Article

Analysis of gear rattle by means of a wavelet-based signal processing procedure

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Abstract

In the paper a wavelet-based signals processing technique for the experimental detection of the gear rattle produced by the teeth impacts in lightly loaded gears is proposed. The Discrete Wavelet Transform is used to decompose the signal of the angular relative motion of an helical gear pair, and the wavelet decomposition details are adopted to analyze the dynamic behavior under rattle condition. In particular the procedure permits to evaluate the quality of the impacts between the teeth, discriminating between the two different sides of teeth contacts when there is a double-sided rattle condition. This technique enables, moreover, to define new indices for metrics of gear rattle especially useful in order to conduct comparisons for different operative conditions. Some examples of application of the proposed technique are reported in the paper adopting experimental signals acquired by two high resolution incremental encoders on a specific gear pair test rig. The experimental investigations regard comparative analyses with respect to the speed fluctuations amplitude, the rattle frequency and the lubrication regime.

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... In 2013, Prasad J. S. et al. reduced gear rattle noises in a passenger compartment by increasing clutch hysteresis [6]. Brancati R. et al. studied on the relationship between the speed fluctuation, the excitation frequency, the lubrication condition and the dynamic characteristics of the gear on the special test bench [7]. Rong Guo et al. discussed the effect of determination of gear rattle noise and the influence of torsional stiffness, hysteresis damping, viscous damping, stiffness transition node, damping coefficient of the active and passive gears, moment of inertia, flywheel speed and the amplitude of fluctuation of angular acceleration on gear rattle [2]. ...
... In order to verify whether multi-stage torsional vibration damper has a better effect than the traditional single-stage torsional vibration damper in terms of attenuating the larger fluctuation of the angular acceleration, the test was conducted on the angular acceleration of input shaft in transmission in the passenger car which equipped with traditional single-stage torsional vibration damper and double-stage torsional vibration damper [7,8]. Then conditions that produce obvious gear rattle noise for testing were chosen, such as 2nd gear acceleration condition, 2nd gear coasting condition, 3rd gear coasting condition, 4th gear coasting condition. ...
Article
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The gear rattle noise of automobile transmission, which belongs to broadband noise, tends to attract the driver’s increasing attention. This paper performs a test on the noise, vibration and harshness (NVH) performance of power train in a passenger car. The results of the test show that the angular acceleration of the input shaft in the transmission increases with the increase of the angular acceleration of the flywheel, and excessive fluctuations of angular acceleration lead to the generation of the gear rattle in transmission. In this paper, a mathematic model of torsional vibration under the working conditions of acceleration, constant speed and deceleration has been established by taking a pair of helical gears as an example. The solving model of the mathematic model is set up by Matlab/Simulink and numerical solution has been solved. The theoretical analyses show that the ability of the traditional single-stage torsional vibration damper to attenuate fluctuations of angular acceleration is limited, while the multi-stage torsional vibration damper can attenuate larger fluctuations of angular acceleration, and the power train can provide good comfort and low fuel consumption. The experimental results in this paper are in accordance with above theories. Dynamic model of torsional direction of helical gears built in this paper is of great significance to the analysis of dynamic characteristics of gears. The multi-stage torsional vibration damper proposed in this paper can attenuate larger fluctuations of angular acceleration effectively, which plays an important role in controlling gear rattles, meanwhile it can enhance the riding comfort of a vehicle and reduce fuel consumption.
... The noise is called as gear-rattling when the transmission is in neutral, and as gear-clattering when the gear is engaged under power [8][9][10][11]. Gear rattle may occur in the teeth of the unloaded or light-loaded gear pairs because of the presence of backlash [8,9,12,13]. There are many factors affecting gear rattle. ...
Article
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Gear rattle induced by backlash between meshing gears results in excessive vibration and noise in many gear systems. A dynamic model of a light-loaded spur gear pair with non-linear damping under no lubrication condition is presented in this paper. Unlike previous models, the effect of backlash on damping is considered, so the damping is not linear. In order to illustrate the effect of non-linear damping on the dynamic response, the dynamic behaviors of gear system with non-linear damping (GSND) and linear damping (GSLD) under different impact status are compared by using the numerical integration method. The results show that the behavior of gear pair with non-linear damping is different from that with linear damping, and the impact vibration of GSND is much greater than GSLD under some conditions. The influences of parameters such as load ratio, load value, meshing stiffness, and damping ratio on the dynamic responses of GSND are also discussed, and some suggestions to reduce impact vibration of gear system are proposed. The results provide a theoretical basis for the design and manufacture of gear system.
... 29 About the analysis of the teeth relative motion, indices based on both Fourier and Wavelet transforms have been described. [30][31][32] In the present study, the analysis of the pinion acceleration during the impact phases is adopted as severity index of the phenomenon. This choice is justified by the fact that the proposed torsional vibration damper is fixed to the pinion shaft tending to minimize its accelerations. ...
Article
An innovative device consisting of a flywheel equipped with a torsional vibration damper, based on the magnetorheo-logical effect in elastomeric spring elements, is proposed in this paper. The feasibility study reports the dynamic behaviour of an automotive driveline equipped with the device aiming to explore the effectiveness of the damper in reducing the torsional oscillations of the flywheel, at low-speed regime, responsible for the vibro-acoustic phenomenon known as ''gear rattle''. The spring elements of the device are constituted by magneto-rheological elastomeric samples, interposed between the flywheel and the damper disk, working for shear strains. Their dynamical characteristics can be properly tuned by varying the magnetic field surrounding the springs in order to mitigate the forced vibration causes of gear tooth impacts. The good attitude of the device in mitigating the rattle phenomenon is demonstrated by comparing the results provided by a numerical drive line model, equipped with a ''monolithic'' flywheel, with those obtained by adopting the present innovative vibration damper. The angular accelerations, resulting from the collisions between the teeth during the operation under ''idle'' conditions at different angular speeds, are thus compared.
... As the increasing of requirement for automobile quality [1] , the transmission rattle noise becomes more and more important for NVH performance. Generally, two factors is significant to the transmission rattle [2] : the external excitation caused by the input speed and torque from the engine, and the internal incentive factors caused by the time-varying stiffness, damping, gear side clearance and mesh error. ...
Article
Full-text available
Based on the vibration dynamics modeling for the single stage gear of transmission system, this paper is to understand the mechanism of transmission rattle. The dynamic model response using MATLAB and Runge-Kutta algorithm is analyzed, and the ways for reducing the rattle noise of the automotive transmission is summarized.
... As the increasing of requirement for automobile quality [1], the transmission rattle noise becomes more and more important for NVH performance. Generally, two factors is significant to the transmission rattle [2]: the external excitation caused by the input speed and torque from the engine, and the internal incentive factors caused by the time-varying stiffness, damping, gear side clearance and mesh error. ...
Chapter
The paper reports the stages of development of an innovative torsional vibration damper employing magnetorheological elastomers as spring elements. Such device could be adopted for reducing torsional vibrations of a vehicle powertrain.
Chapter
In the paper an experimental technique for diagnosing anomalous gear operations, focused on the tribological conditions, is described and tested. The method evaluates vibrational data to find the teeth engagement discontinuity during the transmission due to different lubrication conditions. Lubrication in gears is of great importance because it reduces dissipative actions and temperature. In particular the study considers a “boundary” lubrication regime, i.e. a poor lubrication typical of gear tooth contacts without oil external feeding. The qualitative indexes adopted in the paper, based on a non-linear signal analysis, show a good sensitivity to different behaviors in the various operative conditions.
Article
This paper describes the feasibility analysis of a methodology based on the Hilbert transform in order to detect the gear rattle phenomenon of automotive transmissions. The technique adopts the Hilbert transform to analyze experimental signals of the relative angular motion of gears starting from high-resolution optical encoder measurements. By this procedure it is possible to evaluate the severity of impacts occurring between the teeth of unloaded gears, by examining the root mean square value of the signal. The Hilbert transform is largely adopted in the detection of gear defects, such as tooth cracks, but it has not yet been used to detect gear rattle. This feasibility study highlights the capability in discriminating between impacts occurring on the two different sides of the tooth. The method puts in evidence the influence of oil lubricant between the teeth in reducing the severity of the impacts, by comparing many experimental tests performed with two different oils for transmission gears. Moreover, in order to evaluate the reliability of the proposed methodology some comparisons are conducted with a metric based on the fast Fourier transform, often adopted in this field, to highlight the goodness and simplicity of the technique based on the Hilbert transform.
Chapter
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Chapter
The paper reports a feasibility study for the detection of automotive gear rattle induced by multi-harmonic excitation through the use of a wavelet multi-resolution analysis. The analysis adopts experimental data coming from a helical gear pair under unloaded conditions. The excitation of gear rattle is of periodic type with two harmonic components, which is similar to the excitation of an actual automotive I.C. engine. The dynamic behavior of the gear pair has been analyzed by varying the second order harmonic amplitude of the excitation, for two mean speed values. The analysis gives useful information to develop an index of performances based on the wavelet theory that could be adopted for comparative analyses with respect to the severity of the tooth impacts occurring during the rattle phenomenon.
Article
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Book
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox * Companion website for instructors and selected solutions and code available for students New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox Balances presentation of the mathematics with applications to signal processing.
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This paper describes a model for torsional vibration of automotive manual transmissions and its subsequent analysis. The model is developed for the purpose of analysis and prediction of gear rattles. Efforts have been made to include as many components of power train as possible and to study the rattle responses of all the speeds. Elements of the model include engine, clutch, flywheel, laden and unladen gears, and shafts. Numerical methods available in MATLAB for solving the ordinary differential equations are employed for the dynamic analysis. Results are presented to show the effectiveness of the modelling and analysis scheme. A software package has also been developed to build and analyse any power train model. The package was used to analyse the Daimler-Chrysler T350 transmission and the results are presented in the paper. It is shown that the gear rattle may exhibit three major modes of double-sided, single-sided or irregular impacts. A rattle index has been used to compare the rattle levels produced by different gear pairs. This could be very useful for the purpose of tuning the clutch for the best rattle noise reduction.
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To find an answer to the question ‘how to design low-noise manual automotive transmissions’, it is essential to look at numerous external and internal measures which have already been developed to reduce rattle and clatter proneness. Only very few have been used in mass production. The use of these measures depends not only on the degree of noise reduction achieved but also on the production engineering and economic parameters. The wear characteristics and the level of power loss and the intrinsic noise involved must also be taken into account. Each transmission system and each driveline system must be individually adapted from the large number of various possible solutions. This study focuses on of existing and new measures in the literature and some experimental results which were investigated at the University of Stuttgart Institute of Machine Components. The aim was to create an engineering design catalogue for low-rattle and -clatter manual automotive transmissions using the systematic measurements and the knowledge derived from experience.
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Chapter
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox * Companion website for instructors and selected solutions and code available for students New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox Balances presentation of the mathematics with applications to signal processing.
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This paper deals with gear condition monitoring based on vibration analysis techniques. The detection and diagnostic capability of some of the most effective techniques are discussed and compared on the basis of experimental results, concerning a gear pair affected by a fatigue crack. In particular, the results of new approaches based on time-frequency and cyclostationarity analysis are compared against those obtained by means of the well-accepted cepstrum analysis and time-synchronous average analysis. Moreover, the sensitivity to fault severity is assessed by considering two different depths of the crack. The effect of transducer location and processing options are also shown. In the case of the experimental results considered in this paper, the power cepstrum is practically insensitive to the crack evolution. Conversely, the spectral correlation density function is able to monitor the fault development and does not seem to be significantly influenced by the transducer position. Analysis techniques of the time-synchronous average, such as the ‘residual’ signal and the demodulation technique, are able to localise the damaged tooth; however, the sensitivity of the demodulation technique is strongly dependent on the proper choice of the filtering band and affected by the transducer location. The wavelet transform seems to be a good tool for crack detection; it is particularly effective if the residual part of the time-synchronous averaged signal is processed.
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The impulse response problem in a multi-degree-of-freedom torsional system with multiple clearances is examined with focus on the quantification of the source. This system is related to a vehicle driveline and a map of external transient torque excitations is defined within the operating range of an internal combustion engine. Nonlinear transient solutions are found numerically for the entire excitation map. Proposed metrics include a global metric that indicates the number and nature of impacts, metrics measured just before impact, the relative kinetic energy and relative acceleration of impacting bodies and metrics measured just after impact, initial torque rise, initial velocity rise, peak to peak acceleration and time-windowed mean-square acceleration. Phase plane analysis is applied to explain the differences between the magnitudes of impulses for impact types, illustrating that the relative acceleration between impacting bodies and the relative kinetic energy determine the impact severity. Analysis shows that the metrics measured after impact correlate well. Nonetheless, using numerical or experimental data sets for systems with multiple clearances, it is demonstrated that the windowed mean-square acceleration metric permits an ‘energy’ calculation with multiple impact events that could be either isolated or combined. Chief contributions of this research include better quantification and an understanding of impulsive sources that arise during rapid changes in external torque excitations.
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A method of detecting transients in mechanical systems by matching wavelets with associated signal is proposed, leading to a development of joint time–frequency–scale distribution. The three variables, the time, frequency and scale, have maximised the chance for finding similar signal segments from a system under inspection. The sensitivity is shown to be very high due to closer matching and better choice of wavelet shapes, which is essential for early fault detection and failure prevention. Fundamental types of wavelets are introduced based on the shapes of widely encountered system responses. A method of processing the three-dimensional image is suggested for interpreting the time–frequency–scale wavelet map, where the properties of the object patterns uncover the features of a signal source, so as to understand the defect and to indicate the condition of a diagnosed system. The joint distribution is demonstrated to be useful in detecting transients from different mechanical systems. Implementation and examples are discussed.
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The paper presents an application of the wavelet transform in machinery diagnostics. The theoretical background and some basic properties of the wavelet transform are given. The method is implemented and validated by a series of simulated numerical examples. Finally the method is applied to the detection of a damaged tooth in a spur gear. A fault detection algorithm is presented, based on a similarity analysis of patterns obtained from the modulus of the wavelet transform.
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The wavelet transform is used to represent all possible types of transients in vibration signals generated by faults in a gearbox. It is shown that the transform provides a powerful tool for condition monitoring and fault diagnosis. The vibration signal from a helicopter gearbox is used to demonstrate the application of the suggested wavelet by a simple computer algorithm. The major advantage of the wavelet transform for analyzing the signal is that it possesses multi-resolutions for localizing shirt-time components so that all possible types of gear faults can be displayed by a single time-scale distribution resulting from the transform.
Gearbox fault diagnosis using adaptive wavelet filter Application of the wavelet multi-resolution analysis and Hilbert transform for the prediction of gear tooth defects
  • J Lin
  • Mj Zuo
  • N Ouelaa
  • C Benchaabane
  • Laefer
Lin J, Zuo MJ (2003) Gearbox fault diagnosis using adaptive wavelet filter. Mech Syst Signal Process 17(6):1259–1269 Meccanica (2013) 48:1399–1413 1413 13. Djebala A, Ouelaa N, Benchaabane C, Laefer D (2012) Application of the wavelet multi-resolution analysis and Hilbert transform for the prediction of gear tooth defects. Meccanica 47(7):1601–1612
Gear rattler optimisation
  • F Sbarbati
  • C Grasso
  • M Martorelli
  • P Liccardo
  • L Tosato
  • M Uberti
  • M Malusardi
On the recognition of anomalies in gears by means of the discrete wavelet transform
  • E Rocca
  • R Russo
  • S Savino