Gear Mesh Vibration Research Articles

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.

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.

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.

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.

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.

Signal Identification of Gear Vibration in Engine-Gearbox Systems Based on Auto-Regression and Optimized Resonance-Based Signal Sparse Decomposition

As an essential part of the transmission system, gearboxes are considered as a major source of vibration. Signal identification of gear vibration is necessary for online monitoring of the mechanical systems. However, in engine-gearbox systems, the ignition impact of the engine is strong, so that the gear vibration is generally submerged. To overcome this issue, the resonance-based signal sparse decomposition (RSSD) method is used in this paper based on different oscillatory behaviors of the gear meshing impact and the engine ignition impact. To improve the accuracy of RSSD under interferences, the meshing frequency energy ratio (MF–ER) index is introduced into RSSD to adaptively choose the decomposition parameters. Before applying the RSSD method, the auto-regression (AR) model is used as a pre-whitening step to eliminate the normal gear meshing vibration, which improves the decomposition performance of RSSD. The effectiveness of the proposed AR-ORSSD (AR-based optimized RSSD) algorithm is tested using both simulated signals and measured vibration signals from an engine-gearbox system in a forklift. Comparisons were made with the RSSD algorithm based on a genetic algorithm. Experimental results indicate that the AR-ORSSD algorithm is superior at identifying gear vibration signals especially when under strong interferences.

Linking the modulation of gear mesh vibration in planetary gearboxes to manufacturing deviations

The gear mesh vibration caused by planetary geartrains is modulated. Small planetary gearboxes, commonly used in servo drives, are examined experimentally and numerically. The goal is to link the modulation of the gearbox vibration to the deviations from the ideal geometry caused by manufacturing and assembly. Operational modal analysis shows that, while the dynamical behavior of nominally identical gearboxes is very similar, their modulation is not. The modulation also strongly depends on the operating conditions, such as speed and torque. Therefore, the modulation is aggregated to a vibration signature. In the vibration signature, distinct features are present. These can be linked to the eccentricity of the gears using numerical multi-body simulation and correlation analysis.

An improved phenomenological model of vibrations for planetary gearboxes

Interpreting and understanding vibration characteristics are the cornerstone for health condition monitoring schemes of a planetary gearbox. Phenomenological modeling provides a concise and efficient mathematical description of sensor-related vibration measurements, thus allowing prior guidance for spectrum analysis to be relied on. In this paper, some overlooked problems during the modeling process in previous researches are pointed out and analyzed. Some discoveries are consequently obtained: First, the asymmetry of spectrum structure should be attributed to the magnitude randomness of gear meshing vibration rather than different phase angles of multiple-planet gears; Second, the basic frequency component to constitute a model, namely a product of the rotational frequency of a planet carrier and the number of planet gears, is far from sufficient to describe the actual vibrations; Finally, improper function the phases of multiple-planet gears will lose some sidebands that should have been. For these reasons, we map the phase variation of multiple-planet gears into the time-varying propagating distance, therefore, solving the neutralization phenomena of the frequency components. With consideration of the attenuation effect and random gear meshing magnitudes, an improved model is proposed to provide a more reasonable representation of the vibration behaviors, both for the dominant frequency components and structure. Simulation and experimental studies both demonstrate the higher fidelity and descriptive capability than the traditional models.

Dynamic characteristics for coal shearer cutting unit gearbox housing

Long wall mining is most widely used in coal mining of China, and coal shearer is the most important machine due to its direct role in cutting coal. Nevertheless, coal mining enterprises are suffering from faults of coal shearer, especially cutting unit gearbox housing (CUGH). Published dynamic studies on CUGH have not considered the excitation caused by gear meshing and complete machine vibration. Due to the apparent lack of experimental validation of these published papers, the dynamic response of CUGH is not convincing. In this study, dynamic behavior of CUGH is investigated both theoretically and experimentally for finding out failure mechanism and improving reliability. Complete machine vibration and gear meshing vibration are two excitation sources for CUGH, and vibration is transferred via articulated holes and bearing holes. Hence, complete machine dynamics model is established for obtaining force on articulated holes. Dynamics model of gear transmission system is established for obtaining force on bearing holes. Stochastic cutting forces model is established as external load of complete machine dynamics model. Dynamics response is calculated by finite element model established by ANSYS. A measurement system to capture three-dimensional vibratory motions under realistic working conditions of coal mines is implemented by National Energy Mining Equipment Laboratory of China. Direct comparisons between predicted and measured results are presented to demonstrate the accuracy of the proposed model in predicting three-dimensional vibrations of CUGH. Maximum deformation and stress positions of CUGH are determined, and the excitation sources are investigated.

Gear misalignment diagnosis using statistical features of vibration and airborne sound spectrums

Failure in gears, transmission shafts and drivetrains is very critical in machineries such as aircrafts and helicopters. Real time condition monitoring of these components, using predictive maintenance techniques is hence a proactive task. For effective power transmission and maximum service life, gears are required to remain in prefect alignment but this task is just beyond the bounds of possibility. These components are flexible, thus even if perfect alignment is achieved, random dynamic forces can cause shafts to bend causing gear misalignments. This paper investigates the change in energy levels and statistical parameters including Kurtosis and Skewness of gear mesh vibration and airborne sound signals when subjected to lateral and angular shaft misalignments. Novel regression models are proposed after validation that can be used to predict the degree and type of shaft misalignment, provided the relative change in signal RMS from an aligned condition to any misaligned condition is known.

Deep convolutional neural network based planet bearing fault classification

Condition monitoring and fault diagnosis of the planet bearing is key to operational reliability of the planetary gearbox, and also have remained challenging due to complex modulation phenomenon and strong planetary gear noise. As such, a new fault diagnosis strategy based on the synchrosqueezing transform (SST) and the deep convolutional neural network (DCNN) is proposed in this paper. Specifically, the envelope time-frequency representations (TFRs) of the vibration signals of the planetary gearbox are firstly calculated using the Hilbert transform and the SST. Next, a DCNN is constructed to learn the underlying features from the TFRs and then the fault types can be determined automatically. As its main contribution, the proposed method automatically recognizes the planet bearing fault type, which is free from artificially capturing fault characteristic frequencies in spectrum or time-frequency spectrum that contain many interference items, and effectively avoid missed diagnosis and misdiagnosis. In addition, it is also free from considering frequency band selection, which is difficult duo to the strong interferences of the gear meshing vibration. The analysis results of the planetary gearbox data demonstrate effectiveness of the proposed approach with a classification accuracy better than 98.3%.

Helicopter interior noise reduction using compounded periodic struts

This paper characterizes the performance of a novel compounded gearbox periodic strut on controlling the noise in a helicopter cabin through modelling, simulation and experimental research. The strut exhibits low transmissibility in the specified frequency ranges, called “stop bands”. Based on a certain helicopter model, a dynamic acoustic-structure coupled system is first built by using the finite element method and the transfer matrix method. Subsequently, according to the gear mesh vibration transmission path, analyses of the vibration and noise reduction characteristics are conducted. Compared with the plain strut, attenuations of both vibration and noise in excess of 60 dB are obtained in the simulations. On a specially designed helicopter platform, experimental research is conducted simultaneously on the two aspects of fuselage vibration and cabin noise. The effectiveness of the novel strut used for helicopter cabin broadband noise reduction is demonstrated by the agreement between the simulation and experimentation results, where the attenuations of measured fuselage vibration and cabin noise exceed the levels of 40 dB and 30 dB, respectively, in the frequency range from 300 to 2000 Hz.

A leakage-free resonance sparse decomposition technique for bearing fault detection in gearboxes

Most of rotating machinery deficiencies are related to defects in rolling element bearings. Reliable bearing fault detection still remains a challenging task, especially for bearings in gearboxes as bearing-defect-related features are nonstationary and modulated by gear mesh vibration. A new leakage-free resonance sparse decomposition (LRSD) technique is proposed in this paper for early bearing fault detection of gearboxes. In the proposed LRSD technique, a leakage-free filter is suggested to remove strong gear mesh and shaft running signatures. A kurtosis and cosine distance measure is suggested to select appropriate redundancy r and quality factor Q. The signal residual is processed by signal sparse decomposition for highpass and lowpass resonance analysis to extract representative features for bearing fault detection. The effectiveness of the proposed technique is verified by a succession of experimental tests corresponding to different gearbox and bearing conditions.

Real-Time Order Tracking of Gear Mesh Vibration in High Speed Planetary Gearboxes

Possible approaches to real-time order tracking are discussed. Two methods for real-time order tracking are developed and validated experimentally for the entire audible spectrum. An adaptive heterodyne filter bank is compared to a direct integral transform. The performance of both methods is adequate for usage in an active vibration control (AVC) algorithm. Vold-Kalman filters are not suitable for AVC. The vibration data of three different planetary gearboxes is analyzed using order tracking. While some of the existing research could be reproduced, the data contradicts statements made by several authors. Lastly, the architecture of a novel AVC algorithm is sketched out.

Design and analysis of herringbone gear with sixth-order transmission error based on meshing vibration optimization

To reduce the herringbone gear transmission vibration and noise, an optimization design method about the meshing vibration of herringbone gear is provided with a controllable sixth-order polynomial function of transmission error. First, the polynomial coefficients of sixth-order polynomial function of transmission error curves can be determined by optimizing the aim at minimum root mean square value of herringbone gear meshing vibration acceleration based on loaded tooth contact analysis method and herringbone gear vibration model. Second, because of the existence of second-order frequency factors in the amplitude of loaded transmission error, the root mean square value of meshing vibration acceleration under the optimization of amplitude of loaded transmission error is worse than the value under the optimization of meshing vibration acceleration in resonant frequency. Third, a numerical simulation of example based on herringbone gear with different order transmission errors is performed, which proves tha...

Vibration Characteristics for Planetary Geared Systems with Plastic Gears

A torsional dynamic model and testing model for planetary geared systems are established to study the effects on its vibration characteristics as substituting plastic gears for steel ones successively. The dynamic model is solved by using variable step Runge-Kutta method and the vibration testing experiments for four kinds of combined planetary geared systems are carried out under different rotation speed and load torque. The numerical and experimental results show that the high frequency spectra are suppressed effectively as substituting plastic gears for steel ones. The gear mesh dynamic load and vibration intensity caused by the meshing fundamental frequency and side-frequency reduce markedly when the plastic ring and planet gear substitute for steel ones together. The numerical simulations have a better consistency with the experimental results, which verifies the correctness of the conclusions.