Optimum Determination of Partial Transmission Ratios of Coupled Planetary Gearboxes

This paper presents a new study on optimum determination of the partial ratios of coupled planetary gear sets for getting minimum radial size of the gear sets. In this paper, based on moment equilibrium condition of a mechanic system including two-row planetary gear sets and their regular resistance conditions, an explicit model for calculating the partial ratios of coupled planetary gear sets was proposed. In addition, by giving this effective model, the partial ratios can be calculated simply and accurately.

The Effect of Signal Propagation Delay on the Measured Vibration in Planetary Gearboxes

Modulation of the gear mesh vibration is a major field of research for the condition monitoring of planetary gearboxes.The modulation creates sidebands around the gearmesh frequency in the vibration spectrum,and the distribution of these sidebands has been researched in numerous papers.All publications on the subject assume that the effect of the time varying signal propagation delay between the main vibration source–the gear mesh point(s)–and the(usually fixed)transducer can be neglected.This paper investigates the validity of this assumption.To do so,a planetary gearbox with a transducer mounted on the(fixed)ring gear is studied,and the effect of the propagation delay is modelled as a phase modulation of the gear mesh vibration.General expressions are then derived for the distribution and strength of the modulation sidebands,and these expressions are applied to quantify the effect of the propagation delay on five industrial gearboxes.The results show that the amplitude of the sidebands is negligible and would not interfere with condition assessment based on analysis of the modulation of the gear mesh frequency,and thus the propagation delay can be neglected for practical purposes.

A novel method for vibration signal transmission and attenuation analysis in complex planetary gearboxes

Planetary gearboxes play a crucial role in altering rotary speed and transmitting power in large machines like wind turbines and sophisticated vehicles. There are many nonlinear interfaces, such as splines, bearings, and gear pairs, in planetary gearboxes, and the resulting vibration signal transmission and attenuation mechanisms are still unknown. In this study, a novel method for quantitatively analyzing the transmission and attenuation of vibration signals is proposed. A multibody dynamic model of the planetary gearbox considering nonlinear gear meshing is presented and experimentally validated. To avoid the interference of foundation vibration on the transmission of the fault signal, the fault impact factor(FIF) is used to describe the intensity of the failure, which aligns well with the experimental signals. Based on the FIF, the vibration signal attenuation of nonlinear interfaces such as splines, bearings, and gear meshing interfaces is quantitatively evaluated. To clarify the transfer paths of fault vibration signals inside the gearbox, the transfer path area method(TPAM) based on FIF is proposed. According to the simulated results,the primary transfer paths of fault vibration signals within the gearbox have been identified, which is of great help in understanding the transmission and attenuation of vibration signals in planetary gearboxes.

Wind Turbine Planetary Gearbox Fault Diagnosis via Proportion-Extracting Synchrosqueezing Chirplet Transform

Wind turbine planetary gearboxes usually work under time-varying conditions,leading to nonstationary vibration signals.These signals often consist of multiple time-varying components with close instantaneous frequencies.Therefore,high-quality time-frequency analysis(TFA)is needed to extract the time-frequency feature from such nonstationary signals for fault diagnosis.However,it is difficult to obtain high-quality timefrequency representations(TFRs)through conventional TFA methods due to low resolution and time-frequency blurs.To address this issue,we propose a new TFA method termed the proportion-extracting synchrosqueezing chirplet transform(PESCT).Firstly,the proportion-extracting chirplet transform is employed to generate highresolution underlying TFRs.Then,the energy concentration of the underlying TFRs is enhanced via the synchrosqueezing transform.Finally,wind turbine planetary gearbox fault can be diagnosed by analysis of the dominant time-varying components revealed by the concentrated TFRs with high resolution.The proposed PESCT is suitable for achieving high-quality TFRs for complicated nonstationary signals.Numerical and experimental analyses validate the effectiveness of the PESCT in characterizing the nonstationary signals from wind turbine planetary gearboxes.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis.However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique(IHFST) that combines a distance evaluation technique(DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence,a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

Valuable Impulses and Successful Models of Gearbox Development from Practice

Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.

A dynamic-model-based fault diagnosis method for a wind turbine planetary gearbox using a deep learning network

The planetary gearbox is a critical part of wind turbines,and has great significance for their safety and reliability.Intelligent fault diagnosis methods for these gearboxes have made some achievements based on the availability of large quantities of labeled data.However,the data collected from the diagnosed devices are always unlabeled,and the acquisition of fault data from real gearboxes is time-consuming and laborious.As some gearbox faults can be conveniently simulated by a relatively precise dynamic model,the data from dynamic simulation containing some features are related to those from the actual machines.As a potential tool,transfer learning adapts a network trained in a source domain to its application in a target domain.Therefore,a novel fault diagnosis method combining transfer learning with dynamic model is proposed to identify the health conditions of planetary gearboxes.In the method,a modified lumped-parameter dynamic model of a planetary gear train is established to simulate the resultant vibration signal,while an optimized deep transfer learning network based on a one-dimensional convolutional neural network is built to extract domain-invariant features from different domains to achieve fault classification.Various groups of transfer diagnosis experiments of planetary gearboxes are carried out,and the experimental results demonstrate the effectiveness and the reliability of both the dynamic model and the proposed method.