End Milling: A Neural Approach for Deﬁning Cutting

Conditions

Orlando Duran, Nibaldo Rodriguez and Luiz Airton Consalter

Pontiﬁcia Universidad Catolica de Valparaiso, Av. Brasil 2241, Chile

FEAR Universidade de Passo Fundo, P. Fundo, RS, Brazil

Abstract. The purpose of this paper is to present a new adaptive solution based

on a feed forward neural network (FNN) in order to improve the task of select-

ing cutting conditions for milling operations. From a set of inputs parameters,

such as work material, its mechanical properties, and the type of cutting tool, the

system suggests feed rate and cutting speed values. The four main issues related

to the neural network-based techniques, namely, the selection of a proper topol-

ogy of the neural network, the input representation, the training method and the

output format are discussed. The proposed network was trained using a set of in-

puts parameters provided by cutting operations manuals and tool manufacturers

catalogues. Some tests and results show that adaptative solution proposed yields

performance improvements. Finally, future work and potential applications are

outlined.

1 Introduction

Process planning is a function that establishes a set of manufacturing operations and

their sequence, and speciﬁes the appropriate resources (machines, cutting tools, ﬁx-

tures, inspection instruments, etc.) and process parameters in order to convert a blank

to a ﬁnished component expressed by an engineering drawing and other technical in-

formation. The use of computer tools to assist the process plan generation was ﬁrstly

reported by Niebel [2]. From that work, many other researchers have explored the use of

computer systems to obtain a coherent process plan in an automated manner. Recently,

the term CAPP (computer aided process planning) appears frequently in the technical

literature and can be considered as one of the most active ﬁelds of research in manufac-

turing. In computer integrated manufacturing environments, CAPP can be considered

as the link between the CAD phase and CAM. Many researchers have developed so-

lutions to close the gap between the design phase and the generation of manufacturing

instructions and/or machine control code. A primer reference in CAPP is Chang [1],

who classiﬁes CAPP approaches into two categories, i.e. variant and generative. The

variant approach usually incorporates the use of group technology paradigm to recover

the most suitable process plan that corresponds to the most similar workpiece to that is

being planned. This ﬁrst approach usually lacks in ﬂexibility and does not consider rela-

tionship between features of workpiece. On the other hand, generative process planning

generates in an automated manner, a brand new process plan, only based on experience

and technical knowledge. According to Chang and Chang [3], most generative CAPP

Duran O., Rodriguez N. and Airton Consalter L. (2008).

End Milling: A Neural Approach for Deﬁning Cutting Conditions.

In Proceedings of the 4th International Workshop on Artiﬁcial Neural Networks and Intelligent Information Processing, pages 41-50

DOI: 10.5220/0001495400410050

 SciTePress

lack in learning ability for environmental changes. Because of that reason, recent re-

searches have being focused on integrating variant and generative CAPP with Expert

Systems-based techniques. A number of approaches have been reported in literature

to solve the problems occurring in integrating process planning and other computer

aided manufacturing applications. Leung [4] published an extensive literature review

on CAPP. Other signiﬁcant number of references was reported by Marri et al. [5]. More

recently, Chang and Chang [3] reported artiﬁcial intelligence applications for CAPP

implementations. In an exploratory examination of the CAPP literature it is easy to

conclude that ANN have been intensively used to solve problems such as tool selection,

cutting conditions deﬁnition, sequencing of operations, etc. Unlike the most published

applications of ANN in process planning, where neural networks are used as a means

to create optimization models, the proposed approach involves three key differences:

neural networks are capable of storing knowledge in a distributed manner, neural net-

works are capable of learning to recognize relationships between inputs and outputs,

while such relationships must be explicitly deﬁned in optimization models, and neural

networks are capable of generalizing (i.e., giving a ”closest-ﬁt” answer) when presented

with data not used in deriving the relationships learned. This paper presents a proposal

of artiﬁcial neural network for determining cutting parameters for milling operations.

The subsequent content is organized as follows: The second section discusses the pro-

cess of deﬁnition of cutting conditions and the use of Artiﬁcial Intelligence techniques

for this purpose; the third section presents the suggested approach, speciﬁcally it dis-

cusses the structure of the developed networks, the training data sets, and the details of

the training process. Furthermore, some aspects of the obtained output of the developed

networks are presented. Finally, in the last section some conclusions and future works

are drawn.

2 Artiﬁcial Intelligence and Determination of Cutting Parameters

A workpiece is composed by a set of surfaces or features. These surfaces are obtained

by a sequence of machining operations, such as turning, milling, boring and so on.

For each one of these features process planners must select adequate tools and optimal

cutting parameters. The choice at this stage may be tentative and has to be governed

by experience, intuition and based on information gathered in machining handbooks.

Mainly, this step of process planning considers the selection of the following parame-

ters:

– The cutting speed (vc) and the rotational speed of the part or of the tool (N).

– The feed rate (fn) or the feed speed in translation of the machine elements (vf).

– The depth of cut (ap) or engagement determining the width of the material to be

removed.

Despite the fact that such machining parameters are calculated according to practi-

cal values found in handbooks or from experience, they have to be updated or reﬁned to

adapt the values to match a speciﬁc situation for extracting the best performance of the

cutting resources. Inﬂuence diagrams have been developed for representing complex

decision problems based on incomplete and uncertain information from a variety of

sources. Nestler and Shulz [8] presented a simple example of an inﬂuence diagram for

machining optimizations and discussed their use in optimization of cutting conditions

(Fig1).

Data from machining handbooks were separated into different types of machining

process, such as turning, drilling, boring, end milling, etc. and classiﬁed according to

the workpiece material. As it is well known, workpiece materials are classiﬁed in var-

ious groups covering a wide range of materials according to their hardness: ferrous,

non-ferrous, etc. The machining handbooks provide the machining parameters for dif-

ferent tool-work-piece combinations. A comprehensive review of the information ob-

tained from the literature, and from industry, has indicated that the recommended cut-

ting speeds and feed rates for any machining operation may vary considerably [6]. In

addition to the proper selection of cutting speeds and feed rates, the optimum condition

depends on variables such as part conﬁguration, condition of the machine and ﬁxtur-

ing, tolerances and surface quality. Because the effects of these variables on tool life

are not always precisely known, it becomes difﬁcult to recommend optimum conditions

for a machining operation. Therefore, the recommendations presented in the machining

handbooks are nominal ones and should be adjusted by a certain order of processing

approach [7].



Cutting 

Force 

Tool 

Wear 

Horse 

power 



Temperature 

Acoustic 

Emissionsn 

Cutting 

Speed 

Feed 

rate 

Mat. 

Removal 

rate 

Fig.1. An inﬂuence diagram for determining machining parameters.

Among the applications to determine cutting conditions using an intelligent ap-

proach, one must distinguish the systems that perform the task in an off-line mode

and the systems that operate in an on-line mode. Off-line calculation of cutting condi-

tions consists in deﬁning all the necessary parameters for execute a workpiece before

the process is initiated. According Nestler and Shulz [8], at present, neural networks

are especially used to solve sophisticated problems such as determining and modeling

correlations between input and output parameters. Hashmi et al. [7] points to other di-

rection to use AI tools for deﬁning cutting conditions, the use of fuzzy logic models for

representing knowledge extracted from catalogues or handbooks. According Hashmi

et al. [7] fuzzy logic strategy can simulate an operator’s ‘experience and expertise’ in

decision-making process to facilitate the operator to select drilling parameters from ex-

pert database which can be incorporated in computerized automated systems. On the

other hand, the on-line approach corresponds to an automated attempt to adapt and op-

timize the machining parameters based on sensor information on machining responses

in real time. One of the main differences between off-line and on-line determination

of cutting conditions is the need of information of temperature and acoustic emissions.

Table 1. Subset of training data.

Operation Work Mat Hardness Mill Vc Vf

type Code HB type m/min mm/min

1 30,22 90 1 1000 1910,8

2 30,22 90 1 1100 4904,4

3 30,22 90 1 1250 26871,0

4 30,22 90 1 130 4968,1

1 1,10 125 1 155 288,0

2 1,10 125 1 200 891,7

3 1,10 125 1 375 8061,3

4 1,10 125 1 690 26369,4

1 1,10 125 3 145 450,2

2 1,10 125 3 160 1452,2

1 1,20 150 1 135 257,0

1 7,10 150 1 135 257,9

Fig.2. Types of operations considered in the experiment.

Hence any on-line intelligent system has to be integrated with a sensing device sys-

tem for extracting in real time conditions of cutting processes. AI techniques allows

modeling the information coming from the sensors systems and optimizing machining

parameters by learning from machining events such as tool wear, machine breakdowns

and other failures.

3 Neural Network Model

Several papers recommend that feed forward multilayer backpropagation nets with one

or two hidden layers with 10 to 30 neurons each are appropriate for handling cutting

data selection problems [8]. The approach suggested here is to use two neural networks

one for the selection of cutting speed and the second one for the selection of the feed

speed. Both networks use the same set of inputs. Therefore, the same training and test-

ing sets were used for each one of the nets. There is just one difference between the

two training sets: the second network uses the set of training data plus the correspon-

dent cutting speed values. Thus, the propose here is to link both networks to work in

an integrated manner to produce cutting parameters from the same set of input data,

namely, workpiece material and type of milling operation and cutter. Most of the in-

formation used in the preparation of learning and testing data was extracted from a

Table 2. Alternative Conﬁgurations tested and their performance indicators.

ID of Num.of Num. of Num. of Num. of MAD GF

ANN cfg. hidden layers layer 1 layer 2 layer 3 (mm/min) %

1 3 10 10 10 31,0 100,00

5 2 7 7 0 18,5 90,91

2 3 11 11 11 11,3 85,46

4 3 6 7 8 13,0 83,64

3 2 8 8 0 1,3 83,64

16 2 10 10 0 23,5 80,00

6 2 9 10 0 30,1 78,18

13 2 6 6 0 47,4 74,55

7 2 7 8 0 31,8 74,55

9 3 6 6 6 95,4 72,73

19 2 11 11 0 15,3 72,73

14 3 7 7 7 14,2 72,73

10 3 9 10 11 25,3 69,09

11 3 8 9 10 10,8 69,09

12 3 9 9 9 8,1 69,09

17 2 6 7 0 46,1 67,27

20 2 9 9 0 47,2 65,46

15 2 8 9 0 3,2 63,64

8 3 7 8 9 5,0 60,00

18 3 8 8 8 34,5 58,18

Table 3. Conﬁguration parameters selected for each network.

Network Output Num. of Num. of Num. of Num. of Num. of

ID parameter Inputs Hidden Layers Neurons Lay.1 Neurons Lay.2 Neurons Lay.3

1 Vc 4 3 7 sig 7 sig 7 lin

2 Vf 5 2 8 sig 8 sig -

Sandvik Coromant Catalog. The collected information is in the form of tables, which

show the recommended cutting conditions for different types and geometries of cutters

and materials of workpieces depending on factors affecting machinability. As the orig-

inal information on cutting conditions is given in the form of intervals representations,

the midpoints of such intervals were used as the representative values to construct the

training and testing data sets. In addition, two machining specialists reﬁned these data.

The specialist adapted the data sets assuming a potentially real situation and a given and

known machine tool. By doing so, it will be feasible to incorporate empirical knowledge

to the training process. It was considered for this experiment four types of operations,

as shown in (Fig.2).

The selected input parameters were: milling operation type, workpiece material,

workpiece material hardness and type of mill. Table 1 shows a subset of the used train-

ing data. As can be noticed in table 2, the desired output data are distributed in a wide

interval. This is due to the large number of different types of workpiece materials. This

situation may be seen as a rather complex problem to be handled by any neural net-

work. This situation leads the authors to choose the strategy of two networks, the ﬁrst

Table 4. Percent error according to the operation type.

Operation network 1 network 2

type % %

1 1,44 15,11

2 3,27 24,76

3 2,06 1,91

4 0,44 35,34

Table 5. Percent error according to the workpiece material.

Material network 1 network 2

type (%) (%)

High Alloy Steel 1,37 8,38

Hardened Steel 3,09 18,26

Titanium alloys 0,91 24,11

Aluminium alloys 0,25 1,92

with a single output to estimate the cutting speed and the second one to estimate the

feed speed. The ﬁrst column represents the operations type, namely, the relation be-

tween the depth of cut (ap) and cutting width (ae), as shown in Figure 2. The second

and the third columns in table 1 represent workpiece material and its Brinell hardness.

Different workpieces materials were represented using the Coromant Material Code. In

a similar way, the type of mill was represented as an integer that regards the material

and geometrical conﬁguration of the milling tool. In the experiment four types of com-

mercial end mills were considered. As it was commented previously, network designers

have to test several conﬁgurations, including different numbers of hidden layers and

different number of neurons in each one of the hidden layers. There can be any number

of hidden layers in a neural network. In common use most neural networks will have

only one hidden layer. It is very rare for a neural network to have more than two hidden

layers. The number of neurons for the hidden layer(s) depends on the complexity of

the problem and should be set empirically. With too few neurons the network may not

converge in training, whilst with too many hidden-layer neurons the network starts to

lose generalization ability [9]. In this work, we compare the performance of networks

with two and three hidden layers and the number of neurons in each layer ranging from

5 to 15. Designer selects the network conﬁguration that presents the minimum error and

the fastest rate of convergence. A series of alternative conﬁgurations have been tested

to determine the proper conﬁguration of both networks. Several tests were conducted

varying the number of hidden layers, different numbers of neurons for each layer and

different transitions functions. The learning algorithm adopted in all these tests was

the backpropagation algorithm with momentum. As it is usual in the approaches using

this kind of networks, the set of data was divided into two subsets: the ﬁrst used as

the training data set contains 138 patterns and the second, used as a validation set to

evaluate the responses of the net to unseen information, contains 55 patterns. Through

the use of these two sets, networks parameters can be adjusted and the generalization

ability can be evaluated. To select the most appropriate conﬁguration two traditional

performance indicators were used. We refer to the medium absolute deviation (MAD),

which was computed in two phases, during the training process and the testing process.

The deviations were calculated as the difference between the actual speed and the es-

timated speed, both for the training and testing sets. The second performance indicator

that was used to evaluate the generalization capacity of the tested conﬁgurations is the

Generalization Factor (GF), deﬁned by Eq. (1).

GF =

∗ 100 (1)

Where n is the number of patterns that compose the validation set and k is the

number of such patterns estimated with an error less than 2 % (this value having been

ﬁxed as a threshold level). Table 2 summarizes the results obtained from an alternative

conﬁguration of neural networks for estimating feed speed (network number two). It is

quite evident that the conﬁguration number 1 (with three hidden layers) showed better

generalization performance since GF is 100%. However, the MAD seemed to be a little

high from the operational point of view. If one considers an error of 31 mm/min in the

estimated feed speed, this may lead to undesirable or inappropriate time estimations

and tool life expectations signiﬁcantly overestimated. Thus the selected conﬁguration

was number 3, in Table 2 (with two hidden layers), which MAD is 1,3 mm/min, con-

sidered as acceptable from the operational point of view. Moreover, the generalization

factor of near 85% seems to be adequate, if one consider that the training set takes into

account a wide variety of types of milling tools and workpiece materials. The same type

of analysis was conducted to obtain the architecture of the ﬁrst ANN that performs the

estimation of the cutting speed. Table 3 shows the selected conﬁguration parameters for

both networks. Figure 3 (left) shows the net output and expected cutting speed values

obtained after the network was entirely trained and a comparison between the original

testing data and the parameters estimated by the neural network (Fig.3 right). For the

selection of feed speed a single layer network with one hidden layer was trained using

the same training data set used for training the network that selects the cutting speed.

Figure 4 (left) shows the convergence of the output mean error for the network that

was trained for selecting the cutting speed, where it can be noticed the low number of

epochs needed for attain the minimum required error. Figure 4 (right) shows the con-

vergence of the output mean error for the network during the training process of the

network for selecting the cutting speed. Again, the low number of epochs needed for

attain the minimum required error can be noticed. Figure 5 (left) shows the net out-

put and expected feed speed values obtained after the network was entirely trained and

on the right side of the Figure 5 a comparison between the original testing data and

the parameters estimated by the neural network is shown. To evaluate the performance

of the two developed networks, an additional test set was prepared for simulation and

comparisons ends. The results of the simulation tests were classiﬁed according differ-

ent criteria. Table 4 shows the performance in terms of percent error of the two both

networks according to the operation type (refer Figure 1). Table 5 presents the results

of the test grouped according to the material workpiece. Finally, table 6 presents the re-

sults obtained by the two networks according the hardness of the workpiece. As can be

appreciated, from table 5 and 6, network 1 presented the best results with errors within

the 3%. As it can be observed in the tables shown above, the approach presents different

performance between network 1 and network 2, i.e. network 1 performs better estima-

Fig.3. Comparison between the train data set and the output produced by the trained network(left)

and between by the test data set and the output of the trained network (right).

Fig.4. Convergence during the process of training the ﬁrst network (left) and during the process

of training of the second network (right).

tion of the cutting speed than the estimations performed by the network 2 for the feed

speed. This is caused, we believe, by the great variability of the recommended values

of feed speed among different materials and operations types. The values used in the

test set present a mean value of 6000 mm/min approximately with a standard deviation

of 9000 mm/min. However, and it can be observed in tables 5 and 6, there are some

applications where the networks presented acceptable results (under 10 % of error), i.e.

operation type 3 and milling of High alloy steel and aluminum steel materials.

Table 6. Percent error according to the workpiece material hardness.

Material network 1 network 2

Hardness % %

350 HB 0,76 18,02

350 HB 2,37 13,70

Fig.5. Comparison between the training data and the data obtained by the trained network for

estimating Vf (left) and between test data and the networks output (right side).

4 Conclusions

This paper presented a neural network-based automated approach for cutting conditions

selection in milling operations. Two prototype networks were developed. The ﬁrst net-

work is for selecting cutting speed and the second one for selecting feed speed, both

using almost the same set of input parameters. Both neural networks are interrelated,

since the output produced by the ﬁrst network is used as an input in the second one. The

developed approach aims at selecting cutting parameters in off-line mode. The main

difﬁculty found in the reported experiments was the fact that the training data set con-

siders a great variety of workpiece materials. That situation leads to a wide interval of

cutting conditions affecting convergence mechanism during the training process and the

generalization capabilities during the utilization phase. In spite of this fact, the obtained

results show that the developed networks have an acceptable performance in simulating

cutting conditions selection process, with a generalization performance of about to 85

approximately. Future research points to develop and test new architectures of neural

networks to enhance the selection process performance, especially in estimation of feed

speed. Also, this work should be extended to other process planning functions such as

machine selection, tool and ﬁxture selection and sequence of manufacturing operations.

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