows.

G=WA[C×C={0.4930, 0.5299, 0.5772, 0.7153, 0.7447, 0.6301, 0.6392, 0.4872}

Based on the obtained grey correlation vector, the green comprehensive evaluation

comparison of the 8 functional modules of the gantry machine tool product family is shown in

Figure 11.

Fig.11 Green comprehensive evaluation comparison

5.4 Results and discussion

Since each module is a required variant module, all their generality coefficient is 1 according

to Figure 1 and equation (1). It can be seen from Figure 11 that the green performance order of

each functional module of the gantry machine tool from good to bad is Motor, Spindle, Guide,

Crossbeam, Screw, Column, Bed, Rotary table, that is, the green performance of the motor is the

best, and the green performance of the rotary table is the worst. The worse the green performance

of a functional module of the gantry machine tool is, the more necessary to do green redesign for

the module it is. Therefore, according to the obtained grey correlation vector G and Figure 11, the

priority order of functional module greening redesign is: Rotary table, Bed, Column, Screw,

Crossbeam, Guide, Spindle, Motor, namely the rotary table needs to be green redesigned firstly,

which provides a scientific basis for the company to carry out the greening improvement project

of the gantry machine tool product family.

In current structural design of the rotary table of gantry machine tools in China, traditional

design methods are still widely used, such as adopting a large safety factor to ensure structural

reliability and mechanical performance. Although general calculations and tests are adopted

during the design process, the structural size and weight of the rotary table are still relatively big,

and the potential of the material could not be fully utilized, which increases the manufacturing and

maintenance costs. Therefore, rotary tables have a wide green design space, and the results of the

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case application in this paper also reflect this actual engineering issue.

Analyzing Figures 5-10, it can be seen that among the 8 functional modules of the gantry

machine tool product family, the resource performance, energy performance and economic

performance of the rotary table have the smallest grey correlation degree, that is, these three

performances of the rotary table are relatively bad. Based on the above analysis, in the redesign

process of the rotary table of the gantry machine tool product family, the improvement of resource

performance, energy performance and economic performance should be taken as the optimization

goal firstly, which provides a scientific basis for the green redesign for the rotary table of gantry

machine tools in a more targeted manner.

Through using the proposed method to analyze this case, it is recommended that the optimal

lightweight design and energy-saving design for rotary tables should be emphatically considered

in future work, so as to reduce the material consumption of rotary tables, decrease the

manufacturing and maintenance costs, and improve the energy utilization efficiency of rotary

tables during the work process.

The above research results show that the rotary table of gantry machine tools most should be

redesigned to improve the green performance, which is consistent with the research work of

Croccolo et al. (2018). In the above mentioned research work, the rotary table of a CNC machine

tool had been conducted optimal lightweight design through using the concepts of green design as

well as sustainable development thinking. Therefore, the research results of this paper are in line

with scientific judgments in machine tools’ design engineering.

6 Conclusion and future work

Aiming at the demand on green redesign of the product family of CNC machine tool

companies, a hierarchical model of functional modules of the CNC machine tool product family

was constructed and the types of functional modules were divided, and then the generality

coefficient of the functional module was proposed to reflect the influence of the module type on

the redesign priority order. Starting from the 6 major criterion of green design performance,

resource performance, resources, environmental performance, recycling performance, energy

performance and economic performance, a life cycle-oriented green performance evaluation

system for functional modules of the CNC machine tool product family with 20 indicators was

established. On the above basis, the priority order recognition method of module redesign for the

CNC machine tool product family was constructed based on fuzzy analytic hierarchy process

(FAHP) and grey relational analysis (GRA). The proposed approach was utilized to identify the

priority order of module redesign for a gantry machine tool product family, and research results

show the rotary table module should be green redesigned firstly.

Although a recognition method of module redesign for the CNC machine tool product family

was constructed in this paper, there are still some limitations that needs to be overcome. During

the implementation of the method proposed in this paper, experts used fuzzy scoring to evaluate

the green performance of functional modules of CNC machine tool product family based on

experience to some extent, so it is very necessary to establish more scientific and reliable scoring

standards especially when the machine tools' green performance requirements are much higher;

many experts with different job roles were organized to evaluate the green performance data of

CNC machine tools' modules, and the arithmetic mean of the data determined by the experts was

applied as green performance indicator values, which consumed a lot of human resources and time,

therefore, the approach to obtain and analyze green performance indicator data more efficiently

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and accurately is also an urgent issue to be addressed in future work. The recognition method

proposed in this paper only can reveal the relative sequence of modules of the CNC machine tool

product family, so in the actual application process, researchers/engineers must combine the grey

correlation vector obtained by the method with machine tool manufacturers’ own technical level

and development requirements to reasonably determine modules that should be redesigned to

improve green performance.

Acknowledgments

The work is supported by the National Natural Science Foundation of China (Grant No.

51865008), and the Open Fund Project of Jiangsu Key Laboratory of Precision and

Micro-Manufacturing Technology (Grant No. 201925).

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List of symbols

Fk functional module

Lk generality coefficient

R fuzzy complementary judgment matrix

W weight vector

C grey correlation coefficient matrix

G grey correlation vector

( resolution coefficient

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priority order recognition method of module redesign for

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