Gear Mesh Vibration Research Articles

Effect of Gear Installation Flatness in Main Reducer on Gear Mesh Vibration Based on <i>A</i><i>dams</i> Simulation

This paper takes spiral bevel gear installation planes of a main reducer in a rear axle of a certain car as the research object, using ug to establish three-dimensional model of the main reducer assembly, applies adams simulation and the quantitative and qualitative method to analyze the effect law of the spiral bevel gear installation flatness error on gear mesh vibration, obtains the reasonable area of gear installation flatness error , it provides the reference for parameter design and installation of the spiral bevel gear in the main reducer.

Statistical modeling of gear vibration signals and its application to detecting and diagnosing gear faults

A statistical model of gear mesh vibration signals is proposed in this paper. It is seen that the sample mean is first removed from the gear mesh vibration signal, and the remaining signal components are approximated with a set of sinusoidal functions in the signal model. The signal model parameters can be estimated by the least-square method and the optimal model order is determined based on the Akaike Information Criterion (AIC) or the modified Bayesian Information Criterion (BIC). Within the framework of the signal model, to perform the gear fault diagnosis and analysis, the residual signal between the synchronous signal average and the output of the optimal signal model is further computed and the corresponding kurtosis values are employed for efficiently detecting the gear tooth fault.

Failure Detection of Plastic Gears Based on a Comparison of Fourier Coefficients of a Gear Mesh Vibration Model by Rectangle Pulse Train and Frequency Analysis of Acceleration Response

Failure Detection of Plastic Gears Based on a Comparison of Fourier Coefficients of a Gear Mesh Vibration Model by Rectangle Pulse Train and Frequency Analysis of Acceleration Response

Optimal sinusoidal modelling of gear mesh vibration signals for gear diagnosis and prognosis

In this paper, the synchronous signal average of gear mesh vibration signals is modelled with the multiple modulated sinusoidal representations. The signal model parameters are optimised against the measured signal averages by using the batch learning of the least squares technique. With the optimal signal model, all components of a gear mesh vibration signal, including the amplitude modulations, the phase modulations and the impulse vibration component induced by gear tooth cracking, are identified and analysed with insight of the gear tooth crack development and propagation. In particular, the energy distribution of the impulse vibration signal, extracted from the optimal signal model, provides sufficient information for monitoring and diagnosing the evolution of the tooth cracking process, leading to the prognosis of gear tooth cracking. The new methodologies for gear mesh signal modelling and the diagnosis of the gear tooth fault development and propagation are validated with a set of rig test data, which has shown excellent performance.

Noise resistant time frequency analysis and application in fault diagnosis of rolling element bearings

Rolling element bearings are frequently used in rotary machinery, but they are also fragile mechanical parts. Hence, exact condition monitoring and fault diagnosis for them plays an important role in ensuring machinery's reliable running. Timely diagnosis of early bearing faults is desirable, but the early fault signatures are easily submerged in noise.In this paper, Wigner–Ville spectrum based on cyclic spectral density (CSWVS for a brief notation) is studied, which is able to represent the cyclostationary signals while reducing the masking effect of additive stationary noise. Both simulations and experiments show that CSWVS is a noise resistant time frequency analysis technique for extracting bearing fault patterns, when bearing signals are under influences of random noise and gear vibrations. The 3-D feature of the CSWVS is proved useful in extracting bearing fault pattern from gearbox vibration signals, where bearing signals are affected by gear meshing vibration and noise. Besides, CSWVS utilizes the second order cyclostationary property of the vibration signals produced by bearing distributed fault, and clearly extracts its fault features, which cannot be extracted by envelope analysis.To quantitatively describe the extent of bearing fault, Renyi information encoded in the time frequency diagram of CSWVS is studied. It is shown to be a more sensitive index to reflect bearing performance degradation, compared with the spectral entropy (SE), squared envelope spectrum entropy (SESE) and Renyi informations for WVD, PWVD, especially when SNR is low.

Vibration Signal Processing for Gear Fault Diagnosis Based on Empirical Mode Decomposition and Nonlinear Blind Source Separation

Gear failures happen frequently in the gear mechanisms, and an unexpected serious gear fault may cause severe damage on the machinery. Hence, precise gear fault detection at the early stage is imperative to ensure the normal operation of the machinery. Independent component analysis (ICA) has been paid more and more attention for its powerful ability of separating the useful vibration source from the multi-sensor observations to enhance the fault feature extraction. This is the so called blind source separation (BSS) procedure. However, the popular ICA model may suffer from two limitations. One is the linear mixture assumption, and the other is the lack of sensor channels. Up to now, only limited research considered the nonlinear ICA model in the field of mechanic fault diagnosis, and techniques for the situation where the number of sensor channels is less than the number of independent sources for gear defect detection are scarce. In order to extract the useful source involved with the gear fault characteristics in single-channel vibration signal processing, this work presents a new method based on the empirical mode decomposition (EMD) and nonlinear ICA. The EMD was firstly employed to decompose the vibration signal into a number of intrinsic mode functions (IMFs), and then these IMFs were taken as the multi-channel observations. The post-nonlinear (PNL) ICA model based on the radial basis function (RBF) neural network was applied to the nonlinear BSS procedure on the IMFs. The experimental vibration data acquired from the gear fault test-bed were processed for the validation of the proposed method. The nonlinear ICA method has been compared with the linear ICA and non-ICA based approaches. The analysis results show that the sensitive characteristics of the gear meshing vibration can be separated from the single channel measurement by the proposed method, and the fault diagnosis precision can be enhanced significantly. The detection rate can be increased by 3.75% or better when the ICA based preprocessing is carried out, and the proposed nonlinear ICA outperforms the linear ICA detection model.

Pseudo analytical solution to time periodic stiffness systems

An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudo-closed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange—Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.

Generation Mechanism of Sidebands about Gear Mesh Vibration Considering Amplitudes Asymmetricity

Sidebands of mesh harmonic frequencies are considerable components in gear vibration spectrum. In this study, generation mechanism and characteristics of sidebands are investigated based on a single-degree-of-freedom vibration model of a cylindrical gear pair. Time-varying mesh stiffness and contribution of tooth surface form are formulated in the model. In addition to mesh harmonic components, the first order component of gear rotation is incorporated into each of the time-varying mesh stiffness and the tooth surface form as the effect of gear eccentricity. This model presents that the product of mesh harmonics and low order component of gear rotation frequency produces sidebands on either side of the mesh frequency. Asymmetrical property of sideband amplitudes about mesh frequency is dependent on frequency response function of gear vibration system. Vibration response curves of the sidebands have pseudo resonance peak. These sideband characteristics are verified by comparing simulation result of the gear model with experiment using a single-stage helical gearing.

3112 歯車のかみあい振動における側帯波の特徴把握 : 系がもつ非線形性について(S40-2 第14回卒業研究コンテスト(2),21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

The aim of this work is to investigate the characteristics of sidebands of gear mesh vibration. Because the sidebands of mesh harmonics occur owing to pitch error and gear eccentricity, they are synchronous with the rotation of the gear shaft. The dynamic relations between the sidebands and the gear errors are represented by the single-degree-of-freedom vibration model. Analytical result and experimental result show that the amplitude of the sideband rises to local maximum value when the mesh frequency equal to the natural frequency of the gear pair. This sideband characteristic is due to nonlinearity of the gear vibration, and different from that of the mesh harmonics.

1210 遠心振子式動吸振器による歯車装置の振動低減に関する基礎的研究 : 2段減速機への適用(OS1-3 振動(1))

In this report, authors propose centrifugal vibration absorber to reduce gear mesh vibration due to input shaft pinion. Input shaft of transmission is often cantilever shaft. Shaft bending brings misaligned mesh and high level vibration. Centrifugal vibration absorber is set on input shaft on two stage gear system, and its efficiency is verified experimentaly measuring each shaft rotational vibration.

Variable amplitude Fourier series with its application in gearbox diagnosis—Part I: Principle and simulation

Vibration signal analysis has been an important method in the detection and diagnosis of gearbox faults. The vibration signals measured from a gearbox are complex multi-component signals, which include tooth meshing vibration, gear shaft rotating vibration and gearbox resonance vibrations. They are often non-stationary and time-varying. When conducting gearbox failure detection, it is not simple to interpret the results coming from traditional Fourier analysis; other signal processing methods such as short-time Fourier series (FS) and wavelet analysis are not always sufficient to exactly extract the desired frequency component for a certain gear. In this paper, a novel signal analysis method, which we named the variable amplitude FS (VAFS), is proposed. This method is based on an improvement of the traditional FS analysis and comes from the analysis of the gear meshing vibration signal model. In part I, the principle of the VAFS is introduced, and then an algorithm for calculating VAFS coefficients is presented. The performance of the VAFS is compared with that of a wavelet transform in the analysis of a numerically generated noisy chirp signal. In part II, the VAFS method is applied in the analysis of the vibration signal of a truck gearbox containing a gear in good, cracked and broken condition, and the results are compared with that of the wavelet analysis.

Variable amplitude Fourier series with its application in gearbox diagnosis—Part II: Experiment and application

Vibration signal analysis has been an important method in the detection and diagnosis of gearbox faults. The vibration signals measured from a gearbox are complex multi-component signals, which include tooth meshing vibration, gear shaft rotating vibration and gearbox resonance vibrations. They are often non-stationary and time varying. When conducting gearbox failure detection, it is not simple to interpret the results coming from traditional Fourier analysis; other signal processing methods such as short-time Fourier series and wavelet analysis are not always sufficient to exactly extract the desired frequency component for a certain gear. In this paper, a novel signal analysis method, which we named the variable amplitude Fourier series (VAFS), is proposed. This method is based on an improvement of the traditional Fourier series analysis and comes from the analysis of the gear meshing vibration signal model. In part I, the principle of the VAFS is introduced, and then an algorithm for calculating VAFS coefficients is presented. The performance of the VAFS is compared with that of a wavelet transform in the analysis of a numerically generated noisy chirp signal. In part II, the VAFS method is applied in the analysis of the vibration signal of a truck gearbox containing a gear in good, cracked and broken condition, and the results are compared with that of the wavelet analysis.

はすば歯車軸の振動挙動に関する実験研究(G11-1 軸受,歯車,G11 機素潤滑設計部門)

Gear noise has been becoming a great influence on the comfortable driving, also lightweight transmission is required. Therefore, it is necessary to clarify the physical mechanism of each resonance peak by actual measurement. In this research, a helical gearing apparatus is developed to measure the 3-dimentional vibration of gear and gear shaft. As the result, gear mesh vibration and elastic bending vibration of gear shaft resound on low rotational speed and it causes some characteristic peaks of transverse vibration. Especially, if the drive and driven gears have different shape and weight, both gears vibrate simultaneously along Line of action (LOA), however, each gear vibrates individually at right angles to LOA.

Passive reduction of gear mesh vibration using a periodic drive shaft

In this paper, a passive approach to reduce transmitted vibration generated by gear mesh contact dynamics is presented. The approach utilizes the property of periodic structural components that creates stop band and pass band regions in the frequency spectra. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics and sub-harmonics of the gear mesh frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric variations are considered and each cell is assumed to be identical. A periodic shaft is designed and machined in order to reduce transmitted vibration of a pair of spur gears. Analytical and experimental results indicate that transmitted vibrations from gear mesh contact to the bearing supports are reduced at a variety of operational speeds under static torque preload.

Experimental investigation of the effect of lead errors on helical gear and bearing vibration transmission characteristics

The characteristics of gear meshing vibration undesgo change as the vibration is transmitted from the gear to the housing. Therefore, vibration transmission characteristics of helical gear systems must be understood before the effective methods of reducing gear noise can be found. In this work, using a helical gear with different lead errors, the gear vibration in the rotational direction and the bearing vibration are measured. The frequency characteristics of gear and bearing vibration are investigated and a comparson is also provided.

Multiobjective Optimal Design of Cylindrical Gear Pairs for the Reduction of Gear Size and Meshing Vibration.

In the design of gear pairs, the designer has to make design trade-off between the geometrical volume and the meshing vibration. It is generally known from experience that the two objectives show conflicting tendency. In this paper, the authors demonstrate the analysis results of the relation between the geometrical volume and the vibration of a gear pair, and propose a design method for cylindrical gear pairs to balance the conflicting objectives by using a goal programming formulation. The design method reduces both the geometrical volume and the meshing vibration of cylindrical gear pairs while satisfying strength and geometric constraints. The validity of the method will be shown through the design results of the four cases of design speeds and the redesign of a helical gear pair currently being used in elevator reduction drive.

Model-based condition index for tracking gear wear and fatigue damage

This paper describes a method that utilizes linear dynamic modeling to track the development of gear wear and tooth fatigue crack. A model is created from the gear meshing vibration signal when the gear is new and then the model is applied to vibration data taken over the gear's lifetime to calculate the prediction error. This error is expected to increase over the lifetime as the evolvement of the faults alters meshing stiffness. The method is evaluated by experimental data collected in two tests where gear wear and gear tooth fatigue cracks grew over time. It was found that the method gave more consistent trend when compared with state-of-the-art.

Bifurcations of Higher Subharmonics and Chaos in a Forced Vibratory System with an Asymmetrical Restoring Force

In this paper, we describe the behavioral characteristics of a nonlinear oscillator derived from gear-meshing vibration, which exhibits various successive bifurcations ending in chaos. There are two types of sudden change from a chaotic to a periodic attractor, one of which is called "hysteresis". In a period-doubling bifurcation, a heteroclinic connection between the outset of an inversely unstable fixed point of period 2n and the inset of an inversely unstable fixed point of period n is necessary to generate an n-band chaotic attractor. If a directly unstable fixed point exists in the vicinity of any band attractor and the attractor collides with the inset of the directly unstable fixed point, the attractor expands due to an "interior catastrophe", and transforms into a one-band attractor. In the bifurcation diagram, periodic subharmonic oscillations appear discontinuously as "windows" belonging to the same "family". These "families" are divided into two types : type-I, in which fold bifurcation occurs repeatedly, and type-II, in which fold bifurcation occurs only at both ends of the solution curve. Depending upon whether or not both of the chaotic attractors exist in the same area of the phase plane, either before or after the bifurcation, the discontinuous bifurcation of the chaotic attractor is referred to as an "interior catastrophe" or "hysteresis", respectively.

Bifurcation of Higher Subharmonics and Chaos in Forced Vibratory System with Asymmetrical Restoring Force. 2nd Report. Bifurcation of Periodic Attractors, Window, Hysteresis and Interior Catastrophe above the First Resonance.

In this paper, a nonlinear oscillator derived from the gear meshing vibration is investigated, which exhibits successive different bifurcations ending in chaos above the first resonance. These bifurcations are examined in detail using bifurcation diagrams, Lyapunov exponents, winding numbers, invariant curves, and Poincare maps. In the bifurcation diagram, periodic subharmonic oscillations appearing nonsuccessively as a "window" belong to the same "families", which are divided into two kinds : type- I, in which fold bifurcation occurs iteratively (multifolding) in the family, and type- II, in which fold bifurcation occurs only at both ends of the family. Depending on whether both of the chaotic attractors before/after the bifurcation exist in the same area on the phase plane or not, the chaotic attractor bifurcates discontinuously according to "hysteresis" or "interior catastrophe". In the case that a 2n-band attractor transforms into a 2n-1-band attractor without fold bifurcated directly unstable fixed points, and a periodic directly unstable fixed point exists very close to an inset of a 2n-1-periodic inversely unstable fixed point, the unstable 2n-1-band attractor is suddenly transformed into a one-band attractor upon touching an inset of the periodic directly unstable fixed point.

Early detection of gear failure by vibration analysis i. calculation of the time-frequency distribution

The application of the spectrogram to the calculation of the time-frequency distribution of a gear vibration signal is examined. The spectrogram represents the energy distribution of the signal over the frequency domain at every instant of time. The selection of the window function is discussed, and it is shown that the Gaussian function is well suited to the calculation of the energy distribution, giving a representation which is free from ripple and easy to interpret. The application of the energy distribution is demonstrated using numerically-generated test signals and the experimentally-measured time domain average of the gear meshing vibration from an industrial gearbox. The results suggest that the spectrogram may provide a powerful tool for the early detection of local gear damage.