Gear Meshing Force Research Articles

Automotive powertrain electrification: system methodology to guarantee acoustic comfort

For the past few years, electrification has disrupted the automotive industry. Surprisingly, Noise Vibration and Harshness (NVH) became a major issue as it is located in high frequencies (1 to 5 kHz). The noise has 2 origins: the electromagnetic forces in the electric motor and the gear mesh forces in the reducer. The first part focuses on the methodology developed in collaboration with car-makers in order to integrate the powertrain in a satisfying way in the vehicle. First, this process is focused on the structure-borne noise. Attention is paid on rubber mounts and on their fixation points. Second, the airborne transfer may become an issue. Despite the acoustic power requirement provided, the final vehicle performance is not guaranteed. Examples will illustrate these important topics. The second part pays attention to the prediction of reducer noise. Automotive stakeholders are approaching the gear mesh source by approximate linear tools. Recent works have shown that this methodology has limitations and leads to inaccurate results. This may be a major concern. A few examples will illustrate this risk and show that further simulation developments are necessary.

Modelling of electromechanical coupling dynamics for high-speed EHT system used in HEV and characteristics analysis

As the development of hybrid electric vehicle (HEV) to high-speed, heavy-load, the electromechanical coupling vibration becomes the bottleneck in high-speed electromechanical hybrid transmission (EHT) system. To explore the dynamics characteristics and optimization direction for high-speed EHT system, an electromechanical coupling dynamics model under multi-source excitations is established with lumped-distributed parameter method and verified with experiment data. The dynamics model shows higher accuracy in both time and frequency domain analysis. On this basis, firstly, the comparison between lumped-shaft and distributed-shaft model is studied under time and frequency domain. Comparing with the lumped-shaft model, the distributed-shaft model shows higher accuracy, and can better reflect the coupling vibration of multi-stage planetary gears (PGs). Secondly, the inherent vibration model is derived, and the effect of electromechanical coupling and high-speed working conditions on inherent vibration characteristics are studied. Thirdly, a new method called ‘machine-electricity-magnet coupling interface’ is proposed to reveal the coupling vibration phenomenon. In addition, the signal of stator current and electromagnetic torque includes the frequency of PGs, which is a basis on the fault diagnosis and state monitor of EHT system. Last but not the least, the vibration acceleration of EHT system is analysed under variable speed and load working conditions. Rotation speed and gear meshing force is found as the main influencing factor of series EHT system, and the specific optimization direction is also given.

A novel method for ring-planet gear mesh force identification via SVD-based Kalman filter

Dynamic mesh forces are the primary vibration excitations of the planetary gear transmission systems. However, they are difficult to measure directly, and conventional indirect measurement methods are typically only applicable to specific planetary gear sets with special measuring equipment. This study proposes a more widely applicable method for identifying the mesh forces of ring-planet gear pairs by utilizing vibration signals. To this end, a ring gear dynamic model is established based on the elastic theory of the thick ring in the form of a space state system. The state vector of the model is constructed from parameters of ring gear vibration responses, while the input state vector is derived from parameters of dynamic mesh forces. A singular value decomposition (SVD)-based Kalman filter is employed to provide a stable solution for the estimation of state vector and input vector simultaneously. A mesh force indirect measurement method based on tooth fillet strain signals collected by strain gauges is adopted to evaluate the accuracy of identification results. Results of dynamic experiments conducted in a planetary gear set test rig demonstrate that compared with measured results, the proposed method can obtain acceptable estimated mesh forces of ring-planet gear pairs by using vibration signals.

The Non-Linear Excitation Load-Sharing Method of a High-Powered Nuclear Planetary Gear Train

The paper primarily employs the 3D calculation method of the helical gear-meshing line and meshing position, in addition to the traditional method of the gear-meshing stiffness calculation. This analysis and correction of load-sharing are beneficial for improving the assembly process of high-powered critical equipment. The dynamic models of rigid–flexible coupling, velocity–torque, and the meshing force of planetary gear trains in nuclear power plants are established based on the principles of gear dynamic characteristics. Based on an analysis of the vibration characteristics of a planetary gear train, a load-sharing method for the planetary gear train is proposed. This uniform load-sharing method is explored under different modification values to provide a reference for load-sharing research on high-powered key equipment. In this paper, a dynamic simulation analysis of the gearbox system is conducted, using virtual prototype software to study the load-sharing performance of the planetary gear system. Furthermore, via a vibration frequency analysis of the gear mesh force, the causes of planetary gear train vibration are discussed, particularly their impact on planetary load. This provides a basis for the assembly process of a nuclear power circulation pump gearbox, ensuring that the gearbox for the circulation pump has a longer life that meets the 40-year service life requirement, and provides a foundation for the study of planetary load characteristics.

Dynamic modelling of gear–spline system with nonuniform spline clearance and wear evolution of spline

The gear–spline system consisting of the internal spline of gears and the external spline of shafts is widely used in mechanical transmission systems. However, considering the nonuniform spline clearance caused by the assembly and manufacturing errors, the vibration characteristics of the system and the spline wear mechanism are still unclear. This article proposed a dynamic model of the gear–spline system with nonuniform spline clearance and wear evolution of spline. Compared with the existing models, the new contribution of this article is to reveal the coupling vibration mechanism of the gear–spline system under the condition of nonuniform spline clearance through the dynamic model. On this basis, the support stiffness characteristics and wear evolution law of the spline pair under the dynamic gear meshing force are studied. The results show that under the condition of nonuniform clearance, the displacement response of the system is modulated by the rotation frequency, and the motion trajectory tends to be chaotic. The load distribution of spline teeth and the equivalent stiffness of the spline depends on the number of loaded spline teeth, which in turn depends on the input torque and clearance distribution. In addition, the spline teeth with smaller clearance bear more loads and wear faster, and the wear causes the nonuniform clearance to gradually increase and become uniform. This study can provide theoretical guidance for revealing the vibration mechanism of the gear–spline system and calculating the support stiffness of the spline shaft.

Analysis of the Dynamic Characteristics of a Gear-Rotor-Bearing System with External Excitation

The dynamic response of the rotor system in a ring die granulator is complex and difficult to solve when it operates under joint external, support and gear mesh forces. To solve this problem, a finite element method and extrusion theory was applied in this study to develop a dynamic coupling model for a hollow overhung rotor with external load excitation. A Newmark-β numerical integration method was used to solve for the dynamic response of the overhung rotor under multiple excitation forces. The results included time-domain response diagrams, frequency-domain response diagrams, phase diagrams, Poincaré section diagrams, and bifurcation diagrams. The model and the method were verified by testing a ring die granulator. On this basis, the dynamic response of the system is predicted according to the influence of different parameters. As the bearing support distance increased, the roller eccentricity decreased, the bearing clearance decreased, the response of the rotor system was significantly optimized, and the system tended to stabilize gradually. Therefore, this paper provides a theoretical basis and experimental verification for the optimization of a pelleting machine transmission structure.

Extraction and use of frequency-domain relationships between time-varying gear meshing properties and diagnostic measurements

In gears, the key diagnostic information is carried in the gearmesh stiffness and geometric profile errors. These two key gear meshing properties combine nonlinearly with rotations and displacements of the gear shafts to produce a time-varying gearmesh force. This in turn passes through the system dynamic response before finally resulting in actual diagnostic measurements (e.g., vibration or transmission error). The closed form analysis of such transfer paths is rendered impractical by the complexity of the time-varying gearmesh force, and has therefore so far mostly been studied through time-domain simulations. Inspired by a previous linearisation method, this paper develops a matrix-based procedure on a multiple-degree-of-freedom (MDOF) system to linearise the relationship between time-varying gear meshing properties (stiffness and geometric error) and measurements, thus producing frequency response functions (FRFs) between these key diagnostic inputs and the measurements. This FRFs are then used specifically to study the scarcely employed but highly promising diagnostic measurement of transmission error (TE), which is obtained by combining encoder measurements from the two gear shafts. The analysis of TE includes both an application of its experimental measurement for crack diagnostics under different operating conditions, and a discussion of the properties of the TE-FRF that make TE more robust to different operating conditions.

Active torsional vibration suppression of integrated electric drive system based on optimal harmonic current instruction analytic calculation method

Torque fluctuation caused by flux harmonics in a permanent magnet synchronous motor (PMSM) leads to torsional vibrations in vehicle-integrated electric drive systems. To resolve this fluctuation, the coupling relationship between the torque fluctuation and harmonic current of the PMSM was analyzed by establishing an analytical model of the instantaneous torque of the PMSM. The analysis was performed considering the harmonic and saturation characteristics of the flux chain. An analytical calculation method for the reference harmonic-current instruction was proposed to suppress torque fluctuation. The proportional integral resonant (PIR) controller was designed to accurately control the actual current to follow the reference harmonic-current command. Thus, an active torsional vibration suppression method was developed. Simulation and experimental results showed that the proposed method can effectively reduce the amplitude of the 6th and 12th harmonic torque of the PMSM. The amplitude of each axis torque and gear-meshing force, corresponding to the harmonic frequency of the transmission system, is considerably reduced. The transmission stability is also significantly improved.

Simulation studies around the steering system of the azimuthing propulsor

In this study, the steering load, the steering control and the gear failure of the steering system of the azimuthing propulsor are simulated and investigated respectively. In this research, CFD simulation was used to obtain the steering load moment for a azimuthing propulsor with different advance coefficients in the azimuthing range of 0∘ to 180∘. Then the simulation results were compared to the open water experiment results to analyze the reasons for the similarities and differences. Finally, the reason for the fluctuations and the fluctuations frequency calculation method were discussed. A co-simulation model of the gear transmission system and the hydraulic control system was built to simulate the steering control process. Due to the limited braking speed in small angle position feedback control, a speed feedback position control method was proposed. Taking into account the influence of fluctuating variable load on the hydraulic system pressure and the dynamic gear meshing force, the optimal control parameters were found, and the final control effect was significantly improved. In view of the pressure change of the hydraulic system contains a wealth of information on gear torsional vibration, the influence of gear failure on the hydraulic system pressure was discussed considering the two gear failure modes of broken teeth and uniform wear. The input load is divided into constant load and fluctuating load, and the test results was consistent which provides a basis for diagnosing azimuth gear faults.

Improved vibration AM-FM sideband phenomenon models of planetary gear set with distributed faults and fault-induced speed fluctuation

Vibration modulation features are the important indicators for the planetary gear set fault diagnosis. However, the modulation sidebands caused by the distributed faults of planetary gear set are complicated, especially the FM components related to fault-induced periodic speed fluctuation, which have not been clearly revealed. In this paper, the transfer path function, gear meshing force and measuring-direction projection function with FM components are combined to develop a series of phenomenon models when considering the distributed gear fault-induced speed fluctuation, which can theoretically deduce the vibration modulation sidebands. Field test of the wind turbine planetary gearbox and the fault simulation of experiment platform verify the high consistency of the vibration AM-FM sidebands obtained from the phenomenon models and the practical planetary gear sets. The proposed models contribute a clear explanation for the generation mechanism of vibration AM-FM sidebands even the sidebands with small amplitudes caused by the distributed faults of sun and planet gear, and provide the important and effective frequency features to confirm the condition of planetary gear set.

Establishment and Validation of a Structural Dynamics Model with Power Take-Off Driveline for Agricultural Tractors

As off-road vehicles, in addition to field transportation, another vital function of agricultural tractors is to provide power for field machinery. Therefore, the dynamic performance of the power take-off (PTO) driveline directly affects the field reliability of tractors. Firstly, a torsional vibration coupled spatial dynamics model of the power take-off driveline is proposed according to the classical machine driveline dynamics and gear dynamics theory. In the dynamics model, the interactions among the vertical, lateral, and rotational motions of the driveline parts are fully included. The coupling vibrations from internal excitations (such as tooth surface friction, gear time-varying mesh, and engine pulse) and external excitations (such as field machinery load) are also considered. Secondly, the simulation results of the model are obtained using the numerical solving algorithm ode15s. The actual experiment is carried out on the indoor Tractor PTO Test Bench. Then, the model is verified by comparing the test results with the simulation results. Finally, the dynamic characteristics of the whole driveline are revealed under different drive modes, especially strong interactions between the driveline and field machinery in low-speed and heavy-load mode. The gear mesh forces and the root mean square (RMS) values of the acceleration amplitude for the main parts generally decrease gradually with the increase in the PTO rotation speed and the decrease in PTO torque. Furthermore, the model can be applied to reliability assessment, for instance, vibration, damage, and fatigue of off-road vehicles considering gear transmissions, particularly in a field working environment.

Deformation and Response Analysis of Spur Gear Pairs with Flexible Ring Gears and Localized Spalling Faults

For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.

Optimization of the Quality of the Automatic Transmission Shift and the Power Transmission Characteristics

We have established a simulation platform for the machine–electro-hydraulic coupling system of the transmission system and the control system to study the root causes of the problems of large shifting impact and slow change of the machine tool transmission system. The dynamic analysis of the gear shift work of the gearbox was carried out, and the main factors affecting its shift instability were studied. With the impact and sliding power as the optimization goals, the shift quality is optimized based on the multi-objective genetic algorithm. Through the shift experiment, it was found that the power interruption phenomenon during the shift process was eliminated after optimization, and the quality of the shift was improved. Simulated planetary row wheel gear meshing force was found in the same gear, and the second planetary row gear meshing force was the largest among the planetary rows. The stress of the node near the top of the tooth is greater than the stress of the node near the node circle and the root of the tooth, and the two sides of the tooth top are relatively larger than the intermediate stress. The dynamic simulation model of the planetary gearbox system with rigid–soft hybrid can obtain the stress distribution of the solar wheel at the maximum impact moment and the stationary stage, as well as the dynamic stress of the key nodes of the solar wheel, which lays the foundation for the fatigue strength and life prediction of the gear system.

Dynamic responses of electromechanical transmission system based on a nonlinear hybrid model

A nonlinear hybrid model of electromechanical transmission system is proposed by combining finite element method and lumped parameter method, in which the flexible shaft model is established by using three-dimension nonlinear beam element based on the absolute node coordinate formulation and the gear mesh model is calculated by using nonlinear time-varying lumped parameter model. In the hybrid model, the coupling between the nonlinear deformation of shafts and excitation of gears is considered. The generalized- α implicit time stepping algorithm is used to study the dynamic responses of system. Then, comparisons and analyses are made of the dynamic responses of system between the hybrid model and previous lumped parameter model. Finally, the effects of flexibility of shafts, the geometrical parameters of shaft, the mounting position of the gear on the shaft and the operation conditions on the dynamic responses of system are analyzed. The results show that the presented nonlinear hybrid model is valid and effective in predicting the dynamic behavior of electromechanical transmission system. The gear meshing force is increased by 14.3% and new coupling frequencies are observed due to the effect of the shaft flexibility. Moreover, since the shaft radius of 0.05 m is the critical value for the accurate calculation of the proposed nonlinear hybrid model, the nonlinearity caused by the shaft vibration cannot be ignored. When the gear is installed at the midpoint of the shaft, the maximum von Mises stress of the shaft of 1.8 × 107 Pa is achieved and located at the connected point on the shaft. This study plays an important role in the field of electromechanical transmission design.

Input torque measurements for wind turbine gearboxes using fiber-optic strain sensors

Abstract. Accurate knowledge of the input torque in wind turbine gearboxes is key to improving their reliability. Traditionally, rotor torque is measured using strain gauges bonded to the shaft. Transferring the resulting signal from the rotating shaft to a stationary data acquisition system while powering the sensing devices is complex and costly. The magnitude of the torques involved in wind turbine gearboxes and the high stiffness of the input shaft pose additional difficulties. This paper presents a new alternative method to measure the input torque in wind turbine gearboxes based on deformation measurements of the static first-stage ring gear. We have measured deformation using fiber-optic strain sensors based on fiber Bragg gratings because of their advantages compared to conventional electrical strain gauges. The present study was conducted on a Siemens Gamesa Renewable Energy gearbox with a rated power of 6 MW, in which a total of 54 fiber-optic strain sensors were installed on the outer surface of the first-stage ring gear. The gear mesh forces between the planets and the ring gear cause measurable deformations on the outer surface of the stationary ring gear. The measured strains exhibit a dynamic behavior. The strain values change depending on the relative position of the strain sensors to the planet gears, the instantaneous variations of the input torque, and the way load is shared between planets. A satisfactory correlation has been found between the strain signals measured on the static ring gear and torque. Two signal processing strategies are presented in this paper. The first procedure is based on the peak-to-peak strain values computed for the gear mesh events, and therefore torque can only be estimated when a gear mesh event is detected. The second signal processing procedure combines the strain signals from different sensors using a Coleman coordinate transformation and tracks the magnitude of the fifth harmonic component. With this second procedure, it is possible to estimate torque whenever strain data of all sensors are available, leading to an improved frequency resolution up to the sampling frequency used to acquire strain data. The method presented in this paper could make measuring gearbox torque more cost-effective, which would facilitate its adoption in serial wind turbines and enable novel data-driven control strategies, as well as a more accurate assessment of the consumed fatigue life of the gearboxes throughout their operation.

Dynamic modeling of central bevel gear transmission system in aero-engine

Aero-engine is the most critical part of an aircraft. As its key component, the central bevel gear transmission system is always designed only considering the meshing vibration and ignoring structural characteristics of shafts and bearings, and comprehensive vibration characteristics is not well addressed. The transmission system may suffer severe vibration. To accurately study the dynamic characteristics of the system, a model of a central bevel gear transmission system is developed considering the effects of bevel gear mesh stiffness, shaft stiffness, bearing stiffness, and unbalance excitation in this paper. It has been validated by finite element software ANSYS. On this basis, the influence of variation of bearing stiffness and mesh stiffness on the natural characteristics of the central bevel gear transmission system is investigated. The influence of unbalance on the radial vibration and gear meshing force is studied by the analytical calculation method. A case study is carried out. The results show that variation of stiffness within a certain range will cause dramatic changes in the natural characteristics of the system. The unbalance of the driven bevel gear shaft has an effect on the radial vibration and meshing force of the system. The proposed model can reflect radial vibration characteristics, axial vibration characteristics, torsional vibration characteristics, and some coupled natural characteristics of the system. This research provides a theoretical basis to optimize dynamic performance and reduce the vibration of the system and will be helpful in designing the central bevel gear transmission system.

Vibration characteristics and condition monitoring of internal radial clearance within a ball bearing in a gear-shaft-bearing system

Internal radial clearance is a key factor influencing bearing fatigue life. Moreover, bearings inevitably suffer from various wears and tears, which result in gradual increase of clearance and shorten bearing life. Monitoring bearing clearance changes using vibration can effectively indicate the bearing wear and provide good leading time to perform maintenances. Previous studies show that vibration at ball pass frequency on outer race (BPFO) can be based for clearance monitoring. However, such clearance induced vibration has not been well understood, especially under complicated dynamic interactions such as in a gearbox system. To fill this gap, this paper presents a nonlinear gear-shaft-bearing-housing vibration model with fourteen degree of freedom (DOF) to investigate the vibration responses under the dynamic gear meshing force and progressively changed radial clearances at first. Then, the model was verified through a two-stage spur gearbox. Furthermore, bearing characteristics with different radial clearances under the influence of gear are revealed and indicator based on modulation signal bispectrum-sideband estimator (MSB-SE) was proposed. Finally, vibration data from a run-to-failure gearbox test rig was utilized to verify the effectiveness of the MSB-SE indicator for bearing clearances monitoring. Simulation results show that BPFO is modulated on gear meshing frequency (GMF) and BPFO amplitude from envelope spectrum increases with bearing clearances under the influence of gear meshing. Indicator based on MSB-SE, possessing the capability of purifying the interferences of gear meshing and strong noises, is effective to capture the variance of bearing clearances. The experiment based on a run-to-failure gearbox test rig provided evidence for the effectiveness of the proposed indicator, which is more accurate than BPFO amplitude from conventional envelope analysis and time-domain indicators, such as RMS and kurtosis. These findings are of significance for bearing fault diagnosis and maintenance.

Input Torque Measurements for Wind Turbine Gearboxes Using Fiber Optical Strain Sensors

Abstract. Accurate knowledge of the input torque in wind turbine gearboxes is key to improving their reliability. Traditionally, rotor torque is measured using strain gauges bonded to the shaft. Transferring the resulting signal from the rotating shaft to a stationary data acquisition system while powering the sensing devices is complex and costly. The magnitude of the torques involved in wind turbine gearboxes and the high stiffness of the input shaft pose additional difficulties. This paper presents a new alternative method to measure the input torque in wind turbine gearboxes based on deformation measurements of the static first stage ring gear. We have measured deformation using fiber optic strain sensors based on fiber Bragg gratings because of their advantages compared to conventional electrical strain gauges. The present study was conducted on a Siemens Gamesa Renewable Energy gearbox with a rated power of 6MW, in which a total of 54 fiber optic strain sensors were installed on the outer surface of the first stage ring gear. The gear mesh forces between the planets and the ring gear cause measurable deformations on the outer surface of the stationary ring gear. The measured strains exhibit a dynamic behavior. The strain values change depending on the relative position of the strain sensors to the planet gears, the instantaneous variations of the input torque, and the way load is shared between planets. A satisfactory correlation has been found between the strain signals measured on the static ring gear and torque. Two signal processing strategies are presented in this paper. The first procedure is based on the peak-to-peak strain values computed for the gear mesh events, and therefore, torque can only be estimated when a gear mesh event is detected. The second signal processing procedure combines the strain signals from different sensors using a Coleman coordinate transformation and tracks the magnitude of the fifth harmonic component. With this second procedure, it is possible to estimate torque whenever strain data of all sensors is available, leading to an improved frequency resolution up to the sampling frequency used to acquire strain data. The method presented in this paper could make measuring gearbox torque more cost-effective, which would facilitate its adoption in serial wind turbines and enable novel data-driven control strategies, as well as a more accurate assessment of the consumed fatigue life of the gearboxes throughout their operation.

Fault simulation and forecast of helical cylindrical gear of reducer based on ADAMS

Aiming at the problems that the dynamic speed and meshing force of the helical cylindrical gear of the reducer are difficult to actually measure and the test cost is high, the helical cylindrical gear transmission system of a crane reducer is used as the research object, and the 3D modeling software Solid Works is used to establish the assembly model of the gear transmission system, import the dynamic simulation software ADAMS to establish simulation model, and perform simulation analysis on it. The simulation results show that the gear speed is stable after acceleration, which is basically close to the theoretical calculation value; meshing at different multiples the gear meshing force amplitude is different at different frequencies. As the frequency multiplier increases, the amplitude shows a downward trend. Finally, Ensemble Empirical Mode Decomposition (EEMD) sample entropy and Extreme Learning Machine (ELM) are used for fault prediction to verify the effectiveness of this method. The above can provide a certain reference basis for the condition monitoring and fault prediction of the gearbox of metallurgical cranes, so as to ensure the safe operation of the crane.

Numerical calculation and experimental measurement for gear mesh force of planetary gear transmissions

In this paper, we propose a numerical method to calculate the dynamic mesh forces of planetary gear transmissions (PGTs). In this model, the effects of addendum modification are included in the time-varying mesh stiffness (TVMS) and then the influence of TVMS and relative mesh phase on the dynamic mesh forces are considered in the proposed model. To verify the proposed model, an experimental method is proposed to measure the dynamic ring-planet mesh forces by using gear tooth root-fillet strain signals. Static mesh experiments and dynamic mesh experiments are carried out to obtain the strain signals. To measure the dynamic mesh force, the loaded tooth contact analysis (LTCA) method and quasi-static experiments are carried to determine the coefficient matrix which is used to descript the relationship between the mesh force and tooth root-fillet strain. Finally, calculated mesh forces and measured forces are compared and discussed. Results indicate that the proposed experimental method can effectively measure the dynamic ring-planet mesh forces, and the numerical mesh forces agree well with the measured mesh forces.