Planetary Gear System Research Articles

Evaluating the Time-Varying Mesh Stiffness of Planetary Gear Set With Gear Crack Considering the Friction Force Under Mixed Elastohydrodynamic Lubrication Condition

Abstract The mesh stiffness calculation of the planetary gear system with gear crack is investigated, and gear crack is modeled into end-face and addendum extended crack. Furthermore, the mesh stiffnesses are calculated under the effect of friction force obtained under the mixed elastohydrodynamic lubrication (EHL) condition. The nonuniformly distributed gear cracks on external and internal gear pairs are comprehensively modeled and analyzed, which is rarely investigated in previous studies. Moreover, the influence of crack propagation conditions on the meshing stiffness of the planetary gear system is analyzed. The obtained results show that the mesh stiffnesses experience abrupt variation in the pitch area during meshing, the extent of change is determined by the amplitude of the friction coefficient; in addition, gear crack position and extent could cause mesh stiffness reduction at varying levels at different stages of gear meshing.

Gearbox fault diagnosis based on a fusion model of virtual physical model and data-driven method

Planetary gear system is widely used in wind power, construction machinery and helicopters, because of its large transmission ratio, strong load-bearing capacity and small size. Because the gears are usually in high-speed operation, their key components are subject to severe wear and impact damage. When the gearbox is subjected to a failure, it is often difficult to judge the operating status of the gearbox in real time. Since the gearbox system is complex, moreover, it is still difficult for the simulation model to accurately identify the gearbox fault. To address this issue, this paper proposes a digital twin-based signal fusion model to accurately identify gearbox faults at the signal level. The proposed model can identify minor faults occurring in planetary gearboxes by fusing actual and virtual signals. Firstly, on the basis of virtual prototype and the multibody dynamics software, a digital physical model based on Hertz theory and extended finite element method is proposed for gearbox dynamic monitoring and digital simulation, in which the gearbox can be visualized. Secondly, the data-driven method is used to extract and select features from real and simulation signals, and the fault of the planetary gearbox is detected by feature matching. Finally, the real and simulation signals are fused effectively based on variational mode decomposition and phase correction of generalized cross-correlation coefficient. The fault diagnosis result of the gearbox is finally determined by using the envelope spectrum of the fused signal. The experimental results show that the virtual real fusion method effectively improves the performance of the traditional signal diagnosis methods, and the fusion of the actual and virtual signals strengthens the fault features of the fused signals effectively.

Improved Mesh Stiffness Method and Vibration Analysis of a Planetary Gear System with a Spatial Tooth Crack

Dynamic modeling and analysis are generally regarded as effective tools to investigate the vibration characteristics and fault mechanisms of planetary gear systems with a tooth crack fault. In actual gearboxes, the tooth crack is always a three-dimensional spatial surface, but it was usually simplified as a two-dimensional domain in most previous studies. In this paper, the tooth crack is modeled as a spatial shape that propagates along the crack depth, length and height directions simultaneously. Based on the potential energy principle, an improved analytical method is proposed to calculate the time-varying mesh stiffness (TVMS) of a planetary gear system with a spatial tooth crack. Furthermore, a coupled translational–torsional dynamic model is established for a planetary gear system including time-varying parameters and nonlinear factors. Numerical simulations are conducted to reveal the influences of the spatial crack propagation on the TVMS and vibration responses. In addition, an experimental study is carried out on a gear transmission test rig to verify the proposed analytical method and dynamic model. The mesh stiffness calculation method of the spatial cracked tooth and corresponding analysis results in this study might provide references to detect tooth crack faults in planetary gear systems.

Research on the effect of tooth root defects on the motor-multistage gear transmission system

In this paper, a coupled dynamic model is proposed for a motor and a multistage gears system of a coal mining machine with tooth root defects. The model effectively simulates the influence of the tooth root cracks on the vibration signals in a multistage gears system when the cracks occur in the planetary subsystem and fixed-shaft gear train subsystem. Comparing the Kurtosis and Crest factor indicators of planetary gear dynamic force and vibration velocity signals, the former is more sensitive to tooth root faults and more suitable as a dynamic indicator for evaluating the effect of tooth root defects on the planetary gear system. The electromechanical system is simulated by coupling the dynamic model of three-phase asynchronous motor and gear system, and the effect of gear tooth faults with different crack depths on the dynamic characteristics of motor-multistage gear system is explored. The results show that the motor current signature analysis (MCSA) can be applied to the detection of gear tooth faults in the transmission system. This method greatly reduces the workload of signal acquisition and spectrum analysis, and can be used as an effective supplement to the traditional vibration signal detection technology.

Calculation and influence analysis of tooth surface friction coefficient of planetary gear system in mixed lubrication condition

Based on the gearing theory, the calculation formulas of comprehensive curvature radius, relative sliding speed and tooth surface contact stress of internal and external meshing gear pair of the planetary gear system are deduced in this paper. Combined with load sharing theory and thermal elastohydrodynamic lubrication analysis method, the oil film thickness, film bearing ratio and friction coefficient are solved and the effects of roughness and input power on the friction coefficient are studied. The results show that with the increase of tooth surface roughness, the film bearing ratio decreases and friction coefficient increases; As the input power increases, the film temperature increases, the oil viscosity and film thickness decreases, which causes the tooth surface friction coefficient increases.

Similarity and experimental prediction on load sharing performance of planetary gear transmission system

The uneven load distribution among planetary gears will aggravate the vibration of the system, thus reducing the bearing capacity of the planetary gear transmission system (PGTS) and shortening the service life of the system. It is an effective method to predict and study the load sharing performance of the prototype through the scale model of PGTS. According to similarity theory, the similarity ratio of load sharing coefficient (LSC) of the dynamic model and LSC of the physical experiment model is derived. The LSC of PGTS is predicted and verified under different working conditions and structural flexibility. Based on the comprehensive tangential error similarity, the modified load method and the modified similarity ratio method are established to deal with position error distortion on planetary gear. Then, the dynamic model is used to verify the feasibility of the modification method. A scale model of PGTS is designed according to the similarity theory, and mechanical power closed test bench is established for the scale model. Finally, the load sharing performance of prototype PGTS is predicted through physical experiments under similar working conditions.

Influence of the eccentricity error on the vibrations of a planetary gear

Planetary gear systems are widely used in wind power, ships, aircraft, and construction machinery, etc. In the planetary gear system, when the eccentricity error exists in the planetary gear, the vibrations of the whole system should be affected. However, the influence of the eccentricity error was rarely considered in the previous dynamic models. To solve this problem, a planetary gear system with six planetary gears is established. The influence of the eccentricity error on the vibrations of the planetary gear system is analyzed. Different eccentricity error cases in the planetary gears are considered in the model, as well as the bearings with the radial clearance. The model with the eccentricity error is compared with the normal model. The statistics of dynamic responses of the ring gear and its variations are analyzed. Not that the vibrations of the planetary gear transmission system increase with the eccentricity error of planetary gear. This study can provide a new method for simulating and detecting the eccentricity errors in the planetary gear systems.

Increasing the wind power generation by modifying the windmill mechanism

The population-consuming resources are expanding by the day; the resources are mostly used in a limited fashion. As a result, a technique for connecting natural resources with growing populations is necessary. Wind turbine technology produces the highest power of any currently available renewable energy source, but it only converts energy into electricity in one direction of wind flow. Power creation is constrained since the current technique is intended to produce energy by receiving input from just one direction. This initiative aims to address this problem. This project's mechanism uses wind energy in both clockwise and counter-clockwise directions as input. Under perfect conditions, this system creates a lot more electricity than the existing traditional windmill system. This output is attained by changing the windmill's gearbox transmission system from a planetary gear system to a simple gear train system along with intermediate gear. As a consequence, if the wind blades allowed the two directional effects, then using this system the wind turbine blade's rotational position is reversed. Therefore, it can obtain an increase in power production by the recommended designed mechanism. These effects are analyzed by ANSYS Fluent software and the results are used to prove this increased output energy than the existing domestic windmills. In terms of electricity and energy conservation, this project shows a successful output.

Dynamic modeling and analysis of multistage planetary gear system considering tooth crack fault

Due to the influence of signal modulation and multi-stage coupling, the fault diagnosis of multi-stage planetary gear system is difficult. In this paper, a dynamic model of multi-stage planetary gear system containing sun gear crack is proposed from the perspective of nonlinear dynamics to study the failure mechanism and dynamic characteristics of tooth root crack. The mesh stiffness with root crack is calculated by using the modified energy method. By means of global bifurcation diagram, RMS curve, phase diagram, Poincare map, time series diagram and FFT spectrum, the dynamic responses of the system with and without fault are analyzed and compared. The results show that there are differences in the impact of crack failure on the dynamic characteristics at different rotational speeds. The crack disturbance will cause an abrupt change in the vibration amplitude of the system, which can excite the system into chaos from a quasi-periodic state. The system tends to be unstable due to crack failure, which is manifested by irregular expansion of the attractor, divergence of the phase trajectory, periodic pulses in the time series diagram, and sideband frequencies with the sun gear fault characteristic frequency as interval appearing around the meshing frequency. The chaotic motion range should be avoided during crack fault diagnosis.

A novel hierarchical hyper-parameter search algorithm based on greedy strategy for wind turbine fault diagnosis

With the rise of artificial intelligence, deep learning methods are more and more widely used in the field of intelligent fault diagnosis. However, the actual deep model used in fault diagnosis often exhibits over-fitting or under-fitting. In addition, the training process of these models requires configuration of a large number of hyper-parameters, and the selection of these hyper-parameters relies too much on experience. This makes the process of setting hyper-parameters quite tedious and time-consuming. Therefore, a new hyper-parameter search algorithm for network models is proposed, which is called Hierarchical Grid Scaling Hyper-Parameter Random Search (HGSHRS). The optimized model is verified with the fault simulation data of the wind turbines planetary gear system. First, different modal data are obtained by simulating different fault types and constructing the feature maps corresponding to them. Secondly, the CNN model is reused, and the existing pre-training model is used to accelerate the search for approximate optimal hyper-parameters and models. Finally, the proposed algorithm on the modal data of the planetary gear was verified and discuss the experimental results. Experiments prove that the deep learning model applying HGSHRS algorithm achieves relatively good results in fault diagnosis. The proposed method is of great significance for obtaining better hyper-parameters and models. Moreover, there are also considerable improvements in the reduction of operation and maintenance costs of wind turbine.

Effects of multi-excitation on vibration characteristics of planetary gear system

In this study, the effects of multi-excitation on the vibration responses of each planetary gear component is investigated based on the translational-rotational dynamic model of planetary gear system. The Fourier series are introduced to simulate the excitation sources, and the frequency–response function are applied to determine the effects of excitation sources on the vibration responses of each planetary gear component in the whole frequency. Therefore, the superposition problem of multi-component vibration responses is effectively solved under multi-excitation sources. Based on the analysis approach, the effects on the vibration response of the sun, carrier, ring, and planet gears are evaluated and compared in detail for planet-ring mesh, sun-planet mesh, floating sun gear, motor torque fluctuation, variable load, gearbox translational vibration, and gearbox rotational vibration. From these results, the mapping is revealed about relationship between excitation sources and the vibration response of each planetary gear component. Combined with the mapping relations, the main vibration component of planetary gear system can be predicted.

Design of Real-Time Cobot Planetary Gear System Interfacing with Stepper Motor

Design of Real-Time Cobot Planetary Gear System Interfacing with Stepper Motor

Deterioration state diagnosis and wear evolution evaluation of planetary gearbox using vibration and wear debris analysis

The deterioration state of planetary gearboxes with pitting faults cannot be diagnosed and evaluated effectively with a single type of monitoring signal and traditional features. In this study, a new diagnose method was proposed based on the tribology and vibration signal of planetary gear systems. A new feature extraction approach was exploited to construct a multi-feature fusion relevance vector machine (MFFRVM) model for diagnosing the deterioration state of planetary gearboxes. Meanwhile, a novel index for online wear debris monitoring (ADIDC) was extracted to evaluate the wear evolution of planetary gears. Condition monitoring experiments were conducted on a planetary gearbox. Experimental results show that the diagnostic method combining the MFFRVM model and ADIDC index achieves better accuracy than other methods. This study provides guidance for the wear evolution evaluation of planetary gears with pitting faults and the early fault recognition of planetary gearboxes.

Prognostics of Gear Manufacturing Errors for Planetary Gear Systems Based on Power Flow Theory

Abstract Gear manufacturing errors are key parameters in planetary gear trains and have effects on load sharing, tooth stress, and so on. Accurate estimation of manufacturing errors can help monitor the conditions of planetary gear systems. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analyzed in this paper. The estimated results are accurate when the collected data contain a lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.

Modulation sideband analysis of a two-stage planetary gear system with an elastic continuum ring gear

For a planetary gear system, the flexibility of its components can significantly affect mesh excitation, modal property, and dynamic behavior. However, current research has not revealed the influence of flexibility on the sidebands of vibration spectrum. For this purpose, in our earlier work, we addressed a new elastic-discrete planetary transmission model with an elastic continuum ring gear (originally presented in Wei Liu, Zhijun Shuai, Yibin Guo, Donghua Wang, Modal properties of a two-stage planetary gear system with sliding friction and elastic continuum ring gear. Mechanism and Machine Theory, 135 (2019) 251–270). The previous model study is solely based on free vibration without including sideband analysis. The present work aims to investigate modulation behavior of an elastic two-stage planetary gear (TSPG) system, thus expanding the previous work not only for modal property comparison but also for sideband analysis of the elastic planetary gear. First, gear mesh interface excitations with amplitude modulation (AM) and frequency modulation (FM) due to manufacturing errors are developed to analyze the sideband activity. Then, through loading gear mesh excitations with gear manufacturing errors on the previous model, acceleration spectra with and without sidebands are compared by an analysis with an example. To clearly show the modulation behavior, the effect of ring's elasticity and fluctuating torque on the sidebands is investigated. Finally, a TSPG test bench is proposed to measure the acceleration spectra. The measured spectra are compared to demonstrate the capability of the proposed model in predicting the sidebands of a planetary gear with manufacturing errors.

Study on mesh stiffness and sensitivity analysis of planetary gear system considering the deformation effect of carrier and bearing

The mesh stiffness characteristics and tooth root crack propagation of planetary gear system not only have an important impact on its transmission error, but further affect its vibration and noise level and the bearing capacity of gearbox. It is of great theoretical and engineering significance to study them comprehensively. First, the stiffness-damping model of the planetary gear mechanism is obtained by simplification, and the meshing phase relationships between the studied gear pairs are gotten by theoretical calculation. Then, through the FE modeling, the time-varying mesh stiffness of the sun-planet substructure, ring-planet substructure, and single-branch sun-planet-ring substructure are calculated respectively, and the influence of carrier and bearing flexibility on mesh stiffness is further studied. The mesh stiffness prediction method of the single-branch substructure is proposed and verified, and the overall mesh stiffness of the planetary gear system is predicted and analyzed. Finally, a sensitivity analysis model is established to study the effect of crack propagation at the root of sun and ring on mesh stiffness, capacity, and NVH features. The results show that the sun tooth root crack has a more significant impact on the mean stiffness and bearing capacity, and the ring tooth root crack has a more dramatic influence on the peak-to-peak stiffness and the vibration and noise characteristics of the gear system.

Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Nonlinear dynamics of a two-stage planetary gear system with sliding friction and elastic continuum ring gear

Nonlinear dynamics of a two-stage planetary gear system with sliding friction and elastic continuum ring gear

Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system

Bearing misalignment may be one of the causes of cage fracture fault. However, the research of bearing misalignment on vibration characteristics of the rotating machinery system has not been paid enough attention. In this paper, the effects of axial, radial and tilt misalignments of the rotor support bearing on the dynamic characteristics of the planetary gear set-rotor system are analyzed. Firstly, based on the Hertz contact theory, a nonlinear restoring force model of the ball bearing is proposed under axial, radial, and inner/outer ring tilt misalignments. Secondly, taking the planetary gear transmission system of a tracked vehicle as the research object. The dynamic model of the planetary gear set is established through the lumped parameter method. The rotor is established by the Timoshenko beam element. Finally, the dynamic model of the planetary gear set-ball bearing-rotor system is obtained by coupling these three parts. Based on the proposed model, the dynamic responses are analyzed considering bearing misalignment. The results showed that the three types of misalignments reduce the vibration amplitude due to the strengthened constraint of the bearing on the system, but increase the load-bearing area and contact load. Radial and tilt misalignments increase the varying compliance (VC) frequency amplitude of the bearing. On the contrary, axial misalignment reduces the VC frequency amplitude. The sensitive evaluation indexes of three misalignment states are given. The research results can provide a theoretical basis for fault diagnosis and identification of bearing misalignment in complex rotating machinery system.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.