In this research a new method of improved singular value decomposition (ISVD) is proposed for the vibration signal de-noising of gear pitting fault identification. In this method, the delay time τ and embedding dimension m of the Hankel matrix for SVD are optimized by autocorrelation function and Cao's algorithm respectively. Simulation and experiments are conducted to demonstrate the method. In the simulation, the ISVD method is employed to de-noise the artificial vibration signal in a mathematical model of gear pitting fault, the result demonstrates the signal-noise ratio (SNR) value is SNR = 31.3 dB, and the root-mean-square error (RMSE) value is RMSE = 0.34. In the experiment, the ISVD method is adopted to de-noising the vibration signal of gear pitting fault identification, the results demonstrate SNR is SNR >45 dB, and the RMSE value is RMSE <0.4 of the fault characteristic signals at each measuring point position. The results of simulation and experiment show, the ISVD method is efficient to de-noise the vibration signal of gear pitting fault. Signalentrauschen in Zahnrad-Lochfehler-Identifikation durch eine verbesserte Singular-Value-Zersetzungsmethode Zusammenfassung In dieser Forschung wird eine neue Methode zur verbesserten Singularwertzersetzung (ISVD) für die Schwingungssignalentnosierung von Zahnrad-Lochfehler-Identifikation vorgeschlagen. Bei dieser Methode werden die Verzögerungszeit und die Einbettungsdimension m der Hankel-Matrix für SVD durch die Autokorrelationsfunktion bzw. den Cao-Algorithmus optimiert. Simulationen und Experimente werden durchgeführt, um die Methode zu demonstrieren. In der Simulation wird die ISVD-Methode verwendet, um das künstliche Schwingungssignal in einem mathematischen Modell von Zahnrad-Pitting-Fehlern zu entrauschen; das Ergebnis zeigt den Signal-Rausch-Verhältnis-Wert (SNR) sNR = 31,3 dB und der RMSE-Wert (Root-Mean-Square Error) ist RMSE = 0,34. Im Experiment wird die ISVD-Methode zum Entrauschen des Schwingungssignals der Schaltfehleridentifikation von Zahnrädern angewandt, die Ergebnisse zeigen, dass SNR SNR > 45 dB ist, und der RMSE-Wert ist RMSE-0,4 der Fehlerkennzeichensignale an jeder Messpunktposition. Die Ergebnisse der Simulation und des Experiments zeigen, dass die ISVD-Methode effizient ist, um das Schwingungssignal von Zahnrad-Pitting-Fehlern zu entlärmen. Abbreviations C(τ) The autocorrelation function d Singular value difference spectrum D Singular value difference spectrum matrix Xintao Zhou
The concept of multi-attribute topological graph is proposed in this article to represent the characteristics of both structure and state for typical one-degree-of-freedom planar spur closed planetary gear trains. This method is well applied in power flow analysis and provides a graphical view for the types, values, directions, and transmission relationship of power flow, especially for the recirculation power representation. Furthermore, a template model of multi-attribute topological graph for closed planetary gear trains is also presented, which would be helpful to the multi-attribute topological graph generation for some certain types of closed planetary gear trains just by changing symbols in the template model. A corresponding software is also developed to make the analysis process more convenient. By inputting different parameters, the different visual results can be obtained automatically, thus benefiting engineers in conceptual design.
Multiscale Permutation Entropy (MPE) is a presented nonlinear dynamic technology for measuring the randomness and detecting the nonlinear dynamic change of time sequences and can be used effectively to extract the nonlinear dynamic wear fault feature of gear tooth surface from vibration signals of gear set. To solve the subjectivity drawback of threshold parameter selection process in MPE method, a joint calculation method based on the Mutual Information (MI) and improved False Nearest Neighbor (FNN) principle for calculating threshold parameters for MPE method was presented in this article. Then, the influence of threshold parameters on the identification accuracy of fault features with the MPE was studied by analyzing simulation data. Through the simulation analysis, the effectiveness of the proposed MPE method is validated. Finally, the wear failure test of spur gear was carried out, and the proposed method was applied to analyze the experimental data of fault signal. Meanwhile, the vibration characteristics of the fault signal are acquired. The analysis results show that the proposed method can effectively realize the fault diagnosis of gear box and has higher fault identification accuracy than the existing methods.Keywords: multiscale permutation entropy, mutual information, improved false nearest neighbor, delay time, embedded dimension, scale factor and fault feature.
The detection of mechanical fault signals by singular value decomposition is a commonly used method in fault diagnosis. The delay time of the fault signal time series and the rationality of the value of the phase space embedding dimension, as well as the fluctuation of the characteristic parameters of the fault signal, will cause the singular value decomposition method to have a greater impact on the accuracy of fault feature identification and diagnosis. In this article, the simulation model of the similarity signal is established by the combination of the autocorrelation function method and the Cao’s algorithm. Then, the delay time of the signal sequence and the optimal value of the embedded dimension are obtained through simulation. Next, using this method to study the fluctuation of the characteristic parameters such as the frequency, amplitude and initial phase of the signal, the relationship between the characteristic parameters of the signal and the singular value of the signal is obtained. Finally, through the experimental study of the pitting corrosion of the gear tooth surface, the vibration of the fault feature is obtained. The research shows that the combination of autocorrelation function method and Cao's algorithm can calculate the optimal characteristic parameters for the singular value decomposition method and improve the ability of the method to identify fault features.
The complexity of single-loop gear system transmission structure makes it difficult for traditional modeling methods to establish precise dynamic model, which greatly affects the accuracy of its dynamic characteristics research. Firstly, a structure diagram is established by adopting modularization idea according to the structural properties of single-loop gear system. On this basis, a precise bond graph model of the single-loop gear system is obtained combining the modeling principle of bond graph method and the advantages of rich graphics library. Secondly, the dynamic state equation of single-loop gear system is obtained from bond graph model. The simulation model of gear system is established by numerical simulation method. Eventually, the dynamic characteristics of a single-loop gear system are acquired by calculating two dynamic indexes of the system under linear and weakly nonlinear states. The simulation results show that the bond graph method can accurately describe the mathematical model of single-loop gear train and master the dynamic characteristics of complex gear train. This will provide a reference for the structural design and dynamic characteristics of the transmission system.
The dynamic characteristics of planetary system directly affect the stable state of the whole transmission system. Firstly, an accurate dynamic model of planetary gear system is established by using bond graph method. Formerly, the state equation of the gear train dynamics is obtained based on the bond graph model. On this basis, the simulation model of the gear system was acquired by using the numerical simulation method, and four dynamic indexes including zero-pole diagram, Bode diagram, Nyquist diagram and Nichols diagram of the gear dynamics system were gained. Finally, the analysis results show that the accurate mathematical model is described by the bond graph method and the dynamic characteristics is comprehended of planetary gear system, while will provide a basis for the stability research of the transmission system.
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