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Machines
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Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems
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Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Machine Design and Theory".

Deadline for manuscript submissions: closed (31 March 2026) | Viewed by 10006

Special Issue Editors

Prof. Dr. Lei Hou

E-Mail Website
Guest Editor
School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
Interests: nonlinear dynamics; vibration control; vibration reduction and isolation design
Special Issues, Collections and Topics in MDPI journals
Dr. Nasser A. Saeed

E-Mail Website
Guest Editor
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt
Interests: nonlinear dynamics; nonlinear vibration control; vibration energy harvesting; chaotic systems; perturbation methods; bifurcation theory; delayed differential equations
Special Issues, Collections and Topics in MDPI journals
Dr. Shun Zhong

E-Mail Website
Guest Editor
Department of Mechanics, Tianjin University, Tianjin 100072, China
Interests: nonlinear dynamics; rotor dynamics; deep learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Rotating machinery, such as turbines, compressors, and generators, is integral to industries like aerospace, energy, and manufacturing. These systems operate under demanding conditions, often exhibiting complex nonlinear characteristics, including resonances, multi-mode vibrations, bifurcation, and chaos. As the safety, reliability, and efficiency requirements increase in rotating systems, advancing theoretical understanding and developing innovative monitoring and fault diagnostic techniques are pivotal to optimizing working performance, minimizing downtime, and extending equipment life.

Recent developments in computational methods, sensor technologies, and machine learning have significantly expanded the possibilities for innovation in this field, including the application of multi-physics and multi-scale simulations to capture intricate nonlinear phenomena, the integration of real-time monitoring systems for predictive maintenance, and the utilization of artificial intelligence to predict faults with higher accuracy. The Special Issue aims to invite contributions that push the boundaries of these advancements, explore novel simulation or experimental methodologies, and provide transformative insights into the dynamics and diagnostics of rotating systems.

Topics of interest include, but are not limited to, the following:

  • Novel modeling, solving, and experimental methods for rotating systems;
  • Nonlinear phenomenon analysis of complex rotating systems with high dimensions or multiple nonlinearities;
  • Mechanism of nonlinear dynamics under multiple physical fields;
  • Rapid monitoring and evaluation of key components;
  • Advanced vibration monitoring methods and experimental verification;
  • Advanced fault diagnosis methods and experimental verification;
  • Nonlinear vibration control.

Dr. Lei Hou
Dr. Nasser A. Saeed
Dr. Shun Zhong
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • rotating systems
  • nonlinear dynamics
  • vibration monitoring
  • fault diagnostics
  • intelligent modeling
  • experimental investigation
  • multi-physics and multi-scale
  • artificial intelligence

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Published Papers (9 papers)

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Research

31 pages, 15528 KB  
Article
Rapid Noise Prediction of a Three-Stage Helical Gear Reducer Using a BOA-ISSA-BPNN Surrogate Model
by Zihan Geng, Xutang Zhang, Tianguo Jin, Hongqian Feng and Xinwang Li
Machines 2026, 14(4), 365; https://doi.org/10.3390/machines14040365 - 26 Mar 2026
Viewed by 398
Abstract
To reduce the time and computational cost of vibro-acoustic simulations in gear reducer noise evaluation, this study develops a simulation-driven surrogate modeling framework for a three-stage helical gear reducer. A high-fidelity “vibration–acoustic radiation” simulation chain is established, where the housing vibration responses computed [...] Read more.
To reduce the time and computational cost of vibro-acoustic simulations in gear reducer noise evaluation, this study develops a simulation-driven surrogate modeling framework for a three-stage helical gear reducer. A high-fidelity “vibration–acoustic radiation” simulation chain is established, where the housing vibration responses computed in Romax Designer are mapped into ACTRAN to obtain the radiated noise. Using Optimal Latin Hypercube Sampling, 300 designs are generated by varying the first-stage pinion micro-modification parameters (tooth drum, tooth slope, and tooth profile), and the average RMS sound pressure level over six field points is adopted as the noise metric. A BP neural network (BPNN) surrogate is then constructed, in which Bayesian Optimization (BOA) is used to tune hidden layer nodes and learning rate, and an improved Sparrow Search Algorithm (ISSA) is employed to optimize the initial weights and biases, forming the proposed BOA-ISSA-BPNN model. On the test set, the proposed model achieves R2 = 0.97499, RMSE = 0.91385, and MAE = 0.6547, with an average prediction time of 32.35s. Meanwhile, comparisons with SVM, BPNN, BOA-BPNN, SSA-BPNN, and ISSA-BPNN demonstrate superior prediction accuracy; moreover, relative to the hour-level computational cost of high-fidelity simulations, the proposed surrogate enables rapid noise evaluation on the order of tens of seconds, enabling fast micro-modification design iteration and practical engineering decision-making. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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25 pages, 5602 KB  
Article
Complex Nonlinear Modal Analysis and Resonance Frequency Prediction of a Full-Annular Rubbing Rotor
by Di Liu and Jie Hong
Machines 2026, 14(3), 295; https://doi.org/10.3390/machines14030295 - 5 Mar 2026
Viewed by 342
Abstract
Full-annular rubbing is a common rubbing form in rotor systems. It introduces an additional constraint on the rotor, which produces a significant increase in the resonance frequency. Although many studies have qualitatively discussed the influence of rubbing on rotor dynamics, the quantitative effect [...] Read more.
Full-annular rubbing is a common rubbing form in rotor systems. It introduces an additional constraint on the rotor, which produces a significant increase in the resonance frequency. Although many studies have qualitatively discussed the influence of rubbing on rotor dynamics, the quantitative effect of this constraint still needs to be analyzed with advanced methods and validated by rigorous experiments. The present paper aims to establish a method for predicting the resonance frequency of a rotor undergoing full-annular rubbing. The dynamic feature of a rubbing rotor system is analyzed by complex nonlinear modal analysis, and the numerical results are evaluated against measurements obtained from a rubbing rotor test rig. A modified Jeffcott rotor model is first formulated to clarify the relationship between the modal characteristics and the steady-state response. Experiments are then carried out to investigate the influence of rubbing on rotor dynamics. The results show that the constraint effect caused by rubbing can be quantitatively captured by nonlinear modal analysis. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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23 pages, 13322 KB  
Article
Identification of Turbocharger Noise Sources Taking into Account Design Operating Conditions
by Jozef Doman, Pavel Novotný and Vladimir Chmelko
Machines 2025, 13(10), 948; https://doi.org/10.3390/machines13100948 - 14 Oct 2025
Viewed by 861
Abstract
The paper describes in detail the creation of selected aerodynamic sound sources created by the centrifugal compressor of the turbocharger in operating modes. The description of the creation of aerodynamic sources focuses on the operation of the compressor in a stable area of [...] Read more.
The paper describes in detail the creation of selected aerodynamic sound sources created by the centrifugal compressor of the turbocharger in operating modes. The description of the creation of aerodynamic sources focuses on the operation of the compressor in a stable area of the characteristic. The analysis is based on a detailed survey of selected aerodynamic sources, mainly vortex shedding, TCN, and buzz-saw phenomena, with a focus on the mechanism of the source and the possibility of identifying the source in the frequency spectrum. Based on the survey, the selected sound sources characterize the assumed frequency ranges at which the sources are estimated to originate. Additional source conditions identified in the survey can be used to develop a methodology for identifying aerodynamic sound sources. In the case of aerodynamic sources of a centrifugal compressor, it was necessary to develop an experimental numerical methodology for their identification with regard to the operating condition of the compressor. The result of the proposed procedure is an algorithm that will enable the identification of aerodynamic sound sources in the frequency spectrum with respect to the operating state of the compressor. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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24 pages, 3501 KB  
Article
Piezoelectric Harvester Proportional–Derivative (PHPD) Control for Nonlinear Dynamics Reduction in Underactuated Hybrid Systems
by Fatma Taha El-Bahrawy, Rageh K. Hussein, Ashraf Taha EL-Sayed and Moamen Wafaie
Machines 2025, 13(9), 830; https://doi.org/10.3390/machines13090830 - 9 Sep 2025
Cited by 3 | Viewed by 739
Abstract
This study investigates the nonlinear dynamics and control of an underactuated hybrid system consisting of a Duffing oscillator, a pendulum, and a piezoelectric energy harvester. A novel Piezoelectric Harvester Proportional–Derivative (PHPD) control scheme is introduced, which integrates the harvester’s electrical output directly into [...] Read more.
This study investigates the nonlinear dynamics and control of an underactuated hybrid system consisting of a Duffing oscillator, a pendulum, and a piezoelectric energy harvester. A novel Piezoelectric Harvester Proportional–Derivative (PHPD) control scheme is introduced, which integrates the harvester’s electrical output directly into the feedback loop to achieve simultaneous vibration suppression and energy utilization. The nonlinear governing equations are derived and analyzed using the Multiple-Scale Perturbation Technique (MSPT) to obtain reduced-order dynamics. Bifurcation analysis is employed to identify stability boundaries and critical parameter transitions, while numerical simulations based on the fourth-order Runge–Kutta method validate the analytical predictions. Furthermore, frequency response curves (FRCs) and an ideal system are evaluated under multiple controller and system parameter configurations. Bifurcation classification is performed on the analyzed figure to detect various bifurcations within the system, along with the computation of the Largest Lyapunov Exponent (LLE). The results demonstrate that PHPD control significantly reduces vibration amplitude and accelerates convergence, offering a new pathway for energy-efficient, high-performance control in nonlinear electromechanical systems. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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20 pages, 5084 KB  
Article
Stability Enhancement and Bifurcation Mitigation in Nonlinear Inner Plate Oscillations Through PD Control
by Ashraf Taha EL-Sayed, Rageh K. Hussein, Yasser A. Amer and Marwa A. EL-Sayed
Machines 2025, 13(9), 828; https://doi.org/10.3390/machines13090828 - 8 Sep 2025
Viewed by 1050
Abstract
Axially moving wings offer remarkable aerodynamic efficiency and adaptability; however, they are highly susceptible to detrimental vibrations that may compromise flight stability and structural integrity. Previous studies have mainly focused on simplified linear models or passive control approaches, leaving the nonlinear dynamic behavior [...] Read more.
Axially moving wings offer remarkable aerodynamic efficiency and adaptability; however, they are highly susceptible to detrimental vibrations that may compromise flight stability and structural integrity. Previous studies have mainly focused on simplified linear models or passive control approaches, leaving the nonlinear dynamic behavior and active vibration suppression insufficiently addressed. To overcome these limitations, this study models the wing as a simplified cantilever plate and investigates its nonlinear dynamics under varying load conditions. A proportional–derivative (PD) controller is employed, and approximate analytical solutions to the governing equations are derived using the multiple-scale perturbation method (MSPM). The system’s response under primary resonance is analyzed through frequency response and bifurcation studies, while stability is assessed using the Routh–Hurwitz criterion. Analytical findings are validated with numerical simulations in MATLAB R2023b. Furthermore, the influence of key structural parameters on system dynamics and controller performance is examined. The results demonstrate that the PD controller effectively suppresses vibrations, offering a reliable solution for enhancing the stability of axially moving wing systems. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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28 pages, 14008 KB  
Article
A Novel Dynamic Characteristic for Detecting Breathing Cracks in Blades Based on Vibration Response Envelope Analysis
by Minghao Pan, Yongmin Yang, Fengjiao Guan, Haifeng Hu, Zifang Bian, Wenkang Huang, Bohao Xiao and Ang Li
Machines 2025, 13(5), 399; https://doi.org/10.3390/machines13050399 - 10 May 2025
Viewed by 1063
Abstract
Fatigue cracks in blades pose a significant threat to the safe operation of rotating machinery. Currently, the application of non-contact displacement sensors in blade vibration measurements has enabled the widespread analysis of nonlinear dynamic characteristics, such as natural frequency deviations and spectral anomalies, [...] Read more.
Fatigue cracks in blades pose a significant threat to the safe operation of rotating machinery. Currently, the application of non-contact displacement sensors in blade vibration measurements has enabled the widespread analysis of nonlinear dynamic characteristics, such as natural frequency deviations and spectral anomalies, to enhance crack fault diagnosis in rotating machinery. However, these two dynamic characteristics are not distinguishable for crack changes, especially for incipient cracks, leading to potential misdiagnosis. In this paper, a dynamic characteristic called the envelope diagram image of vibration responses (EDIVR) was extracted from blade tip displacement signals collected during acceleration–deceleration cycles for crack diagnosis. Initially, considering the breathing effect of fatigue cracks, a structural dynamics finite element model of a blade containing a breathing crack is established to calculate its dynamic response under aerodynamic force. Subsequently, the sensitivity of three characteristics (natural frequency, frequency spectrum, and EDIVR) to crack fault changes is quantitatively compared based on the simulated response signals. Experimental validation confirms the accuracy of the proposed dynamic model and the effectiveness of the proposed feature. The study shows that under identical operational conditions, blades with cracks of equivalent depth and location exhibit maximum sensitivity to crack detection when EDIVR dynamic characteristics are employed as the fault diagnostic criterion. Moreover, this characteristic is less susceptible to signal noise interference compared to other dynamic characteristics, enhancing its potential for crack diagnosis in engineering applications. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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23 pages, 12486 KB  
Article
Nonlinear Vibration Analysis of Turbocharger Rotor Supported on Rolling Bearing by Modified Incremental Harmonic Balance Method
by Tangwei Li, Hulun Guo, Zhenyu Cheng, Rixiu Men, Jun Li and Yushu Chen
Machines 2025, 13(5), 360; https://doi.org/10.3390/machines13050360 - 25 Apr 2025
Cited by 1 | Viewed by 1651
Abstract
High-speed rolling bearings exhibit low friction, high mechanical efficiency, low lubrication requirements, and excellent acceleration performance. The replacement of floating ring bearings in turbochargers with rolling bearings is an important tendency for modern turbochargers. However, due to the nonlinearity in rolling bearings, the [...] Read more.
High-speed rolling bearings exhibit low friction, high mechanical efficiency, low lubrication requirements, and excellent acceleration performance. The replacement of floating ring bearings in turbochargers with rolling bearings is an important tendency for modern turbochargers. However, due to the nonlinearity in rolling bearings, the nonlinear vibration characteristics of the turbocharger rotor system need to be clearly revealed. The turbocharger rotor is modeled by a lumped mass model. The nonlinear rolling bearing model is derived using the Hertz contact theory. The vibration responses of the nonlinear system are obtained by the modified incremental harmonic balance (MIHB) method. The results demonstrate that the MIHB method significantly improves computational efficiency compared to the traditional fourth-order Runge–Kutta method for solving this class of problems while also being capable of obtaining complete solution branches of the system. The stability of the responses is determined by the Floquet theory. Based on the present rotor dynamic model, the conical mode and cylindrical mode are found. Resonance peaks at 4.5 × 104 rpm (conical mode) and 1.1 × 105 rpm (bending mode) are identified as critical vibration thresholds. Moreover, the vibration amplitude results show that the resonance peak of the bending mode is mainly due to the nonlinearity of the rolling bearings, which also causes the amplitude jumping phenomenon. Changing the parameters of the rolling bearing could avoid the resonance peak appearing in the working speed range. The amplitude of the system under different rotating speeds could be suppressed by choosing the appropriate parameters of the rolling bearing. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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16 pages, 3060 KB  
Article
Influence of Excitation Disturbances on Oscillation of a Belt System with Collisions
by Marek Lampart and Jaroslav Zapoměl
Machines 2025, 13(5), 345; https://doi.org/10.3390/machines13050345 - 23 Apr 2025
Cited by 2 | Viewed by 647
Abstract
In addition to technological influences, real-world belt and conveyor systems must contend with loading effects characterized primarily by randomness. Evaluating the impact of these effects on system behavior involves the creation of a computational model. In this innovative approach, disturbances are expressed by [...] Read more.
In addition to technological influences, real-world belt and conveyor systems must contend with loading effects characterized primarily by randomness. Evaluating the impact of these effects on system behavior involves the creation of a computational model. In this innovative approach, disturbances are expressed by discretization and round-off errors arising throughout the solution of the controlling equations. Simulations conducted under this model demonstrate that these disturbances have the potential to generate hidden and co-existing attractors. Additionally, they have the potential to initiate shifts between oscillations of varying periods or transitions from regular to chaotic motions. This exploration sheds light on the intricate dynamics and behaviors exhibited by belt and conveyor systems in the face of various disturbances. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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22 pages, 7429 KB  
Article
Nonlinear Dynamic Modeling of a Gear-Bearing Transmission System Based on Dynamic Meshing Parameters
by Jinzhou Song, Lei Hou, Rui Ma, Zhonggang Li, Rongzhou Lin, Yi Chen, Yushu Chen and Nasser A. Saeed
Machines 2025, 13(3), 230; https://doi.org/10.3390/machines13030230 - 12 Mar 2025
Cited by 8 | Viewed by 2162
Abstract
The nonlinear contact force between gears and bearings exhibits intricate dynamics. This paper focuses on the coupling relationship between the time-varying meshing parameters of the gears, dynamic backlash, and dynamic bearing clearance in gear-bearing transmission systems. A dynamic model of a gear-bearing transmission [...] Read more.
The nonlinear contact force between gears and bearings exhibits intricate dynamics. This paper focuses on the coupling relationship between the time-varying meshing parameters of the gears, dynamic backlash, and dynamic bearing clearance in gear-bearing transmission systems. A dynamic model of a gear-bearing transmission system considering dynamic meshing parameters is established. The coupling mechanism between meshing stiffness, gear backlash, bearing clearance, and gear vibration response in gear transmission systems is analyzed. The results demonstrate a negative correlation between the gears’ geometric center distance and meshing stiffness amplitude. Gear vibration can affect the relative position of the gears. Changes in the relative position of the gears lead to an increase in the number of frequency components in the frequency domain of gear meshing stiffness. During gear rotation, the meshing parameters of the gears and tooth side clearance fluctuate with gear vibration. With increasing speed, the model’s dynamic meshing parameters also increase accordingly. The model achieves a feedback calculation of the system parameters and vibration responses in gear-bearing system dynamics. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Vibration Monitoring and Fault Diagnostics in Rotating Systems)
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