1007

Sensors and Materials, Vol. 31, No. 3 (2019) 1007–1020
MYU Tokyo
S & M 1831

Temperature Sensing and Two-stage Integrated Modelingof the Thermal Error for a Computer-numerical Control
Swiss-type Turning Center
Kun-Chieh Wang, Hui-Cun Shen, Chi-Hsin Yang,* and Hong-Yi Chen
Zhaoqing University, Zhaoqing City, Guangdong Province 526061, P.R. China(Received November 23, 2018; accepted January 30, 2019)

Keywords: data mining, support vector regression, thermal error compensation, CNC machine tools

For tool machinery, the most crucial factor affecting the machining precision is thermal
deformation. Thus far, the most popular method of reducing thermal deformation has been
considered as the compensation method, and many mathematical compensation methods havebeen proposed. However, attempts to develop a more comprehensive model are continuing. To
improve the prediction accuracy, in this study, we propose a two-stage integrated data-mining
scheme. The first stage, using rough set theory, focuses on how to manipulate the measured
problem-dependent temperature and deformation data. The second stage, using a deep-learningneural network scheme, models the relationship between the temperature increase and thethermal error. Comparisons of the proposed method with other methods are also made. Results
show that marked improvements are obtained using our proposed integrated data mining
scheme.

1.

Introduction

The machining precision directly affects the dimensional accuracy of workpieces. The
issue of how to eliminate the machining error has continuously drawn much attention fromscholars and engineers attempting to develop precision machine tools. The machining error
mainly originates from the mechanism kinematics, thermal deformation, machining, structure
dynamics, controller inaccuracy, and deviation from the control rules. Among these factors,
thermal deformation has the largest contribution and may reach a value as high as 75% of thetotal error.(1)There are two sources of thermal deformation in a machine tool, internal and external,
which may induce a temperature rise and thermal deformation. The internal heat sources
include heat generation from the cutting process, heat generation from friction during motion,and heat generation from electronic systems and motors. The external heat sources include
environmental temperature changes and human body radiation. Through the propagation of
conduction, convection, and radiation, the generated heat affects all the components of thestructure and causes an undesired thermal error. The thermal error of a Swiss-type turning*

Corresponding author: e-mail: yangchihsin1969@gmail.com
https://doi.org/10.18494/SAM.2019.2225
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 31, No. 3 (2019)

center (see Fig. 1) may be considered as the position error of the tip of the tool clamped in theturret relative to the center of the workpiece clamped in the first (major) or second spindle
system. Table 1 shows the details of the thermal sources and errors for a computer-numericalcontrol (CNC) turning center.
In general, there are three ways of reducing the thermal error of a machine tool: designinga thermally stable structure, reducing heat sources, and compensating the thermal error.
Reducing the heat sources has become a mature method and this concept has been widely usedin manufacturing machine tools. In the design of thermally robust structures, there is a limit to
the accuracy that can be achieved. Thus far, thermal error compensation has been successful
because it is easy to implement and cost-effective. The procedure used to perform thermal
error compensation is as follows: (1) selection of the target machine, (2) determination of thetest and verification conditions, (3) determination of the key thermal points for temperature
measurement, (4) setting up of temperature- and displacement-sensing systems, (5) data
reduction, (6) thermal error modeling, and (7) model verification.
In the above procedure, the main difficulty lies in the data reduction and thereafter thethermal error modeling. Many papers have used different mathematical relationships to build
thermal error models of machine tools or their key modules. For example, Du et al.(2) used amodified regression method to build a thermal error model of a machining center. Kim andPark(3) proposed a difference-equation-based state space model for the two axes of a CNC lathe.

Fig. 1.

(Color online) Target Swiss-type CNC lathe.

Table 1
Thermal error and heat sources of a CNC turning center.
Generation in machine:
Heat generationelectronic system, mechanism system, during machining
friction during motion, motors
processes
Components Components, modules, assemblies, structure, mechanism, bed structure, turret structure, first spindle
affectedsystem, second spindle system
Error types
Configuration error, dimension error
Total error of whole turning machine

Heat sources

Room
Heat dissipation
environment of cooling system

Human
body

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Moreover, methods based on an artificial neural network (ANN)(4) and PSO combined with an
ANN(5) have been reported as means of dealing with the problem of thermal error modeling.
Recently, to enhance model accuracy, the concept of data preprocessing has been added.
Liu et al.(6) used a linear regression model, incorporating fuzzy clustering and grey relation,
which was used for data preprocessing. Wang and Tseng(7) built a linear regression model that
employed the rough set theory (RST) for data preprocessing for a vertical machining center.
Wang(8) used an ANN auxiliary with grey system theory for data preprocessing for a doublecolumn machining center. It was found that the two-stage thermal error modeling methods(one scheme for data preprocessing and one scheme for building a mathematical relationship)
can be comprehensively used. Moreover, past literature surveys(1–3,7–9) showed that different
machine structures lead to different thermal behaviors, in which they required more appropriate
and accurate thermal error modeling schemes. Thus far, there have been no publications about
the studies of thermal error compensation for a CNC Swiss-type machining center, which has
a main spindle system structure considerably different from that of a traditional CNC lathe.
In the main spindle system, bar-type workpieces are fed from its left-hand side and come out
from the right spindle hole. This complicated system generates heat in usual ways and thus its
thermal behavior needs an appropriate thermal error modelling scheme.
Regarding the above discussions, the aim of this study is to build a thermal error model
for a Swiss-type machining center. We intend first to carefully study this machine’s thermal
behavior. Then, we develop a proper measuring method and a measurement system. A
suitable integrated two-stage thermal modeling scheme, including the RST and deep-learningneural network methods, is used to establish a comprehensive mathematical relationship. The
modeling results are thereafter verified by specifically designed experiments.

2.

Methodology

The methodology used for thermal error modeling is shown in Fig. 2. The key thermal
points on the machine were chosen by considering the heat sources in the machine underoperation. The measured temperature at the key thermal points and the displacement of thetwo spindle noses were accumulated and grouped using RST.(10) The grouping results provide
the relatively important temperature variables for the main and second spindle systems. Then,
we used a deep-learning neural network scheme(11) to establish a thermal error model basedon the grouping results, which includes a reduced number of temperature variables and thecorresponding thermal deformation for each spindle system.

3.

Experimental Procedure

3.1

Measurement system and test conditions

The sensing units were composed of thermal and displacement sensors. Resistancethermometers (PT100) were employed as temperature sensors to detect the temperature
variation of the key thermal points on the machine, and eddy current displacement sensors were

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Sensors and Materials, Vol. 31, No. 3 (2019)

Fig. 2.

Procedure used for thermal error compensation.

used to detect the thermal errors of the first and second spindles. The key thermal points for thetemperature measurements should be carefully chosen since the number of temperature sensors
and their location strongly affect the accuracy of the thermal error modeling and compensation
results. In general, the selected key thermal points should be (1) close to the main heat sources, (2)capable of reflecting the temperature field of the system, and (3) strongly related to the thermal
error.(12) On the basis of these suggestions, 12 thermal sensors were stamped at the selected key
points, as listed in Table 2 and shown in Fig. 3. In addition, an invar rod was mounted on thefirst and second spindles. Also, to detect the deformation of the first spindle, an eddy current
displacement sensor was mounted on a fixture connected to the upper turret. Similarly, anothereddy current displacement sensor was mounted on another fixture connected to the lower turretto detect the deformation of the second spindle.
3.2

Test conditions

To investigate the thermal behavior of our target two-spindle, two-turret CNC turn-millmachining center, the test conditions used for modeling and verification were designed tosimulate real cutting cases and are given in Tables 3 and 4, respectively.

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Table 2
Locations of key temperature sensors.
Sensor No.
T1
T2
T3
T4
T5
T6

Location
Environment
Chucking cylinder
Spindle motor
Spindle motor
Chucking cylinder
Servo motor

Fig. 3.

Sensor No.
T7
T8
T9
T10
T11
T12

Location
Turret cylinder housing
Servo motor
Turret cylinder housing
Linear guideway seatLinear guideway seat
Bed

Thermal key points of temperature sensing.

Table 3
Test conditions for modelling.

Table 4
Test conditions for verification.

First (major) spindle
Second spindle
systemsystemTurretTurretOperation
Spindlespeed
Spindle
speed
time
speed
(mm/s)
speed(mm/s) in(min/total
(rpm)
in x
(rpm)
x direction
time)
direction
0–10
3000
20
3000
20
10–20
2000
20
2000
20
20–30
2500
20
2500
20
30–40
1500
20
1500
20
40–50
0
0
0
0
50–60
500
10
500
10
60–70
1000
10
1000
10
70–80
1500
10
1500
10
80–90
2000
10
2000
10
90–100
2500
10
2500
10

First (major) spindle
Second spindle
systemsystemTurretTurretOperation
Spindlespeed
Spindle
speed
time
speed
(mm/s)
speed(mm/s) in(min/total
(rpm)
in x
(rpm)
x direction
time)
direction
0–10
1400
10
1400
10
10–20
2000
10
2000
10
20–30
2600
15
2600
15
30–40
3200
15
3200
15
40–50
2000
15
2000
15
50–60
1500
10
1500
10
60–0
1000
10
1000
10

Test

Test

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3.3

Sensors and Materials, Vol. 31, No. 3 (2019)

Measurement of temperature and thermal deformation

The temperature and capacitance sensors were integrated into one system so as to retrieve
the temperature and deformation readings synchronically. The variation of the measured
temperature with time at different sensors on the target machine is shown in Figs. 4(a) and
4(b). It was found that the temperature of the machine ranges from 26 (room temperature) to
62 ℃. The temperature variation with time changes among the key thermal points. Moreover,the variation of the thermal drift of the spindles in the axial direction is shown in Fig. 5. The
MX1 curve represents the measured thermal drift with time for the first spindle system, whichreaches a maximum of 46 μm after 15 min of operation. Similarly, the MX2 curve represents
the measured thermal drift with time for the second spindle system, which reaches a maximumof −48 μm after 15 min (slightly larger than that of MX1).

(a)

(b)
Fig. 4. Temperature variation with time at key thermal points. (a) Variation of temperature at T1, T4, T5, T6, T7,
T11, and T12 with time. (b) Variations of temperature at T1, T2, T3, T8, T9, T10, and T12 with time.

Sensors and Materials, Vol. 31, No. 3 (2019)

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Fig. 5. (Color online) Measured (MX1, MX2) and predicted (EX1, EX2) thermal drifts with time for the first andsecond spindle systems.

4.

Thermal Error Model

4.1

Stage 1: Data trimming

The measured temperature and deformation data are trimmed by RST, which is an effective
scheme developed in the field of data mining. Since Pawlak proposed the RST in 1982,(10)this theory has been well studied by many researchers, resulting in major advances.(13,14) The
following is a brief introduction of RST used in this study.
Information systems
In RST, information systems are used to represent knowledge. An information system
S = (U , A ) consists of the following:U– a nonempty, finite set called the universe;
A– a nonempty, finite set of attributes;
A= C ∪ D , in which C is a finite set of condition attributes and D is a finite set of decisionattributes (see Table 5).
The universe includes many objects. Objects can be interpreted as cases, states,
processes, patients, and observations. Attributes can be interpreted as features, variables, andcharacteristic conditions. A simple information system is shown in Table 5, in which Ni = N1 –N5 represent the objects of the universe (U = {Ni}), X i = X1 , X 2 , X 3 are the condition attributes(C = {Xi}), and Y is the decision attribute (D = {Y}).
Reducts and core
An important process in RST is attribute reduction. Attribute reduction should be carriedout in such a way that the reduced set of attributes provides the same quality of approximation
as the original set. Reducts and the core are two fundamental concepts related to attribute
reduction. The minimal subsets of attributes that discern all equivalence classes of the relation

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Sensors and Materials, Vol. 31, No. 3 (2019)

Table 5
Information table of a sample database.
Universe
U
Ni
N1
N2
N3
N4
N5

Nonempty, finite set of attributes A
Decision
Condition attributes C
attribute D
X1
X2
X3
Y
2
1
3
1
3
2
1
1
1
3
3
0
2
1
1
0
1
1
3
1

D discernable by the entire set of attributes are called reducts. The core is the common
part of all reducts. To find the core of an information system, the discernibility matrix anddiscernibility function should be constructed.
First, the discernibility matrix M = [mij ] is defined as

mij = { X ∈ C :X ( Ni ) ≠ X ( Nj ) ∧ (Y ∈ D, Y ( Ni ) ≠ Y ( Nj ))} ,(1)

where i, j = 1, 2, …, n, and n denotes the number of objects in U. To calculate the elements mij,
one must find the set of attributes that discern the objects Ni and Nj and those that do not belong
to the same equivalence class of D.
The overall rule can be written as X 2 ∧ X 3 → Y , which implies that the decision attribute (Y)only depends on the two core attributes of X2 and X3.
Using Eq. (1), the discernibility matrix corresponding to the sample database shown in Table
5 with U = {N1, N2, N3, N4, N5}, C = { X1 , X 2 , X 3}, D = {Y} is obtained and shown in Table 6.
For instance, when discerning the sets between the sets N1 and N3, the result m13 = { X1 , X 2 } is
obtained. This means that with regard to decision Y, object N1 (Y = 1) differs from object N3 (Y = 0)
in attributes X1 and X2. When discerning the sets between N3 and N5, the result m35 = { X 2 } is
obtained. This is because the attribute X2 alone is sufficient for distinguishing between N3 (Y = 0)
and N5 (Y = 1).
Secondly, the discernibility function can be constructed via the discernibility matrix.
The discernibility function f ( A ) is a Boolean function constructed as follows. (1) To eachelement, a Boolean variable ‘X’ is assigned (e.g., m13 = { X1 , X 2 }); (2) for each element mij, theBoolean form of the union operation is assigned [(e.g., X1 ∨ X 2 (the union of X1 and X2)]; (3) for
different elements, the Boolean form of the intersection operation is assigned [(e.g., X1 ∧ X 2 (theintersection of X1 and X2)]. Accordingly, the discernibility function of all the data in Table 6
can be constructed asf ( A) = ( X1 ∨ X 2 ) ∧ X 3 ∧ ( X1 ∨ X 2 ∨ X 3 ) ∧ ( X1 ∨ X 2 ) ∧ X 2 ∧ ( X1 ∨ X 3 ).

(2)

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Finally, to calculate the final form of f(A), the absorption law is applied. The absorption
law can be defined as the minimal absorbent construction for a given tolerance information
system, which can be easily transformed to the problem of finding the minimal prime implicant
for the Boolean function corresponding to this system. According to the absorption law, forinstance, to discern the sets among N1, N3, and N5, when m13 = { X1 , X 2 } and m35 = { X 2 } are
obtained, the discernibility function f(A) can be further expressed and reduced to the formf ( A) = ( X1 ∨ X 2 ) ∨ ( X 2 ) = X 2, and one final reduct X2 of the considered set of attributes isfound. Moreover, by applying the absorption law to Eq. (2) for all the data in Table 6, the final=) X 2 ∧ X 3 (see Table 6). We can represent our system and rules
two cores are obtained as f ( A
as in Table 7.
The data analysis through the decision rule of the RST can display the knowledge rule of thethermal error of a machine tool. In addition, the core factors can be found.
Cores:The two cores of this database are f ( A=) X 2 ∧ X 3 (X2 and X3).
Rules:(1) (X 2 =1) ∧ ( X 3 =3) → (Y =1) , i.e.,
if X2 = 1 and X3 = 3, then decision = 1, see sample N1.
(2) (X 2 =2) ∧ ( X 3 =1) → (Y =1), i.e.,
if X2 = 2 and X3 = 1, then decision = 1, see sample N2.
(3) (X 2 =3) ∧ ( X 3 =3) → (Y =0), i.e.,
if X2 = 3 and X3 = 3, then decision = 0, see sample N3.
(4) (X 2 =1) ∧ ( X 3 =1) → (Y =0), i.e.,
if X2 = 1 and X3 = 1, then decision = 0, see sample N4.
(5) (X 2 =1) ∧ ( X 3 =3) → (Y =1), i.e.,
if X2 = 1 and X3 = 3, then decision = 1, see sample N5.
The overall rule can be written as X 2 ∧ X 3 → Y , which means that the decision attribute (Y)only depends on two core attributes of X2 and X3.
In this study, Xi denotes the temperature at different key points, Xi = Ti, i = 1 – 12; Y denotes
MX1 or MX2. Following the procedures of the above-mentioned discernibility matrix method,
we obtain the two overall rules(3)

T 1 ∧ T 2 ∧ T 3 ∧ T 4 ∧ T 5 ∧ T 6 ∧ T 8 → MX 1

Table 6
Discernibility matrix M corresponding to the sample
database shown in Table 1.
mij
N1
N2
N3
N4
N5

N1
N2
—
—
—
—
X1, X2 X1, X2, X3
X1, X2,
X3
—
—

N3
—
—
—
—
X2

N4
—
—
—
—
X1, X3

N5
—
—
—
—
—

Table 7
Findings of core and decision rules.
U
Ni
N1
N2
N3
N4
N5

X2
1
2
3
1
1

C

X3
3
1
3
1
3

D
Y
1
1
0
0
1

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Sensors and Materials, Vol. 31, No. 3 (2019)andT 1 ∧ T 2 ∧ T 3 ∧ T 4 ∧ T 5 ∧ T 6 ∧ T 8 → MX 2.

(4)

It is found that the obtained influence rules are the same for both MX1 and MX2. Using
these high-weighting temperature parameters, a mathematical relationship may be derived
between the temperature at key points and axial deformation in a simple manner since thenumber of condition parameters (Ti) is reduced.
4.2

Stage 2: Mathematical relationship

Using the resultant rules obtained from RST, we can neglect the effects of T7, T10, T11,
and T12 on both MX1 and MX2. Then, a mathematical relationship between temperatures andthermal drifts is established via a deep-learning neural network, described as follows.
A convolutional neural network (CNN) is a state-of-the-art comprehensive network of
DNNs, capable of mapping multiple outputs with multiple inputs in modeling problems. This
technique was developed in the 1980s and 1990s.(15) Since 2012, when it was dramaticallyrevived, this technique has conquered most computer vision fields and is growing rapidly. A
CNN consists of a neural network that extracts features of the input image and another neuralnetwork that classifies the feature image. The fundamentals of a CNN are as follows.
The simplest neural network is called a multilayer perception (MLP). The nth layer of an
MLP can be expressed as
xn,i = ϕ  ∑ wn,i , j xn −1, j  .
 j




(5)

Many different functions such as step functions, the sigmoid function, and the hyperbolic
tangent, can be chosen. Here, we adopt a rectified linear unit (ReLU). The ReLU function isdefined as the positive component of its input as follows:x ≤ 0 :x > 0 :ϕRe LU ( x) = 

0
.
x

(6)

It was discovered that even a single hidden layer is sufficient for an MLP to express any
continuous function with arbitrary precision (universal approximation theorem). However, theconstruction of such a neural network is still based on trial and error. Expressing complicatedfunctions is rather expensive for a two-layer MLP since a hidden layer requires a very large
number of neurons. Instead, DNN researchers have used networks with multiple narrow layers.
The trade-off and challenge in DNNs lie in how to tune them to solve a given problem. A CNN
adopts a machine learning algorithm that consists of a set of rules for using and updating a set of

Sensors and Materials, Vol. 31, No. 3 (2019)1017

parameters (i.e., tuning weights) in accordance with the labeled data provided to it. Moreover,the learning type of the CNN in this study is chosen as reinforcement learning, which is related
to supervised learning but decouples the form of the training outputs from that of the inference
output. The output of reinforcement learning is called an action, and the label for each training
input is called a reward.
x, r → M
		Training phase				

Inference phase		M ( x′) → y ′A model infers some output action from its input, the action produces some reward froman external system, and then the initial input and subsequent reward are used to update themodel. Furthermore, it is difficult to decide the initial distribution of random values of model
parameters. It is suggested that these values should be small and random. Here, we chose thecross-entropy loss function to evaluate the difference between the true and estimated outputs.

1e yi L( y, yˆ ) = − ∑ ln
n i  ∑ e y j 
j



(7)

This loss function is chosen for its capability of dealing with the relationship between
multiple inputs and multiple outputs. Finally, to adjust the model weights to minimize theloss function, we use the stochastic gradient descent (SGD) method in conjunction with the
backpropagation technique to complete the training of the model. A CNN is similar to a large
MLP in which many of the weights in a layer are tied together in a specific pattern. In the
training, when a gradient update is applied to one of these weights, it is applied to all of them.
Second, using the above nine relatively important temperature rises as the input and the three
grinding head deformations as the output, we construct a CNN. This CNN has five layers: one
input layer, one convolution layer (twelve neurons), one pooling layer, one hidden layer (eightneurons), and one output layer (two neurons). Only three layers, the convolution, hidden, andoutput layers, contain weight matrices that require training. Through the training, the weightsof the neurons in each layer are determined. We trained our model using the SGD with a batch
size of 100 examples, a momentum of 0.79, and a weight decay of 0.0007. We initialized theweights in each required layer using a Gaussian distribution with zero mean and a standard
deviation of 0.01. We used an equal learning rate (initialized at 0.01) for all required layers.
The typical architecture of the CNN is shown in Fig. 6.
The results obtained after training are expressed in the form of a prediction curve of thethermal error. Figure 5 shows a comparison between the measured (MX1, MX2) and predicted(EX1, EX2) results. It can be seen that the maximum original measured thermal errors are 46
and −48 μm. Moreover, after compensation with our CNN prediction model, the maximum
thermal errors are reduced to 0.3 and −0.5 μm, corresponding to reductions of 99.3% and98.9%, respectively.

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Sensors and Materials, Vol. 31, No. 3 (2019)

Fig. 6.

(Color online) Typical architecture of CNN.

Table 8New test conditions.
Test
Operation time(min/total time)
0–10
10–20
20–30
30–40
40–50
50–60
60–70

4.3

First (major) spindle system
Spindle speed Turret speed (mm/s)(rpm)
in x direction
1400
10
2000
10
2600
15
3200
15
2000
15
1500
10
1000
10

Second spindle system
Spindle speed Turret speed (mm/s)(rpm)
in x direction
1400
10
2000
10
2600
15
3200
15
2000
15
1500
10
1000
10

Verification

To verify our proposed new thermal error modelling methodology, we now perform anotherexperiment. The new test condition is arranged according to some actual cutting conditions,as shown in Table 8. We measure the temperature variations only at the reduced number ofkey points, i.e., T1, T2, T3, T4, T5, T6, and T8, and neglect the other five temperatures (T7, T9,
T10, T11, and T12). The temperature measurement results are shown in Fig. 7. The thermal
errors at the first and second spindle noses are also measured, and the results are shown in Fig.
8. Figure 8 also shows a comparison between the measured and predicted thermal errors forthe first and second spindle systems with the new test conditions. It is seen that the maximum
measured thermal errors are 49.1 and 51.3 μm at the first and second spindle noses, respectively.

Sensors and Materials, Vol. 31, No. 3 (2019)

Fig. 7.

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Temperature variation at reduced numbers of key points in the new experiment.

Fig. 8. (Color online) Measured (MX1, MX2) and predicted (EX1, EX2) thermal deformations with time for the
first and second spindle systems with the new test conditions.

Moreover, after compensation with our prediction model, the maximum thermal errors can be
reduced to 0.35 and –0.52 μm, corresponding to reductions of 99.28% and 98.98%, respectively.
The comparison thus shows satisfying results.

5.

Conclusion

The two-stage thermal error modeling of a CNC Swiss-type turning center has been
performed in this study. The new proposed modeling technique includes a data mining scheme
based on a rough set theory to reduce the number of key points where the temperature must
be monitored and a deep-learning neural network to accurately establish the mathematical
relationship between variations in the temperature and deformation. The results for thepredicted thermal errors are accurate. The thermal errors after compensation are 0.45 and −0.5μm for the first and second spindle noses, respectively, in the verification experiment. In this1020

Sensors and Materials, Vol. 31, No. 3 (2019)study, we explored the thermal behavior of a specific target, a CNC Swiss-type turning center,and established an accurate and efficient two-stage modeling scheme that may be extensively
applied to the thermal error modeling problems for a wide range of CNC machine tools.

References
1 J. Mayra, J. Jedrzejewskic, E. Uhlmann, M. A. Donmez, W. Knapp, F. Hartig, K. Wendt, T. Moriwaki, P. Shore, R.
Schmitt, C. Brecher, T. Wurz, and K. Wegener: CIRP Ann. Manuf. Technol. 2 (2012) 1. https://doi.org/10.1016/
j.cirp.2012.05.008
2 Z. C. Du, J. G. Yang, Z. Q. Yao, and B. Y. Xue: J. Mater. Process. Technol. 129 (2002) 619.
3 B. S. Kim and J. K. Park: Proc. 2014 9th Int. Workshop on Microfactories (IWMF2014).
4 C. D. Mize and J. C. Ziegert: Precis. Eng. 24 (2000) 338.
5 H. Wu, H. Zhang, Q. Guo, X. Wang, and J. Yang: J. Mater. Process. Technol. 207 (2008) 172.
6 H. Liu, E. Miao, Z. Xindong, X. Zhuang, and X. Wei: Precis. Eng. 51 (2018) 169. https://doi.org/10.1016/
j.precision.2017.08.007
7 K. C. Wang and P. C. Tseng: J. Adv. Mech. Des. Sys. Manuf. 4 (2010) 516.
8 K. C. Wang: J. Grey Sys. 4 (2010) 353.
9 W. Feng, Z. Li, Q. Gu, and J. Yang: Int. J. Mach. Tools Manuf. 93 (2015) 26.
10 Z. Pawlak: Int. J. Comput. Inf. Sci. 11 (1982) 341.
11 Y. L. Cun, B. Bower, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel: Proc. Advancesin Neural Information Processing Systems (1990) 396.
12 D. Zhang, X. Liu, H. Shi, and R. Y. Chen: Proc. Int. Conf. Intelligent Manufacturing, Int. Society for Optics
and Photonics (1995) 468.
13 C. Goh and R. Law: Tourism Manage. 24 (2003) 511.
14 S. Lee and G. Vachtsevanos: Math. Comput. Simul. 60 (2002) 225.
15 A. Krizhevsky and G. E. Hinton: ESANN (2011).