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International Journal of Computer Integrated

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Adaptive control optimisation system for minimising

production cost in hard milling operations
a

Jorge A. Silva , Jos V. Abelln-Nebot , Hector R. Siller & Federico Guedea-Elizalde

Center for Innovation in Design and Technology, Tecnolgico de Monterrey, Monterrey,

Mxico
b

Department of Industrial Systems Engineering and Design,, Universitat Jaume I, Castelln,

Spain
Version of record first published: 19 Dec 2012.

To cite this article: Jorge A. Silva , Jos V. Abelln-Nebot , Hector R. Siller & Federico Guedea-Elizalde (2012): Adaptive
control optimisation system for minimising production cost in hard milling operations, International Journal of Computer
Integrated Manufacturing, DOI:10.1080/0951192X.2012.749535
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International Journal of Computer Integrated Manufacturing

2013, 113, iFirst article

Adaptive control optimisation system for minimising production cost in hard milling operations
Jorge A. Silvaa, Jose V. Abellan-Nebotb, Hector R. Sillera* and Federico Guedea-Elizaldea
a

Center for Innovation in Design and Technology, Tecnologico de Monterrey, Monterrey, Mexico; bDepartment of Industrial
Systems Engineering and Design, Universitat Jaume I, Castellon, Spain

Downloaded by [Hector Siller] at 06:09 21 December 2012

(Received 22 February 2012; nal version received 21 October 2012)

This paper proposes an adaptive control with optimisation (ACO) methodology for optimising the production cost
subjected to quality constraints in high-performance milling operations of hardened steel (5862 HRC). Unlike
traditional approaches for optimising production cost, this paper deals with optimising the cutting operation
considering the current state of the cutting tool. Articial intelligence techniques for modelling (articial neural
networks) and optimising (genetic algorithms and mesh adaptive direct search algorithms) are applied for this
purpose. As a result, the production cost estimation from the proposed approach is 13% lower than the one
obtained by the traditional approach with 76% less uncertainty.
Keywords: articial neural networks; production cost; adaptive control with optimisation (ACO); genetic algorithms;
mesh adaptive direct search algorithms; hard milling

1.

Introduction

The machining of hardened steels (5862 HRC) for

moulds and dies requires costly and time-consuming
operations such as electrical discharge machining and
grinding operations in order to meet part quality
specications. Recently, the emerging eld of hard
cutting to avoid these inecient operations is gaining
popularity. In hard cutting, high-performance machining centres with special cutting tools such as Cubic
Boron Nitride (CBN) tools are used to meet quality
specications without conducting subsequent grinding
operations. In this eld, rst introductory steps have
been made in automotive, gear, bearing, tool and die
making industry (Tonsho et al. 2000).
Cutting parameter selection for minimising production cost in hard cutting operations requires the
evaluation of cutting-tool costs and non-quality costs.
Current practices for selecting optimal cutting parameters are based on minimising the manufacturing cost
assuming that the estimation of cutting-tool life and
surface roughness from heuristic and analytical (combined) models is reliable for process planning (Wang
et al. 2005, Valentincic et al. 2007). Furthermore, the
surface roughness is assumed to be independent of
other variables such as cutting-tool wear or built-up
edge, and then, the selection of optimal cutting
parameters can be conducted o-line (Samanta 2009).
In this paper, the o-line selection of optimal cutting
parameters for minimising production cost is referred
to as traditional approach. In this eld, some

*Corresponding author. Email: hector.siller@itesm.mx

ISSN 0951-192X print/ISSN 1362-3052 online
2013 Taylor & Francis
http://dx.doi.org/10.1080/0951192X.2012.749535
http://www.tandfonline.com

interesting research works have been reported in the

past. In Zuperl and Cus (2003), a multi-objective
function for optimising the machining process is
presented, considering three conicting objectives:
production rate, operation cost and quality of machining. An articial neural networks (ANN) was trained
in order to model the relationship between the
parameters cutting speed, feed rate and depth of cut,
and the multi-objective function. The optimal cutting
parameters are found by searching for the extreme
value of the multi-objective function. This work was
improved by the same authors (Zuperl et al. 2004),
where the optimisation of cutting parameters was
conducted based on the minimum cost per product
criterion. The cost function was modelled by combining an ANN and an analytical module that selects the
optimum cutting conditions from commercial databases with respect to minimum machining costs. In
Cus and Balic (2003), the optimal cutting parameters
in order to minimise the unit production cost were
conducted using analytical models to describe the
material removal rate (MRR), production rate, tool
life, operation cost, cutting forces and cutting quality.
The optimisation procedure was based on genetic
algorithms (GA) subjected to cutting power and
cutting force constraints. In Gopal and Rao (2003),
optimal cutting parameters to maximise the MRR
subjected to surface roughness and surface damage
constraints in grinding operations were studied. In
order to model surface roughness and surface damage,

Downloaded by [Hector Siller] at 06:09 21 December 2012

J.A. Silva et al.

a design of experiments (DoE) was conducted and the

experimental results were used to model the variable
responses using multiple regressions. The optimisation
procedure was based on GA.
These research works presented methods to optimise cutting parameters but assuming that part quality
is independent of the cutting-tool state. However,
several research works have shown that cutting-tool
wear together with other factors can directly impact on
surface roughness, especially in hard cutting operations (Benardos and Vosniakos 2002, Siller et al. 2008).
Figure 1 shows a set of factors that may aect the
surface roughness. Therefore, in hard cutting operations where cutting-tool wear eect on surface roughness has been clearly identied as a key factor to keep
parts within specications (Siller et al. 2008), the
production cost optimisation procedure should consider the life cycle of the cutting tool during its
operation and its impact on non-quality costs. Under
this approach, one can expect dierent cutting

parameters according to the state of the cutting tool,

so the adaptation of cutting parameters is required for
a real minimum production cost.
In the literature, the adaptation of cutting parameters according to the state of the machining
operation has been successfully implemented under
three major strategies (Koren 1989):
(1) Geometric adaptive control (GAC).
(2) Adaptive control with optimisation (ACO).
(3) Adaptive control with constraints (ACC).
In the GAC systems, process parameters are
modied to maintain product quality such as dimensional accuracy and/or surface nish (Coker and Shin
1996). In ACO systems, a given performance index
(usually an economic function) is optimised subject to
process and system constraints (Koren 1989, Liang
et al. 2004). Traditionally, ACO systems have dealt
with adjusting cutting parameters (feed rate, spindle

Figure 1. Fishbone diagram of parameters that aect surface roughness (adapted from Benardos and Vosniakos 2003, AbellanNebot 2010).

Production cost
ACO (adaptation of cutting parameters)
To present in this paper

Analytical and ANN models.

Analytical and regression models.
Knowledge-based machining data.
Analytical and ANN models.
Genetic Algorithms and
MADS for optimisation.
Chiang et al. (1995)
Billatos and Tseng (1991)

Abellan-Nebot et al. (2008)

Liu et al. (1999)

Cus and Balic (2003)

ACC (adaptation of cutting parameters)

ACO (adaptation of cutting parameters)

Multi-objective function based on desirability

functions of cutting-tool life, surface
roughness and material removal rate.
Feed rate
Material removal rate

Material removal rate

Production cost

Material removal rate

Gopal and Rao (2003)

Analytical and ANN models. Experimental

data from manufacturers databases.
Analytical and regression models.
GA algorithms for optimisation.
Analytical models and GA algorithms
for optimisation.
ANN models, expert rules and
GA algorithms for optimisation.
Analytical, regression, and ANN models.
Search algorithms for optimisation.
Zuperl et al. (2004)

Traditional approach
(xed cutting parameters)
Traditional approach
(xed cutting parameters)
Traditional approach
(xed cutting parameters)
ACO and ACC
(adaptation of cutting parameters)
ACO (adaptation of cutting parameters)

Multi-objective function based on: production

rate, operation cost and quality of
machining.
Production cost
Analytical and ANN models
Zuperl and Cus (2003)

Traditional approach
(xed cutting parameters)

Optimised performance index

Approach
Modelling and optimisation techniques applied
Reference

Literature review and paper contribution.

speed and depth of cut) to maximise MRR or other

performance indices subjected to constraints such as
surface roughness, power consumption, cutting forces,
etc. (Koren 1989). In these systems, an in-process
monitoring of process performance is used to determine
the new optimised set of cutting parameters, enabling
autonomous self-optimisation. Unlike ACO, ACC
systems do not utilise a performance index and are
based on maximising a machining variable (e.g. feed
rate) subjected to process and machine constraints (e.g.
allowable cutting force on the tool, or maximum power
of the machine). In the literature, several research works
have been reported in order to adapt cutting parameters
during the machining process, and good reviews of the
applicability of adaptive control in machining can be
found in Koren (1989) and Ulsoy and Koren (1989). In
Chiang et al. (1995), an ACC system was analysed to
maximise feed rate in end milling operations constrained to maximum cutting forces relative to threshold
tool breakage conditions. They proposed the use of two
neural networks, a rst one to model the cutting process
and the second one to determine optimal cutting
parameters for a maximum feed rate. In Billatos and
Tseng (1991), an ACO system was researched to
determine the optimum feed rate and spindle speed in
order to maximise the MRR. In this work, tool life and
cutting force models were obtained tting a linearised
Taylor model with experimental data. In Liu et al.
(1999), an ACO and ACC system was proposed in
milling processes. The ACO system was applied for
optimising the MRR, and it was based on an ANN and
GA. On the other hand, the ACC system was applied to
modify the feed rate constrained to a maximum force
value, and it was based on ANN and expert rules. Both
systems were proved to present a higher machining
eciency than selecting cutting parameters from handbooks. In Abellan-Nebot et al. (2008), an ACO system
was proposed to optimise a multi-objective function
dened by an overall desirability function composed of
three desirability functions related to MRR, surface
roughness and cutting-tool life. This work compared the
ACO results with the traditional approach using both
regression and ANN models.
Despite previous research eorts, to the best of
authors knowledge, there is no ACO system studied for
minimising the production cost, mainly because, as
reported above, production costs have been assumed
independent of the cutting-tool state. In this paper, an
ACO method for product cost optimisation of hard
milling operations is proposed and analysed. The
proposed system adjusts cutting parameters during the
cutting-tool life cycle every time a tool pass is over in
order to minimise the cutting-tool pass cost, and then,
the total production cost. Table 1 shows the literature
review and the paper contribution in the eld.

Table 1.

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International Journal of Computer Integrated Manufacturing

Downloaded by [Hector Siller] at 06:09 21 December 2012

J.A. Silva et al.

The rest of the paper is organised as follows.

Section 2 describes the traditional approach applied to
obtain optimal cutting parameters for minimising the
production cost in a machining process and the models
commonly applied for Ra and T. Section 3 describes
the ACO system proposed to overcome the traditional
approach limitations. In Section 4, an experimental
case study is analysed for both traditional and ACO
approaches in order to prove the higher performance
of the ACO system for minimising production cost.
Finally, Section 5 presents the conclusions of the
paper.

where D is the rotary cutting-tool diameter, L the

workpiece length to be machined, Vc the cutting
speed, fz the feed per tooth, np the number of parts to
be machined, z the number of teeth, e the overtravel of the milling cutter on the workpiece, e the
thickness of the workpiece to be machined and ap the
axial depth of cut. Denoting Dt as the workpiece
diameter and fr as the feed per revolution, the
machining time equation for turning operations is
dened as Equation (3):

2.

The production cost for a part lot (Cu) can be

formulated as Equation (4):

Traditional cutting parameters optimisation

The traditional machining economics problem consists

in determining the optimal cutting parameters in order
to maximise or minimise an objective function based
on a desired economic criterion and subjected to the
constraints applicable to the machining system. Three
economic criteria are commonly applied: production
time, production cost and prot rate. The maximum
production objective (minimum production time) seeks
to identify the cutting conditions that best balance the
MRR and tool life to produce the highest output. The
production cost objective seeks to nd a balance
between MRR and tool life to produce at the lowest
cost. For the case of the maximum rate of prot
criteria, there is a balance between the contributions of
both minimum production cost and production time
criteria into the objective function. For practical
purposes, it has been found that unless the prot
margin is very high, the optimum conditions predicted
by the maximum prot rate criterion tends to lie close
to the minimum production cost (Stephenson and
Agapiou 1997). In this paper, without loss of generality, the economic criterion analysed is the minimum
production cost.
2.1.

Production cost

In machining systems, the time to produce a part lot

(Tu) can be dened by Equation (1):
Tu ts tm ttc

tm
;
T

where ts is the set up time, tm the machining time, ttc

the tool change time and T the expected cutting-tool
life.
For milling operations, the machining time is
dened by Equation (2) (Stephenson and Agapiou
1997):
tm

p  D  L e  e=ap  np
;
1000  z  Vc  fz

tm

p  D t  L  np
:
1000  Vc  fr

Cu cmat c1 c0 ts c1 c0 tm
tm
c1 ttc ct c0 ttc ;
T

where cmat is the cost of the raw material per part, c1 is

the labour cost, c0 is the overhead cost and ct is the cost
of the cutting tool. Additionally, in hard cutting
operations, the cost of quality loss due to the deviation
of the part surface quality (measured as the surface
roughness Ra) from its desired value should be
considered. For this purpose, the Taguchis loss quality
function for the nominal-the-best case can be added as
an additional cost, and it is formulated as Equation (5)
(Li 2000):
Cq Arw

b2
np ;
D2

where Arw is the part cost if the part is outside of

specications, np the number of parts to be machined,
b 2 is the mean square deviation of Ra and D2 is the
maximum admissible square deviation of Ra from
specications, which are expressed as Equations (6)
and (7), respectively, as follows:
D2 Ra max  Ra tgt 2 ;

b2 Ra avg  Ra tgt 2 :

From previous equations, Ra max is the maximum Ra

dened by the specications, Ra tgt is the desired Ra and
Ra avg is the expected average Ra of the machined
workpiece. Therefore, the minimum production cost,
denoted as Ctot, will be obtained by minimising the
following equation:
Ctot Cu Cq :

International Journal of Computer Integrated Manufacturing

2.2.

Constraints

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Due to the limitations of the cutting process, the

cutting-tool manufacturers limit the range of the
cutting parameters to avoid premature failures, unsafe
operations and undesired cutting eects. Therefore,
according to manufacturers specications, the cutting
parameters are constrained to:
Vcmin  Vc  Vcmax ;

fzmin  fz  fzmax ;

10

ap  apmax :

11

Furthermore, cutting parameters are constrained to

ensure that machined parts meet the design specications of Ra which are limited by a maximum admissible
value. Thus, the following constraint also applies:
Ra  Ra max :

estimations. First, the use of Taylors equation for

estimating T in cutting-tool materials such as CBN
tools may be not accurate enough as reported in Trent
and Wright (2000). Second, surface roughness generation is inuenced by additional mechanisms such as
vibrations, engagement of the cutting tool, built up
edge and tool wear among others, especially in hard
cutting machining operations (Siller et al. 2008).
Therefore, Equation (14) may be inadequate to model
Ra for actual machining operations when tool wear
gradually occurs and when the operation is subjected
to stochastic phenomena. Additionally, even if these
models were accurate enough, the traditional optimisation methods cannot consider the current state of the
cutting tool during the operation since this optimisation procedure is conducted o-line in order to dene
the cutting parameters for the whole cutting-tool life. It
seems that a more ecient approach would result if the
cutting conditions can be modied according to the
current state of the cutting tool and the actual surface
roughness values.

12
3.

2.3.

Process models

The traditional optimisation approach requires the use

of theoretical/empirical models that relate cutting
parameters with tool life T and surface roughness Ra
since both process variables are included in Equation
(8) and they are closely related to cutting parameters.
The relation between T and cutting parameters is
usually expressed by empirical models such as the wellknown Taylors formula shown in Equation (13),
adapted from (Schey 2000), where KT, a1, a2 and a3
are empirical coecients which can be usually
obtained from handbooks or cutting data catalogues.
T

KT
:
a3
Va1

fa2
c
z  ap

13

On the other hand, Ra is usually estimated by

analytical or empirical expressions such as Equation
(14) presented in (Cus and Balic 2003), where k, a, b
and c are empirical coecients.
Ra avg k  Vac  fbz  acp :

2.4.

14

Limitations

The minimisation of the production cost requires

reliable process models for Ra and T. According to
the traditional approach, these models are based on
Equations (13) and (14). However, for hard cutting
operations, these models tend to generate inaccurate

Proposed adaptive control optimisation system

The proposed ACO system overcomes the limitations

of traditional optimisation approaches using in-process sensor measurements as well as robust and reliable
articial intelligent (AI) process models. The proposed
ACO system is described in Figure 2 and its operation
is described as follows. After each cutting-tool pass,
the ACO system obtains information of the operation
by sensors installed in the machine-tool. After conditioning the signals and extracting their descriptors
(signicant values such as average, root mean square
(RMS), etc.), these values are used by the process
models to estimate the current performance of the
machining (current tool wear (Tw), Ra and T). The
process models are based on AI techniques and were
previously learnt from experimental data. Using the
estimations from the AI models, the objective function
is optimised by a combination of optimisation
techniques for black box models such as GA and
mesh adaptive direct search (MADS) algorithms (Shan
and Wang 2010). The optimisation provides the
optimal cutting parameters for the next cutting-tool
pass, which are sent to the numerical control system of
the machine-tool.
In order to evaluate the objective function in terms
of production cost per pass, the traditional optimisation approach should be transformed into a cuttingtool pass optimisation approach. For this purpose,
Equation (8) can be transformed into cutting-tool pass
costs including the eect of the cutting-tool wear (Tw)
on Ra along all the life cycle of the cutting tool.
Considering only the production cost terms that

Downloaded by [Hector Siller] at 06:09 21 December 2012

Figure 2.

J.A. Silva et al.

Adaptive control with optimisation (ACO) scheme (adapted from Schey 2000).

depend on cutting parameters and dening tith

m as the
machining time of each ith cutting pass, Equation (8)
can be rewritten as:
ith
Cith
tot c1 c0 tm c1 ttc ct c0 ttc

tith
b2
m
Arw ith
;
T
D2
15

where the term tith

m =T means the percentage of usage of
the cutting tool in the ith cutting pass and b2ith is the
expected surface roughness mean square deviation of
the ith pass. Note that the eect of Tw on Ra is shown
in the term b2ith, since the expected average Ra depends
on the cutting-tool state. Equation (15) is the objective
function to be minimised every cutting-tool pass in the
ACO system.

powerful modelling technique is called as a universal

function approximator due to its capacity to adjust
any function. The model is built learning from
experimental data the relationships between variables
which is done by updating the network architecture
and the connection weights. In the eld of machining
processes, ANNs have been extensively applied for
modelling surface roughness (Zain et al. 2010), cuttingtool wear (Kondayya and Krishna 2012) and cutting
forces (El-Mounayri and Deng 2010). Good reviews of
ANNs applied in machining can be found in Sick
(2002) and Abellan-Nebot (2010). In this paper, the
recommendations presented in Abellan-Nebot (2010)
are followed for modelling surface roughness, cuttingtool life and cutting-tool wear using ANNs.
4.
4.1.

3.1. Selection of AI technique for process modelling

Machining processes are non-linear and time-dependant
processes that are dicult to be accurately modelled by
traditional methods. For this reason, the introduction
of new techniques such as the ones based on AI has had
a great impact in this eld. The use of AI in machining
monitoring systems has been recently reviewed in
Abellan-Nebot and Romero (2010), where it was
remarked that the use of ANNs represented almost
the 60% of AI approaches reported in the literature.
Basically, an ANN is a mathematical model that
mimics the human reasoning and neurobiology. This

Experimental case study

Experimental setup

A manufacturing process of moulds for the tile

industry was analysed to implement the ACO system
proposed in this paper. The workpiece material are
squared plates of AISI D3 steel (250 6 250 mm; 60
HRC), and the cutting tool used is a CBN round insert
with an eective cutting diameter of 40 mm. For
completing the full tool path for manufacturing a
feature of the workpiece, eight face milling cutting-tool
passes are conducted under a vertical machining centre
suited for mould components manufacturing. The
xed cutting conditions, part specications and cost
constants are shown in Table 2.

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International Journal of Computer Integrated Manufacturing

For this application, the cutting parameters Vc and
fz have to be selected for minimum production cost. In
order to model the process variables, a full factorial
DoE was conducted. Three levels per each factor were
considered to acquire lineal and quadratic eects. The
factor combinations used are shown in Table 3. For
each experiment, the face milling operation was carried
out until the cutting-tool edge was worn (VB 4 0.3
mm, usual value for face milling nishing operations
according to ISO standards (ISO 1989)) or the Ra was
out of specications. For each cutting-tool pass,
detailed measurements of surface roughness and
machining forces were obtained. Ra was measured
using a MitutoyoTM Surftest 301 prolometer using a
sampling length l 0.8 mm, a number of spans
n 5 and with a measure repeatability of 0.02 mm.
Cutting forces were acquired from a Kistler piezoelectric dynamometer model 9366AB installed on the
machine-tool table and the descriptor analysed was the
RMS value of the cutting force, with a sensitivity
of 7 3.7 pC/N in the x and y axis and 7 3.8 pC/N in
the z axis. After the experimentation, a dataset of 160
samples was obtained due to the tool wear reaching its
limit value for each combination of cutting conditions.
The full data on Ra is shown in Table 4.
4.2. Traditional optimisation results
In order to conduct the traditional optimisation
procedure, the process models of T and Ra, dened
Table 2.

by Equations (13) and (14), respectively, were tted

from the experimental data shown in Table 3. The T
model was tted with a coecient of determination of
R2 90% and a standard deviation of the error
between the model and the experimental results
sT 0.2 min; and the Ra model was tted with
R2 67.4% and sR a 0.0221 mm. Tables 5 and 6
show the results of the analysis of variances for both
models. The Ra model was not very accurate as
indicated by the low value of R2 which is an important
limitation for the reliability of the production cost
estimation.The resulting process models of T and Ra
are:
T

16

Ra avg 0:254  V0:0088

 f0:206
c
z

17

For the traditional method, the optimisation of

Equation (15) is conducted through any conventional
optimisation technique. Note that Ra is expected to be
constant for a given cutting parameter combination
(Ra is assumed to be independent of tool wear), and
then, the optimal cutting conditions are constant for
the whole cutting operation. The resulting optimal
parameters were Vc 200 m/min and fz 0.089 mm/
tooth, which determines a production cost per part of
79.1 e . Figure 3 shows the resulting model and the
location of the optimal point.

Cutting conditions and cost constants for ACO system experimental setup.

Cutting conditions

Cost constants

Radial depth of cut

Axial depth of cut

ae
ap

Part specications
Surface roughness

Ra

Tool constants
Tool change time

ttc

Table 3.

1230
V1:32
 f0:881
c
z

31.25 mm
0.4 mm
50.2 m m

Tool cost
Overhead cost

Ct
C0

90 e
10 e /hr

Labour cost
Piece rework cost

C1
Arw

40 e /hr
75 e

Lot size

np

50 pcs

10 s

Design of experiments, parameters and results for each parameter combinations.

Parameters

DoE scheme

Results

Combination numbers

Vc (m/min)

fz (mm)

T (min)

Ra1 ( m m)

1
2
3
4
5
6
7
8
9

100
100
100
150
150
150
200
200
200

0.04
0.08
0.12
0.04
0.08
0.12
0.04
0.08
0.12

43.36
31.17
19.88
37.94
10.84
10.24
18.97
10.84
9.03

0.120
0.144
0.168
0.119
0.134
0.157
0.142
0.134
0.154

Note: 1Average of Ra along all cutting passes of each parameter combination.

8
Table 4.

J.A. Silva et al.

Ra [mm] results of training samples for the ACO system.

Downloaded by [Hector Siller] at 06:09 21 December 2012

Pass
Condition

10

11

12

1
2
3
4
5
6
7
8
9
Condition
1
2
3
4
5
6
7
8
9

0.10
0.11
0.13
0.09
0.11
0.14
0.15
0.11
0.11
13
0.16
0.16
0.19
0.13

0.08
0.11
0.14
0.11
0.12
0.14
0.12
0.11
0.13
14
0.15
0.17
0.18
0.13

0.09
0.11
0.13
0.11
0.11
0.15
0.11
0.14
0.15
15
0.15
0.17
0.21
0.13

0.09
0.11
0.12
0.11
0.12
0.14
0.13
0.11
0.17
16
0.14
0.18
0.21
0.13

0.12
0.11
0.13
0.12
0.18
0.16
0.13
0.13
0.17
17

0.14
0.13
0.15
0.13
0.14
0.15
0.15
0.12
0.17
18

0.13
0.14
0.15
0.11
0.14
0.18
0.17
0.14
0.17
19

0.13
0.13
0.16
0.12
0.15
0.15
0.16
0.15
0.17
20

0.11
0.11
0.16
0.14
0.14
0.15
0.13
0.13
0.15
21

0.1
0.12
0.18
0.11
0.14
0.15
0.15
0.12
0.14
22

0.13
0.15
0.15
0.12
0.14
0.16
0.14
0.14
0.13
23

0.12
0.14
0.18
0.10
0.12
0.16
0.15
0.15
0.14

0.17
0.18
0.12

0.17
0.20
0.12

0.17
0.20
0.12

0.17
0.21
0.12

0.16
0.19
0.14

0.17
0.20

0.18

0.18
0.13
0.14
0.15

0.17
0.18
0.14
0.15

0.17

0.18

0.16
0.16

0.16
0.17

0.15

0.15

0.17

0.20

Table 5.

Analysis of variances for tool-life (T).

Source
Regression
Residual error
Total

Table 6.

Degrees of freedom

Sum of squares

Mean of the sum of squares

2
6
8

0.50347
0.05606
0.55953

0.25173
0.00934

26.94

0.001
R2 90%

Analysis of variances for surface roughness (Ra).

Source
Regression
Residual error
Total

Degrees of freedom

Sum of squares

Mean of the Sum of Squares

2
6
8

0.014137
0.006832
0.020969

0.007068
0.001139

6.21

0.035

4.3.

Figure 3. Production cost model for the traditional

optimisation approach. Optimal parameters [Vc 200 m/
min and fz 0.089 mm/tooth].

R2 67.4%

Proposed ACO system optimisation results

The ACO system implemented is composed of three

process models: Tw model for diagnosing the state of the
cutting tool (percentage of eective cutting machining
life time); Ra model for predicting the Taguchis quality
loss; and T model. All models were developed using
back-propagation ANNs to model the non-linear
relationships in machining processes. The characteristics of the ANN models are described in Table 7.
The operation of the ACO system is as follows.
After a cutting-tool pass, the ACO system receives the
cutting forces measured from the dynamometer and it
evaluates the resultant RMS force value. This value is
introduced into the tool wear model along with Vc and
fz in order to get an estimation of the percentage of
eective machining life time of the cutting tool given the
cutting parameters at the moment of measuring the

International Journal of Computer Integrated Manufacturing

Table 7.

ANN models description for cutting tool wear, surface roughness and tool life.
ANN models

Modelling variable

Cutting-tool wear model, Tw

Surface roughness model, Ra

Tool life model, T

Type
Inputs
Outputs
Hidden layers
Neurons
Mapping function
Training method
Epochs
Learning

Back propagation
Vc, fz, Fc (RMS)
Tw
1
3
Logarithmic sigmoid
Lev-Marq
300
0.05

Back propagation
Vc, fz, Tw
Ra
1
3
Logarithmic sigmoid
Lev-Marq
100
0.05

Back propagation
V c, f z
T
1
2
Logarithmic sigmoid
Lev-Marq
200
0.05

Table 8.

Optimisation algorithms description for the operation of the ACO system (genetic algorithm).

Downloaded by [Hector Siller] at 06:09 21 December 2012

Genetic algorithm
Variables to optimise
Population size
Stall generations
Stall time
Crossover frac.

Table 9.

V c, f z
10
7
6 sec
0.8

Elite count
Mutation function
Selection function
Generations
Initial ranges

2
Gaussian
Stochastic
15
Vc [100, 200]; fz [0.04, 0.12]

Optimisation algorithms description for the operation of the ACO system (mesh adaptive direct search).
Mesh adaptive direct search

Variables to optimise
Initial mesh size
Maximum mesh size
Minimum mesh size
Expansion factor

V c, f z
0.05
Inf
Inf
2

cutting forces, which was named as the variable Tw

(units in percentage). Knowing the cutting-tool state,
the production cost function for the next pass is updated
according to the expected value of Ra that depends on
Tw, Vc and fz parameters and to the expected cuttingtool life T that depends on Vc and fz. Then, the expected
production cost per pass Equation (15) is optimised
applying sequentially a GA and a MADS algorithm.
Basically, the GA is rstly applied to nd the general
region where the objective function is a minimum. Then,
the MADS renes the search using the GA solution as
the starting point of the mesh. The optimisation results
are the optimal parameters for the next machining pass
(Vc and fz), as well as the expected values for Ra andCith
tot .
The procedure is repeated until the cutting-tool wear
(Tw) is estimated by the model to be higher than 95% of
the tool lifetime, when a cutting-tool replacement is
conducted. The characteristics of the GA and MADS
algorithm are shown in Tables 8 and 9, respectively,
followed by the owchart for both algorithms in Figure
4 and 5.

Contraction
Poll method
Polling order
Stop criterion

2
Positive basis 2N
Consecutive
Tolerance mesh: 5 6 1074

The error standard deviation of the models for T

and Ra were found to be sT 0.006 min and
sR a 0.0155 mm. An example of the optimisation
results from the ACO system is shown in Figures 6 and
7. Figure 6 shows the production cost per pass when
Tw 24% of the tool life time, with optimal parameters Vc 116 m/min and fz 0.087 mm/tooth;
Figure 7 shows the production cost per pass for a
Tw 84%, where the optimal parameters Vc 195 m/
min and fz 0.115 mm/tooth.
4.4.

Comparison and validation results

For comparison and validation purposes, two plates

were machined: one using the parameters obtained from
the ACO system and a second one using the parameters
from the traditional approach. Figure 8 shows the comparison of the surface roughness per pass obtained for each
case, and Figure 9 shows the production cost expected
results from the optimisation procedures (simulated)
and the actual results after machining (experimental).

Downloaded by [Hector Siller] at 06:09 21 December 2012

10

Figure 4.

J.A. Silva et al.

Genetic algorithm for optimisation of cutting parameters.

For the rst plate, the proposed optimisation

approach resulted in an expected production cost of
61.41 e; and experimentally, the production cost was
64.17 e. For the second plate, the traditional approach
resulted in an expected production cost of 79.15 e, and
experimentally, the production cost was 73.46 e.
Therefore, the proposed optimisation approach reduces the cost in a 13% experimentally. It is worth
mentioning that the Ra was also well contained within
the limits of its specication (Ra 5 0.2 mm) at all times
(see Figure 8).
4.5. Uncertainty of production cost estimation
It should be noted that the cost estimation is subjected
to an uncertainty since models are not perfect. In order
to estimate the range in which the real production cost

will lie due to the models uncertainty, the derivative of

Equation (15) should be analysed. Equation (18) shows
the derivative of Equation (15) with respect to T and
Ra. The values for dT and dRa represent the error of
the estimation of T and Ra and are calculated
as + 2 s , for a 95% condence of the resulting value
being in this range, and it is obtained from the
standard deviation of the error of the T and Ra models.





@Ctot 



dT @Ctot dRa
ECtot dCith


18
tot
 @T 
 @R 
a

(
 
 tm  

ECtot    c1 ttc ct co ttc 2 dT 


T


)
 2A n 





rw p

19
R

R
dR

a
a
a
tgt


D2

Downloaded by [Hector Siller] at 06:09 21 December 2012

International Journal of Computer Integrated Manufacturing

Figure 5.

MADS algorithm for optimisation of cutting parameters.

Figure 6.

Total cutting-tool pass cost for a tool wear of 24%.

Figure 7.

11

Total cutting-tool pass cost for a tool wear of 84%.

12

J.A. Silva et al.

Downloaded by [Hector Siller] at 06:09 21 December 2012

Figure 8. Expected and experimental surface roughness

from the traditional and proposed optimisation approaches.

Figure 9. Expected and experimental production cost from

the traditional and proposed optimisation approaches.


n 
o
tm 


ECtot   98:333 2 2sT  j1875Ra  0:12sRa j
T
20
Evaluating Equation (20) using the traditional and the
proposed approach, the uncertainties of the production cost estimation per part are + 44.32 e and
+10.76 e, respectively. Therefore, the uncertainty of
the cost estimation is greatly reduced (76%) which is
mainly explained by the better performance of ANN
models to estimate the machining process variables.
5.

Conclusion and future work

An ACO system based on AI techniques and a

dynamometer for minimising production cost every
cutting-tool pass considering the eect of tool wear on
surface roughness was presented in this paper. Unlike
traditional optimisation techniques, this methodology

allows the system to adapt the cutting parameters

according to the cutting-tool state for reaching a real
minimum production cost. The proposed ACO system
was experimentally compared with the traditional
optimisation procedure on a hard milling process
with CBN tools.
The expected optimal cutting conditions by the
traditional approach were Vc 200 m/min and fz
0.089 mm with a total production cost per part of
73.46 e. On the other hand, the proposed ACO system
decreases the nal production cost per part to
64.17 e by adapting the cutting conditions each cutting
pass, which means a decrease of 13% in the production
cost. Furthermore, the uncertainty of the production
cost estimation was 76% lower with the proposed
approach than with the traditional one. The better
performance of the proposed approach was mainly due
to two reasons. First, the ANN process models showed
a more accurate estimation than empirical regression
models, so the optimal parameters are closer to the
reality. Second, the on-line nature of the ACO system
allows adapting the cutting parameters every cutting
pass so the system is more exible to adapt to any
change in the objective function during the cutting-tool
life-cycle, minimising the total production cost per part
considerably.
As future work, the authors suggest to investigate
the implementation of ACO systems based on other
non-intrusive sensor systems such as current sensors or
accelerometers. The use of the presented ACO system
based on dynamometer has limited industrial applicability due to the intrusive nature on the process.
Furthermore, for the case study analysed, the high
impact of workpiece hardness variability on surface
roughness should be investigated in more detail to
ensure a real optimal production cost.
Acknowledgements
The authors would like to express their gratitude to the
Department of Engineering Systems and Design at the
Universitat Jaume I, to the Intelligent Machines Research
Group at Tecnologico de Monterrey, to CONACYT
exchange scholarship program for its support and to
Miguel Aymerich for his help in gathering the experimental
data.

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