| A transmission system plays a vital role in mechanical equipment.A gearbox is an essential part in a transmission system and it is of great significance to prolong its service life by diagnosing and prognosing the undergoing/potential failures through analyzing intrinsic characteristics of the gearbox.Attractor in Chaos theory has been accepted as a standard indicator to measure the development trend of a chaotic system towards a certain steady state.A gearbox system is a typical chaotic system and the vibration signals contain lots of information which can reflect characteristics of gearbox.Aiming at the lack of research on the chaotic characters of the gearbox,especially on the characteristics and evolution of chaotic attractors in high dimension,and the inner relationship between chaotic characteristics and faults is not explored in the feature extraction.Therefore,it is a new theoretical research perspective to investigate the chaotic characteristics of the system with chaotic attractors to reveal essential properties of different operating states of the gearbox.In order to reveal the intrinsic properties of the gearbox system,the phase space reconstruction theory were applied to make the one-dimensional vibration signal to the high dimension space which can reveal the implicit information of the single variable time series.Moreover,the trajectory of chaotic attractors,phase distribution and recursive features have been explored which are helpful to reveal the chaotic characteristics.Furthermore,the chaotic attractors characterizing of gearbox have been accomplished for feature extraction and fault identification.This thesis deeply studies the chaotic characteristics of the gearbox and fault diagnosis methods.The main contributions of this thesis are described as followings:First of all,experimental tests were carried out on the fault gearbox simulation rig.In order to study the chaotic characteristic of the gearbox,gear fault tests in different operation states were carried out.The time domain analysis and frequency domain analysis have been accomplished.It is found that the vibration signal contains lots of noise which have high similarity,and the mesh frequency and its harmonic components exist and a series of side frequency bands formed.The Wavelet analysis and Complete Ensemble Empirical Mode Decomposition with the Adaptive Noise method have adopted for noise reduction respectively.It is found that the high frequency components can be suppressed to some extent and the characteristics information of the original signal in the low frequency can be remained after the two methods processing.Compare to the Wavelet analysis,CEEMDAN method have more advantageous to eliminate the influence of environmental noise and helpful to reveal the inherent characteristic information which can provide the necessary and important experimental basis for fault identification and diagnostics.In order to reveal the chaotic characteristics of gearbox,the chaotic features of gearbox under different operating conditions are proved.The quantitative discriminant methods based on phase space reconstruction are introduced,which are Correlation dimension,Lyapunov index,Kolmogorov entropy.At the same time the qualitative discriminant method power spectrum is also been introduced.In order to verify the validity of these four methods,the Lorenz chaotic system have been proved.Then the gearbox under different operation has been verified.It is found that the correlation dimension is fractal,the maximum Lynapunv index and Kolmogorov entropy are greater than zero,the power spectrum have continuous broadband spectrum.In order to explore the spacial distribution characteristics of the gearbox,Firstly,chaotic attractors with different running states of gears were constructed,and the influence of embedding dimension and delay time were discussed.Secondly the phase trajectory map and three-dimensional histogram of phase points were used to present the morphology and structure of gearbox chaotic attractors in three-dimensional space.Thirdly The phase point distribution and spatial structure of gearbox chaotic attractors were characterized qualitatively.Finally the quantitative parameters such as correlation dimension,inclusion sphere radius,the number of boxes and the maximum value of phase points number were used to characterize the dynamic features quantitatively and the pattern recognition of different running states of gearbox have been carried out.The results showed that the pattern recognition of different operating states can be realized intuitively from the phase trajectory map of the chaotic attractors,and the inclusion sphere radius is an effective index based on phase points distribution,which can be used to realize the different operating states pattern recognition.Furthermore the chaotic dynamics characteristics of the gearbox hidden in the one-dimensional time series were explored effectively.In practice,a gearbox always suffers various failures.In order to address this problem,this thesis proposed a new method for faults detection which combine CEEMDAN and recurrence analysis method to extract qualitative and quantitative features of different faults.Firstly,the mapping relationship between the recurrence mode and fault type for gearbox system was investigated from chaotic characteristics aspect which open a new view compared to the traditional methods.Then,Four quantitative features were selected including Recurrence Rate(RR),Determinism(DET),Laminarity(LAM),Entropy(ENTR)for diagnosis and identification of the gearbox health conditions.The results demonstrated the four quantitative index are all valid for gearbox different state identification.In addition,the RR and ENTR are more sensitive and effective than the DET and LAM in identifying faults.Compared with Wavelet denoising combing recurrence,the results showed that the accuracy of CEEMDAN combining recurrence analysis method is more higher and effective to diagnose the gearbox faults.In addition,comparing to the characterization parameters based on the chaotic attractors phase trajectory,the two recursive indexes Recurrence Rate and Entropy were found to have better diagnostic effect.As a result,it may provide a new practical method for multiple faults diagnosis using recurrence index from the chaotic view.Considering the harsh working environment of gearboxes in real practice,the vibration of the gearboxes is often influenced by the multi-frequency excitation.To this avail,the multi-frequency excitation effect was proposed in the nonlinear dynamics model built in this work.A numerical calculation process was implemented to investigate the primary resonance and the dynamic response of the gear nonlinear model,where a gear-meshing stiffness coefficient was defined.When the secondary excitation force added into the model,the system embody obvious chaotic characteristics.The established multi-frequency excitation dynamic gear model is more accurate than the traditional single frequency excitation model in describing the gear-meshing dynamics.Furthermore,the maximum Lyapunov index of the gear crack vibration signal was calculated to identify the crack severity.The results demonstrated that the maximum Lyapunov index increased with the increase of the level of the crack fault,and hence,it can be used as an effective indicator for the discrimination and detection of gear crack degree.This paper enrich the chaotic theory of gearbox and provide effective tool for gearbox health assessment and is beneficial to improving the reliability level of mechanical equipment and prolonging their service life.This paper has 98 figures,19 tables and 170 references. |
PDF Full Text Request