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The identification of compound fault components of a planetary gearbox is especially important for keeping the mechanical equipment working safely. However, the recognition performance of existing deep learning-based methods is limited by insufficient compound fault samples and single label classification principles. To solve the issue, a capsule neural network with an improved feature extractor, named LTSS-BoW-CapsNet, is proposed for the intelligent recognition of compound fault components. Firstly, a feature extractor is constructed to extract fault feature vectors from raw signals, which is based on local temporal self-similarity coupled with bag-of-words models (LTSS-BoW). Then, a multi-label classifier based on a capsule network (CapsNet) is designed, in which the dynamic routing algorithm and average threshold are adopted. The effectiveness of the proposed LTSS-BoW-CapsNet method is validated by processing three compound fault diagnosis tasks. The experimental results demonstrate that our method can via decoupling effectively identify the multi-fault components of different compound fault patterns. The testing accuracy is more than 97%, which is better than the other four traditional classification models. [ABSTRACT FROM AUTHOR]

The carrier eccentricity error and gear compound faults are most likely to occur simultaneously in an actual planetary gear train (PGT). Various faults and errors are coupled with each other to generate a complex dynamic response, which makes the diagnosis of PGT faults difficult in practice. In order to analyze the joint effect of the error and the compound faults in a PGT, a carrier eccentricity error model is proposed and incorporated into the TVMS model by considering the time-varying center distance, line of action (LOA), meshing angle, and contact ratio. Then, the TVMS of the cracked gear is derived based on the potential energy method. On this basis, the dynamic model of a PGT with both the carrier eccentricity error and compound gear cracks as internal excitations are established. Furthermore, the meshing characteristics and dynamic responses of the PGT are simulated to investigate the compound fault features. A series of experiments are conducted to further analyze the influence of the compound fault on the vibration response. The relevant conclusions can provide a reference for the compound fault diagnosis of a PGT in practice. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel fault diagnosis method based on variational mode decomposition (VMD) and generalized composite multi-scale symbol dynamic entropy (GCMSDE) to identify the different health conditions of planetary gearboxes. First, VMD is adopted to remove the noises and highlight the fault symptoms. Second, GCMSDE is utilized to extract the fault features from the denoised vibration signals. Third, the Laplacian score (LS) approach is employed to refine the fault features. Finally, the new features are fed into Softmax regression to identify the health conditions of planetary gearboxes. The proposed method is numerically and experimentally demonstrated to be able to differentiate seven localized fault types on the sun gear, planet gear and ring gear of planetary gearboxes. Highlights • A method called GCMSDE is developed to enhance the fault extraction ability. • We first combined VMD and GCMSDE, which highlight the fault signatures. • Simulated and experiments have validated good performance of the proposed method. [ABSTRACT FROM AUTHOR]

The fault diagnosis of planetary gearboxes is crucial to reduce the maintenance costs and economic losses. This paper proposes a novel fault diagnosis method based on adaptive multi-scale morphological filter (AMMF) and modified hierarchical permutation entropy (MHPE) to identify the different health conditions of planetary gearboxes. In this method, AMMF is firstly adopted to remove the fault-unrelated components and enhance the fault characteristics. Second, MHPE is utilized to extract the fault features from the denoised vibration signals. Third, Laplacian score (LS) approach is employed to refine the fault features. In the end, the obtained features are fed into the binary tree support vector machine (BT-SVM) to accomplish the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault categories of planetary gearboxes. [ABSTRACT FROM AUTHOR]

Health condition identification of planetary gearboxes is crucial to reduce the downtime and maximize productivity. This paper aims to develop a novel fault diagnosis method based on modified multi-scale symbolic dynamic entropy (MMSDE) and minimum redundancy maximum relevance (mRMR) to identify the different health conditions of planetary gearbox. MMSDE is proposed to quantify the regularity of time series, which can assess the dynamical characteristics over a range of scales. MMSDE has obvious advantages in the detection of dynamical changes and computation efficiency. Then, the mRMR approach is introduced to refine the fault features. Lastly, the obtained new features are fed into the least square support vector machine (LSSVM) to complete the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault types of planetary gearboxes. [ABSTRACT FROM AUTHOR]

• A novel mathematical model of the transmission path effect is proposed. • Path effect depends only on the geometric parameters and material properties. • A phenomenological vibration model is used to simulate all vibration sources. • Vibration characteristics are analyzed and validated through experiments. Model-based vibration signal analysis to interpret and understand vibration characteristics can provide prior guidance for the condition monitoring and fault diagnosis of planetary gearboxes (PGs). Transmission path effects due to the rotational motion of planet gears with respect to the accelerometer mounted on the PG housing make understanding its real dynamic behavior challenging. To overcome this challenge, a novel mathematical model of the transmission path effect is proposed to support the construction of more realistic dynamic response of PGs. This model is derived only from the geometric parameters and material properties, and it has higher applicability than traditional models. Subsequently, a phenomenological vibration model is used to simulate all vibration sources, including sun–planet and ring–planet gear meshes. On these bases, a comprehensive vibration signal model is proposed by considering all vibration sources and the corresponding transmission path effects. Moreover, the theoretical spectral structure is deduced via Fourier series analysis. Finally, the vibration characteristics of the vibration signals obtained using the proposed mathematical model are analyzed and validated through simulations and experiments in the time and frequency domains. [ABSTRACT FROM AUTHOR]

• An improved phenomenological model of a gear pair with local fault is proposed. • Relative phases of planetary gearboxes are calculated by a modified phase model. • The local fault characteristic frequencies of gears are deduced based on models. • The conclusions are validated based on five experiments conducted on a test rig. Planetary gearboxes (PGs) are prone to gear local faults, such as cracking, pitting, and spalling, because of their difficult working environment. These faults may lead to significant capital losses and catastrophic events. Numerous phenomenological modulation models of vibration signals of PGs have been proposed for diagnosis purposes. However, local fault diagnosis remains extremely challenging due to two aspects: (1) Most vibration modulation models cannot reflect the local fault-induced pulse modulation characteristic. (2) Studies on local fault characteristic frequencies (LFCFs) of gears lack a unified mechanism explanation. To solve these problems, an improved phenomenological vibration model of a gear pair with local fault is first proposed. This model can reflect the pulse modulation characteristic. Then, relative phases between multiple gear pairs in the PG are calculated based on a modified phase model. Based on these, phenomenological vibration models of PGs with/without local faults are established, spectral structures are derived using Fourier series analysis, and LFCFs are deduced for local fault diagnosis. Simulation and experimental studies demonstrate the effectiveness of the proposed models, which exhibit higher descriptive capability than traditional models. [ABSTRACT FROM AUTHOR]