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Machine Learning Based Predictive Modeling of
Machining Induced Microhardness and Grain Size in
Ti-6Al-4V Alloy
a
a
Yiğit M. Arisoy & Tuğrul Özel
a
Manufacturing and Automation Research Laboratory, Department of Industrial and Systems
Engineering, Rutgers University, Piscataway, New Jersey, USA
Accepted author version posted online: 25 Sep 2014.
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To cite this article: Yiğit M. Arisoy & Tuğrul Özel (2014): Machine Learning Based Predictive Modeling of Machining Induced
Microhardness and Grain Size in Ti-6Al-4V Alloy, Materials and Manufacturing Processes, DOI: 10.1080/10426914.2014.961476
To link to this article: http://dx.doi.org/10.1080/10426914.2014.961476
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Machine Learning Based Predictive Modeling of Machining Induced Microhardness
and Grain Size in Ti-6Al-4V Alloy
Yiğit M. Arisoy1, Tuğrul Özel1
1
Manufacturing and Automation Research Laboratory, Department of Industrial and
Systems Engineering, Rutgers University, Piscataway, New Jersey, USA
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Corresponding author, Manufacturing and Automation Research Laboratory, Department
of Industrial and Systems Engineering, Rutgers University, Piscataway, New Jersey,
08854, USA E-mail: ozel@rutgers.edu
Abstract
Titanium and its alloys are today used in many industries including aerospace,
automotive and medical device and among those Ti-6Al-4V alloy is the most suitable
because of favorable properties such as high strength-to-weight ratio, toughness, superb
corrosion resistance and bio-compatibility. Machining induced surface integrity and
microstructure alterations size play a critical role in product fatigue life and reliability.
Cutting tool geometry, coating type, and cutting conditions can affect surface and
subsurface hardness as well as grain size. In this paper, predictions of machining induced
microhardness and grain size are performed by using 3D finite element simulations of
machining and machine learning models. Microhardness and microstructure of machined
surfaces of Ti-6Al-4V are investigated. Hardness measurements are conducted at
elevated temperatures to develop a predictive model by utilizing FEM based temperature
fields for hardness profile. Measured hardness, grain size and fractions are utilized in
developing predictive models. Predicted microhardness profiles and grain sizes are then
utilized in understanding the effect of machining parameters such as cutting speed, tool
1
coating and edge radius on the surface integrity. Optimization using genetic algorithms is
performed to identify most favorable tool edge radius and cutting conditions.
KEYWORDS: Machining, Titanium, Machine Learning, Microhardness, Grain size
INTRODUCTION
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Titanium alloys, specifically Ti-6Al-4V (Ti64), are commonly used in the aerospace
industry due to their high strength to weight ratio, toughness and corrosion resistance.
They are also considered bio-compatible and can be used in medical devices. Surface
integrity is one of the most relevant parameters used for evaluating the quality of finish
machined surfaces, as the critical structural components in industry are manufactured
with the objective to reach high reliability levels. Microhardness is an important aspect of
surface integrity, and it can play an important role throughout the product’s lifecycle as
reviewed in [1].
Microhardness is affected by the machining induced strain, stress and temperature fields
in the workpiece and although there are some analytical modeling efforts, they require a
great understanding of the microstructure of the specific material and are not easily
implemented [1, 2]. However, it is known that machining parameters such as cutting
speed, depth of cut, tool radius and tool coating have an effect on stress and temperature
fields; therefore it is possible to obtain a relationship between the machining parameters
and microhardness.
2
In a recent paper, Moussaoui et al. [3] investigated the effects of milling to microhardness
and microstructure in Ti-6Al-4V. They state that machining causes a softening effect on
the material due to high temperatures during cutting which cause Vanadium to diffuse
into the α phase from the β phase of the alloy, without changing the microstructure. They
also state that it is difficult to take traditional hardness measurements from two phase
alloys such as the Ti-6Al-4V, and the results are dispersed. Jovanovic et al. [4]
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investigated how the mechanical properties and microstructure of investment cast Ti-6Al4V change with different annealing temperatures and cooling rates. They found out that
higher annealing temperatures and faster cooling rates yield higher tensile strength and
hardness. Jovanovic et al. [4] reported microhardness measurements of annealed Ti-6Al4V between 360-375 HV using 10 N force (about 1.02 kg). Moussaoui et al. [3] reported
microhardness measurements that were made 300 g force (about 2.94 N) for Ti-6Al-4V
as 335.65 HV mean with 19.24 standard deviation. Rotella et al. [5] measured surface and
subsurface microhardness values as 354 HV for as received (annealed) Ti-6Al-4V using
50 g force (0.49 N).
In this paper, as continuation of the study by Özel and Ulutan [6, 7] on machining
induced surface integrity where residual stresses were analyzed using experiments and
3D FE simulations, we perform microhardness analysis using similar experiments,
simulations, and machine learning based pseudo models in order to achieve an
understanding about how cutting conditions affect the machining induced microhardness
on Ti-6Al-4V titanium alloy. Genetic algorithms are utilized to determine optimum
cutting tool and machining conditions for minimizing microstructure alteration.
3
MACHINING EXPERIMENTS
Face turning experiments, using four different cutting tools and 16 cutting conditions,
were conducted on the Ti-6Al-4V specimen obtained as a cylindrical billet. To
accomplish this, the specimen was machined in circular tracks, each track representing a
different cutting condition with the same cutting tool. The machined face was then cut
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from the billet to form about 3 mm thick disk. The billet was then annealed at 704 C and
the surface was cleaned with a few finishing passes prior to starting a new set of
experiments. This procedure was repeated using different tools (uncoated WC/Co and
TiAlN coated WC/Co) until all disks were obtained with different tracks representing
different cutting conditions and cutting tools. In the experiments, WC/Co inserts with
edge radii of r = 25 µm, r = 10 µm, r = 5 µm (sharp) and TiAlN coated WC/Co inserts
with edge radius of r = 10 µm have been tested in face turning of Ti-6Al-4V disks. A
depth of cut of ap = 2mm, two cutting speeds of vc=55m/min and 90m/min, and two feeds
of f = 0.05 mm/rev and 0.1 mm/rev were selected as cutting conditions. Hardness
measurements were taken on machined tracks of the disks using a Rockwell type tester in
the HR15N scale (15N or 1.53 kg) and the values were then converted to Vickers
Hardness (HV) scale. In some sets, some spreading was observed in hardness
measurements. The measurements together with mean and standard deviation values are
given in Table 1. The workpiece was annealed at 704 °C in the furnace in between
experiments, after each disk was cut off. Hardness measurements were taken from the
untouched back surface of the cylindrical billet after each annealing process, and the
mean and standard deviation are reported as 335.7 HV and 13.5 HV respectively. Grain
4
size measurements were taken from the side surface of the billet, and the average grain
size and its standard deviation were found to be 15.84 μm and 4.56 μm, respectively.
Hardness measurements were also taken from the workpiece after air cooling down to
room temperature from 700 °C, 600 °C, 500 °C, and 400 °C. About thirty hardness
measurements were taken for each case. The mean and standard deviation of hardness
values for all cooled cases are shown in Fig. 1 and Table 2. Hot hardness measurements
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were performed on a cylindrical workpiece that was left over from the disk machining
experiments. This piece also shares a surface that was used in taking the hardness
measurements after annealing, allowing a valid comparison. Temperature measurements
were taken with an infrared thermometer, and the values were fit into exponential curves
to smooth the noisy data. Fig. 2 shows the hardness versus temperature curves for each
initial temperature. Hot hardness values were used to generate a temperature based
instantaneous hardness model for the Ti-6Al-4V alloy, which is explained in Section 4.
Note that the first measurements do not precisely represent the furnace heated
temperature levels due to setup delays and machine measurement limitations.
It is known that microstructure of Ti-6Al-4V is affected by thermo-mechanical
processing [9] such as machining [5]. Therefore, microstructural analysis of machined Ti6Al-4V alloy disks was performed after hardness measurements. Firstly Ti-64 disk
specimens were prepared for microstructure analysis by polishing with 300, 600, and
1200 grit SiC sand paper and subsequent etching with Kroll’s agent (2 ml HF, 6 ml
HNO3, 92 ml distilled water). Then Scanning Electron Microscopy (SEM) imaging
together with a proprietary image processing program written in MATLAB has been
5
utilized to obtain grain size measurements. Grain diameters and volume fractions were
determined from these SEM images as shown in Fig. 3 for Ti-64 subsurfaces. Predictive
models are developed using Random Forests method as described in Section 4.
FINITE ELEMENT BASED SIMULATION OF MACHINING
In order to calculate temperature rises in the machined workpiece, 3-D Finite Element
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simulations of machining Ti-6Al-4V titanium alloy have been utilized. These predicted
temperature fields will be used as input to predict resultant microhardness profiles on the
machined surfaces. A constitutive model relating the flow stress to strain, strain rate and
temperature is required for the simulations for the Ti-6Al-4V. This model is often
obtained from the Split-Hopkinson pressure bar tests performed under various strain rates
and temperatures, and is generally valid in certain ranges. The model given in Eq. (1) that
was proposed by Sima and Özel [6] accounts for strain and strain rate hardening,
temperature-dependent flow softening and thermal softening effects and it is used in this
work.
A B
n
1
exp
1 Cln
a
˙
1
0
T Tr
Tm Tr
s
m
D2
1 D2
tanh
1
p2
(1)
where D2
1
T
Tm
d
, and p2
Here, σ is flow stress, ε and
T
Tm
b
.
are true strain and true strain rate, εo is reference true
strain, and T, Tm and To are work, material melting and ambient temperatures
respectively. The material model parameters are; A=725 MPa, B=300 MPa, n=0.65,
6
r
C=0.035, m=1, a=0.5, b=2, d=0.5, r=12, s=-0.05. The melting temperature for Ti-6Al-4V
is Tm = 1604°C.
3D Finite Element software DEFORM was used with workpiece being considered as
viscoplastic and tool being considered as rigid bodies [7]. Hence, it was assumed that the
workpiece deformations are predominantly viscoplastic. The workpiece was modeled as a
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4-degree disk sector geometry with the same diameter used in the experiments and it was
discretized with 1.5x10 5 elements, giving a minimum element size of 0.005 mm as shown
in Fig. 4a. The tool was modeled using a small segment around the corner radius area of
the cutting insert (r =0.8 mm with 11° relief angle) and its mesh consists of 1.0x105
elements with minimum element size of 0.015 mm. A very fine mesh was utilized in the
cutting zone and the tip of the tool in order to accurately represent the tool characteristics.
Boundary conditions were defined for heat transfer from the workpiece to the tool. A
very high heat conduction coefficient (h=100 kW/m2 /°C) was adopted to allow a rapid
temperature change in the tool. Temperature-dependent material properties i.e. elasticity
modulus E(T) (MPa), thermal expansion α(T) (1/°C), thermal conduction λ(T) (W/m/°C)
and heat capacity cp(T) (N/mm2/°C) were used in simulations as shown in Table 3. The
tool-chip contact friction was computed by a hybrid model where a shear region (with
m=τ/k where is the shear stress and k is the shear flow stress) was defined around the
tool edge radius curvature and a sliding region with the coefficient μ was defined along
the rest of the rake face. The coefficients were taken as m=0.9 and 0.6 μ
0.8 . All FE
simulations were run for a fixed cutting distance of 1.8 mm corresponding to simulation
times about 2 ms (v c=90m/min) and 1.2 ms (v c=90m/min) during which it was assumed
7
that the temperature rise in the workpiece reached to near steady-state. The simulation
output temperature fields were obtained as shown in Fig.4b&c, which were in turn
utilized in predictive modeling of microhardness profiles.
PREDICTIVE MODELING USING MACHINE LEARNING
The Random Forests Method
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In order to find a relationship and create a predictive model between the temperature of
the workpiece during machining and the microhardness, we utilize machine learning
algorithms. Once properly configured, machine learning algorithms inspect, extract and
use the relationships and patterns that exist within the given dataset, which is very
convenient for the user. Among machine learning algorithms, the Random Forests (RF)
method proposed by Breiman [10] is an adaptive nearest neighbor algorithm that can be
used for classification and regression. By making use of an ensemble of regression trees,
it can easily capture nonlinear relationships between an input data set and a target data
set. Regression trees work by recursively partitioning the data. Starting from the root
node that contains the whole dataset, a tree is grown by generating two branches. The
partitioning is done to minimize the sum of the squared errors over all splitting variables
α (input parameters and predictor types) and split points β as shown in Eq. (2) where 1
and 2 denote the first and second regions respectively. It should be noted that this
equation is a general expression and available in literature.
NL
min
α,β
yi1
i 1
y1
2
NR
yi 2
y2
2
(2)
i 1
8
The splitting process continues at each new node until certain criteria are met; such as
meeting a minimum error improvement δ for a split, or setting a minimum number of
data points in each branch. When a node cannot be split anymore, it is called a terminal
node or a leaf node. Usually, trees are grown until a minimum number of leaves exist.
However, over fitting is very common especially if the trees are fully grown. In this case,
the bias will be small but small changes in the training data will yield a high variance due
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to the number of degrees of freedom in the tree. This can be prevented by pruning the
trees but it will reduce the model’s ability to capture complicated relationships in the
data. The RF method remedies this issue with the introduction of bagging (bootstrap
aggregating), which is essentially a random selection of training data for each tree
(bootstrapping) combined with an aggregation of predictions from different trees. Also, at
each node during the growth of a tree, m out of p input parameters are selected randomly
to determine the split instead of using all p parameters. This isolates the trees from each
other and reduces the correlation between them, thus improving the accuracy of the
predictions. In general, the Random Forest method can be considered similar to genetic
programming as well.
Prediction Methodology
The input and target vectors must first be determined carefully in order to train a model
that achieves desirable results. Two separate RF models were constructed to predict
instantaneous hardness during machining and final hardness of the workpiece after
cooling down to room temperature. The training of the instantaneous model was
performed using hot hardness measurements as the target vector, where the temperature
9
and hardness values were measured and recorded. The input vectors were chosen as
maximum temperature, instantaneous temperature and the cooling time. An input matrix
was constructed by assigning each vector to a column and each row to a different
measurement. The RF regression model was trained using 800 trees. A representative tree
from the model is shown in Fig. 5a. After the model was trained, FE simulation results
were used as inputs to the model to obtain instantaneous hardness values during the
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machining operations. During the training of the model, 10% of the input data was
reserved as test data and was not used in training. Fig. 5b also shows the goodness of the
fit. The fit has R2= 0.965, MAE=0.51 and RMSE=0.933. The secondary RF model was
trained to calculate the hardness of the cooled down workpiece. The temperatures shown
in Fig. 1 and Table 2 were used as the input dataset and the hardness measurements are
used as the target dataset, with the exception of the hardness measurements from the
furnace cooled 704°C data which was used as the default room temperature hardness for
the model to converge to, by setting the temperature to 20°C instead. For the prediction
phase, FE simulation data was extracted in the form of nodal temperatures and passed to
MATLAB. A line of 0.1 mm depth from the surface was selected close to the middle of
the workpiece in order to see the effects of the tool. The temperature data was
interpolated using MATLAB. The resulting data was fed into the RF model, and hardness
values were calculated. It is important to note that current model is purely temperature
dependent and is not intended to capture the work deformation induced effects. For
instance, localized heating, an important factor that affects surface integrity during
machining, is not present in the hot hardness measurements. Moreover, plastic
10
deformation was not included in this current model. However, a more complicated and
accurate model can be developed in a similar manner.
Simulations that were conducted at first eight cutting conditions listed in Table 1 were
used in the hardness predictions. Two distinct steps of hardness predictions were done. At
first an instantaneous change in microhardness was computed based on the temperature
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rise. The evolution of temperature and hardness on the depth into the material line over
time is shown in Fig. 6 for a representative cutting condition (TiAlN coated tool, vc= 90
m/min, and f=0.1 mm/rev condition). It is observed that the machined surface layer
experiences an instantaneous hardness state due to localized heating during cutting
process, and cools down to a lower temperature. During this repeated heating and cooling
process, machined surface and subsurface go through changes in the microhardness. Fig.
7 shows the effects of different cutting conditions and tool coating on instantaneous
hardness during various stages of the machining process. Microhardness state into the
depth below the surface is shown just prior to chip formation (cutting) process for all
cutting conditions in Fig. 7a. Higher feeds create larger change in surface hardness while
this effect diminishes after 50 µm depth into the machined surface. In general coated tool
influences hardness more than uncoated tool. In addition, instantenous hardness change
prior to and after the cutting process was also investigated. Machined surface was cooled
down to the room temperature and resultant hardness profile was calculated as shown in
Fig. 7b&c. Higher feed rate and a larger edge radius are found responsible for greater
alterations in microhardness profiles. Fig. 7b shows that the heated surface is predicted to
be softer than the relatively colder interior parts of the workpiece, which follows the hot
11
hardness measurement data. Fig. 7c shows the predicted final hardness of the surface,
after being processed and reveals the differences.
Microhardness And Grain Size Predictions
In order to develop a predictive model for microhardness and grain size of the machined
surfaces in Ti-6Al-4V, all 16 experimental cutting conditions listed in Table 1 were
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utilized and Random Forests based models were trained separately for surface hardness
and grain size and volume fractions.
The RF method [10] was also used to create predictive models that relate cutting
conditions, grain size and fractions, and hardness measurements to each other. Fig. 8
shows the 3 different RF models. The RF1 x model predicts hardness (HV) from
cutting conditions, RF2 x model predicts Ti-6Al-4V’s
grain size (davg) from cutting
conditions, and the RF3 x model predicts hardness from grain size and volume
fractions. Cutting conditions are given as v c, f, rβ, and c, which represent cutting speed,
feed rate, tool edge radius, and a binary parameter that describes whether coating exists
or not (i.e. uncoated c=0 WC/Co uncoated and c=1 for TiAlN coating) respectively.
Therefore, the input variable set for RF1 x and RF2 x is x
RF3 x is x
d avg , f
vc , f , r , c and for
. Mean values of the hardness and grain size measurements
were obtained for each of the 16 cutting conditions (2 levels of cutting speed and feed,
and 4 different tools). The data was partitioned into training and testing sets such that the
12
testing set contained 4 conditions, selected from 4 different tool types at varying cutting
speeds and feeds. The training set contained the remaining 12 conditions.
In addition, using the grain sizes and distributions obtained via SEM, an expression was
constructed and proposed to estimate microhardness based on grain size and phase
fraction relation and by following a general Hall-Petch (H-P) type equation for grain size
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and strength relation available in literature:
HV
c0
m1
n1
c1 d avg
f avg
(3)
where HV is microhardness, davg, and f are α grain size and α or
volume fraction,
respectively. The c0 and c1 are model constants and m1 and n1 are exponents. Model
parameters were obtained via nonlinear optimization using genetic algorithm from SEM
measurements for α grain sizes and
volume fractions (Eq. 4) and α grain sizes and
volume fractions (Eq. 5) to generate a hardness model for predicting machining induced
microhardness in Ti-6Al-4V titanium alloy. These equations can be used to determine the
hardness of the particular material that has undergone similar machining conditions from
microstructure information.
HV
0.07
175.79 112.36 d avg
f
HV
0.08 0.11
176.26 120.53 d avg
f
Predicted
0.04
(4)
(5)
grain sizes in Ti-6Al-4V using RF2 x
model were compared against
measured ones and predicted microhardness of machined surfaces using RF3 x model
and Hall-Petch type equation as given in Eqs. (4) & (5) against measured mean
microhardness given in Table 1. Fig. 9 shows the grain size comparisons between
13
measurements and RF2 x model predictions for different cutting speeds, feeds and
tools. The predicted values are very close to each other, and while they follow a trend, the
accuracy is not spectacular even for the training set, with MSE = 0.9203 (across testing
data). This suggests that there are other factors that should be taken into account that
determine the final grain size. In fact, it is known that grain sizes in the machined
subsurfaces are determined by strain, strain rate and temperature history of the area,
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which cannot be accurately described solely by the machining conditions. Fig. 10 shows
the hardness comparisons between measurements, RF3 x
model predictions (and
predictions based on the H-P like equation. In this case, the RF3 model performs better
than Eq. (5), with MSE= 38.3370 (across testing data) and MSE= 59.9408 (across all
data) for H-P like equation. However, standard deviations of measured grain size and
Microhardness which represent uncertainty are utilized in obtaining separate RF models
and used in predicting these uncertainties (as error bars) in Figs. 9 & 10.
GENETIC ALGORITHMS BASED OPTIMIZATION
Genetic algorithms and evolutionary computation have been used in optimization
problems in materials and manufacturing processes successfully ranging from carbon
nanotubes to the process optimization [8, 11, 12]. Recently, a review was provided on the
soft computing techniques used in designing metal alloys based on composition-processmicrostructure-property relations by Datta and Chattopadhyay [13] and a critical
assessment of this field was given by Chakraborti [14]. In this work, the optimization
problem can be formulated as determining cutting conditions using genetic algorithms for
minimizing the machining induced hardness alteration. Random Forests based
14
predictions by using the model for cutting condition to hardness RF1 x
HVpredicted
were utilized to represent a function that can be used in the optimization problem. Then,
the objective function f x is the square of the difference between annealed hardness
and predicted hardness f x
HVannealed
HV predicted
limitations with a set of decision variables ( x
x1 ,
2
subject to constraints and process
, xn ) (i.e. n number of process
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parameters), and X is the space with all feasible solutions. The decision variables are
cutting speed (v c), feed (f), edge radius (rβ) and coating indicator (c), where rβ and c are
forced to be integers i.e. x
Minimize
subject to
vc , f , r , c .
f x
gj x
b j for j 1, 2, , 4 , x
r
5, 6, 7, 25
c
0,1
X
This mixed-integer optimization problem was solved in MATLAB using the genetic
algorithm with default settings (function tolerance = 1e-6, constraint tolerance = 1e-6,
stall generations = 50, elite count = 2, crossover fraction = 0.8) and a population size of
500. The optimization took about 15 seconds when run in parallel on an Intel i7-3770K
processor, and converged in about 50 generations. Optimal cutting conditions, calculated
from this method are listed in Table 4, for different constraints. In Approach 1, all
feasible ranges of decision variables i.e. tool type, cutting speed, and feed were included
in the search space. In Approach 2, constraints were used to limit the cutting speed to a
low setting so that the optimum tool type can be identified in which TiAlN coated tool
was determined to be the best choice for minimizing microhardness alterations. As it can
15
(6)
be seen from optimization results, a small edge radius tool (r = 6 µm) is being favored
and a cutting speed of 85 m/min for uncoated WC/Co tool and a cutting speed of 58
m/min for TiAlN coated tool with a feed of about 0.07 mm/rev are found optimum values
within the ranges of experimental data.
CONCLUSIONS
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In this paper, machining induced microstructure alterations such as hardness, grain size
and fractions have been investigated by using face turning experiments, Finite Element
simulations, and machine learning based predictive modeling for Ti-6Al-4V titanium
alloy. 3-D Finite Element simulations have been utilized to calculate the temperature
fields experience during machining of Ti-6Al-4V. Together with hot hardness
measurements conducted at these temperature ranges, prediction of microhardness profile
into machined subsurface Ti-6Al-4V is achieved. Furthermore, microstructure is
investigated by taking grain size and phase fraction measurements. Effects of tool edge
radius and coating as well as cutting conditions on surface microhardness and
microstructure i.e. grain size and fractions are identified. It was found that the
microhardness of the machined surface and subsurface is affected by the machining
process and cutting conditions especially with a large edge radius, high cutting speed and
feed rates. Some of the specific conclusions can be given as:
Softening occurs in some cutting conditions possibly due to high localized
temperatures, dynamic recrystallization and grain coarsening on the machined surfaces of
Ti-6Al-4V.
16
Predictive modeling utilizing FE simulations combined with Random Forests
method is found effective in capturing temperature affected microhardness profile into
the machined subsurface as well as machining induced microstructure alterations such as
grain size and fractions.
Genetic algorithm is a viable method to conduct optimization for selecting tool
type and machining parameters in relation to most desirable microstructure, strength and
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microhardness.
ACKNOWLEDGEMENTS
The authors greatly acknowledge the financial support provided by United States
National Science Foundation- Grant# CMMI-113078 for this research.
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[4]
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Table 1 Hardness measurements on the machined tracks.
Tool
Edge
Cutting
Feed
Mean
SD
Avg.
SD
Volume
Type
radius
Speed
f
Hardness
Hardness
Grain
Grain
fraction
r
vc
(mm/rev) (HV)
(HV)
Size
Size
of
(mm)
(m/min)
davg
davg
matrix
(µm)
(µm)
grains
WC/Co 25
55
0.05
316.9
8.9
13.03
3.04
0.22
WC/Co 25
55
0.1
301.6
16.0
14.39
2.73
0.27
WC/Co 25
90
0.05
316.7
18.9
16.17
3.45
0.19
WC/Co 25
90
0.1
310.0
37.9
13.57
2.85
0.28
TiAlN
10
55
0.05
326.5
9.5
14.66
3.43
0.17
TiAlN
10
55
0.1
323.3
17.4
13.09
2.59
0.18
TiAlN
10
90
0.05
319.1
13.3
14.40
3.18
0.19
TiAlN
10
90
0.1
324.2
16.3
14.95
3.63
0.17
WC/Co 10
55
0.05
313.9
24.8
13.20
2.69
0.27
WC/Co 10
55
0.1
319.6
11.4
12.82
2.69
0.24
WC/Co 10
90
0.05
319.6
23.4
14.39
2.79
0.29
WC/Co 10
90
0.1
310.1
23.9
13.66
2.62
0.23
WC/Co 5
55
0.05
321.2
22.3
10.70
2.41
0.34
WC/Co 5
55
0.1
324.8
11.2
13.63
3.07
0.23
WC/Co 5
90
0.05
332.3
10.2
16.29
2.95
0.25
WC/Co 5
90
0.1
332.1
14.5
14.57
3.23
0.27
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Table 2 Hardness measurements at room temperature after cooling down
Condition
Temperature (°C) Mean Hardness (HV) SD Hardnesss (HV)
335.8
13.3
Air Cooled
700
323.8
13.1
Air Cooled
600
332.8
8.9
Air Cooled
500
326.4
18.9
Air Cooled
400
312.1
20.1
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Furnace Cooled 704
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Table 3 Mechanical and thermo-physical properties of work and tool materials used in FE
simulations [6].
Ti-6Al-4V
WC/Co
(Ti,Al)N
E(T)
0.7412T+113375 5.6x105
6.0x105
α(T)
3.10-9T+7.10-6
4.7x10-6
9.4x10-6
7.039e0.0011T
55
0.0081T+11.95
(T)
0.0005T+2.07 0.0003T+0.57
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cp(T) 2.24e0.0007T
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Table 4 Optimization results.
Optimization Constraints
Approach 1
55 ≤ vc ≤ 90 & 0.05
WC/Co
≤ f ≤ 0.10
uncoated
55 ≤ vc ≤ 60 & 0.05
TiAlN
≤ f ≤ 0.10
coated
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Approach 2
Tool
23
Edge radius,
vc
f
r (µm)
(m/min)
(mm/rev)
6
84.9
0.069
6
58.3
0.073
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Figure 1 Hardness measurements at room temperature after cooling down
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Figure 2 Hot hardness measurements for different initial temperatures.
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Figure 3 Microstructure of Ti-6Al-4V (a) unmachined and machined subsurfaces (b)
WC/Co tool, r = 5 µm (sharp), vc=55 m/min, f=0.10 mm/rev, (c) TiAlN coated WC/Co
tool, vc=90 m/min, f=0.10 mm/rev (d) WC/Co tool, r = 10 µm, vc=55 m/min, f=0.10
mm/rev (e) WC/Co tool, r = 25 µm, v c=55 m/min, f=0.10 mm/rev (f) WC/Co tool, r = 25
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µm, vc=90 m/min, f=0.05 mm/rev.
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Figure 4 3D FE model for machining and predicted machining induced temperature
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fields.
27
Figure 5 Representation of a regression tree in the instantaneous hardness model (a) and
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RF model fit for hot hardness (b).
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Figure 6 Temperature in ºC (a) and hardness in HV (b) over line section on the workpiece
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during machining over time.
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Figure 7 Instantaneous hardness (a) prior to chip formation, (b) after the cutting process,
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and (c) after cooling down to r. t.
30
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Figure 8 Random Forests based prediction models for hardness and grain size.
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Figure 9 Measured and predicted average grain size.
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Figure 10 Measured and predicted hardness.
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