Geared Rotor System Research Articles

Dynamic Analysis of Geared Rotor System with Hybrid Uncertainties

Current research on the dynamics and vibrations of geared rotor systems primarily focuses on deterministic models. However, uncertainties inevitably exist in the gear system, which cause uncertainties in system parameters and subsequently influence the accurate evaluation of system dynamic behavior. In this study, a dynamic model of a geared rotor system with mixed parameters and model uncertainties is proposed. Initially, the dynamic model of the geared rotor-bearing system with deterministic parameters is established using a finite element method. Subsequently, a nonparametric method is introduced to model the hybrid uncertainties in the dynamic model. Deviation coefficients and dispersion parameters are used to reflect the levels of parameter and model uncertainty. For example, the study evaluates the effects of uncertain bearing and mesh stiffness on the vibration responses of a geared rotor system. The results demonstrate that the influence of uncertainty varies among different model types. Model uncertainties have a more significant than parametric uncertainties, whereas hybrid uncertainties increase the nonlinearities and complexities of the system’s dynamic responses. These findings provide valuable insights into understanding the dynamic behavior of geared system with hybrid uncertainties.

Torsional vibration suppression of a gear-rotor system using an inerter magnet nonlinear energy sink

The novel inerter magnet nonlinear energy sink (IMNES) utilizes chiral compression-torsion coupling effects to achieve mass augmentation, effectively mitigating torsional vibrations in a gear-rotor system with gear meshing clearance. The positive stiffness generated by the piecewise linear beam combines with the negative stiffness produced by the permanent magnet pair, resulting in the establishment of the IMNES’s nonlinear stiffness. Subsequently, a dynamic model of the IMNES-gear-rotor system is developed. Optimal parameters for the IMNES are determined through analysis of vibrational response surfaces under both transient and steady-state conditions. The numerical calculation of torsional vibration in the IMNES-gear rotor system is conducted across various gear meshing clearances. The results demonstrate that across different gear mesh clearances, the IMNES effectively attenuates torsional vibrations in the gear-rotor system. Under transient excitation, implementation of the IMNES leads to an 87% reduction rate in displacement within the gear-rotor system. In terms of steady-state excitation, simulations show a significant enhancement with a 65% increase in vibration suppression percentage.

Dynamic characteristics of gear-rotor system with gear eccentricity and wear fault

Dynamic characteristics of gear-rotor system with gear eccentricity and wear fault

Identification of the Asymmetric Transmission Error and Gear Mesh Dynamic Parameters using Full-Spectrum Responses in a Geared-Rotor System

A dominant source of vibration in geared-rotor systems are the gear mesh fault parameters. They include the asymmetric transmission error, phases of transmission error, the gear mesh stiffness, the gear mesh damping and the gear runouts. The present work deals with the experimental identification of aforementioned parameters. A mathematical model of geared-rotor system has been developed using Lagrangian dynamics. Equations of motion are transformed into frequency domain using the full-spectrum response analysis. These transformed equations are used to develop an identification algorithm based on least-squares fit to estimate the transmission error and gear mesh dynamic parameters. The system identification algorithm is initially verified using numerical simulations. The robustness of the algorithm is checked by introducing white Gaussian noise in the simulated responses. A geared-rotor experimental rig was developed and used to measure responses at gear locations in two orthogonal directions. Measured responses are transformed in frequency domain using the full-spectrum analysis and used in the present novel identification algorithm to identify the gear parameters. The identified parameters are validated by comparing the numerically generated full-spectrum response using experimentally estimated parameters and that from the experimental rig. Conflict of Interest Statement The authors declare no conflicts of interest.

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.

Research Progress on the Dynamic Characteristics of Planetary Gear Transmission in a Non-Inertial System

Planetary gear systems have many advantages over other gear systems. Previous studies on its dynamic characteristics mostly used Earth as the reference system, which is inconsistent with the actual working conditions of many planetary gear systems, such as aircraft maneuvering, vehicle movement changes, etc. By analyzing representative research papers, this study summarizes the lumped-parameter, finite element, and rigid–flexible coupling models commonly used in studying the traditional dynamic characteristics. Then, the research status of gear–rotor and planetary gear systems in inertial and non-inertial systems is summarized. The research progress of load characteristics, vibration characteristics, and vibration control of the traditional planetary gear system is summarized. Finally, some suggestions for future development are put forward. There are a few studies on the non-inertial dynamics of planetary gear systems. The three analysis models have distinct characteristics and applications but can all be used in non-inertial systems. The dynamic analysis method of non-inertial rotor systems can be combined with the dynamic study of gear systems. It is of practical significance to study the non-inertial dynamic characteristics of planetary gear systems. Scholars can refer to the non-inertial dynamic research of the gear–rotor system, select the analysis model according to the needs, and continue to study the dynamic characteristics of the planetary gear system under the non-inertial system.

Vibration attenuation characteristics of squeeze film dampers in spiral bevel gear systems

A central drive bevel gear system of aero-engines extracts power from a high-pressure rotor. The high speed of the high-pressure rotor aggravates the gear system's vibration. This work adopts squeeze film dampers (SFD) as damping devices to suppress excessive vibration of the spiral bevel gear rotor system. This paper establishes the general Reynolds equation of SFD and calculates the nonlinear oil-film force of SFD in real-time based on the finite element method. Besides, the finite element method and Timoshenko beam element are employed to model the flexible gear shaft. Then, the dynamic model of the spiral bevel gear system supported by SFDs is established, including the nonlinear oil-film force of SFD and time-varying meshing stiffness of the gear system. The dynamic response of the spiral bevel gear system is analyzed theoretically and experimentally to study the vibration attenuation characteristics of SFD. The findings indicate that SFD can effectively suppress the vibration amplitude of the system at high speeds. The theoretical analysis and experimental amplitude are within an order of magnitude, and the changing trend is consistent.

Dynamic modeling of GTF star gear-rotor coupling system considering structural flexibility

This paper establishes a dynamic model of Geared turbofan (GTF) star gear-rotor coupling system, in which the flexibility of shaft, disk, shell, diaphragm coupling, ring gear, and carrier are all taken into consideration. Additionally, an internal meshing model for flexible ring gear is developed, and the matrix reduction techniques is introduced to enhance the computational efficiency. Based on the dynamic model, the modal characteristics of the coupling system are extracted, and the influence of structural flexibility are investigated. Considering gyroscopic effect of the rotor, the Campbell diagram and the critical speeds are obtained. In addition, the vibration amplitudes under unbalanced excitation and time-varying mesh stiffness (TVMS) excitation are calculated and compared. The results of modal characteristics analysis indicate that many of the star gear train models are greatly affected by structural flexibility. Besides, the counter-rotating between the low-pressure rotor and the fan rotor results in frequency veering in the Campbell diagram, which is rarely observed in parallel gear-rotor system. The vibration responses indicate that unbalanced excitation of the rotor has relatively less effect on the gear vibration, while the low frequency excitation at star gear train is capable of exciting resonant vibration of the rotor.

The Coupled Thermal-Structural Resonance Reliability Sensitivity Analysis of Gear-Rotor System with Random Parameters

The resonance of the gear-rotor system will produce a large number of responses that do not exceed the threshold value, resulting in structural fatigue failure and transmission failure, affecting its life and reliability. It is particularly critical to consider the temperature rise under high-speed and heavy-load conditions. Therefore, the research will take the main drive gear-rotor system of a certain type of aeroengine accessory gearbox as the research object, consider the influence of the temperature field on the natural frequency of the gear-rotor system, and take the difference between the natural frequency of the gear-rotor system and the excitation frequency (gear meshing frequency) as the performance function. The PC-Kriging and adaptive design of experimental strategies are applied to the thermal-structural coupling parametric model to analyze the resonance reliability and sensitivity of the gear-rotor system. For complex mechanical mechanisms, the method has better accuracy than other surrogate models and greatly saves the time of finite element simulation in reliability analysis. The results show that the natural frequency of a gear rotor decreases with an increase in temperature, and the natural frequency of different orders varies with the change in temperature. The influence of the sensitivity of different random parameters on the resonance reliability of the gear-rotor system is obtained. Reliability research on resonance failure of high-speed and heavy-load aviation gear-rotor systems considering random parameters under a temperature rise field has important practical engineering application value and scientific research significance.

Escape through parametric instabilities in a non-ideal motor driven geared rotor shaft driveline

Periodically-varying gear mesh stiffness is a source of parametric excitation, which causes torsional instabilities in geared rotor systems. Unbounded amplitude growth at instability requires energy to be continuously pumped into the torsional modes from some ideal source of infinite power. However, real or non-ideal drives can only provide a limited amount of power; hence, the amplitude growth of torsional oscillations is bounded even at the unstable regions. In this paper, the coupled electro-mechanical dynamics of a geared rotor system driven by a non-ideal DC motor is investigated. It is shown that the system exhibits symptoms of Sommerfeld effect when driven through a torsionally unstable zone. As the system transitions through an unstable speed range, harmful torsional vibrations of the rotor-shafts consume a major part of the motor power, thereby reducing the power available to spin the rotor-shafts. Under some conditions, the spin speed gets captured at the instability zone, from where an escape occurs in the form of a speed jump on supplying a certain minimum threshold power. The design guidelines to suppress this harmful Sommerfeld effect are then proposed.

Effects of supporting stiffness of deep groove ball bearings with raceway misalignment on vibration behaviors of a gear-rotor system

The raceway misalignment of deep groove ball bearings is a typical engineering problem that dramatically influences the supporting stiffness and vibration behaviors of gear transmission systems. Considering the influences of meshing of the spur gear pair, the connection of the spline, and the flexibility of the shaft in the practical transmission system, a method for calculating the stiffness of bearings with raceway misalignment is proposed. The effects of misalignment angle, input torque and rotational speed on radial, axial and coupling stiffness are analyzed. Subsequently, the dynamic model of the gear-rotor-bearing system is established, and the influences of the time-varying and coupling characteristics of bearing stiffness on the vibration of the system are analyzed. The results show that the raceway misalignment enhances the radial and axial coupling characteristics of the bearing stiffness and aggravates the axial vibration of the system, which is mainly manifested in the increase of the amplitude of the axial meshing frequency. The vibration amplitude of the system is easily affected by high-order resonance in the case of raceway misalignment.

Modal sensitivity of three-dimensional planetary geared rotor systems to planet gear parameters

A parameter study is presented to determine effects of planet gear design parameters on the global modal behaviour of planetary geared rotor systems. The modal sensitivity analysis is conducted using a three-dimensional dynamic model of a planetary geared rotor system for the number of planet gears, planet mistuning, mass of planet gears, gear mesh stiffness and planet gear speed. These parameters have varying impacts on both natural frequencies and mode shapes, therefore the sensitivity of the planetary geared rotor vibration modes to the planet gear parameters is determined by computing the frequency shifts and comparing the mode shapes. The results show that the mass and mesh stiffness of planet gears have a larger influence on the global dynamic response. Torsional modes and coupled torsional-axial modes are more sensitive to gear mesh stiffness whereas lateral vibration modes are more sensitive to gearbox mass. Planet mistuning results in coupling between lateral and torsional vibrations. The planetary gearbox becomes more rigid in the torsional-axial modes and more flexible in the lateral modes with an increase in the number of planet gears. Planet gears are also found to be having significant gyroscopic effects inside the planetary gearbox. The main original findings in this study can be directly used as initial guidelines for planetary geared rotor design.

Comprehensive diagnosis and analysis of spur gears with pitting-crack coupling faults

As an important part of power transmission in mechanical system, the health status of gear needs to be judged accurately. However, most of researchers focus on single fault gear, and very few papers are reported on the performance of multiple faults. So the gear mathematical model with pitting-crack coupling faults is derived in this study, and it is validated by a three-dimensional finite element model. Furthermore, several types of fault combinations from health to severity are presented to investigate the effect of coupling fault evolution on gear time-varying meshing stiffness. The stiffness excitation is applied into an 8 degrees of freedom model to obtain the dynamic characteristics of the gear-rotor system in terms of displacement and acceleration, and a reasonable diagnosis of the gear status can be made by analyzing the dynamic characteristics in time domain and frequency domain. In the next step of research, the statistical indicators are applied to further reveal the degree of coupling faults, which provides effective reference on the diagnosis of coupling fault gears.

Experimental study on vibration control of spur geared rotor system with active magnetic bearings

The gearbox vibrations and noise caused by variation of contact forces often causes failure in the components of gearbox, which are then transmitted to the surrounding structures. The concept of active control of gearbox vibrations with piezoelectric actuators at the mounting points has been analysed earlier in several studies, then with certain limitations. There has been little research on how Active Magnetic Bearings (AMBs) might mitigate gear vibrations. AMBs are used in this study to investigate active internal shaft vibration control caused by rotor unbalance, gear runout, transmission error, which usually resides within the gearbox. Hence, minimizing the effect of vibrational amplitude at gear mesh frequency and its harmonics to have quieter gear operation. A mathematical model is developed for the torsional-lateral dynamic analysis of a spur geared rotor-AMB system. Responses are computed numerically with different gear-rotor faults. Based on the mathematical model, setted up an experimental test rig in the laboratory, and the effectiveness of the proposed model is compared with and without the application of AMBs. The approach is based on active control of the shaft transverse vibration with an electromagnetic actuator. The control forces are applied to the rotor shafts supported on conventional rolling element bearings by an eight-pole radial AMB, as an auxiliary component and a closed-loop linear output feedback control is employed for stable, reliable, and robust operation. A linear PID controller working on differential mode is used to generate the appropriate control signals and the experimental results are presented. It was found that there is a considerable amount of reduction in the geared rotor vibration levels and correspondingly in overall measured gear noise levels.

Application of active magnetic bearings in control and estimation of geared-rotor faults in high speed offset spur gear transmission system

This study is focused on the mathematical modelling, analysis, active transverse vibration control and fault analysis of a single-stage spur geared-rotor system. It uses Active Magnetic Bearings (AMBs) as an auxiliary bearing in addition to the conventional mechanical bearing in rotor fault detection considering the dynamic model with gyroscopic effects. The change in dynamic forces primarily due to the mesh deformation, gear runout, and variable transmission error are considered, which causes unwanted vibration and noise. To prevent the damage of gears and other supporting structures, these forced vibrations and control currents are meticulously investigated. From the dynamic responses of geared-rotor, the AMB control the stiffness and damping to minimize the transmission of forced vibrations to the mountings by closed-loop feedback control system. For an accurate modelling the dynamic transmission error is taken in two orthogonal transverse directions, which has asymmetric transmission error characteristics. Full spectrum is used for frequency domain analysis with tilting phenomena of the gears at high spin speed. An identification algorithm is developed for fault detection and estimation of system parameters from vibration and current of the proposed geared-rotor-AMB system. The robustness of the proposed algorithm is verified with different added percentage of noise and modeling errors.

Dynamic modeling of the gear-rotor systems with spatial propagation crack and complicated foundation structure

Considering both spatial crack fault and complex foundation structure, the dynamic finite element model and multi-body dynamic model are established simultaneously to analyze the dynamic characteristics of gear-rotor systems. Firstly, the extended finite element method is used to simulate the three-dimensional crack propagation paths of spur gears under partial load. Then, based on the proposed three-dimensional loaded tooth contact analysis (3D-LTCA) method, the mesh stiffness of spur gears with the spatial crack and complex foundation is calculated and the results are verified by the finite element method. Finally, the dynamic finite element model and multi-body dynamic model of the gear-rotor system are established. The dynamic responses under different crack levels are analyzed. The advantages and disadvantages of these two dynamic models are evaluated. According to the above analysis, it is indicated that the 3D-LTCA can accurately consider the influence of complex foundation and spatial crack on mesh stiffness. The finite element model and multi-body dynamic model can effectively analyze the influence of crack fault and foundation structure on dynamic responses.

Nonlinear analysis of herringbone gear rotor system based on the surface waviness excitation of journal bearing

Nonlinear analysis of herringbone gear rotor system based on the surface waviness excitation of journal bearing

Dynamic and gradual coupled reliability analysis of the transmission system of a shearer cutting arm

The strong impact and heavy load imposed on the transmission system of a shearer cutting arm is a potential cause of system variation and deterioration. And the overall equipment performance and output efficiency of a drum shearer cutting arm depends to a large degree on the reliability of the transmission system. Therefore, the current study proposes an innovative method for precise prediction of the reliability of the transmission system considering dynamic characteristic and performance degradation. Firstly, for the sake of quantifying the time-dependent reliability with deterioration parameters, a dynamic model of the geared rotor system is established based on the finite element method and the dynamic response is derived based on the main failure mode and the stochastic process model. Then the reliability and reliability sensitivity are estimated based on the probability perturbation theory and the fourth-order moment method. Finally, the proposed method is validated through a comparison to the canonical Monte Carlo Simulation method, which exhibits an average discrepancy of merely 3%. The present method serves as a theoretical guidance and applicable tool for both design and manufacture of coal shearers.

Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances.

Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.

Dynamic analysis for a spur geared rotor system with tooth tip chipping based on an improved time-varying mesh stiffness model

This study conducts a comprehensive analysis of a spur geared rotor system with tooth tip chipping from the viewpoints of dynamic modeling and fault detection. An improved tooth tip chipping model is proposed, and analytical equations of time-varying mesh stiffness (TVMS) for a chipped tooth is derived. A new term called “torsional stiffness” is introduced into the overall TVMS due to the chipping defect. On this basis, a finite element dynamic model of a spur geared rotor system is established. The mass unbalance caused by the chipping defect is emphasized in the dynamic model. The nonlinear frequency responses of the geared rotor system are obtained to study the system vibration behaviors. The influences of chipping defects on the TVMS, time histories and frequency spectrums of vibration signals are revealed. Several statistic indicators are applied to evaluate the fault conditions under different rotational speeds. Finally, a comparative study is carried out to show the effects of unbalance excitations caused by chipping defects on the system vibration responses. This study could provide a comprehensive methodology and some meaningful references for the modeling, dynamic analysis and fault diagnosis of gear transmission systems with local defects.