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1 INTERNATIONAL CONFERENCE ON HEAT TREATMENT
AND SURFACE ENGINEERING OF TOOLS AND DIES
IFHTSE 2005
Pula, Croatia, 08 - 11 June, 2005
THE APPLICATION OF ARTIFICIAL INTELLIGENCE METHODS
IN HEAT TREATMENT
Tomislav Filetin, Irena Žmak, Dragutin Lisjak, Davor Novak, Darko Landek
University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture (FMENA),
Department of Materials, I. Lučića 5, HR-10000 Zagreb, Croatia
E-mail: [email protected]
ABSTRACT:
Over the past few years a detailed study of artificial neural network, genetic algorithm and
programming, as well as the expert systems in predicting the steel properties and determination of heat
treatment process parameters has been performed at the Department for Materials of FMENA. This
paper presents the short overview of applied methods and results in predicting different properties of
the heat treatable steels and process parameters. Based on known chemical composition and heat
treatment condition the following properties has been predicted by means of neural network:
tempering curve of tool steels, coefficient of heat conductivity. The duration and surface hardness of
gas and plasma nitriding has been also successfully determined using neural network. The genetic
algorithm and genetic programming has been used for definition of the relations between different
variables, for optimisation of neural network parameters, as well as for determination of carburising
parameters. The expert system for selection of steel and surface modification treatment has been
developed, which integrate the above-mentioned methods.
The results are encouraging and open the wide possibilities for further investigation in heat
treatment and surface engineering technologies.
Keywords:
steel properties, heat treatment parameters, neural network, genetic algorithm, expert
system
1. INTRODUCTION
This paper presents the applied methods of artificial intelligence - neural network, genetic algorithm,
expert systems and results in predicting different steel properties and heat treatment parameters. The
use of neural network (NN) as an artificial intelligence method has been rapidly increased over the
past 10 years in many different science and technology fields. Some of them are: chemical science,
molecular structure design and polymer properties prediction, weld deposits structures and properties
prediction, as a function of a very large number of variables [2], process control etc. In the own
investigations we were focused on the applications of neural network for prediction the hardenability
(Jominy curve) of structural steels [3,4,5,16] and tempering curve of tool steels [5,6,16], using the
given chemical composition and austenising temperature. Another very important physical property
that has been investigated was the heat conductivity of different steel types [7,16]. Heat conductivity
versus temperature is needed in calculation and simulation of heating and cooling processes. The
duration of gas and plasma nitriding and surface hardness has been also successfully determined for
defined steel type and layer thickness using neural network [8,16].
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The genetic algorithm and genetic programming has been used for definition of the relations between
different variables, for optimisation of neural network parameters, as well as for determination of
carburising parameters [12,23]. The expert system for selection of steel and surface modification
treatment has been developed, which integrate the above-mentioned methods and additionally the
expert rules and frames [13,14,15].
2. PREDICTING THE STEEL PROPERTIES AND HEAT TREATMENT
PARAMETERS BY MEANS OF NEURAL NETWORK
Artificial error back propagation neural networks were used for predicting different steel properties,
and some heat treatment parameters [16]. Some of the research work that will be presented in this
paper include predicting the tempering curves of tool steels, predicting the coefficients of thermal
conductivity of steel types at different elevated temperatures, and determining the required plasma
nitriding time for a defined steel and layer thickness.
2.1.
Predicting the tempering curves for the tool steels
Data from the tempering curves of tool steels for neural network learning were collected from the
catalogue [17]. For different standard tool steels the producer specifies, among other data, data of
average chemical composition, expressed in weight contents, and the austenising temperature. These
data were the independent data for the artificial neural network, i.e. its inputs. Dependent variables, or
neural network outputs were the hardness at different tempering temperatures. Previous research has
shown that great differences in chemical composition between different groups of tool steel make it
very difficult for the neural network to learn and the generalize [18]. For this reason tool steel were
grouped according to the field of application into: non-alloyed cold work tool steels, alloyed cold work
tool steels, alloyed hot work tool steels, and high speed steels. Data used to test the ability of the
neural network to generalize, i.e. for the testing, were collected from literature [19].
Table I presents the results of statistical analysis of absolute error in predicting tempering curve of
non-alloyed tool steels.
Table I. Statistical analysis of absolute errors in predicting tempering curve of non-alloyed tool steels
Group for:
Learning
Testing
Hardness, HRC
Min.
Average
Max.
St. dev.
u rel , %
0
0.2
0.65
1.98
7.78
3.63
1
1.17
1.22
3.75
Statistical parameters
2
NRMS
R
R
0.13
0.2438
0.992
0.9802
0.9841
0.9608
Steel S 18-0-1
70
65
60
55
50
45
40
Hardness, HV
Hardness, HRC
Figure 1 presents two examples of predicted and measured tempering curves of two high-speed steels HS18-0-1 from the learning data set, and HS6-5-2 from the testing data set.
0
900
800
700
600
500
400
300
Steel S 6-5-2
0
200 400
600 800
Tempering temperature, °C
200
400
600
800
Tempering temperature, °C
Measured
NN Predicted
Measured
NN Predicted
Figure 1: Predicted and measured tempering curves of high-speed steels HS18-0-1 from the learning
data set, and HS6-5-2 from the testing data set
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2.2.
Predicting the coefficients of thermal conductivity of steels at different temperatures
Data of coefficient of thermal conductivity of different steels at elevated temperatures were collected
from literature [15,16]. Input parameters were the weight content of alloying elements, and the sum of
these contents (called the alloying level). Output data were the coefficients of thermal conductivity at
different elevated temperatures: 20, 100, 200, … and 700 °C. Steels were divided into the groups of:
structural steels, tool steels for hot work, high-speed steels, stainless steels, heat resistant steels,
austenitic steels for elevated temperatures, and cobalt steels and alloys for elevated temperatures.
Table II presents the results of statistical analysis of absolute error in predicting the coefficient of
thermal conductivity of steels. Results are presented for both the learning and testing data sets. Figure
2 presents two examples of predicted and measured coefficients of thermal conductivity vs.
temperature of steels: one for the steel 56NiCrMoV7 from the learning data set, and the other from the
testing data set - steel X7CrNiAl17-7.
Table II: Absolute errors in predicting the coefficient of thermal conductivity of steels
-1
Group for:
Statistical parameters
Min.
Average
Max.
St. dev.
u rel , %
NRMS
R
R
0.01
0
0.7
0.82
3.62
1.71
0.63
0.5
2.92
4.16
0.1
0.3568
0.995
0.9416
0.99
0.8866
Steel 56NiCrMoV7
-1
60
50
40
30
20
10
0
-1
λ , Wm K
-1
λ , Wm K
-1
Learning
Testing
-1
λ, Wm K
0
200
400
600
800
Temperature, °C
Measured
NN Predicted
60
50
40
30
20
10
0
2
Steel X7CrNiAl17-7
0
200
400
600
800
Temperature, °C
Measured
NN Predicted
Figure 2: Predicted and measured coefficients of thermal conductivity vs. temperature of the steels
56NiCrMoV7 from the learning data set, and steel X7CrNiAl17-7 from the testing data set
2.3.
Determining nitriding time
Original data for predicting nitriding time, depending on the achieved effective nitriding layer
thickness, nitriding temperature, and chemical composition of steels were collected from literature
[19]. Input parameters for neural network learning were the sum of nitride forming alloying elements,
nitriding temperature, and effective layer thickness. Output variable was the needed nitriding time.
Since nitriding time is linearly dependent to the square of nitriding thickness, input data of effective
nitriding thickness were squared before presented to the neural network.
Table III presents the results of statistical analysis of absolute error in predicting nitriding time.
Results are presented for both the learning and testing data sets. Figure 3 presents curves of predicted
and really required nitriding time vs. effective nitriding thickness for different nitriding temperatures
for two steels: X40CrMoV5-1 with alloying level LN = 8.4% from the learning data set, and steel
32CrMoV12-10 with LN = 4.3% from the testing data set.
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Table III: Statistical analysis of absolute errors in predicting plasma nitriding time
Nitriding time, h
Group for:
Learning
Testing
Min.
Average
Max.
St. dev.
u rel , %
NRMS
R
R
0
0.01
0.41
0.88
2.26
6.11
0.37
1.02
7.9
13
0.032
0.095
0.9995
0.9972
0.999
0.994
0.2
600° 550°
0.3
600° 550° 500°
450°C
0.15
Steel X40CrMoV5-1
L N = 8.4%
0.1
0.05
0
10
20
30
40
Nitriding time, h
Effective nitriding
thickness, mm
Effective nitriding
thickness, mm
0.3
0.25
Parameters
500°
2
450°C
0.25
0.2
0.15
Steel 32CrMoV12-10
L N = 4.3%
0.1
0.05
50
0
10
20
30 40
Nitriding time, h
50
Figure 3: Predicted and required plasma nitriding time vs. effective nitriding thickness at different
nitriding temperatures for two steels: X40CrMoV5-1 (LN = 8.4%) from the learning data set,
and steel 32CrMoV12-10 (LN = 4.3%) from the testing data set
3.
DETERMINATION OF CARBURIZING PARAMETERS BY MEANS GENETIC
ALGORITHM
Genetic algorithms belong to the class of stochastic search methods. Whereas most stochastic search
methods operate on a single solution to the problem at hand, genetic algorithms operate on a
population of solutions. In genetic algorithm problem must be encoded in a structure that can be stored
in the computer. This object is a genome (or chromosome). The genetic algorithm creates a population
of genomes and applies crossover and mutation to the individuals (potential solution of problem) in
the population to generate new individuals. It uses various selection criteria so that it picking out the
best individuals for mating (and subsequent crossover). Objective function determines how 'good' each
individual is and is most important for improvements of solution. In carburising, the surface carbon
content should be from 0.8-0.9 %C, also the carbon flow should be uniform (constant) up to a certain
distance from the surface. Thus, maximal surface hardness is achieved, and a rapid hardness drop with
the distance from the surface is minimized. At the required, i.e. effective carburising depth Eht, carbon
concentration will be about 0.35 %C, which enables the achieving of the "limit" hardness in hardening
HG = 550 HV1 as per DIN 50190. However, these, more or less ideal requirements can be hardly
achieved in case of high carburising depths, particularly if the carburising process is performed with
only one C-potential. Using a mathematical model of the carburising process [22] enables the
simulation of the process where C-potential changes. Model for carburising with three changes of Cpotential (three carburising phases) was developed [23]. The temperature, duration and C-potential are
the most important process parameters of carburising, therefore they were selected as parameters for
optimising. The genetic algorithm was used for determining the parameters, as it performed very
successfully in solving the optimisation problems with more variables. In this case, the defined
mathematical model of the carburising process can monitor the influence of duration of the carburising
process and of C-potential on the result of the carburising process. Therefore, optimal parameters of
the carburising process will be determined, while the specified requirements on carbon flow in the
surface layer are met, and total process duration will be as short as possible.
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During optimisation, each solution was evaluated by an objective function. The objective function was
defined as follows:
2
0.4
O bjective _ function = ∑ (10 ⋅ ( carbon _ concentration x - 0.8 ) ) + t SU M
x=0
→
min
where carbon_concentrationx is the carbon content at a distance x from the surface, calculated by a
mathematical model, and tSUM is the total process duration (t1 + t2 + t3). The first part of the objective
function is the requirement that the carbon flow up to 0.4 mm depth should be 0.8%C, while the other
part of the function takes into account the total process duration.
Carburising parameters were determined for non-alloyed steel C15E which chemical composition was:
0.146 %C, 0.27 %Si, 0.49 %Mn, 0.051 %Cr, 0.058 %Ni and 0.074 %Mo.
The optimal values of carburising parameters obtained by the genetic algorithm for the selected steel:
Cpot1=1.2 %C; Cpot2=1.19 %C ; Cpot3=0.71 %C; t1=98 min; t2=102 min; t3=131 min.
Figure 4 presents carbon content curves, generated by a mathematical model, for the parameters
optimised by the genetic algorithm. Carburising and hardening of the selected steel were performed in
accordance with the optimised parameters and the results of the carburising process are presented in
Figure 5.
d
t
s
rd
phase → end of carburizing
Figure 4: Modelled carbon content curves at the
Figure 5: Hardness curve after the performed
end of each phase of the carburizing process,
carburising process, for steel C15E
obtained by a mathematical model for the steel
(measured)
C15E
The achieved carburising depth is 0.66 mm, which meets the specified requirement. As hardness
depends on the carbon content, it is to be assumed that the measured hardness distribution is in
accordance with the carbon content (curve 3 in Fig. 4) obtained by the mathematical model.
4.
EXPERT SYSTEMS
Expert systems are computer programs, which, based on implanted human knowledge (most
frequently in the form of the rules) solve certain problem from specific area [20,21]. Implanted
knowledge, beside facts, contains information that are used for connecting facts in logical deduction
sequence. The most important components in every expert system structure are: knowledge base and
deduction mechanism. Knowledge base in encoded form contains collection of required knowledge
elements from the examined problem area. Deduction component task is to choose knowledge
elements from knowledge base and, at the end, connect them into meaningful deduction. Deduction
quality which knowledge mechanism is bringing depends on, so called, expert system communication
elements. Their main task is to provide needed information most often through the dialog with user
(questions - answers). Unlike the knowledge base, deduction mechanism doesn’t depend on analysed
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problem type. Increased efficiency expert systems often include previously described artificial
intelligence methods which are gained by hybrid expert system. Figure 6. shows possible way for
integration of artificial intelligent methods (neural networks, fuzzy logic, neurofuzzy logic, genetic
algorithm) within hybrid expert system deduction mechanism suitable for solving wear problems.
Figure 6: Integration of artificial intelligence methods within hybrid expert system for selection of
wear resistant materials and surface modification processes [20]
After conducted partial or complete conversation with user, system is qualified to bring conclusions
about: wear type, dominant wear mechanism, suitable surface modification process and suitable base
material for layer deposition. In the early application stage, system has limited knowledge about
analyzed wear problem. System begins to give acceptable solutions just after solving certain number
of real wear problems from which he learns. Figure 7. shows an explanation for certain wear problem
solution.
5.
CONCLUSION
The results of neural network method application in predicting the properties of steels are very
satisfying, and they encourage further investigation. The accuracy of prediction depends on the
accuracy of measured data, and they should reflect real relations between chemical composition and
properties. Neural network application has shown that it is possible predict accurately predict the
tempering curve, and the thermal conductivity for similar new heats in the production or for every new
steel which is similar to some previously used one. It is also possible to optimise the steel chemical
composition for the desired tool steels tempering resistance, or the thermal conductivity. This method
also makes it possible to avoid postproduction property testing.
To achieve better accuracy in neural network application, additional activities are needed - selecting
the optimum learning dataset size, and also such dataset that would contain the most representative
data, in order to be able to successfully predict properties of similar steels. The learning datasets
should be as wide as possible, and should contain enough different steel types. It would also be
interesting to test the network with a number of heats from different sources, and to compare these
results. It is also possible to use other neural network algorithms.
Neural networks and genetic algorithms are also successfully applied for determination of parameters
of thermo-chemical treatments (nitriding and carburising).
Presented method of integration of artificial intelligence methods (neural networks, fuzzy logic and
genetic algorithms) within conclusion making mechanism of hybrid expert system enhances selection
of logic solutions for selecting material and surface modification treatment.
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Figure 7:
Explanation of solved given wear problem by hybrid expert system for selection of wear
resistant materials and surface modification processes [20]
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REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
J.M. Zurada, Artificial Neural Systems, W. P. Company, USA, 1992.
H.D.H.K. Bhadeshia, Neural Networks in Materials Science, ISIJ International, Vol. 39(1999), No. 10, pp
966-979
T. Filetin, D. Majetić, I. Žmak, Prediction of the Jominy curves by means of neural networks, Proceedings
of the 11th Congress of the International Federation for Heat Treatment and Surface engineering, Florence:
IFHTSE, 1998. p. 353-361.
W.G. Vermeulen, P.J. van der Wolk, A.P. de Weijer, S. van der Zwaag, Journal of Materials Engineering
and Performance, Vol. 5, No. 1, 1996. p.57
V. Colla, L.M. Reyneri, M. Sgarbi, Neuro-Wavelet Parametric Characterization of Hardness Profiles,
ESANN’1999 Proceedings - European Symposium on Artificial Neural Networks, Bruges, 1999, pp. 141146.
T. Filetin, D. Majetić, I. Žmak, Predicting the tempering curve of tool steels using neural networks, In: 2nd
international conference on industrial tools, Maribor: ICIT, 1999. p. 424- 427.
T. Filetin, I. Žmak, D. Markučič, D. Novak, Determination of physical properties of heat treatable steels,
Proceedings of the 8th Seminar of Int. Federation for Heat Treatment and Surface Eng. - Integration of heat
treatment and surface engineering in the manufacture of engineering components. Cavtat/Dubrovnik,
Croatia, 2001. pp. 399-406.
T. Filetin, I. Žmak, D. Novak, Determining Nitriding Parameters with Neural Networks, Journal of ASTM
International (on line Journal), May 2005, Vol. 2, No. 5
L.A. Dobrzański, W. Sitek, J. Zacłona, R. Bachul, Modelowanie wybranych własnosci stali szybkotnacych,
Proceedings of the scientific Conference Materials and Mechanical Engineering, Gliwice, Poland, 2000, pp.
155-158.
L.A. Dobrzański, W. Sitek, J. Zacłona, The modelling of high-speed steels’ properties using neural network,
Proceedings of the 8th Seminar of Int. Federation for Heat Treatment and Surface Engineering - Integration
of Heat Treatment and Surface Eng. in the Manufacture of Engineering Components, Cavtat, Croatia, 2001,
pp. 367-372
I. Žmak, Application of artificial neural network in predicting material properties (in Croatian), Master's
thesis (In Croatian), University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture,
Zagreb, Croatia, 2003.
..., Naši proizvodi, Slovenske železarne n. sol. o., Ravne na Koroškem, Slovenia, 1984.
A. Rose, Atlas zur Wärmebehandlung der Stähle, Band 4, Verlag Stahleisen m.b.H., Düsseldorf, Germany,
1954./56
B. Edenhofer, H. Trenkler, Einfluß der Nitrierdaten und der Stahlzusammensetzung auf die Härte von
Nitrierschichten, HTM Härterei-Technische Mitteilungen, 35 (1980) 5, 220-229.
K. Bugardt, W. Spyra, Wärmeleitfähigkeit unlegierter und legierter Stähle und Legierungen bei
Temperaturen zwischen 20 und 700 ºC, Archiv für das Eisenhüttenwesen, 36 (1965) 4, 1-11.
F. Richter, Die wichtigsten physikalischen Eigenschaften von Eisenwerkstoffen, Verlag Stahleisen m.b.H.,
Düsseldorf, 1973.
M. Stupnišek, Študij izmenjave ogljika med plinsko atmosfero in jeklom pri njegovi termični obdelavi,
Doctoral Thesis, (In Slowenian) Univerza Edvarda Kardelja v Ljubljani, VDO Fakulteta za naravoslovje in
tehnologijo, Ljubljana, 1981.
D. Novak, D. Lisjak, T. Filetin, Determination of Carburizing Parameters using Genetic Algorithms,
Transactions of FAMENA (1333-1124),28 (2004)2, p. 11-18.
D. Novak, Determining of the parameters of heat treatment of metals using genetic algorithms, (in
Croatian), Master's Thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval
Architecture, Zagreb, Croatia 2003.
D. Lisjak, Application of the artificial intelligence methods in selection of materials (in Croatian),
Dissertation, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb,
2004.
D. Lisjak, T. Filetin, ABRex - Description of the Abrasion Wear Expert System, Database and Expert
Systems Applications’, Eighth International Workshop on Database and Expert Systems Applications, IEEE
Computer Society, Los Alamitos, CA 90720-1314, 1997, p. 576-581.
476