Gear Mesh Excitation Research Articles

Vertical dynamics analysis and multi-objective optimization of electric vehicle considering the integrated powertrain system

Integrated powertrain system, mainly composed of driving motor and reducer, is one of the excitation sources to electric vehicle vibration but is limited in coupling with the vertical vehicle dynamic in the existing research, which restricts the reliability of dynamics investigation of vehicle and integrated powertrain system. This work proposes a novel vertical dynamic model of the electric vehicle considering the integrated powertrain system, enabling the way to access the coupled vibration among the chassis, unsprung mass, and integrated powertrain system. The road irregularity, unbalanced magnetic pull, and gear mesh excitation are developed and are further applied to the novel vehicle dynamic model with ten degrees of freedom (DOFs). Then, the dynamic response between the novel model and traditional one is compared. Further, the effects of the stiffness and damping of suspension and mounting on the vibration of chassis and integrated powertrain system are explored by numerical calculation. Finally, a multi-objective optimization model is proposed and is driven by the dragonfly algorithm to minimize the vibration of chassis and integrated powertrain system. The research results shown that there will be present the new complex dynamic characteristics with considering the excitation from the integrated powertrain system. The suspension and mounting parameters have the nonlinear effects on the vehicle vibration. And the system vibration can be globally optimized with the optimization algorithm.

A Fully Integrated Simulation Approach of Drive Trains towards Tonality Free Wind Turbines

Wind turbine manufacturers are now facing stricter noise regulations as turbines are being placed closer to urban areas. While rotor blade aero-acoustic noise is the dominant noise component in the total sound pressure level of a wind turbine, mechanical noise originating from gears and generators are gaining importance as well, especially when producing tonal noise. To minimize the tonal noise originating from the gears it is crucial to compare different drivetrain concepts and gear designs early in the design phase and consider the NVH performance as part of the design selection criteria. Unfortunately, the software available on the market allows the prediction of the acoustic performance of a drivetrain design when all details are already known, but these software’s are unable to do this in the early concept design phase when making design choices have the biggest impact. Therefore, an integrated simulation platform has been developed to predict wind turbine tonality, considering factors like gear mesh excitation and aero-acoustic masking, which is already applicable in the design concept phase when lots of design details are not known yet. This platform, linked to optimization software, allows ZF to proactively develop strategies to mitigate Noise, Vibration, and Harshness risks, resulting in cost-effective and harmonized solutions across their product platforms.

NONLINEAR DYNAMIC RESPONSES OF LOCOMOTIVE EXCITED BY RAIL CORRUGATION AND GEAR TIME-VARYING MESH STIFFNESS

Rail corrugation is usually generated in modern railway transportations, such as high-speed railway, urban railway, and heavy-haul railway. It is one of the major excitations to the wheel–rail dynamic interaction, which will cause extra vibration and noise, failures, or even risk of derailment to the vehicle and its components. A dynamics model of a heavy-haul locomotive considering the traction power from the electric motor to the wheelset through gear transmission is employed to investigate the nonlinear dynamic responses of the locomotive. This dynamics model couples the motions of the vehicle, the track, and the gear transmission together. In this dynamics model, excitations from the rail corrugation, the nonlinear wheel–rail contact, the time-varying mesh stiffness, and the nonlinear gear backlash are considered. Then, numerical simulations are performed to reveal the dynamic responses of the locomotive. The calculated results indicate that different nonlinear phenomenon can be observed under the excitation of the rail corrugation with different amplitude and wavelength. The high frequency vibrations excited by the time-varying mesh stiffness are usually modulated by the low frequency vibrations caused by the rail corrugation. However, this is likely to vanish under the chaotic conditions with some corrugation wavelength. The vibration level of the vehicle and the gear transmission increases generally with the corrugation amplitude. However, some corrugation lengths have been found to be more responsible for the vibration of the dynamics system, which should be concerned greatly during the locomotive operation. Meanwhile, involvement of gear transmission systems will cause different dynamic responses between the wheelsets under rail corrugation and gear mesh excitations.

Reducing noise and vibrations in wind power plants with DFIG and planetary gearbox through improved rotor current control

Planetary gears in wind power plants transmit force excitations to the mechanical structure due to alternating tooth meshes. Structure-borne sound is generated and proceeds to tower and nacelle where it is radiated to the environment and may be a noise pollution to residents. In addition, unwanted vibrations can decrease the durability of the gearbox. So far, structural vibrations are being avoided by constructive measures or active absorbers. In contrast to this, our approach is to reduce gear mesh excitations only with the existing electric generator. Therefore, the rotor current control of the machine is enhanced to inject high frequency oscillations so that the wind power generator produces a specific oscillating torque. This anti-noise torque ripple is transmitted via the shaft to the gear stage and minimizes the gear mesh orders so that less force excitations are exposed to the mechanical structure at the bearings. In our knowledge this anti-noise torque approach using the electric generator and its current control is completely new in the field of wind power plants. Simulation is performed using a multi-body-model of the drivetrain to identify an optimal torque oscillation. Afterwards a control circuit model of the generator and the power converter for the rotor circuit is shown. Hence, it is possible to calculate the behavior of the system in high level of detail on the mechanical and the electrical side. Resulting bearing forces are analyzed to prove that excitation can be reduced significantly. No additional hardware, especially no additional actor is needed.

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.

Dynamic modeling and analysis of Ravigneaux planetary gear set with unloaded floating ring gear

A Ravigneaux planetary gear set (RPGS) system with an unloaded floating ring gear is studied in this paper. Aiming at investigating the three-dimensional vibration response of the long planet and the dynamic load on the floating ring gear, a flexible-rigid coupling dynamic (FRCD) model is proposed by coupling the condensed substructure of finite element (FE) flexible bodies with rigid dynamic model. Relative positions of different force elements are taken into consideration, as well as time-varying mesh stiffness and gear backlash. Based on this model, the effect of sun gear positions on the dynamic response of the long planet is performed and the mechanism for the vibration of the floating ring gear is revealed. The results show that the bearing force of the long planet varies nearly linearity with sun gear positions, and dynamic loads on the floating ring gear are induced by gear mesh excitations and carrier vibrations, while the former affects impact amplitudes and the latter influences impact frequencies. A further investigation is conducted on the effects of gear backlash and support stiffness, and it is indicated that increasing the support stiffness of the floating ring gear can reduce its dynamic load significantly.

Gear mesh excitation and non-uniform Rational B-Splines

Gear mesh excitation and non-uniform Rational B-Splines

Dynamic modelling of traction motor bearings in locomotive-track spatially coupled dynamics system

For railway locomotive, its motor bearing is one of the key components, which is likely to be damaged due to the intensified vibration conditions caused by the wheel-rail interaction and gear mesh. In this paper, a locomotive-track spatially coupled dynamics model considering the dynamic effect of the traction power transmission is established to investigate the dynamic responses of traction motor bearings. The detailed structure of the traction motor, complex internal interactions of the rolling bearing itself, time-varying gear mesh stiffness, and wheel-rail interaction are considered. The simulated results indicate that the gear mesh excitation and internal interactions of the motor bearings significantly affect the dynamic characteristics of the rotor. The motor bearing at the driving end surfers more dynamic loads, and the internal interactions between the components are more intensified than that of the bearing at the non-driving end. Moreover, the skidding phenomenon of the motor bearing at the driving end is alleviated by the greater radial load. Additionally, the wheel-rail interaction with track random irregularity will deteriorate the working conditions of the motor bearings. The modelling method and results can provide helpful theoretical guidance for the motor bearing design and structure optimization of the locomotive traction motor.

Vibration and dynamics analysis of electric vehicle drivetrains

The importance of the vibration and dynamics of electric vehicle drivetrains has increased because of noise and durability concerns. In this study, the important dynamic responses of drivetrains, including the dynamic mesh force acting at the gear teeth, dynamic loads acting at the bearings, and torsional fluctuation of the tire or load under major vibration excitations, such as motor torque fluctuation excitation and spiral bevel gear mesh excitation, were investigated. The results demonstrate that at a lower motor speed, dynamic responses such as the dynamic mesh force, dynamic bearing loads, and dynamic torsional displacement of the tire or load under motor torque fluctuation are dominant. At a higher motor speed, however, the dynamic responses under the gear mesh excitation are dominant. In addition, increasing the pinion-motor torsional compliance is an effective approach for suppressing the dynamic responses of drivetrains under motor torque fluctuation.

Modeling and Analysis of Amplitude-Frequency Characteristics of Torsional Vibration for Automotive Powertrain

In the present paper, the amplitude-frequency characteristics of torsional vibration are discussed theoretically and experimentally for automotive powertrain. A bending-torsional-lateral-rocking coupled dynamic model with time-dependent mesh stiffness, backlash, transmission error etc. is proposed by the lumped-mass method to analysis the amplitude-frequency characteristic of torsional vibration for practical purposes, and equations of motive are derived. The Runge–Kutta method is employed to conduct a sweep frequency response analysis numerically. Furthermore, a torsional experiment is performed and validates the feasibility of the theoretical model. As a result, some torsional characteristics of automotive powertrain are obtained. The first three-order nature torsional frequencies are predicted. Torsional behaviors only affect the vibration characteristics of a complete vehicle at low-speed condition and will be reinforced expectedly while increasing torque fluctuation. Gear mesh excitations have little effects on torsional responses for such components located before mesh point but a lot for ones behind it. In particular, it is noted that the torsional system has a stiffness-softening characteristic with respect to torque fluctuation.

Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations

Time-varying mesh stiffness and gear transmission errors are the major excitations to gear dynamics system. How to calculate them more accurately and efficiently has attracted much attention worldwide for a long period. Especially consideration of the gear body structure coupling effect and the tooth profile error will make interactions between the tooth pairs in mesh more complicated so that traditional analytical methods could not applicable any more. In this paper, a comprehensive and general analytical gear mesh model is proposed by considering all the deformations including the teeth deformation, teeth contact deformation, fillet-foundation deformation, and gear body structure coupling effect, as well as tooth profile deviations. The calculation formulas for the mesh stiffness, load sharing ratio and static transmission error are derived, and the corresponding efficient solving method is also proposed. Based on the proposed model, the influencing mechanism of the gear body structure coupling effect on the total mesh stiffness is revealed. The proposed mesh stiffness calculation model is proven to be more general and comprehensive since the traditional analytical models are the special cases of the proposed model.

Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

Reduction of the tonality of gear noise by application of topography scattering

In the design process of transmissions, one major criterion is the resulting noise emission of the powertrain due to the gear excitation. Within the past years, a lot of investigations have shown that the noise emission can be correlated to the quasi-static transmission error. Therefore, the transmission error can be used as a characteristic value for quality assurance by conducting experimental inspections as well as a tooth contact analysis in the design process.An optimization approach to solve gear whine issues is the reduction of the gear mesh excitation. In this report, a novel optimization approach for gears is presented. A targeted topography scatter from tooth to tooth is applied on the teeth of the gear set, in order to manipulate the composition of the gear mesh excitation. As a result of the slight deviations for each tooth mesh, the regularity of the transmission error excitation is broken up leading to a reduction of the tonality of the resulting gear whine.In the first step, different topography scatter variants are calculated in the tooth contact analysis. Based on the transmission error spectra, two variants with a topography scatter are chosen for manufacturing. The evaluation of the predicted excitation behavior is evaluated on a conventional bevel gear tester by means of single flank tests. A test fixture for the evaluation of the operational behavior under loaded and dynamic conditions is used to compare the measured and simulated dynamic excitation behavior. In order to simulate the dynamic behavior, a torsional multi-body-simulation model of the powertrain is developed that uses the stiffness of the gear mesh calculated by the tooth contact analysis as input data for the excitation forces. The force-coupling-element connects the drive and the driven train and forms the excitation of the gearing.Finally, it is the aim to evaluate the impact of the targeted topography scatter psychoacoustic parameters, such as loudness, sharpness, roughness and tonality. The potentials of the topography deviation for the optimization of ground bevel gears in terms of tonality reduction will be shown by means dynamic test rig trials.

Research on Vibration Characteristics and Stress Analysis of Gearbox Housing in High-Speed Trains

Gearbox housing in high-speed trains has two kinds of excitation sources: the internal excitation of gear mesh excitation and the external excitation that contains the wheel polygonization and the input torque. To study the effect of the torque on the vibration and stress of the gearbox housing, a multibody dynamic model is established by the Simpack, in which the elastic deformation of the wheelset and the gearbox housing are considered. A traction drive system is modeled by the MATLAB/Simulink to calculate the traction torque, which is transformed to drive the high-speed train to overcome the basic resistance and run with a constant speed. The accuracy of the model is verified by comparing the simulation results with the measurement results. Based on the electromechanical model, the vibration acceleration of the gearbox housing in the case of without torque, with ideal torque, and with harmonic torque is calculated and analyzed, as well as its dynamic stress. The results show that the traction torque plays a role in amplifying the vibration acceleration and dynamic stress. When the fatigue damage of the gearbox housing is calculated, it will obtain a more accurate result to consider the effect of the traction torque.

Multiphysics coupling between periodic gear mesh excitation and input/output fluctuating torques: Application to a roots vacuum pump

This paper presents the analysis of multiphysics coupling between periodic gear mesh excitation and upstream/downstream fluctuating loads using an iterative spectral methodology. This one is based on the resolution of the parametric equations of motion in the spectral domain. Its efficiency makes possible to treat both low and high frequency excitations for systems having a large number of degrees-of-freedom. The different excitation sources, the dynamic coupled equations of motion, the spectral methodology and the iterative resolution principle are described. The dynamic responses of a roots vacuum pump for which the spur gear high mesh frequency parametric excitation is coupled with a low fluidic drag torque frequency. The coupling between excitations generates a frequency enrichment of the dynamic response which is reflected on waterfall plots by emergence of numerous sidebands around harmonics of the mesh frequency.

A Dynamic Model for Double-Planet Planetary Gearsets

In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

An experimental and theoretical study of the dynamic behavior of double-helical gear sets

In this study, dynamic behavior of a double-helical gear pair is investigated both experimentally and theoretically. In the experimental side, a new double-helical test set-up consisting of a test machine and test specimens is developed for operating a double-helical gear pair under realistic torque and speed ranges. A test gear pair formed by novel three-piece double-helical gears is developed to allow adjustable right-to-left stagger angles. A measurement system to capture three-dimensional vibratory motions and dynamic motion transmission error under high-speed conditions is implemented. A test matrix that included various combinations of key system parameters is executed under realistic torque values within a wide speed range to establish a database. In view of this experimental data, a linear, time-invariant dynamic model of double-helical gear pair systems including shafts and bearing supports is proposed, also allowing for any stagger angle between the right and left sides of a double-helical gear pair through proper definition of phasing between the two gear mesh excitations. Direct comparisons to measurements are presented to demonstrate the accuracy of the proposed model in predicting three-dimensional gear vibrations. The right-to-left stagger angle is shown to be the most critical parameter impacting dynamic response.

A dynamic model of a double-helical planetary gear set

A linear, time-invariant model of a double-helical planetary gear set is proposed in this paper. The model formulation allows the analysis of a gear set with any number of planets, any planet phasing and spacing configurations and any support conditions. Torsional, transverse, axial and rotational (rocking) motions of gears and the planet carrier are included in this three-dimensional model. Planets are allowed to be positioned equally or unequally spaced around the sun gear. The natural modes are computed by solving the corresponding Eigen value problem. The modal summation technique is used to find the forced response due to periodic gear mesh excitations under constant or proportional modal damping conditions. An example gear set consisting of four equally-spaced planets is considered at the end to demonstrate the influence of key design parameters including right-to-left stagger angle, and support conditions on the dynamic response of the double-helical planetary gear system. Numerous modes with dominant tilting motions are predicted to underline the essence of using a 3D formulation for double helical gears. Staggering of gear teeth is shown to impact the dynamic response of the gear system substantially. Different values of stagger are shown excite different types of modes, resulting in different dynamic response curves. It is also found that left and right sides of double helical gears can carry equal or different dynamic load amplitudes based on the right-to-left stagger values. Likewise the influence of the sun support conditions is shown to be more pronounced for the case of a non-zero stagger.

Dynamic Modelling of Planetary Gears of Automatic Transmissions

In this paper, a generalized dynamic model for multi-stage planetary gear trains of automotive automatic transmissions is proposed. The planetary gear train is formed by N number of planetary gear sets of different types (single-planet, double-planet, or complex-compound), connected to each other in any given kinematic configuration. In addition, each planetary stage can have any number of parallel planet branches. A generalized power flow formulation and a gear mesh load distribution model are used to determine the stiffnesses, displacement excitations, and fundamental frequencies at the gear mesh interfaces. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. At the end, the model is applied to a three-stage planetary gear train representative of an automotive automatic transmission application to demonstrate the influence of coupling stiffnesses and the kinematic configurations on the natural modes and the dynamic response.

Vibration Analysis of the Helical Gear System Using the Integrated Excitation Model

The vibration of the helical gear system is generated by three kinds of excitation. The first cause is a displacement excitation due to the tooth surface error. The second is a parametric excitation by the periodical change of the tooth mesh stiffness. The third is a moving load on the tooth surface during the progress of mesh of the teeth. In mesh of a pair of helical gears, the composite load of the distributed load along a contact line moves its operating location from one end of face width to the other end during the process of mesh progress. This moving load causes fluctuation of bearing load that excites the housing. Therefore, it is important to treat gear mesh excitation as moving load problem. For this purpose, a tooth mesh model, in which three different types of excitations above are incorporated, is proposed. In this model, a pair of gear tooth is represented by the multiple springs and the moving load can be taken into account by the multiple mesh excitation forces that have the phase differences from each other. This model is applied to the vibration analysis of a single stage gearbox. The analytical and experimental results show that this method is accurate and effective enough for practical use.