Meshing Vibration Research Articles

Influence of meshing stiffness variation on the vibration characteristics of main reduction gears

Abstract The meshing stiffness of the main and passive gears of the main reducer of the rear axle of a commercial vehicle is taken as the object of this study, aiming to optimize the influence of the meshing stiffness of the main and passive gears on the vibration and noise, enhance the meshing performance of the gear teeth, reduce the vibration and noise of the main reducer, and improve the vibration performance of the main reducer. Through UG 3D modeling software and ADAMS dynamics simulation, the dynamics characteristics of hypoid gears under different gear tooth meshing stiffness coefficients are analyzed and simulated. It is concluded that under the meshing stiffness coefficients of 0.8 to 0.9 times, the translational vibration acceleration and angular acceleration of the passive gears are smaller, the translational vibration and torsional vibration are smoother, and it can improve the performance of the meshing vibration of the gear system of the main gear reducer.

Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment

Abstract Gear drive is one of the most widely used transmission forms. Its vibration analysis plays an important role in design and operation. Considering the gear meshing resonance phenomenon (MRP), the paper analyzes the influences of rotating speed and load on meshing resonance intensity (MRI). Based on the gear meshing impact mechanism, meshing force variation during the engagement process were obtained. It was considered as meshing impacts exerted on the gear system. By comparing the maximum meshing force under different circumstances, it was found that rotating speeds and loads were positively related to meshing forces. The vibration signals with different load torques and rotating speeds obtained from the gear pair were analyzed. The experiment results showed that the intensity of meshing impact increased with the increases of both rotating speed and load. It was also observed that due to the MRP, the gear meshing frequency was modulated to the resonance frequency band as meshing impacts. Consequently, the resonance frequency band contained most of the energy of the meshing impact. An indicator called resonance energy ratio (RER) was defined to represent the proportion of resonance energy due to meshing impact. The simulation and experiment result show that the proposed RER indicator can well assess the intensity of the vibration. By comparing the RER values of 20 sets of gear vibration data, the influences of rotating speed and load on MRI were discussed. The result shows that the proposed method is helpful to the vibration assessment and condition monitoring in different operational states.

Fundamental study on estimation of tooth contact area based on combined image from temperature monitor images of tooth surface with a high-speed-camera thermography and on meshing vibration for high reduction ratio hypoid gear with a three-tooth pinion

Fundamental study on estimation of tooth contact area based on combined image from temperature monitor images of tooth surface with a high-speed-camera thermography and on meshing vibration for high reduction ratio hypoid gear with a three-tooth pinion

Dynamic Responses of the Planetary Gear Mechanism Considering Dynamic Wear Effects

Gear wear is unavoidable and results in vibrations and decreased performance in a planetary gear system. In this work, the wear phenomenon of the gear teeth surface and the dynamic responses of the planetary gear mechanism are investigated through a computational methodology. Dynamic responses are presented by considering the dynamic wear effects. First, the model of the planetary gear mechanism dynamics is established by considering the nonlinear stiffness and friction of gear surfaces. The dynamic wear model of the gear is then established based on Archard’s wear model. Further, the coupling between the dynamics and wear characteristics of the planetary gear mechanism is presented by considering the dynamic wear effects. Finally, a numerical investigation is conducted. The simulation results reveal severe wear between the sun and planet gears. The wear depth and meshing vibration responses exhibit prominent nonlinear characteristics. The low-order resonance of the meshing frequency becomes more marked as the mesh times and wear increase.

Vibration response mechanism of fixed-shaft gear train with cracks based on rigid-flexible coupling dynamics and signal convolution model

Affected by external flexible transfer path of fixed-shaft gear train, internal gear meshing vibration signals that representing the healthy state of gear will convolve with modal information of gearbox housing and become much more complicated. Moreover, gear crack fault features of fixed-shaft gear train are relatively weak and complex, which are difficult to diagnose. Therefore, to reveal the origination mechanism of crack fault, a rigid-flexible coupling dynamics model of fixed-shaft gear train with full consideration of flexible housing is firstly established, then a signal convolution model is proposed to solve housing vibration response signal by combining internal excitation and external transfer path. Thereinto, as internal influence factor, time-varying meshing stiffness that drives excitation forces is used to reflect excitation characteristics under normal and crack state; as external influence factor, flexible transfer path that includes modal characteristics of gearbox housing is calculated by finite-element-method. Through the established models, modulation sideband features of housing vibration response signals are selected as crack fault indicator. Corresponding vibration response mechanism is revealed clearly under normal and different crack degrees in simulations. Experimental results keep good consistency at crack fault features with simulation signals and verify the effectiveness of the proposed models.

A new method for calculating time‐varying torsional stiffness of RV reducers with variable loads and tooth modifications

AbstractRotate vector (RV) reducers have advantages of high torque ratio, and extremely reliable functioning under dynamic load conditions, and so forth, and they are extensively used in precision transmissions, such as industrial robots. The torsional stiffness of RV reducers is a main parameter affecting the meshing vibration and transmission performance. In addition, the variable loads and tooth modifications have significant influence on the torsional stiffness of RV reducers. In this paper, a new method of calculating torsional stiffness for RV reducers considering variable loads and tooth modifications is presented. The dynamic stress and deformation of meshing teeth are calculated based on Hertz formulation, and the number of meshing teeth is determined by analyzing the dynamic stress of meshing teeth. Then, the torsional stiffness of RV reducers is obtained. Finite element method is applied to calculate the deformation of cycloidal‐pin gear in the maximum force position δmax. The influence of variable applied loads and different tooth modifications of cycloidal‐pin gear transmission on torsional stiffness are also studied. The results show that variable applied loads and different tooth modifications influence the torsional stiffness of RV reducers by changing teeth deformation and clearance, respectively.

Analysis of electromechanical coupling characteristics of electrics vehicle electric drive system considering current harmonic excitation

In order to study the electromechanical coupling dynamics characteristics of the drive motor and gear transmission system in the electric vehicle electric drive system, firstly, an electromechanical coupling dynamics model of the electric vehicle electric drive system is established; the electromechanical coupling vibration characteristics of the electric drive system under current harmonic excitation is compared and analyzed. The influence law of permanent magnet synchronous motor current harmonics on the meshing vibration of gear transmission system is revealed. The simulation results show that there is an obvious electromechanical coupling effect in the electric drive system; the harmonics of the drive motor can aggravate seriously the vibration state of the mechanical drive system; the research results provide a theoretical reference for further research on the vibration source positioning and active vibration reduction control strategy for the electric drive system of electric vehicles.

Modeling of Traction Drive in Elastohydrodynamic Lubrication Contact and Traction Coefficient Enhancement Using Surface Texture Under High-Speed Conditions of up to 50,000 rpm

Abstract A high-speed electric motor with a small reducer that has high-power transmission efficiency can be used to realize a high-power-density powertrain system because electric motors can be miniaturized to increase the rotational speed. A traction drive has low vibration noise due to its lack of meshing vibration, making it suitable as a transmission element for high-speed reducers. However, the traction coefficient, which greatly affects transmission performance, decreases with increasing rotational speed. In this study, to increase the traction coefficient using a surface texture, a model that takes into account transient temperature changes under high-speed conditions and the effects of micro-surface geometry was developed. The traction coefficient was measured using a high-speed test machine capable of operating at a maximum speed of 50,000 rpm. The model was able to predict the experimental values with an error of at most 6%. The high-pressure rheological properties of the oil were examined to develop design guidelines for the surface texture and a model was used to optimize the texture parameters. The designed texture was manufactured and evaluated. Experimental results show that the traction coefficient can be improved by up to 19%.

Multi-meshing-state and disengaging-proportion analyses of a gear-bearing system considering deterministic-random excitation based on nonlinear dynamics

Backlash induces gear-teeth separation or back-side tooth mesh (BTM), resulting in gear disengagement (GD), which heavily aggravates the dynamic performance and transmission quality of gear drivetrains. This study focuses on the disengaging proportion (DP) characteristics of a gear- bearing systems based on a multi-meshing-state (MMS) model. A new nonlinear dynamic model of gear-bearing system with MMS and deterministic-random external excitation is established considering the synergistic effect of backlash and non-integer contact ratio. A modified time-varying mesh stiffness with temperature stiffness is included in the model. Afterwards, the effect of the gear pair meshing vibration on bearing radial vibration is studied. The bifurcation and evolution of the MMS behavior are investigated changing the system parameters. An algorithm of DP is proposed in the time domain based on the established MMS model. The characteristics of DP are systematically discussed with the effects of dynamic response type, phase trajectory topology, bifurcation and chaos, and correlation between parameters. The results demonstrate that grazing bifurcation reduces the number of GD and chaos is prone to BTM. The disengaging proportion is highly dependent on the phase trajectory topology and generally increases from period-1 to quasi-periodic and then to chaotic responses. Bifurcation changes the variation trend of DP, thus there is a peak near period-doubling bifurcation and a trough near grazing bifurcation. The chaotic response leads to a jump in DP. The correlation between parameters considerably dominates the DP. This study provides a reference for revealing the mechanism of gear system disengagement and improving the dynamic performance.

Design and validation of a wheel-rail adhesion simulator in PLS-Circulator

A 1:4 scaled test rig called 'PLS-Circulator' is introduced for wheel-rail contact research under large slip conditions, which is composed of two wheel assemblies, 2 m diameter ring track with sprinklers surrounded, gearbox and two servo motors. On this basis, a wheel-rail adhesion simulator was designed to generate and measure the wheel-rail contact force. The slip ratio is the specific value of two motor speeds, which brings convenience to precisely control. SIMPACK simulation results showed that the slip ratio converged to the target value after the initial time in consideration of gear meshing vibration. The validation of the adhesion recovery was carried out utilizing PLS-Circulator under large slip conditions. Experimental results showed that in both steady and dynamic slip ratio experiments the adhesion coefficient could increase up to 26% from a lower adhesion caused by wet wheel-rail interface at the vehicle velocity of 20 km/h.

Study on Electrical Parameter Matching of Piezoelectric Stack Periodic Strut for Helicopter Cabin Noise Control

The gear meshing noise generated by the helicopter main reducer is one of the important sources of noise in the helicopter cabin. By improving the isolation performance of the struts supporting reducer to the gear meshing vibration, the purpose of reducing the gear meshing noise in the helicopter cabin can be achieved. Piezoelectric stack periodic strut (PSPS) composed of piezoelectric stacks and passive materials periodically arranged is an original type of strut with active and passive hybrid isolation characteristics. Piezoelectric stacks and passive materials form a periodic structure, which makes PSPS have a unique stopband characteristic. The propagation of elastic waves in the stopband frequency range is attenuated, which can improve the broadband passive vibration isolation capability of the PSPS; The piezoelectric stacks can adjust the elastic wave propagation in the PSPS and improve the single-frequency or multifrequency active isolation performance of the PSPS. Since the driving voltage and current range of the piezoelectric stacks significantly affect the isolation performance of the PSPS, this article focuses on the relationship between the isolation performance of the PSPS and the voltage and current required by the piezoelectric stacks. Firstly, based on the passive material periodic structure transfer matrix model, the driving voltage and current of the piezoelectric stacks are introduced into the model, and a PSPS electromechanical coupling model based on the transfer matrix form is established. Secondly, the correctness of the model is verified by the finite element software. Based on the model, the design process of PSPS parameters is proposed. The optimal isolation performance of PSPS is predicted under the limitation of maximum driving voltage and current. The effects of damping loss factor, exciting force, period number and passive material on the requirements of electrical parameters for active control are studied. A three-period PSPS strut composed of piezoelectric stack actuator and PV strut is used for experimental research, and the matching of electrical parameters of this PSPS in the test is analyzed.

The Effect of Signal Propagation Delay on the Measured Vibration in Planetary Gearboxes

Modulation of the gear mesh vibration is a major field of research for the condition monitoring of planetary gearboxes. The modulation creates sidebands around the gearmesh frequency in the vibration spectrum, and the distribution of these sidebands has been researched in numerous papers. All publications on the subject assume that the effect of the time varying signal propagation delay between the main vibration source – the gear mesh point(s) – and the (usually fixed) transducer can beneglected. This paper investigates the validity of this assumption. To do so, a planetary gearbox with a transducer mounted on the (fixed) ring gear is studied, and the effect of the propagation delay is modelled as a phase modulation of the gear mesh vibration. General expressions are then derived for the distribution and strength of the modulation sidebands, and these expressions are applied to quantify the effect of the propagation delay on five industrial gearboxes. The results show that the amplitude of the sidebands is negligible and would not interfere with condition assessment based on analysis of the modulation of the gear mesh frequency, and thus the propagation delay can be neglected for practical purposes.

A novel method to reduce the fluctuation of mesh stiffness by high-order phasing gear sets: Theoretical analysis and experiment

The vibration, triggered by the periodic fluctuation of time-varying mesh stiffness, is difficult to be reduced especially for the traditional spur gear transmission. In this paper, to reduce the fluctuation of mesh stiffness, a novel high-order phasing gear is proposed and verified by theoretical analysis and experiments. The contact line is studied in terms of the high-order phasing gear pair. Based on the time-varying mesh stiffness of spur gear pair, the mesh stiffness of the high-order phasing gear pair is derived. And the phasing parameters of the high-order phasing gear pair are optimized with the aim of achieving the near zero fluctuation of mesh stiffness. Moreover, it is proved that the application of the phasing gear sets effectively decreases gear meshing vibration, and the optimal staggered phase angle is verified by experiment.

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.

Suitable Design of Tooth Profile Modification for Noise Reduction in Spur Gear Pump

This study has carried out for noise reduction of spur gear pump. The previous report was published at JSME 2021 annual conference, which reported the noise source analyses result of test gear pump. According to the report, it was concluded that the most effective way to reduce noise was to reduce the meshing vibration of gears. Therefore, the authors aimed to reduce gear meshing vibration by modifying the tooth profile. For this purpose, the effect of tooth profile modification on the tooth root stress form was investigated. Then, the appropriate tooth modification amount was decided by the tooth root stress calculation. Furthermore, several kind of function which determines the shape of tooth profile modification has applied to the calculation to make clear the most effective shape of tooth profile modification for noise reduction. The major conclusions of this research are as follows; (1) The most effective value to tooth root stress waveform was depth of tooth profile modification. (2)The type of functions which determine the shape of tooth profile modification was less effective to tooth root stress waveform.

Research on improving durability of high-strength spheroidal graphite cast iron gears by nitriding heat treatment

The vibration damping property of high-strength spheroidal graphite cast iron is higher than that of steel materials, and it is possible to reduce gear meshing vibration, which is effective in reducing noise in gear devices. This material is significantly stronger than conventional spheroidal graphite cast iron. However, the problem is that the fatigue strength is inferior at the as-cast material level compared to conventional railway gear materials. Gas nitriding can significantly improve the fatigue strength of cast iron. In this study, we report the results of material fatigue test and improvement of nitriding heat treatment property by adding alloying elements in order to determine the optimum gas nitriding treatment conditions for cast iron gears. Furthermore, we manufactured the nitriding gear for railway vehicles and this noise performance was evaluated by rotation test. The thermal strain of the gear due to the nitriding heat treatment is less than that of carburizing, and the noise is reduced by about 2 dB on average compared to the conventional material tooth grinding gear.

Generation mechanism and evolution of five-state meshing behavior of a spur gear system considering gear-tooth time-varying contact characteristics

Teeth disengagement or back-side teeth engagement induced by backlash reduces the transmission quality and dynamic performance of gear systems, and the accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is established based on the time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is revealed using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single- or double-tooth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.

Wavelet Packet Transform-Assisted Least Squares Support Vector Machine for Gear Wear Degree Diagnosis

Wear degree detection of gears is an effective way to prevent faults. However, due to the interference of high-speed meshing vibration and environmental noise, the weak vibration signal generated by the gear is easily covered by the noise, which makes it difficult to detect the degree of wear. To address this issue, this paper proposes a novel gear wear degree diagnosis method based on local weighted scatter smoothing method (LOWESS), wavelet packet transform (WPT), and least square support vector machine (APSO-LSSVM) optimized by adaptive particle swarm algorithm. According to the low signal-to-noise ratio characteristic of gear vibration signal, LOWESS is first used to preprocess the signal spectrum. Then, the characteristic parameters used to characterize gear wear are extracted from different decomposition depths by WPT and, finally, combined with APSO-SVM to diagnose the degree of gear wear. Compared with the basic least squares support vector machine, the improved method has better performance in sample classification. The experimental results show that the method in this paper can effectively reduce the diagnosis error caused by background noise, and the diagnosis accuracy reaches 98.33%, which can provide a solution for the health status monitoring of gears.

A mathematical model of vibration signal for multistage wind turbine gearboxes with transmission path effect analysis

The sensor-perceived vibration signals of multistage wind turbine gearboxes have more complex frequency features than that of single-stage gearboxes since there are more meshing vibration sources and more complicated transmission paths inside them, which lead to difficulties in condition monitoring and fault diagnosis. Aiming to understand the vibration frequency features of multistage wind turbine gearboxes, a mathematical vibration model of healthy wind turbine gearboxes is developed and the spectral structure of the model is deduced by adopting Fourier series analysis. In the vibration model, the time-varying transmission paths from all the meshing vibration sources to the fixed sensor are considered, and the equivalent transmission path functions of the time-varying transmission paths are proposed for the first time. The theoretical derivations are validated by both simulations and engineering tests using two cases of 2.0MW industrial wind turbine gearboxes. The findings in this work are not only applicable to the gearboxes studied in this paper, but also to other similar multistage gearboxes, which can provide a priori spectral structure for the multistage gearbox to assist its condition monitoring and fault diagnosis.

Vibrational Monitoring of Nested Planetary Geartrain with Unground Pinion

The nested planetary gear train, which has two integrated single-stage planetary gearsets, is one of the newly developed compound gear train that has been successfully applied to the automobile transmissions. In the current study, a certain type of gear fault in the nested gear train, ungrounded pinion, is investigated using a non-destructive approach monitoring its vibration levels. A novel experimental test stand with open and vertical setup has been designed to collect the vibrational data by mounting the accelerometer directly to the gear clutches. Each of the two layers of the compound gear was tested separately. The measured vibrational data were processed with several signal processing techniques, which includes (a) frequency spectrum analysis, (b) time synchronous averaging (TSA) and (c) modulation sideband analysis. The experimental results show that the existence of the ungrounded pinion can be identified with the frequency spectrum analysis of the vibrational data. In addition, the modulation sidebands are also modeled using a modified version of the traditional technique of physical signal modeling. It is shown that the relative phase of the planet and the meshing vibration strength changed by the unground gear is the critical factor for determining the modulation sideband behavior. In addition, the location of the ungrounded pinion can also be determined by the time history processed by TSA.