Rotor System Research Articles

Comparing the Performance of Robust Controllers for Vibration Suppression in Long Rotor Systems

In this paper, the vibration control of the multivariable model of rotor bearing systems is considered for investigation. Some simply structured controllers that can suppress vibrational disturbances are tested for their robustness via the H∞ optimality criteria. Initially, intelligent optimisation techniques are used to minimize the H∞ mixed-sensitivity norm of the Linear Fractional Transformation (LFT) of the simple two-term PI controllers acting on the rotor system models. This results in some controllers that can suppress the vibration but with a slow oscillatory response. After this, an appropriate interpretation of the Bode plot singular values of the combined sensitivity and control effort matrix is used to explain the performance shortcomings of this controller. Moreover, the existing simply structured controllers in the literature exhibiting a faster performance are examined by using singular value plots. It is shown that when the maximum singular value of the control effort matrix drops below the 0 db line, the performance will be boosted. Finally, the H∞ controllers are designed by using the robust control toolbox in MATLAB. This resulted in rapid disturbance rejection, with the vibration amplitude diminishing to zero after 0.3 s due to double-step disturbances. However, these controllers in the frequency domain have an order of eight and may not be realizable to be implemented in practice. It is concluded that examining the Bode plot of the maximum singular value of the control effort matrix is a useful tool for evaluating performance in the frequency domain. However, designing robust controllers by toolboxes in the time domain can lead to superb performance with higher-order controllers.

Nonlinear Modeling and Vibration Response Analysis of a Dual-Rotor System with an Inter-Shaft Graphite Seal

The inter-shaft graphite seal is a common structure in the dual-rotor system, and may generate nonlinear lateral excitation when there is large relative angular motion at the seal position. This paper represents the first attempt to study the nonlinear behaviors of a dual-rotor system with inter-shaft graphite seal excitations. First, an excitation model of the inter-shaft graphite seal is proposed by the analytical method. This model is then introduced into the beam finite element model of a dual rotor system, and the dynamic equations of the whole system are finally obtained. The vibration responses under the effect of the inter-shaft seal are clarified by analyzing 3D waterfall plots, rotor orbits, and time and frequency domain waveforms. The results show that the inter-shaft seal can lead to vibration coupling between HP and LP rotors. The axial spring stiffness and contact end face friction coefficient of the graphite seal have a significant effect on rotor vibration. When those two parameters are small, only coupling vibration phenomena can be observed, i.e., the rotation frequency of one rotor can be observed in another rotor vibration. With the increase in axial spring stiffness or contact end face friction coefficient, multiple modes of LP and HP rotors are excited, which dominates the vibration behaviors of the dual rotor system.

Modeling of flexible bevel gear rotor systems: Modal and dynamic characterization

Bevel gears, a crucial part of aircraft transmission systems, are more susceptible to wheel body vibration issues as lightweight requirements rise. In the past, the gear wheel body was often considered rigid while assessing the dynamic properties of gear systems. Constructing a bevel gear model with a thin-walled structure might not be appropriate for this modeling technique; this research suggests a dynamic model that considers the flexibility of bevel gears. The web and teeth structure of the gear are preserved by realistic modeling using three-dimensional hexahedral components. The component mode synthesis (CMS) approach reduces the model order for increased computational efficiency. To confirm the accuracy of the modeling method, the modal frequencies and vibration shapes of the proposed model single-gear shaft are compared with results from experiments and ABAQUS. By contrasting ABAQUS system-level meshing modal frequencies and vibration shapes, the accuracy of the system model assembly is further confirmed. The model examines the impact of bevel gear flexibility on the modal frequencies, modal vibration shapes, and system dynamic properties. The mode shape diagram at dangerous modal frequencies found using the modal strain energy technique and the vibration displacement cloud maps at resonance speeds computed using the Newmark-β method are mutually verified, and this demonstrates that lightweight bevel gears are more susceptible to excitation due to nodal diameter type vibrations. Proposed and traditional models anticipate substantially different resonance speeds since the traditional model assumes that the gear, being a rigid disk, can only excite the shaft's bending mode of vibration. The proposed model provides a more comprehensive description of the dynamic characteristics of bevel gear systems, providing a theoretical basis and optimization tool for the high-performance design, vibration reduction, and noise control of high-speed lightweight gear transmission systems.

Dynamic analysis of slant cracked rotor system considering nonlinear oil film force.

In this paper, considering the combined effects of nonlinear oil film forces and cracks on the rotor-bearing system, the differential equations of motion with 4 degrees of freedom are established by Lagrangian method. Then, the Lundgren-Kutta method is used to solve them and the results of the model are compared with the experimental data. The study demonstrate that the cracked rotor-bearing system is relatively stable at subcritical speeds, mostly in the period-1 motion. But near 1/3 of the critical speed, there is an inner loop in its whirl orbit and a significant increase in the 2x frequency component. When the system speed rises to the region near 1/2 of the critical speed, though the bifurcation motion and a relatively high 2x frequency can be observed, there are no other reliable fault characteristics. The study proves that the rotor crack fault diagnosis method based on the whirl orbits is convincing for slant cracked rotors.

Nonlinear dynamics of full-ceramic bearing-rotor system considering structural defects in cage pockets

Full ceramic bearings provide exceptional characteristics, including elevated accuracy and substantial load-bearing capability, rendering them indispensable in high-end rotating machinery. Still, the long-term use of the bearing will lead to the gradual wear and defects of the cage pocket, which may affect the unstable operation of the rotor system. This study examines the vibration characteristics of cage failure through simulation and experiments. To study the dynamic characteristics of the bearing-rotor system, a dimensionless model is established by using the lumped mass method, and a cage failure model is added to the model, which can study the influence of cage failure on the system stability. Phase trajectories, Poincaré plots, and bifurcation diagrams are employed to analyze the impact of individual parameters on the nonlinear vibration of the system. Ultimately, to gather cage vibration data from two different types of faulty, the experimental approaches are used. The findings indicate that in the event of cage failure, the system’s amplitude amplifies and the time-domain vibration signal exhibits distinct periodicity. Then, the vibration energy gradually focuses on low-frequency vibrations. Additionally, the spectrograms allow for easier identification of frequency components associated with the cage frequency, such as nfc and mfs ± nfc, the largest error is 3.32% when comparing the two models’ simulated results with the experimental data. The model accurately depicts the frequency characteristics of failures resulting from wear and defects in full ceramic bearing cages. It offers crucial information for detecting failures and monitoring the health of full ceramic bearings.

Model verification and vibration analysis of the four-disk hollow flexible shaft rotor system

Rotor unbalances failure due to various factors such as manufacturing defects, mounting errors, and material inhomogeneity is inevitable, and will be aggravated by bearing pulse displacement excitation caused by maneuvering flight. Therefore, the purpose of this paper is to study the vibration of the rotor system under disk unbalance forces and bearing pulse displacement excitation. Firstly, the differential equation of motion for four-disk flexible hollow shaft rotor system modeling with a simple finite element model(SFEM) is established by the Lagrangian method in non-inertial systems, and the shaft is modeled using Timoshenko beam theory. Then, the dynamic characteristics of the four-disk flexible hollow shaft rotor are analyzed and compared with the 3D finite element model(3D FEM) to verify the accuracy of the model. To analyze the effects of different disk unbalanced positions and pulse displacement excitation on the vibration characteristics of the rotor, the characteristic vector method and the Runge–Kutta method are used to obtain the steady-state solution and the transient solution, respectively. In addition, the simulation results show that suitable in-shaft damping has a stable effect on the rotor during the start-up. Disk2 and Disk3 are more sensitive to synchronous harmonic excitation and pulse displacement excitation than Disk1 and Disk4. The research of this paper provides an important basis for vibration monitoring and control, and vibration transmission analysis of aero-engine rotor system.

Penerapan Lean Manufacturing Menggunakan Value Stream Mapping pada VCT Rotor di PT. XYZ

XYZ is an automotive component manufacturing company with two lines of production: the Shock Absorber Line and the VCT Line. One of the products on the VCT Line is the VCT rotor, with issues surrounding waste. Utilizing Lean Manufacturing approaches using the Waste Assessment Model and the Value Stream Analysis Tools is an effective way to solve issues and enhance efficiency in the VCT rotor system and production process at PT. XYZ. Total time savings as a result of the process change is 9,108.25 seconds, and the total lead time reduction in inventory is 34 days. The highest type of waste found in the VCT rotor is inventory, which accounts for 23,29% of the total waste. Overproduction contributes to 23,23% of the waste, while defect is responsible for 19,04%.

Transient investigations of teeth on rotor and teeth on stator modified labyrinth seals

Teeth-on-rotor (TOR) and teeth-on-stator (TOS) layouts are compared in this paper to explore better arrangement for different labyrinth seals. The diaphragm labyrinth seal (DLS) and hole diaphragm labyrinth seal (HDLS) are both redesigned into TOR and TOS layouts. To accurately predict the rotordynamics and leakage performance of different seals, a one-motion transient computational fluid dynamics (CFD) method based on the simplified multi-frequency transient method is proposed. A comparison of the experimental results, two-motion transient CFD method and proposed method showcase the better accuracy of the current method in rotordynamic performance prediction. The results shows the better rotordynamic characteristics of the TOS layout for different layouts and of the HDLS type seals for three labyrinth type seals. Even though, the TOR layout cannot increase the stability of the rotor system, a clear circumferential velocity reduction in the DLS and HDLS seals can be observed in both the TOS and TOR layouts. However, the changes in leakage performance for DLS and HDLS seals are different from those for traditional LSs. Unlike TOR-LS and TOR-HDLS, which exhibit relatively large increases in leakage compared with the TOS layout, TOR-DLS achieves a maximum 1.7% leakage reduction at a 15000 rpm rotation speed. A decrease in the jet flow length and increase in the turbulence kinetic energy in TOR-DLS compared with those in TOS-DLS further explain this abnormal phenomenon.

Study on the Mechanism and Suppression of Harmonic Vibration of AMB-Rotor System

The AMB-rotor system is complex and has strong coupling characteristics, which allows multi-harmonic disturbances to enter the system through different ways to produce vibrations with rich spectrum components, which has a great influence on the improvement of micro-vibration accuracy of the rotor system. To further achieve active control of the micro-vibration in the AMB-rotor system, firstly, the mechanism of multi-source disturbance is analyzed according to the working principle of the AMB-rotor system, and the mathematical and physical relationship between the mechanism of disturbance generation and the inducement is deeply studied. Then, the structure of a novel adaptive notch filter, the method of adaptive frequency estimation and analysis of harmonic current suppression in the AMB system are presented. Finally, simulation and experimental research using an MSCMG system demonstrate the feasibility of the proposed method regarding the elimination of harmonic control current.

Rub-impact dynamic analysis of a dual-rotor system with bolted joint structure: Theoretical and experimental investigations

Large gas turbines often utilize dual-rotor structures to improve efficiency. To facilitate manufacture and maintenance, the large rotor systems are typically constructed by connecting components made from different materials together through the bolted joint. In this work, a dynamic model of a dual-rotor system with bolted joint included in the high-pressure (HP) rotor is established based upon the finite element theory of Timoshenko beam element, as well as taking into account the bearing forces and fixed-point rubbing fault. To evaluate the influence of rubbing faults on the dynamic behavior of a dual-rotor system, this study analyzed the response characteristics of the rotor under the cases of the LP rotor and the HP rotor subjected to the rubbing fault, respectively. In order to further reveal the effect of bolted joint structure on the system response while rubbing fault occurs, piecewise linear bending stiffness is also considered in this study. The nonlinear vibration responses of the bolted joint dual rotor-bearing system are studied through numerical simulation. Effect of rotor–stator contact stiffness and the occurrence of rubbing faults at the low-pressure (LP) rotor and the HP rotor are investigated through frequency-amplitude curves, waterfall diagrams, time-domain responses, and bending stiffness of the bolted joint. The results indicate that the presence of rubbing faults, whether occurring at the LP rotor or the HP rotor, leads to a decrease in the critical speed. Furthermore, under a rubbing fault, the bending stiffness of the bolted joint enters the stiffness softening region earlier and exhibits a wider range, which is exacerbated with increased contact stiffness. This phenomenon is considered one of the main causes of system response instability. Finally, the experimental studies are carried out on a bolted joint dual-rotor test rig to validate the numerical simulation results.

Development of Rotor Balancing Algorithm for a High-Precision Rotor System considering Dynamic Reliability through Automatic-Adaptive DBSCAN

Recently, the demand for high-precision balancing of rotors has increased in the automobile industry, as more rotors are designed to rotate at ever-higher speeds to maximize energy efficiency. The accumulation of measurement uncertainty in the balancing process decreases the accuracy of the unbalanced mass estimation, which is the ultimate goal of balancing. Here, the problem of uncertainty is shown through a Monte Carlo simulation of signals acquired from an actual production line. To reduce the effect of measurement uncertainty in the balancing procedures, a signal-processing technique that increases the dynamic reliability of the signal is proposed. The suggested method is based on density-based spatial clustering of applications with noise (DBSCAN) with the use of the orthogonality-based averaging method. Specifically, by adjusting radius values while clustering samples through the use of the DBSCAN method, the outliers that arise due to uncertainty are successfully removed. In this work, our proposed automatic-adaptive DBSCAN (AA-DBSCAN) method is validated by applying it to a balancing machine used for blower rotors in fuel cell electric vehicles. The results show that the deviation of the extracted influence coefficients is up to 0.0050, whereas the proposed method reduced it to less than 0.0037. In addition, the suggested procedure reduced the deviations of the unbalanced mass phase estimation by 35.2% as compared to the results found by the conventional method. Consequently, through the validation test, the suggested method was found to have the largest vibration decrease of any method considered in the study.

Dynamic Response Analysis of a Magnetically Suspended Dual-Rotor System Considering the Uncertainty of Interference-Fit Value

Interference fit is often used in rotating machinery to transmit torque and force. The actual interference value is uncertain due to factors such as manufacturing errors and operating conditions, resulting in a gap between the response of the system and theoretical results. Therefore, the interval method is used to study the magnetically suspended dual-rotor system (MSDS) with uncertainty of interference-fit value. Firstly, a theoretical model of the MSDS was established using the finite element method, and the influence mechanism of the interference value on the rotor bending stiffness was derived. Then, the rotor stiffness range was obtained from the uncertain range of interference value. Finally, the dynamic response of the MSDS was studied based on the Chebyshev interval method. The research results indicate that the uncertainty of interference value has an effect on the vibration response of the MSDS. The vibration response of the system is most affected near the first-order bending critical speed, and the effect on rotor response is relatively small in other angular speed regions. The research results can provide a basis for the design of rotor systems.

A parametric study of a bolted joint rotor-bearing system with an unbalanced offset disk

The turbine disk is the core component of an aero-engine whose position and unbalanced force seriously affect the vibration stability of the rotor system. Ignoring the influence of the offset disk may result in discrepancies between real-world scenarios and numerical simulation results. The present work aims to explore the nonlinear dynamic characteristics of rotor systems under the coupling of bolted joint and offset disk effect, as well as the influence of offset disk position and its unbalanced force on the system dynamic behavior and bending stiffness of bolted joint also investigated. The governing equations of a bolted joint rotor-bearing system with an offset disk were established based on the finite element method and derived as a dimensionless expression in the first. Then, the Newmark method was employed for the numerical solution of the motion equations, and then a bifurcation analysis of the rotor system and the evolution of bending stiffness for the bolted joint was studied. Next, by comparing the frequency-amplitude diagrams, bifurcation diagrams, time history, shaft obits, and bending stiffness diagrams of the bolted joint, the effect of the offset disk position and its unbalanced force on the nonlinear system dynamic was revealed. Finally, an experimental study was carried out to verify the numerical result using the bolted joint rotor test rig with an offset disk. The analysis result of the present work can provide theoretical guidance for structure design and stability analysis on the aero-engine.

The Inertial Disturbances of Fluid Movement in the Chamber of a Liquid Autobalancer

This article analyses the problem of automatic balancing rotors with a liquid balancer, which is a cylindrical chamber partially filled liquid of a certain density. This problem is related to the problem of the dynamics of bodies with cavities partially filled with liquid. As part of this task, we analyzed disturbances in the relative motion of the fluid in the ABD chamber caused by the Coriolis force inertia. The distortions of the free surface of the liquid were found, resonant phenomena in the flow of the working fluid were investigated, and the physical explanation of the received results given should be taken into account when designing the corresponding ones self-balancing devices. It was established that the axial component of the Coriolis inertial force causes peculiar wave phenomena in the correcting fluid movement. For the given nature of undisturbed motion, the conditions of this phenomenon’s occurrence are determined only by the geometric dimensions of the cylindrical chamber and the thickness of the liquid layer in undisturbed motion, and do not depend on the intensity of rotation of the liquid, nor on its density. It is shown that a decrease in the “ABD chamber height–radius” ratio leads to stabilization of the movement of the system. Experimental verification has been performed; theoretical results on the developed stand for work research rotor system with a vertical axis of rotation.

Physics-informed Neural Network for system identification of rotors

The condition of the rotor system remains difficult to assess due to system nonlinearity and nosiy measurements. To deal with the problem, we proposed a hierarchical physics-informed neural network (HPINN) to discover the ordinary differential equation (ODE) of a healthy/faulty rotor system from noise measurements and then assess the machine condition based on the discovered ODE. Specifically, the ODE of a healthy rotor system is first stably identified from noise measurement through HPINN guided by rotor dynamics. Based on the identified healthy ODE, the extra fault terms in the ODE of the faulty rotor system are then sparsely regressed from the predefined library embedded in HPINN. Moreover, with the mathematical terms of discovered fault, the potential fault and the health indicator (HI) are diagnosed and constructed to assess the condition of the rotor system, respectively. Finally, the effectiveness of the proposed method is verified by the data set collected on the circulating water test bench, showing the potential for practical applications.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

Coupling dynamics of pedestal looseness and impact-rub for rotor system with nonlinear support

It is easy for the rotor system to produce the plastic deformation at the support after a long-term operation, this change will cause looseness of the bolt. Due to the particularity of the material and the structure for the bearing base and foundation, the elastic force of the support is nonlinear. Larger vibration of the loosening rotor under the nonlinear support will occur, resulting in the impact-rub between the rotor and stator. In order to study the dynamic behaviors of the loosening-rubbing coupling rotor system under the nonlinear support, the model is established to analyze the influencing mechanism of the key parameters such as the eccentricity, the disk offset, the looseness gap, the rubbing gap, and the nonlinear parameters on the vibrational responses of the system. The piecewise cubic nonlinear expression is applied to describe the nonlinear support with the loosing bolt; Coulomb friction is employed to characterize the rubbing of the impact-rub. The research results show that the nonlinear support will stimulate and amplify the nonlinear dynamic behaviors of the rotor system; there exists a threshold for the effect of the loosening gap on the vibrational characteristics of the system; increasing nonlinear parameters to a certain degree will cause the increase of the proportion of quasi-period and chaos. The research focus and conclusions are certain innovative in this paper. The work is of great value for fault diagnosis and structural design.

Unbalanced Feature Identification of Rotor System Based on Fused Cross‐Correlation Fast Fourier Transform

Rotor system unbalance is one of the most important factors that affects the operating accuracy and stability in aerospace engineering. The extraction and identification of unbalanced features is the premise for the dynamic balance of rotor system. In order to accurately identify the unbalanced vibration feature, based on the fused cross‐correlation fast Fourier transform (FC‐CFFT) method, an unbalanced feature extraction method of the rotor system is proposed. The convolution window weighs the data of the vibration sequence and carries out delay processing. Through spectrum calculation, the phase information of the vibration signal is obtained. And the amplitude information of the vibration feature can be acquired through cross‐correlation calculation. The unbalanced features of the rotor system vibration signals are identified under different working conditions through simulation and experiment. The results show that this method is more accurate than FFT, the cross‐power method, and the sine‐approximation method in extracting different unbalanced vibration features of the rotor system. The extraction accuracy of unbalanced feature phase and amplitude reaches 98.61% and 97.27%, respectively. After the unbalanced feature is extracted, the dynamic balance experiment can be carried out. The unbalanced feature is used for dynamic balance compensation. In this way, the average amplitude decreased by 76.35%. The high accuracy of the FC‐CFFT method for extracting the unbalanced feature has been verified. This research provides a theoretical foundation for the vibration signal processing and dynamic balance control of the rotor system.

Accounting for the Temperature Dependence of Hardness in Numerical Simulation of Wear in Pivot-Jewel Bearings

Pivot-jewel bearings are important components in rotor systems and flywheel energy storage systems; the relative rotation speed can reach about 10³ rps under nominal operating conditions, while the lifespan can amount to years. Wear calculations of the contact surfaces are necessary in such scenarios to assess the life cycle of friction joints. Accounting for the variation in the surface hardness due to friction heating can considerably affect the amount of wear in the contact surface.

Progress in Rotorcraft Design: 1974–2024

Fundamental advancements in aircraft design over the past 50 years have enabled a range of vertical takeoff and landing (VTOL) air vehicle configurations and have significantly enhanced aircraft performance, safety, and reliability. This summary paper chronicles the evolution of rotorcraft design from 1974 to 2024. It is segregated into three key pillars of aircraft design preceded by an aircraft design overview. The three pillars are processes and tools, technology, and air vehicle configuration. The first pillar, on design processes and tools, describes advancements in technology, methodologies, and computational capabilities such as the transition from design solely by wind tunnel testing, physical models, and hand calculations to computer-aided design/synthesis and simulation in a model-based engineering digital-twin environment. The second pillar, on technology, focuses on advances in disciplinary technologies and how they have been incorporated into aircraft design. Technologies discussed include composite materials; rotor systems; propulsion systems, ranging from advancements in turbine engines to all- and more-electric propulsion technologies utilizing various energy storage systems to convertible engines; fly-by-wire systems; avionics and cockpit architectures, including digital displays, navigation aids, and communication equipment; and autonomous and semiautonomous systems. The third pillar, on air vehicle configuration, focuses on platform architectures. Major architectures discussed are high-speed VTOLs such as the thrust-vectored aircraft, tiltrotors, lift/thrust compounded helicopters, and all- and more-electric aircraft.