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)
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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
upsBed Column Screw Spindle Motor Crossbeam Guide
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
upsBed Column Screw Spindle Motor Crossbeam Guide
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
upsBed Column Screw Spindle Motor Crossbeam Guide
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
upsBed Column Screw Spindle Motor Crossbeam Guide
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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