Mesh Harmonics Research Articles

Vibration analysis of planet gear bore-rim failure using enhanced planet time synchronous averaging

It is a worldwide challenge to detect planet gear bore-rim cracking using vibration data analytics, especially for large helicopters like the Airbus Super Puma that has experienced two fatal accidents since 2009 due to planet gear bore-rim cracking. For helicopter safety, it is of vital importance to equip helicopter vibration health monitoring systems with the capability of detecting and monitoring the progression of planet gear bore-rim cracking. When a crack reaches sufficient size in the rim of the gear, the weakening stiffness caused by the crack allows the planet gear teeth near the crack to distort as they come into and out of mesh, resulting in vibration impacts. A key challenge for detecting a planet gear bore-rim crack lies in isolating these impacts from the dominating gear mesh harmonics. In this paper, we propose a method of vibration data analytics based on enhanced planet gear time synchronous averaging (EP-TSA). The method takes advantage of visualizing the impacts from planet-ring and planet-sun gear meshes over the planet-ring hunting tooth period of the planetary gear system. We firstly process the raw vibration signal using time-synchronous averaging with respect to the relative rotation of the planet gear over a number of hunting tooth periods. The method employs a novel resampling scheme, termed boosted synchronous resampling scheme (BSRS), which facilitates simultaneous removal of multiple shaft and gear mesh harmonics and their intermodulation components using the spectrum of the averaged signal in order to derive a residual signal. By construction, the BSRS facilitates three-dimensional (3-D) plotting of the squared envelope of the residual signal, comprising multiple individual revolutions of the planet gear over the hunting tooth period. With crack-induced impacts visualized in 3-D, we can identify those planet gear revolutions where the crack-induced impacts are in close proximity to the vibration transducer to obtain a final feature signal reflecting the characteristics of the bore-rim cracking. We call the final feature signal the enhanced planet residual signals (EPRS), which is those individual residual signals at the selected planet gear revolutions with the largest kurtoses above a certain threshold. Where possible we should look at multiple planet gear revolutions to reinforce the detection of vibration impacts. Lastly, we confirm the detection of planet gear bore-rim cracking by the consistent pattern of two spikes in each planet revolution that are associated with the planet-ring and planet-sun gear meshes. The method is validated using vibration data generated from a small industrial planetary gearbox with simulated cracks inserted in the bore-rim from one side of a planet gear. The results show that the BSRS can be very effective in removing multiple sets of shaft harmonics and their intermodulation sidebands. We have demonstrated that the visualization tool can provide strong evidence of the crack-induced impacts. In comparison to other methods our results have shown that we can detect the planet gear bore-rim crack more effectively using the enhanced planet time synchronous averaging method.

Experimental Analysis of an Active Vibration Frequency Control in Gearbox

Aiming at the vibrations of the multistage gear transmission system aroused by the gear meshing excitation, a novel active vibration control structure with built‐in piezoelectric actuators (PZT) was established. The active control forces generated by the PZT were transmitted to the shafts through the additional supporting bearings. In addition, an adaptive fuzzy proportion integration differentiation (AFPID) control algorithm was proposed as the primary control algorithm to reduce the transverse vibrations of the gear shaft. According to the control law of PID parameters, a fuzzy inference module was designed to adaptively adjust the PID parameters to obtain the optimal control effect. An experimental platform was set up to verify the control effect of the algorithm. The experiments performed show 10 dB reduction in housing vibrations at certain targeted mesh harmonics over a range of operating speeds.

Fault features analysis of a compound planetary gear set with damaged planet gears

The fault properties of compound planetary gear set are much more complicated than the simple planetary gear set. A damaged planet will induce two periodic transient impulses in the raw signals and generates modulation sidebands around the mesh harmonics. This paper aims to investigate the fault properties of a compound planetary gear set in damaged planet conditions. A dynamic model is proposed to simulate the vibration signals. The time interval between the fault-induced close impulses in the time domain is used as a significant feature to locate the faulty planet. Considering the phase relations, the time-varying mesh stiffness is obtained. Then, the fault properties are demonstrated in the simulation, and the theoretical derivations are experimentally verified.

Stereo music visualization through manifold harmonics

Music visualizations are nowadays included with virtually any media player. They usually rely on harmonic analysis of each sound channel, which automatically generate parameters for procedural image generation. However, only few music visualizations make use of 3d shapes. This paper proposes to use spectral mesh processing techniques, here manifold harmonics, to produce 3d stereo music visualization. The images are generated from 3d models by deforming an initial shape, mapping the sound frequencies to the mesh harmonics. A symmetry criterion is introduced to enhance the stereo effects on the deformed shape. A concise representation of the frequency mapping is proposed to allow for an animated gallery interface with genetic reproduction. Such galleries let the user quickly navigate between visual effects. Rendering such animated galleries in real time is a challenging task, since it requires computing and rendering the deformed shapes at a very high rate. This paper introduces a direct GPU implementation of manifold harmonics filters, which allows the displaying of the animated galleries.

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.

Novel adaptation of the demodulation technology for gear damage detection to variable amplitudes of mesh harmonics

In this paper, a novel adaptive demodulation technique including a new diagnostic feature is proposed for gear diagnosis in conditions of variable amplitudes of the mesh harmonics. This vibration technique employs the time synchronous average (TSA) of vibration signals. The new adaptive diagnostic feature is defined as the ratio of the sum of the sideband components of the envelope spectrum of a mesh harmonic to the measured power of the mesh harmonic. The proposed adaptation of the technique is justified theoretically and experimentally by the high level of the positive covariance between amplitudes of the mesh harmonics and the sidebands in conditions of variable amplitudes of the mesh harmonics. It is shown that the adaptive demodulation technique preserves effectiveness of local fault detection of gears operating in conditions of variable mesh amplitudes.

Construction of Semianalytical Solutions to Spur Gear Dynamics Given Periodic Mesh Stiffness and Sliding Friction Functions

Gear dynamic models with time-varying mesh stiffness, viscous mesh damping, and sliding friction forces and moments lead to complex periodic differential equations. For example, the multiplicative effect generates higher mesh harmonics. In prior studies, time-domain integration and fast Fourier transform analysis have been utilized, but these methods are computationally sensitive. Therefore, semianalytical single- and multiterm harmonic balance methods are developed for an efficient construction of the frequency responses. First, an analytical single-degree-of-freedom, linear time-varying system model is developed for a spur gear pair in terms of the dynamic transmission error. Harmonic solutions are then derived and validated by comparing with numerical integration results. Next, harmonic solutions are extended to a six-degree-of-freedom system model for the prediction of (normal) mesh loads, friction forces, and pinion/gear displacements (in both line-of-action and off-line-of-action directions). Semianalytical predictions compare well with numerical simulations under nonresonant conditions and provide insights into the interaction between sliding friction and mesh stiffness.

Optimal filtering of gear signals for early damage detection based on the spectral kurtosis

In this paper, we propose a methodology for the enhancement of small transients in gear vibration signals in order to detect local tooth faults, such as pitting, at an early stage of damage. We propose to apply the optimal denoising (Wiener) filter based on the spectral kurtosis (SK). The originality is to estimate and apply this filter to the gear residual signal, as classically obtained after removing the mesh harmonics from the time synchronous average (TSA). This presents several advantages over the direct estimation from the raw vibration signal: improved signal/noise ratio, reduced interferences from other stages of the gearbox and easier detection of excited structural resonance(s) within the range of the mesh harmonic components. From the SK-based filtered residual signal, called SK-residual, we define the local power as the smoothed squared envelope, which reflects both the energy and the degree of non-stationarity of the fault-induced transients. The methodology is then applied to an industrial case and shows the possibility of detection of relatively small tooth surface pitting (less than 10%) in a two-stage helical reduction gearbox. The adjustment of the resolution for the SK estimation appears to be optimal when the length of the analysis window is approximately matched with the mesh period of the gear. The proposed approach is also compared to an inverse filtering (blind deconvolution) approach. However, the latter turns out to be more unstable and sensitive to noise and shows a lower degree of separation, quantified by the Fisher criterion, between the estimated diagnostic features in the pitted and unpitted cases. Thus, the proposed optimal filtering methodology based on the SK appears to be well adapted for the early detection of local tooth damage in gears.

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.

Experimental active vibration control of gear mesh harmonics in a power recirculationgearbox system using a piezoelectric stack actuator

An experimental study of an active shaft transverse vibration control system forsuppressing gear mesh vibratory response due to transmission error excitation in a highpower density gearbox is presented. The proposed active control concept employsa piezoelectric stack actuator to deliver the control force through a secondarybearing. A versatile test stand that includes a closed-loop, power recirculating,dual-gearbox set-up capable of high load transfer is specially designed for this work. Theunderlying controller for computing the actuation signal is based on a modifiedfiltered-x LMS algorithm with a robust frequency estimation technique. In order to avoid thecommon out-of-band overshoot problem, an integrated adaptive linear enhancer is alsoapplied. Both single mesh frequency and multi-harmonic control cases are examined toevaluate the performance of the active control system. Additionally, the impact of theadaptive linear enhancer order as well as the controller adaptation step size on activecontrol performance is evaluated. The experiments performed show more than 10 dBreduction in housing vibrations at certain targeted mesh harmonics over a range ofoperating speeds.

Experimental analysis of an active vibration control system for gearboxes

An internal active vibration control system for suppressing gearbox housing vibrations dueto gear transmission error excitation is developed and evaluated experimentally. Theapproach is based on an active shaft transverse vibration control concept that resideswithin the gearbox. The system contains a piezoelectric stack actuator for applyingcontrol forces to the shaft via a secondary rolling element bearing. An enhancedfiltered-x least mean squares control algorithm with frequency estimation capability is employed togenerate the appropriate actuation signal. The experimental results show up to about 20 dBreduction in the vibration levels of the first two mesh harmonics at the control positions onthe housing structure for a range of operating speeds. The experimental studiesalso indicate that, under certain narrow operating conditions, the vibrations atsome non-control positions may be amplified slightly due possibly to the effect ofunmodeled dynamics. In spite of this limitation, the proposed active vibration controlapproach is quite promising for reducing gear vibration and ultimately gear noise.

Linear dynamic analysis of multi-mesh transmissions containing external, rigid gears

This paper extends the multi-body dynamics modeling strategy for a gear pair [6] to multi-mesh transmissions with external, fixed center, helical or spur gears. Each gear is modeled as a rigid body with six degrees of freedom. A multi-dimensional, position-dependent formulation is used to describe the gear mesh stiffness which is assumed to be distributed along the line of action. A simplified model of the shaft-bearing subsystems is included since the focus of this study is on the gear dynamics. Excitation to the system is considered in the form of either external torque pulsation or internal static transmission error. The governing equations are linearized to yield a formulation with position or time-varying coefficients (LTV). Subsequently, three examples of linearized time-invariant (LTI) transmission systems are solved, and eigensolution predictions of the multi-body dynamics model compare very well with finite element calculations. Then the periodic response of a non-unity gear pair system is studied in depth. New results including a comparison between LTI and LTV models are presented. It has been demonstrated that both time and frequency domain solutions can be efficiently and accurately constructed by using the multi-term harmonic balance method, provided that several shaft and gear mesh harmonics are included.