=Paper=
{{Paper
|id=Vol-3869/p04
|storemode=property
|title=Simulation and Analysis of Dual Unbalanced Rotor Effects
on Natural Frequency in a Digital Twin Shaft Model
|pdfUrl=https://ceur-ws.org/Vol-3869/p04.pdf
|volume=Vol-3869
|authors=Fadhel Abbas Abdulla,Ahmed Imad Abbood
|dblpUrl=https://dblp.org/rec/conf/icyrime/AbdullaA24
}}
==Simulation and Analysis of Dual Unbalanced Rotor Effects
on Natural Frequency in a Digital Twin Shaft Model==
https://ceur-ws.org/Vol-3869/p04.pdf
Simulation and Analysis of Dual Unbalanced Rotor Effects
on Natural Frequency in a Digital Twin Shaft Model
Fadhel Abbas Abdulla1,* , Ahmed Imad Abbood1
1
Department of Mechanical Engineering, Mustansiriyah University, Baghdad, Iraq
Abstract
Blades are one of the basic components of a gas turbine and its main function is to rotate the shaft associated with the
generator motor. Gas turbine model MS9001E used power plants at south Baghdad station, the blades are subjected to harsh
working conditions such as high vibration, temperatures and pressures, thus highlighting the importance of studying the
materials used in Manufacture of blades that work under harsh operating conditions. In this research, stress, strain and
deformation produced by the centrifugal force that the blade is subjected to be studied, as well as studying the natural
frequencies of the blades. Three-dimensional was created through the program solidwork 2018 and then exported to the
program ansys 2019 for analyzing. Two alloys of materials (GTD-111) and (IN-738) were analyzed and compared between
them, and the results showed that alloy (GTD-11) is the best and is suitable for use in the manufacture of blades.
Keywords
Rotors, Natural frequency, Deformation, vibrations frequency, Modal analysis
1. Introduction den accidents. Numerous researchers have focused on
investigating the impact of cracks on the efficiency of
The dynamic rotor plays a crucial role in the behavior rotating shafts. Some have conducted analytical analyses
of rotary machines, ranging from large-scale systems to study these issues, while others have approached them
like power plant rotors and turbo-generators to smaller approximately. One key factor in minimizing undesired
systems such as tooth drills, pumps, and air compressors vibrations is effectively controlling the rotor’s geometric
[1, 2, 3]. Understanding the history of rotor dynamics is imbalance [20, 21, 22]. By employing calculations and
essential as it highlights the fundamental challenges in understanding the mass of unbalance during rotation,
developing and implementing rolling bearings for vari- it is possible to measure the vibration response of any
ous applications [4, 5, 6, 7, 8] when stability and quality system. Multiple researchers have conducted studies on
must be assured [9]. The study of dynamic behavior the impact of externally applied axial force and torque on
in rotating machinery began in the early years of the the lateral vibration of shafts. Alaa et al. [23] derived the
19th century when the industrial revolution increased equation of motion for a flexible rotating shaft subjected
the demand for analyzing rotational motion also in the to a constant compressive axial load by incorporating
robotic industry [10, 11, 12, 13]. Since the fifties, numer- gyroscopic moments consistently. In the study [24] exam-
ous researchers have conducted studies on crack prop- ined the stability of a rotating cantilever shaft carrying
agation in shafts, and some of these findings have been a rigid disk at its free end, considering follower axial
extended to real-world rotors, providing valuable insights force and torque loads. Chen and Sheu [25] analytically
for designers [14, 15, 16]. Typically, rotors operate un- investigated the stability behavior of a rotating Timo-
der cyclic pressure, making them susceptible to various shenko shaft with an intermediate attached disk under
operational issues, such as fatigue cracks. These cracks longitudinal force, providing frequency equations for var-
tend to occur when the rotors’ natural frequencies and ious boundary conditions and numerically determining
critical speeds increase as the shaft length decreases and critical axial and follower forces. Chen et al. [26] The
the cross-sectional area increases [17]. It is crucial to influence of inertial forces on shafts and beams can result
identify the vibration characteristics of cracked shafts in axial stresses. Researchers have also examined the
to develop a control system that can detect operational rotation of beams around an axis perpendicular to their
errors and early-stage cracks [18, 19] and prevent sud- beam axis, where centrifugal force directly induces axial
stress in the beam. In this study [27] utilized the dynamic
ICYRIME 2024: 9th International Conference of Yearly Reports on
Informatics, Mathematics, and Engineering. Catania, July 29-August stiffness matrix for an Euler-Bernoulli beam subjected to
1, 2024 axial force to analyze the vibration of rotating uniform
*
Corresponding author. and tapered beams. In the investigation reported [28, 29]
$ fadhel975@uomustansiriyah.edu.iq (F. A. Abdulla); derived the governing equation for the linear vibration of
ahmed.abbood@uomustansiriyah.edu.iq (A. I. Abbood)
a rotating Timoshenko beam, considering the coupling
0000-0002-7840-0659 (F. A. Abdulla); 0009-0006-8763-7160
(A. I. Abbood) between extensional and flexural deformation by lineariz-
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License ing the fully geometrically nonlinear beam theory. They
Attribution 4.0 International (CC BY 4.0).
32
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Fadhel Abbas Abdulla et al. CEUR Workshop Proceedings 32–37
proposed a power series solution method to determine of 1200mm, while the rotors have diameters of 230mm,
the natural frequency of the rotating Timoshenko beam. as shown in Figure (1a). The bearings are positioned at
This study introduces a new phenomenon that can influ- three locations, with the midspan position being partic-
ence the performance of rotating shafts. The change in ularly interesting for identifying the optimal position.
natural frequency is attributed to the position of rotors The system’s geometry was created using SolidWorks
and the midspan between double rotors. Unlike previous 2020 and then exported to ANSYS 2019 software. The
studies, the disks located equal spaces between fixtures rotor system geometry was discretized in the initial stage
and rotors. To accomplish this objective, the lateral de- using tetrahedral elements. The model comprises 160,022
formation and natural frequency need to be calculated, nodes and 40,196 elements, as depicted in Figure (1b).
then evaluating the impact of this distance on the lat-
eral natural frequency of the shaft. The paper presents a
numerical solution to evaluate the systems.
2. Materials and Method
A modal analysis was conducted on a structural steel
shaft, and commercially available rotors were used. The
material properties of the structural steel are provided
in Table 1. Finite element analysis (FEA) was chosen
as it offers more comprehensive results compared to ex-
perimental studies, with the added benefits of speed and
cost-effectiveness [30, 31, 32] also in term of missing data
reconstruction or imputation [33, 34]. The FEA employed (a)
a finite element discretization approach to solve complex
structural equations by dividing the structure into spe-
cific finite elements[31, 32, 35, 36]. The unbalanced rotors
were designed using FEA, utilizing a mesh system com-
posed of interconnected nodes. The model, created in
SOLIDWORKS 2020, was exported to ANSYS 2019 soft-
ware. The ANSYS model then meshed, and boundary
conditions were applied. The software solved the system
equations to determine the model’s natural frequencies.
Table 1
Material Properties of Rotating shaft and Rotors
PROPERTIES VALUE
Specific Heat (J/Kg K) 485
Young’s Modulus (GPa) 210
Density (kg/m3) 7850
Poison’s ratio 0.30
Thermal conductivity (W/mk) 60
Thermal expansion (oC) 14 × 10−6
Yield strength (Mpa) 450 (b)
Shear Modulus (GPa) 80
Figure 1: a. The geometry of rotor system in SOLIDWORKS,
b. Meshed model using ANSYS
3. Modelling and Analysis of The geometry of the rotor is affected by the unbalanced
mass and the rotating velocity of 200 RPM in ANSYS
Rotating shaft and Dual Rotors Modal. The boundary conditions shown in Figure (2), the
The model developed aims to simulate rotating machin- two ends of the shaft are fixed support and the position
ery with unbalanced rotating components. The model of bearings are BEARING boundary conditions in ANSYS
consists of two main components to simplify the sys- Model. The geometry of the rotor and shaft are meshed
tem: the rotors and the shaft. The shaft has a length with ELEMENT 186 to adept to different shapes.
ANSYS Modal analysis uses the following equations
33
Fadhel Abbas Abdulla et al. CEUR Workshop Proceedings 32–37
(a) 1𝑠𝑡 mode 162.43Hz
Figure 2: Boundary conditions in ANSYS.
to solve vibration problems:
1. Mass Matrix Equation: [𝑀 ]𝜓 + [𝐾]𝜓 = 0
2. In this equation: [M] is the mass matrix, which
represents the distribution of masses in the system. 𝜓 is
the vector of mode shapes or modal displacements. [K] (b) 2𝑛𝑑 mode 418.48Hz
is the stiffness matrix, which represents the stiffness of
the system.
3. Eigenvalue Equation: [𝐾]𝜓 = 𝜆[𝑀 ]𝜓
4. In this equation: 𝜆 represents the eigenvalues, which
determine the natural frequencies of the system. [K] is
the stiffness matrix. 𝜓 is the vector of mode shapes.
By solving the above equations, ANSYS Modal analy-
sis calculates the natural frequencies (eigenvalues) and
corresponding mode shapes (modal displacements) of the
system.
(c) 3𝑟𝑑 mode 569.65Hz
4. Results and Discussion
The outcomes derived from ANSYS 2019R3 depend on
various elements such as the system’s shape, length of the
shaft, elastic characteristics, rotor spacing, and boundary
conditions. These factors impact the inherent frequency
of the system. A higher inherent frequency signifies an
improved design by reducing vibration amplitude and (d) 4𝑡ℎ mode 601.04Hz
lowering the likelihood of component malfunction [37].
The modal analysis offers a valuable understanding of
these outcomes, aiding in assessing and enhancing the
system’s performance. Figure (3) shows the mode shapes
for the first five modes for the 916mm midspan. Defor-
mation (11.69 mm) at a frequency (162.43Hz) 1st mode,
and deformation (12.22 mm) at a frequency (418.48Hz)
2nd mode. The following three modes show an increase (e) 5𝑡ℎ mode 648.08Hz
in frequency, and deformation will reach the peak at 4th
mode for the 3rd ,4th, and 5th modes; the frequency and
deformation are 569.65Hz, 35.22mm; 601.04Hz, 35.74mm; Figure 3: The first five mode shapes of rotor midspan 916mm
which are extracted by ANSYS19, are labeled (a) to (e) respec-
and 648.08Hz, 29.22mm respectively.
tively
34
Fadhel Abbas Abdulla et al. CEUR Workshop Proceedings 32–37
(a)
(b)
Figure 4: Shape modes and the Natural frequency in (Hz).
Figure (4a) shows the change in natural frequency of 5. Conclusions
the unbalanced rotating shaft with the mode shape num-
ber. It is noticed that the 1st and 5th modes are having The following conclusions can be derived from the find-
same value, the change in natural frequency occur in ings of this study:
the other three modes. Figure (4b) gives a lock at the 1. Using midspan at the highest value increase the
three modes 2nd,3rd, and 4th, for midspan 916mm gives value of natural frequency and reduces the effect of
highest frequency in the second mode while lowest fre- whirling.
quency for the midspan 756mm for the same mode. The 2. The position of the rotors does affect much on the
third mode midspan 796mm and 756mm approximately rotating shaft’s natural frequency because of the deforma-
have the same frequency about 570 Hz and the 796mm tion in the rotating disk, which has the same dimensions.
midspan has same value with 756mm midspan. 836mm 3. The second mode is affected by the position of rotors
midspan has a value between them. 4th mode midspan which give high natural frequency at a high midspan
756mm has the lowest frequency 591 Hz and the mid value.
span 836mm has the highest value 607Hz. 4. As well as the distance between two rotating discs
is higher, the system balance increases too.
In future works, new optimization methods based on
35
Fadhel Abbas Abdulla et al. CEUR Workshop Proceedings 32–37
neural approaches will be explored [38, 39]. impaired people with a following robotic assistant
by means of end-to-end visual target navigation
and reinforcement learning approaches, in: CEUR
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