Simulation and Analysis of Dual Unbalanced Rotor Efects on Natural Frequency in a Digital Twin Shaft Model Fadhel Abbas Abdulla 0 Ahmed Imad Abbood 0 Department of Mechanical Engineering, Mustansiriyah University , Baghdad , Iraq 32 37

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.

 eol>Rotors Natural frequency Deformation vibrations frequency Modal analysis 1. Introduction

den accidents. Numerous researchers have focused on investigating the impact of cracks on the eficiency 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 efectively 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 ] examous 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 Timoder 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 vartend 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 IInCfYoRrmIMaEtic2s,02M4a:th9tehmaIntitcesr,naantidonEanlgiCnoeenrfienrgen.CceatoafnYiae,aJrulylyR2e9p-oArutsguosnt stifness 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 ahm00e0d0.a-b00b0o2o-d7@84u0o-0m6u5s9ta(Fn.sAir.iyAabhd.eudllua.)i;q0(0A0.9I-.0A00b6b-o8o7d6)3-7160 a rotating Timoshenko beam, considering the coupling (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). 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 particence 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 lateral 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 ofers more comprehensive results compared to experimental studies, with the added benefits of speed and cost-efectiveness [ 30, 31, 32 ] also in term of missing data reconstruction or imputation [33, 34]. The FEA employed a finite element discretization approach to solve complex structural equations by dividing the structure into specific finite elements[ 31, 32, 35, 36 ]. The unbalanced rotors were designed using FEA, utilizing a mesh system composed of interconnected nodes. The model, created in SOLIDWORKS 2020, was exported to ANSYS 2019 software. The ANSYS model then meshed, and boundary conditions were applied. The software solved the system equations to determine the model’s natural frequencies.

3. Modelling and Analysis of Rotating shaft and Dual Rotors

The model developed aims to simulate rotating machinery with unbalanced rotating components. The model consists of two main components to simplify the system: the rotors and the shaft. The shaft has a length

The geometry of the rotor is afected by the unbalanced mass and the rotating velocity of 200 RPM in ANSYS Modal. The boundary conditions shown in Figure (2), the two ends of the shaft are fixed support and the position of bearings are BEARING boundary conditions in ANSYS Model. The geometry of the rotor and shaft are meshed with ELEMENT 186 to adept to diferent shapes.

ANSYS Modal analysis uses the following equations to solve vibration problems: 1. Mass Matrix Equation: [ ] + [] = 0 2. In this equation: [M] is the mass matrix, which represents the distribution of masses in the system. is the vector of mode shapes or modal displacements. [K] is the stifness matrix, which represents the stifness of the system.

3. Eigenvalue Equation: [] = [ ] 4. In this equation: represents the eigenvalues, which determine the natural frequencies of the system. [K] is the stifness matrix. is the vector of mode shapes.

By solving the above equations, ANSYS Modal analysis calculates the natural frequencies (eigenvalues) and corresponding mode shapes (modal displacements) of the system.

 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 lowering the likelihood of component malfunction [37]. The modal analysis ofers 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. Deformation (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 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; and 648.08Hz, 29.22mm respectively. (e) 5ℎ mode 648.08Hz

 5. Conclusions

The following conclusions can be derived from the findings of this study:

1. Using midspan at the highest value increase the value of natural frequency and reduces the efect of whirling.

2. The position of the rotors does afect much on the rotating shaft’s natural frequency because of the deformation in the rotating disk, which has the same dimensions.

3. The second mode is afected by the position of rotors which give high natural frequency at a high midspan value.

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

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