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In this paper, the graph theory model of the kinematics of the double internal meshing planetary gear is established by splitting the k value of the planetary gear, the system matrix of the dual-state logic planetary gear transmission is assembled, the logic characteristics of the dual-state logic planetary gear transmission control are analyzed, the logic characteristic table of the 32-gear control is established, and the system model of the kinematics analysis and calculation of the entire planetary gear transmission is established. The expressions of rotational speed and transmission ratio of each component (including planetary gear) of the planetary gear in 32 gears are solved and obtained. The efficiency expression of each gear is derived through the Kleinas method, the calculation of the transmission ratio and efficiency of the 32 gears is completed, and the system efficiency diagram is drawn, which provides a reliable basis for the structural design, shift dynamic simulation analysis, and test verification of the dual-state logic planetary transmission.

In the operation and maintenance of planetary gearboxes, the growth of monitoring data is often faster than its analysis and classification. Careful data analysis is generally considered to require more expertise. Rendering the machine learning algorithm able to provide more information, not just the diagnosis conclusion, is promising work. This paper proposes an analysis and diagnosis two-stage framework based on time-frequency information analysis. In the first stage, a U-net model is used for the semantic segmentation of vibration time-frequency spectrum to highlight faulty feature regions. Shape features are then calculated to extract useful information from the segmented image. In the second stage, the decision tree algorithm completes the health state classification of the planetary gearboxes using the input of shape features. The real data of wind turbine planetary gearboxes and augmented data are utilized to verify the proposed framework’s effectiveness and superiority. The F1-score of segmentation and the classification accuracy reach 0.942 and 97.4%, respectively, while in the environmental robustness experiment, they reached 0.747 and 83.1%. Equipping the two-stage framework with different analytical methods and diagnostic algorithms can construct flexible diagnostic systems for similar problems in the community.

A planetary gearbox is more complex in structure and motion than a gearbox with a fixed shaft, making it difficult to monitor and make a fault diagnosis in practice. Components must be frequently inspected to avoid excessive wear, but there is no simple way to directly measure wear. The most direct method is to log vibration and temperature signals using external sensors. Wireless sensors offer more space advantages than a wired one, so this study developed a measurement system that features a three-axis MEMS accelerometer, temperature sensing and wireless modules that are integrated into a planetary gearbox. Along with the system, a virtual instrument (VI) utilizing graphics programming language LabVIEW was developed to acquire and display data time and frequency domains to detect the gear’s faults. To determine the root cause of vibrations in a planetary gearbox, determine the vibration signal model of amplitude modulation (AM) and frequency modulation (FM) due to gear damage and derive the characteristic frequencies of vibrations for a planetary gearbox, the characteristic frequencies and AMFM modulation were summarized in closed form. Different degrees of each gear damage were then detected in the planetary gearbox. The vibration signal model was validated by experiments to indicate the sideband around the gear meshing frequency and its feasibility for fault diagnosis of a planetary gearbox with the wireless embedded sensor.

Existing studies on the dynamic characteristics of planetary gearboxes are generally based on traditional modeling methods. The models were idealized because of various uncertain factors that affect the dynamic characteristics of the planetary gearbox. The influence of non-mechanical components, such as driving motors, on dynamic analysis, is often ignored. Digital twin technology can not only simulate the data characteristics of physical entities to realize the real-time state evaluation and fault diagnosis of complex equipment but also reflect the entity characteristics of the modeled object completely. Therefore, a digital twin multi-body dynamic model of a planetary gearbox is established for detecting the combined fault of the sun gear missing teeth and the planetary gear missing teeth or pitting under different working conditions. The dynamic characteristics of a planetary gearbox subjected to electromechanical coupling were studied. The sun gear fault frequency, planetary gear fault frequency, and both related modulation frequencies appear in the experiment, and the corresponding fault characteristic frequencies also appear in the digital twin simulation. The validity of the proposed model was experimentally verified. Finally, the root-mean-square index was used to analyze the fault sensitivity of the traditional and digital twin models. The results show that the fault diagnosis effect of the digital twin model has a significant advantage, thus verifying the necessity of considering the effect of electromechanical coupling on the dynamic characteristics of the planetary gearbox.

Multi-view information fusion can provide more accurate, complete and reliable data descriptions for monitoring objects, effectively improve the limitations and unreliability of single-view data. Existing multi-view information fusion based on deep learning mostly focuses on the feature level and decision level, with large information loss, and does not distinguish the view weight in the fusion process. To this end, a multi-view data level information fusion model CAM_MCFCNN with view weight was proposed based on a channel attention mechanism and convolutional neural network. The model used the channel characteristics to implement multi-view information fusion at the data level stage, which made the fusion position and mode more natural and reduced the loss of information. A multi-channel fusion convolutional neural network was used for feature learning. In addition, the channel attention mechanism was used to learn the view weight, so that the algorithm could pay more attention to the views that contribute more to the fault identification task during the training process, and more reasonably integrate the information of different views. The proposed method was verified by the data of the planetary gearbox experimental platform. The multi-view data and single-view data were used as the input of the CAM_MCFCNN model and single-channel CNN model respectively for comparison. The average accuracy of CAM_MCFCNN on three constant-speed datasets reached 99.95%, 99.87% and 99.92%, which was an improvement of 0.95%, 2.25%, and 0.04%, compared with the single view with the highest diagnostic accuracy, respectively. When facing limited samples, CAM_MCFCNN had similar performance. Finally, compared with different multi-view information fusion algorithms, CAM_MCFCNN showed better stability and higher accuracy. The experimental results showed that the proposed method had better performance, higher diagnostic accuracy and was more reliable, compared with other methods.

Deep neural network (DNN), with the capacity for feature inference and nonlinear mapping, has demonstrated its effectiveness in end-to-end fault diagnosis. However, the intermediate learning process of the DNN architecture is invisible, making it an uninterpretable black-box model. In this paper, a stacked residual multi-attention network (SRMANet) is proposed as a means of feature extraction of vibration signals, and visualizing the model training process, designing Squeeze-excitation residual (SE-Res) blocks to obtain additive features with minimal redundancy and sparsity. This study recommends the use of the attention fusion unit to ensure the interpretability of the model and ultimately to obtain representative features. By feeding the output gradient of the attention layer back to the original signal, the key feature components in the time domain signal can be effectively captured. Finally, the interpretability, identification accuracy and adaptability of the model under different operating conditions are verified on 12 different fault tasks in the planetary gearbox.

Planetary gearboxes are more and more widely used in large and complex construction machinery such as those used in aviation, aerospace fields, and so on. However, the movement of the gear is a typical complex motion and is often under variable conditions in real environments, which may make vibration signals of planetary gearboxes nonlinear and nonstationary. It is more difficult and complex to achieve fault diagnosis than to fix the axis gearboxes effectively. A fault diagnosis method for planetary gearboxes based on improved complementary ensemble empirical mode decomposition (ICEEMD)-time-frequency information entropy and variable predictive model-based class discriminate (VPMCD) is proposed in this paper. First, the vibration signal of planetary gearboxes is decomposed into several intrinsic mode functions (IMFs) by using the ICEEMD algorithm, which is used to determine the noise component by using the magnitude of the entropy and to remove the noise components. Then, the time-frequency information entropy of intrinsic modal function under the new decomposition is calculated and regarded as the characteristic matrix. Finally, the fault mode is classified by the VPMCD method. The experimental results demonstrate that the method proposed in this paper can not only solve the fault diagnosis of planetary gearboxes under different operation conditions, but can also be used for fault diagnosis under variable operation conditions. Simultaneously, the proposed method is superior to the wavelet entropy method and variational mode decomposition (VMD)-time-frequency information entropy.

Planetary gearbox vibration signals have strong modulation features due to the amplitude modulation and frequency modulation (AM-FM) effect of gear faults, as well as the amplitude modulation (AM) effect of time-varying vibration transfer paths, on gear meshing vibrations. This results in an involute sidebands structure in Fourier spectrum, possibly misleading fault diagnosis. The modulating frequency of both amplitude modulation (AM) and frequency modulation (FM) parts is closely related to the gear fault characteristic frequency. This inspires the idea of joint amplitude and frequency demodulation analysis, thus addressing the complex sidebands issue inherent in Fourier spectrum. Demodulation analysis requires mono-component signals for accurate estimation of instantaneous frequency, and proper selection of an AM-FM component sensitive to gear fault. To this end, we firstly decompose the complex signal into intrinsic mode functions (IMFs) via variational mode decomposition (VMD), by exploiting its capability in decomposing complex modulated signal into constituent AM-FM components. For effective application of VMD in complex planetary gearbox signal analysis, we propose a method to determine a key parameter in VMD, i.e. the number of IMFs to be separated. For accurate instantaneous frequency estimation, we decompose IMFs via empirical AM-FM decomposition, to remove the influence of AM on instantaneous frequency estimation. Then, we select the sensitive IMF that contains the main gear fault information for further demodulation analysis. In order to properly select the sensitive IMF, we propose a criterion based on the gear vibration characteristics and the VMD properties. Finally, we obtain the amplitude and frequency demodulated spectra by applying Fourier transform to the amplitude envelope and instantaneous frequency of the selected sensitive IMF. According to the characteristics exhibited in the demodulated spectra, we can detect planetary gearbox fault. The proposed method is illustrated via a numerical simulated planetary gearbox vibration signal, and is further validated using lab experimental vibration signals of a planetary gearbox. Faults on all the three types of gear (sun, planet and ring) are successfully identified.

In this paper, the direct current (DC) offset cancellation and S transform-based diagnosis method is verified using three case studies. For DC offset cancellation, correlated kurtosis (CK) is used instead of the cross-correlation coefficient in order to determine the optimal iteration number. Compared to the cross-correlation coefficient, CK enhances the DC offset cancellation ability enormously because of its excellent periodic impulse signal detection ability. Here, it has been proven experimentally that it can effectively diagnose the implanted bearing fault. However, the proposed method is less effective in the case of simultaneously present bearing and gear faults, especially for extremely weak bearing faults. In this circumstance, the iteration number of DC offset cancellation is determined directly by the high-speed shaft gear mesh frequency order. For the planetary gearbox, the application of the proposed method differs from the fixed-axis gearbox, because of its complex structure. For those small fault frequency parts, such as planet gear and ring gear, the DC offset cancellation’s ability is less effective than for the fixed-axis gearbox. In these studies, the S transform is used to display the time-frequency characteristics of the DC offset cancellation processed results; the performances are evaluated, and the discussions are given. The fault information can be more easily observed in the time-frequency contour than the frequency domain.