Received: 13 May 2022 Revised: 5 August 2022 Accepted: 9 August 2022 The Journal of Engineering
DOI: 10.1049/tje2.12189
ORIGINAL RESEARCH
Mechanical vibration monitoring system for electrocardiogram
machine based on Hilbert-Huang transformations
Zhu Yongbo1 Xu Lijun1 Issah Abubakari Samori2
1Hunan Mechanical and Electrical Polytechnic, Abstract
Changsha, China The monitoring of health and the technologies that are related to it are an exciting area
2School of Engineering Sciences, University of of research. The paper proposes a mechanical manufacturing vibration monitoring system
Ghana, Accra, Ghana that is based on Hilbert-Huang transformation (HHT) feature extraction to monitor the
running state of the spindle of a mechanical numerical control (NC) machine tool of an
Correspondence
Issah Abubakari Samori, School of Engineering electrocardiogram (ECG) machine. Real-time monitoring of the time–frequency charac-
Sciences, University of Ghana, Accra, Ghana. teristic quantity of the spindle vibration signal for ECG signals has been made possible
Email: iasamori@st.ug.edu.gh due to the online empirical mode decomposition (EMD) method, which is used to obtain
the time–frequency characteristic quantity of the spindle vibration signal based on HHT.
The experiment shows that the frequency doubling characteristic components in the time–
frequency distribution are obvious in the time interval without copper rod contact, but they
disappear in the time interval during which copper rods are in contact (0.3 1.1 s, 3 4s in the
figure). It has been demonstrated that the system is capable of not only accurately moni-
toring the characteristic quantity in the frequency domain of the vibration signal produced
by the NC machine tool spindle, but also of successfully implementing the monitoring of
the time–frequency characteristic quantity in real time.
1 INTRODUCTION the influence of various environmental excitation. Under the
action of natural factors such as earthquake, climbing wind, and
In the field of biomedical, electrocardiogram (ECG) machines waves, as well as long-term fatigue and corrosion, its structure
stand out to be one of the important machines for analysis will produce varying degrees of damage and damage. The eval-
health of an individual. The analysis of ECG signals needs to be uation of the state of the structure is of great significance to
handled with utmost care. In this paper the mechanical vibra- ensure social economic security and personal safety. Through
tions of these machines are analyzed. Mechanical vibration is a the modal analysis method, the vibration components of each
common phenomenon in modern industrial production. Strong mode in vibration are analyzed, and the modal parameters
vibration will have an adverse impact on the normal operation are identified accordingly, which can better identify the natural
of equipment, lead to component loss, greatly shorten the ser- vibration characteristics of mechanical equipment and structure,
vice life of mechanical equipment, and may have more serious so as to evaluate its structural characteristics and working state
accidents, and even endanger the life safety of workers [1]. Any [3–6].
structure or mechanical equipment will produce certain vibra- The ECG is a biomedical equipment that is used to analyze
tion under dynamic conditions. When the mechanical system the heart signals and electrical activity. It makes use of sen-
is running, if the excitation load is close to the natural fre- sors that are attached to various part of the human chest and
quency component of the system, it will cause the resonance then electrical signals are captured each time the heart beats.
of the system. This large-scale vibration may affect the normal These electrical signals are then processed and analyzed through
operation of the mechanical system, and even lead to system a graph in order to check the condition of the human heart. In
damage and major accidents [2]. Large bridges, buildings and this paper these signals are analyzed and features are extracted
other engineering structures will also produce vibration under in order to reduce the faults that can arise.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the
original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
© 2022 The Authors. The Journal of Engineering published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
1104 wileyonlinelibrary.com/iet-joe J. Eng. 2022;2022:1104–1113.
YONGBO ET AL. 1105
FIGURE 1 Schematic diagram of mechanical manufacturing vibration system detection
Feature extraction is the core of fault diagnosis. The accuracy accelerometer measures the changing acceleration with a level of
of signal processing and feature extraction will directly affect accuracy that is satisfactory. The high-performance digital signal
the reliability of fault diagnosis. Traditional fault feature extrac- processors that make up the VC-3100 vibration comparator
tion methods include wavelet transform, Fourier transform, offer three fundamental capabilities: detection, measurement,
short-time Fourier transform and other methods [7]. Hilbert- and evaluation. The accelerometer sends signals to the compara-
Huang transform (HHT) is an adaptive time–frequency analysis tor, and the comparator uses those signals to detect irregularities
method, which overcomes the defects of traditional spectrum in the machine (detection), measure vibration levels (measure-
analysis methods. The HHT method is used to analyze the ment), and judge vibration levels based on the measurements
signal, which has good time–frequency aggregation, can obtain (judgement). It is possible to listen to the vibration sound
very high time–frequency resolution, and is very suitable for by attaching a regular set of headphones to your device and
analyzing the non-stationary signals that may be included in doing so. An output of the vibration sound is provided for
the rotor vibration signal [8]. In this paper, taking the spindle each band, which enables verification of specific vibration
of mechanical manufacturing numerical control (NC) machine occurrences.
tool as an example, the mechanical manufacturing vibration Recent developments in medical and biological technology
monitoring system based on HHT feature extraction is studied. have resulted in an explosion in the volume of data pertaining to
Whether the spindle of NC machine tool operates normally biological and physiological processes. Examples of this include
or not directly affects the machining quality and production medical imaging, electroencephalography, genomic sequences,
efficiency of the machine tool. The spindle vibration signal and protein sequences. Understanding human health and dis-
contains a large amount of information reflecting its working ease is made easier by the use of this data as a learning resource.
condition characteristics. The real-time monitoring of spindle As a result of developments in high-throughput technology, the
vibration is of great significance to ensure the machining quality past several decades have seen a meteoric rise in the amount of
and production efficiency of machine tools. In recent years, biomedical data, such as genomic sequences, protein structures,
the vibration monitoring method of NC machine tool spindle and medical pictures. This expansion has been observed across
has been widely studied, and the corresponding monitoring a wide range of disciplines. This flood of biomedical big data
system has been developed. When the working conditions of makes it necessary to develop computational tools that are both
NC machine tool spindle change or faults occur, its vibration effective and efficient in order to store, analyze, and interpret
signal has obvious non-stationary characteristics [9]. Therefore, the data. The paper focuses on vibration monitoring systems;
the strong non-stationary local characteristics in the spindle however, in the previous researches there are three analysis
vibration signal can characterize the change of working condi- techniques, namely, acoustic analysis, vibration signal analysis,
tions and the existence of some faults. Figure 1 is the schematic and thermal imaging analysis. The acoustic and vibration signal
diagram of mechanical manufacturing vibration system detec- analyses stand out as two of the most common options avail-
tion. Accelerometers, velocity sensors, proximity probes, and able among these studies. This is due to the fact that numerous
laser displacement sensors are some examples of the various issues can be found without the machine needing to be stopped
types of sensors that can be utilized in the process of measuring or taken apart. The variations in these signals frequently serve
vibration. A built-in accelerometer can be seen in Figure 1; this as an early warning sign of the existence of a problem. In
1106 YONGBO ET AL.
addition to its excellent recognition efficiency and non- 2 LITERATURE REVIEW
destructive testing capabilities, acoustic analysis benefits from a
relatively quick analysis time. However, it is extremely difficult In recent years, the vibration monitoring method of NC
to capture the acoustic signals in an accurate manner due to a machine tool spindle has been widely studied, and the corre-
number of elements including environmental conditions. Analy- sponding monitoring system has been developed. Teng et al.
sis of vibration signals comes with its own set of benefits as well analyzed the machine tool spindle signal based on the weak
as drawbacks. Vibration analysis is one method that can be uti- feature extraction method of cascaded bistable stochastic reso-
lized to accomplish real-time machine monitoring, and there are nance system, and developed the condition monitoring system
a variety of highly developed signal processing techniques that [10–12]. Zhao et al. designed an optical fibre monitoring system
can be utilized. Noise contamination and the correct mounting for collecting vibration signals during mechanical operation
position of the vibration sensors are two factors that prevent to monitor the mechanical operation status in real time [13].
vibration analysis from being completely accurate. Lastly, the Huang et al. developed the spindle vibration monitoring system
thermal imaging analysis method can be utilized for the purpose of NC machine tool based on spectrum analysis on the basis of
of monitoring and diagnosing mechanical systems. For the pur- analyzing the spectrum characteristics of vibration signal [14,
pose of this investigation, an infrared camera is typically utilized 15]. Abdeljaber et al. described the vibration signal monitoring
to identify several electrical defects in the machine on the basis system of medical equipment products based on servers, nodes,
of the thermal irregularities. The thermal pictures that were and sensors [16]. Zafarani et al. designed the working condition
obtained are helpful in detecting and localizing the flaws that monitoring system of vibrating screen based on wireless com-
are present in the equipment. However, this method is time- munication, and used the method of vibration signal analysis
consuming and costly, and it takes significantly more effort to to judge the working state of machinery [17, 18]. Wszoek et al.
analyze thermal images than it does auditory or vibration data. applied the wavelet method to spindle vibration monitoring
It is generally agreed that vibration analysis is the most accurate and developed a spindle vibration monitoring system with
way for determining the state of a machine. Based on the above- strong anti-interference ability [19]. Casamenti et al. studied the
mentioned reasons the paper focuses on monitoring vibration influence of load, position, and instantaneous acceleration on
signals for ECG machines using the HHT feature extraction the measured signal, and proposed a machine tool condition
method. monitoring system that can trace the fault source [20, 21]. Yang
Main contributions of the paper are: et al. developed the vibration monitoring system of spindle
bearing of NC machine tool with virtual instrument technology
1. The proposed model aims to monitor the running state based on LabVIEW [22]. Nazolin et al. used wavelet transform
of spindle of mechanical NC machine tool of ECG to analyze the time–frequency characteristics of machine tool
machine that is a vibration monitoring system based on spindle vibration signal, but the essence of wavelet transform
HHT. is Fourier transform with adjustable window. Once the local
2. The method that includes the design of spindle vibration feature scale of the signal is smaller than the feature scale of
monitoring system of mechanical NC machine tool. the selected base wavelet, it is difficult to accurately describe
3. The experiment uses characteristic quantity in frequency the local features with strong non-stationary in the spindle
domain of vibration signal produced by NC machine tool vibration signal of NC machine tool due to working condition
spindle and monitoring of time–frequency characteristic change or fault [23, 24]. The authors of [41] are concerned
quantity in real time. with the construction of a new fractional-order controller for
4. The experimental results prove the disappearance and recur- the autonomous rudder of underactuated surface vessels. This
rence time points of frequency doubling characteristics controller is to be developed with the required gain and phase
components in the time–frequency energy distribution are margin. They offered two different models for USV course
consistent with the generation and termination time points control and discovered that the performance of their controllers
of external excitation. was superior to that of the other controllers that were already in
use. Reference [42] is an attempt to solve the issue of poor diag-
The organization of this paper is as follows: Section 2 nosis effect, which is brought on by the mutual interference of
discusses the associated literature; Section 3 illustrates the many fault responses. They proposed a unique new method for
research methods by categorizing it into four parts: First the diagnosis of compound faults that they called MDSRCFD.
part explain the basic details of HHT method, second part This method is based on optimal maximum correlation kurtosis
explains the overall design of spindle vibration monitoring deconvolution (MCKD), and it uses sparse representation.
system of mechanical NC biomedical machine tool, third The findings of both the simulation and the actual application
part introduces the hardware development of the monitor- demonstrate that the proposed MDSRCFD is able to effi-
ing system, and the last part discusses the software design ciently separate and extract the compound fault characteristics
of monitoring system including the time–frequency feature of rolling bearings, which allows for the accurate diagnosis
extraction method; Section 4 discusses and analyzes the results of compound faults. Reference [43] investigated the clinical
obtained; Section 5 presents the conclusion and scope for future outcomes of individuals with a high-risk diabetic foot who
work. had been provided with custom-moulded offloading footwear
YONGBO ET AL. 1107
and who had been subjected to varying levels of adherence to ing into account time-varying vehicle speeds, fuel consumption,
their treatment regimens. The suggested [44] approach has the carbon emissions, and customers’ time windows led to the uti-
ability to successfully boost PS convergence and distribution lization of a satisfaction measure function based on a time
while also improving PF variety and distribution. An adaptive window as well as a measure function of the economic cost.
crossover approach is intended to assure the development of In conclusion, the results of the experiments demonstrate that
a high-quality offspring population while also weighing the the recommended strategies are highly effective in lowering total
impact of two distinct techniques on the variety of decision distribution costs, fostering energy saving, and improving cus-
and object space. This is done by examining how two distinct tomer satisfaction. The proposed model in [55] would increase
crossover procedures optimize their application to two distinct the time–frequency energy aggregation of non-stationary sig-
environments. In [45], the authors suggest a novel defect diag- nals as well as the immunity to cross-term interference. The goal
nostic approach for rolling elements of rolling bearings based is to obtain a time–frequency representation of the signal while
on variational mode decomposition (VMD) and MCKD. This also aggregating a significant amount of energy. The findings
method is called VMD-MCKD-FD. The goal of this method of the experiment demonstrate that the proposed model is able
is to improve the diagnosis accuracy and solve the problem to process non-stationary signals successfully, despite the fact
of a weak fault signal caused by the long transmission path of that the simulated signal and genuine fault signals have changing
the rolling element of the rolling bearing. The findings of the instantaneous frequencies (Table 1).
experiments indicate that the VMD-MCKD-FD approach is This paper analyzes the advantages of non-stationary data
capable of accurately diagnosing rolling element faults in rolling combined with the HHT method. Based on the on-line EMD
bearings and achieving higher levels of fault precision. The method, a feature extraction method of NC machine tool spin-
authors of the paper [46] build hybrid machine learning (ML) dle vibration signal based on HHT is proposed and applied to
classifiers for biomedical data using a meta-heuristic feature the developed NC machine tool spindle vibration monitoring
selection technique. The model is validated with data derived system to monitor the time–frequency characteristics of spindle
from biomedical studies of cardiac disease. In conjunction with vibration signal on-line.
the E-GWO feature selection technique, seven different types
of hybrid classifiers were applied, including NBBT, RFBT,
DTBT, KNNBT, NNBT, ABBT, and GBBT. The K-fold cross- 3 RESEARCH METHODS
validation technique was utilized in order to verify the accuracy
of the produced models. The innovative E-GWO feature selec- 3.1 Basic theory of HHT
tion algorithm chooses important features from among all of
the available ones. The purpose of [47] is to analyze data using In the traditional spectrum analysis, the global spectrum and
ML classification algorithms so that heart disease can be pre- energy distribution of the signal are generally obtained. This
dicted. It has been suggested that cloud-based IoMT diagnostics method is effective for processing stationary signals, but when
could be used for cardiac disease. A rapid analysis of patient processing non-stationary signals, the information that the
data using ML classification methods can be performed with the frequency of the signal changes with time will be lost, so it
help of the fog layer. The performance of the healthcare model needs time–frequency analysis to process it. The frequency of
is evaluated using a variety of simulations, which represents non-stationary ECG signal changes with time, which can be
a significant improvement in comparison to earlier models. regarded as a function of time. Therefore, in order to obtain the
The proposed algorithm [48] classifies healthcare data, selects frequency information of signal at a certain time, it is necessary
appropriate gateways for data transfer, and improves transmis- to define its instantaneous frequency. In the HHT method,
sion quality by considering throughput, end-to-end delay, and the Hilbert transform (HT) of the signal is generally used to
jitter. Proposed algorithms classify healthcare data and deliver obtain the instantaneous frequency information [25, 26]. For
high-risk data to end-user using best gateway. The goal of [49] is any time-series X (t), the definition of HT Y (t) is shown in
to apply a variety of ML approaches to the data that was created. formula (1):
For the purpose of early diagnosis of cardiac disease through
+∞
the Internet of Things, a ML framework has been developed. 1 X (𝜏)
Y (t ) = P d𝜏 (1)
The authors of [52] compared their suggested model to other 𝜋 ∫−∞ t − 𝜏
algorithms already in use for TSP in order to determine which
provided superior results in terms of solution quality, robust- where P is the Cauchy principal value. HT exists for all
ness, and space distribution. The model serves as a reference plant level functions. Different from Fourier transform, HT
for resolving the large-scale TSP in order to get more desirable is a transformation from time domain to time domain. As
path lengths. The problem of low reliability in the detection of can be seen from Equation (1), HT of a signal represents
features and tracking boxes in visual object tracking is addressed the convolution of X(T) and 1/t, emphasizing the locality
by [53]. The authors have provided evidence to demonstrate of X(t).
that their proposed model may be incorporated into any track- An analytical signal can be constructed from the original time
ing model by making use of a variety of attributes. The authors series X (t) and its HT Y (r), as shown in formula (2)
of [54] present a method for calculating the amount of time
needed for travel by road for a variety of time periods. Tak- Z (t ) = X (t ) + iY (t ) = a (t ) ei𝜃(t ) (2)
1108 YONGBO ET AL.
TABLE 1 Qualitative comparison with current state-of-the-art techniques
Related work Objective Model Advantages
Our paper To design and implement the mechanical Proposed model Efficiently monitor the time–frequency
manufacturing vibration monitoring characteristics of spindle vibration signal
system for ECG signal monitoring based on-line
on HHT feature extraction
[50] To develop local frequency to extract the Hybrid adaptive waveform Accurately distinguish the different fault
limitation of traditional frequency decomposition and normalized states of rolling bearings
Lempel-Ziv complexity method
[51] To facilitate an appropriate distribution Multidimensional form Could be used to generalize the existing
selection in a specific application approaches defined in either the Fourier
or the DCT domain
The amplitude function is shown in formula (3):
[ ]
2 2 1∕2a (t ) = X (t ) +Y (t ) (3)
The phase function is shown in formula (4):
( )
Y (t )
𝜃 (t ) = arctan (4)
X (t )
The instantaneous frequency can be defined as the deriva-
tive of the phase function of z(t), as shown in formulas (5)
and (6):
FIGURE 2 Structural block diagram of spindle vibration monitoring
d𝜃 (t ) system of mechanical NC machine tool
𝜔 (t ) = (5)
dt
1 d𝜃 (t ) 3.2 Overall design of spindle vibration
f (t ) = (6)
2𝜋 dt monitoring system of mechanical NC
biomedical machine tool
It can be seen from Equations (5) and (6) that the instan-
taneous frequency of the signal obtained by HT is a single Combined with the characteristics of spindle vibration signal
value function of time, so it can only reflect the frequency of mechanical NC machine tools, and based on the study of
value of one component of the signal. To use the instanta- a large number of rotating machinery condition monitoring
neous frequency to analyze the signal, it is required that the systems, this paper designs the spindle vibration monitoring
signal is a single component. Therefore, Cohen introduced the system of NC biomedical machine tools. The structural block
concept of ‘single component’ function to make the instan- diagram is shown in Figure 2. During the working process of
taneous frequency have physical meaning. However, there is NC machine tool, the spindle vibration acceleration signal is
still no clear definition of ‘single component’ function. Nar- transmitted to the upper computer through the data acquisi-
row band condition and symmetry condition are usually used tion module. The upper computer software system includes two
to judge ‘single component’ function. The preceding investi- modules: time domain waveform monitoring and characteris-
gation demonstrates that the HT cannot directly supply the tic data monitoring. The characteristic data monitoring module
entire frequency information of a complex signal. As a result, has the function of monitoring frequency domain character-
Huang established the concept of intrinsic mode function. The istic quantity and time–frequency characteristic quantity. The
intrinsic mode function he invented fulfils two conditions: the power spectral density of vibration signal is selected as the fre-
whole data set has the same number of extreme points and quency domain characteristic of vibration response of machine
zero crossings. The envelopes created by the local maximum tool spindle [28, 29]. The time–frequency distribution based on
and local minimum are locally symmetrical along the time axis, HHT is selected as the monitored time–frequency characteristic
which means that the upper and lower envelopes have the quantity, which describes the time and frequency domain infor-
same mean value. These two limitations ensure that the imme- mation of the vibration response of the machine tool spindle at
diate frequency of the natural mode function is meaningful the same time, and can effectively reflect the variation law of the
[27, 28]. characteristic frequency with time.
YONGBO ET AL. 1109
FIGURE 3 Hardware structure block diagram of spindle vibration monitoring system of NC machine tool
3.3 Hardware development of monitoring tool’s spindle vibration signal. The HHT method is a non-
system stationary signal analysis method based on empirical mode
decomposition (EMD), in which the frequency domain signal
The real-time and accuracy of the data collected by the system is decomposed into several IMF frequency components rang-
hardware and the speed of data transmission are the primary ing from high to low frequency, and then HT is applied to each
premise to realize the spindle vibration monitoring of NC IMF component to describe the time–frequency characteristics
biomedical machine tools. Based on the above requirements, of non-stationary signals. HHT incorporates both EMD and
this paper divides the hardware of CNC machine tool spin- HT. EMD decomposition of signal x(t).
dle monitoring system into sensor, signal conditioning module, The basic idea of the proposed algorithm is as follows:
data acquisition module, and data communication module.
The system hardware structure block diagram is shown in Step 1: All the maximum and minimum points of x(t) are
Figure 3. Among them, the sensor converts the spindle vibra- interpolated by cubic spline curve to obtain the upper
tion displacement and speed into electrical signals, the signal and lower envelopes of x(t).
conditioning module regulates the sensor electrical signals to Step 2: Calculate the mean m(t) of the upper and lower
meet the data acquisition requirements, the data acquisition envelopes.
module converts the electrical signals into A/D, and the data Step 3: Remove the mean m(T) in the signal and extract the
communication module uploads the real-time data to the upper detailed components of the signald (t ) = x(t ) − m(t ),
computer [30]. and use it to extract the first-order IMF.
Step 4: Remove the first-order IMF from x(t), repeat steps
1 to 4 as a new signal, and extract each order IMF suc-
3.4 Software design of monitoring system cessively. During extraction, d(t) screening operation in
step 3 is required [33]. When d(t) satisfies the IMF def-
The spindle vibration monitoring system of NC biomedical inition and iteration termination conditions at the same
machine tool generally adopts the classical signal process- time, the screening operation is terminated. After EMD
ing method based on stationary process, which is difficult to decomposition, x(t) can be expressed as the sum of
accurately describe the local characteristics with strong non- each order of IMF and trend term [34–36], as shown
stationarity caused by working condition changes or faults. in formula (7)
Therefore, the spindle vibration monitoring system of NC
biomedical machine tool needs to be able to monitor not only ∑k
the time domain waveform and frequency domain character- x (t ) = dk (t ) (7)
istic quantity of vibration signal, but also the time–frequency k=1
characteristic quantity that can reflect the local characteristics of
vibration signal [31, 32]. where K is the number of IMF components;
dk(t )(k = 1 ∼ (k − 1)) is the kth order IMF component
and is recorded as the kth order IMF [37, 38].
3.4.1 Time–frequency feature extraction HT is performed for each order of IMF, as shown in formula
method (8):
+∞
The HHT approach is used to extract time–frequency infor- 1 d (𝜏)D (t ) = PV k d𝜏 (8)
mation from the non-stationary properties of an NC machine k 𝜋 ∫−∞ t − 𝜏
1110 YONGBO ET AL.
where PV is Cauchy Principal component. Form dk(t ) and
Dk(t ) into the analytical form of the kth order IMF [39, 40],
as shown in formula (9):
[
Zk (t ) = ak (t ) exp i𝜃k (t )] (9)
Among them
√
a 2 2k (t ) = d (t ) + D (t )k k (10)
[ ]
D (t )
𝜃k (t )
k
= arctan (11)
dk (t )
where ak(t ) is signal amplitude; 𝜃k(t ) is the signal phase.
The instantaneous frequency of the signal is defined as the
derivative of D, as shown in formula (12): FIGURE 4 Time domain waveform of spindle vibration of NC machine
tool without copper bar contact
1 d𝜃
(t ) k
(t )
𝜔k = (12)2𝜋 dt
The original signal x(t) is expressed as shown in formula (13):
∑k−1 ( )
x (t ) = (reat ) ak (t ) exp i ∫ 𝜔k (t ) dt (13)
k=1
As a function of time t, the frequency components of non-
linear and non-stationary signals at each time can be accurately
described by the signal x(t), amplitude ak(t ), and instantaneous
frequency 𝜔k(t ) of Equation (13).
4 RESULT DISCUSSION
In order to verify the effectiveness of the spindle vibration
monitoring system of CNC biomedical machine tools, the spin- FIGURE 5 Time domain waveform of spindle vibration of NC machine
dle vibration of Takumi vertical machining centre is monitored tool when copper bar contacts
by the system [25]. In the test, the sampling frequency of the
system is 1280 Hz, and the time-domain waveform displayed by
the original data monitoring module is set to 0.2 s. Adjust the
spindle speed of the NC machine tool to 3840 r/min. after the
spindle runs stably for a period of time, contact the spindle with
a copper rod to make the speed fluctuate. The system monitors
the time domain waveform of spindle vibration signal when
there is no copper rod contact, as shown in Figure 4. The time
domain waveform of the spindle vibration signal monitored by
the system when the copper bar contacts is shown in Figure 5.
Comparing Figures 4 and 5, it is difficult to see the difference
between them from the time domain waveform. The power
spectral density reflects the average energy distribution charac-
teristics of the frequency components of the energy signal in a
certain time interval, and can be used as the frequency domain
characteristic analysis of the monitored signal. The stationary
characteristic quantity (power spectrum) monitored by the
system is shown in Figure 6. The frequency conversion (64 Hz)
characteristic quantity and frequency doubling (128 Hz) FIGURE 6 Frequency domain distribution of system monitoring
YONGBO ET AL. 1111
the machine tool speed fluctuates slightly, so that the frequency
doubling frequency is far away from the radial first-order nat-
ural frequency of the spindle system, and the subharmonic
resonance phenomenon disappears. In the time interval of 1.1
to 3 s, because the copper rod leaves the spindle, the spin-
dle rotation frequency is stabilized at 1/2 radial first-order
natural frequency again, and the subharmonic resonance phe-
nomenon reappears. In the same way, it can be explained that
the frequency composition of vibration signal when copper rod
touches the main shaft within 3 to 4 s interval. Therefore, the
time–frequency characteristic monitoring sub-module of CNC
machine tool spindle vibration monitoring system based on
HHT can not only describe the frequency domain information
of CNC machine tool spindle vibration signal, but also track the
change of frequency component with time, which can provide a
basis for analyzing the causes of no stationarity of CNCmachine
FIGURE 7 Time–frequency distribution of system monitoring tool spindle vibration signal.
characteristic quantity are obvious, and the high-order fre- 5 CONCLUSION
quency doubling characteristic quantity is small. However, the
occurrence time and duration of external excitation (copper rod HHT is a very suitable analysis method for analyzing non-linear
contact) of rotor system cannot be judged from the monitored and non-stationary signals. In this paper, the mechanical man-
stationary characteristic quantity. ufacturing vibration monitoring system for ECG signal moni-
The time–frequency distribution obtained by the HHT toring based on HHT feature extraction is designed and imple-
method can reflect the variation law of characteristic frequency mented. The combination of main control module and PC104
with time. The time–frequency distribution of vibration signal bus can ensure the real-time performance of data acquisition
HHT is shown in Figure 7. To describe the time–frequency and the accuracy of data transmission. The test results of spindle
properties of non-stationary signals, the frequency domain sig- vibration signal of mechanical NCmachine tool show that while
nal is first decomposed into several IMF frequency components, monitoring the time-domain waveform and spectrum distribu-
going from high frequency to low frequency, and then the HT is tion of signal, the system can use the instantaneous frequency
performed for each of those IMF frequency components. The description characteristics of HHT to realize the real-timemoni-
components with a frequency doubling feature can be found toring of time–frequency distribution of spindle vibration signal
in the time–frequency distribution. A frequency multiplier is a of NC machine tool. The goal is to develop and implement
non-linear circuit that, when it receives an input signal, distorts a system for monitoring ECG signals based on HHT feature
that signal and, as a result, generates harmonics that are related extraction, and this systemwill be utilized in mechanical produc-
to the original signal. After that, a bandpass filter picks the har- tion vibration monitoring. The system will be used in mechan-
monic frequency that is needed and eliminates the undesirable ical production vibration monitoring. As can be seen from the
fundamental as well as any other harmonics that are present in results of the experiments that were carried out, the suggested
the output. model has the capacity to monitor the time–frequency char-
It can be seen from Figure 7 that the frequency doubling acteristics of the spindle vibration signal in an efficient and
characteristic components in the time–frequency distribution effective manner while it is being transmitted online. The pro-
are obvious in the time interval without copper rod contact posed work is limited in that it cannot be applied to further
and disappear in the copper rod contact time interval (0.3–1.1 biomedical tools that include signal analysis and processes like
s, 3—4 s in the Figure). The disappearance and reappearance MRI machines. This is one of the limitations of the study.
time points of frequency doubling characteristic components
in time–frequency energy distribution are consistent with the AUTHOR CONTRIBUTIONS
occurrence and termination time points of external excitation. Zhu Yongbo: Conceptualization; Formal analysis; Investiga-
According to the subharmonic resonance theory, when the spin- tion; Methodology. Xu Lijun: Investigation; Methodology;
dle frequency is close to 1/2 of the radial first-order natural Validation; Writing – original draft. Issah Samori: Resources;
frequency of the spindle system, the double frequency com- Validation; Writing review – editing.
ponent of the frequency conversion will be excited. There are
obvious frequency conversion (64 Hz) and double frequency CONFLICT OF INTEREST
(128 Hz) components in the time interval of 0 to 0.3 s. It is The authors declare no conflict of Interest.
inferred that the machine tool spindle has subharmonic reso-
nance due to misalignment. In the time interval of 0.3 to 1.1 FUNDING INFORMATION
s, due to the friction between the copper bar and the spindle, None.
1112 YONGBO ET AL.
DATA AVAILABILITY STATEMENT 18. Zafarani, M., Hosseini, B.J., Akin, B.: Lateral and torsional vibration mon-
The data shall be available on request from the corresponding itoring of multistack rotor induction motors. IEEE Trans. Ind. Electron.
author. 68(4), 3494–3505 (2021)
19. Wszoek, G., et al.: Vibration monitoring of CNC machinery using mems
sensors. J. Vibroeng. 22(3), 735–750 (2020)
ORCID 20. Chen, J., Chen, L., Shabaz, M.: Image fusion algorithm at pixel level based
Issah Abubakari Samori https://orcid.org/0000-0001-9990- on edge detection. In: Singh, D. (ed.). J. Health. Eng. 2021, 1–10 (2021).
5552 https://doi.org/10.1155/2021/5760660
21. Casamenti, E., et al.: Vibration monitoring based on optical sensing of
mechanical nonlinearities in glass suspended waveguides. Opt. Express,
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