Xihui Liang

Evaluating the Time-Varying Mesh Stiffness of a Planetary Gear Set Using the Potential Energy Method

Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.

Understanding vibration properties of a planetary gear set for fault detection

This paper investigates the vibration properties of a planetary gear set. A two-dimensional lumped mass model is developed to simulate the vibration signals of a planetary gear set in the perfect and crack situations. Through dynamic simulation, the vibration signals of each individual component can be simulated, including the vibration signals of the sun gear, each planet gear, and the ring gear. By incorporating the effect of transmission path, resultant vibration signals of the gearbox at the transducer location are obtained. Results show obvious fault symptoms in the signals of an individual component, such as the sun gear. After going through the transmission path, amplitude modulation is shown in the resultant vibration signals. When there is a crack on a sun gear tooth, a large amount of sidebands appears in the vibration spectrum. The locations of these sidebands are investigated and identified, which are helpful for fault detection.

Early Fault Diagnosis of Rotating Machinery by Combining Differential Rational Spline-Based LMD and K–L Divergence

First, an improved local mean decomposition (LMD) method called differential rational spline-based LMD (DRS) is developed for signal decomposition. Differential and integral operations are introduced in LMD, which can weaken the mode mixing problem. Meanwhile, an optimized rational spline interpolation is proposed to calculate the envelope functions aiming to reduce the large errors caused by moving average in the traditional LMD. A series of product functions (PFs) is obtained after the application of the proposed DRS-LMD. Then, Kullback–Leibler (K–L) divergence is adopted to select main PF components that contain most fault information. The machine fault can be easily identified from the amplitude spectrum of the selected PF component. The effectiveness of the proposed DRS-LMD and K–L strategy is tested on simulated vibration signals and experimental vibration signals. Results show that the proposed method can increase the decomposition accuracy of the signals and can be used to detect early faults on the gears and rolling bearings.

A mesh stiffness evaluation model to reflect tooth pitting growth of a pair of external spur gears

Tooth pitting is a common failure mode of a gearbox. With the growth of tooth pitting, gear mesh stiffness shape changes and consequently the dynamic properties of the gear system change. An efficient and effective way to evaluate the time-varying mesh stiffness is essential for comprehensive understanding of dynamic properties and fault detection of a gear system. This study is devoted to modeling gear tooth pitting growth using circular pits and analytically evaluating the influence of tooth pitting on the mesh stiffness of a pair of external spur gears. Equations of the mesh stiffness are derived using the potential energy method. The relationship between pitting severity and mesh stiffness is established.

Dependence analysis of planetary gearbox vibration marginals

Time-frequency distribution (TFD) methods have been widely used for planetary gearbox fault detection. The aim of TFD is to represent a signal by a joint energy distribution in the time-frequency domain. Positivity is one of the most important properties for TFDs. Copula-based positive TFD construction methods utilize the time marginal, the frequency marginal and the dependence structure between the marginals. In this study, the dependence between the time marginal and the frequency marginal is studied explicitly by numerical and graphical rank-based statistics. Rank-based statistics are invariant with monotone transformations of the marginal distributions. This study demonstrates that the dependence does exist between the time marginal and the frequency marginal. The findings build one theoretical foundation for further study on copula-based TFD construction for one planetary gearbox vibration. Moreover, the results show that with the increase of the gearbox degradation, the Kendalls Taus absolute value increases as well. This indicates that the more severe the fault is, the stronger the dependence would be.

Health indicator extraction based on sparse representation of vibration signal for planetary gearbox

The general methods of health indicators extraction for planetary gearbox are based on the vibration signals which acquired by sensors equipped on the casing of the gearbox and sampled in the frame of Shannon sampling theory. Therefore, it is necessary to sample and save abundant original vibration data in the process of uninterrupted monitoring, and this will generate masses of original data which would burden the storage and transmission. For this issue, a health indicator extraction method based on sparse representation and reconstruction theory is proposed in this paper. It only needs to sample and save fewer compressive measurements of vibration signal directly compared to original signal. There is no need to recover the original signal accurately for extract health indicators, while it just requires some sparse representation and reconstruction results based on the redundant dictionary of the original signals. The effectiveness of the method proposed is validated with simulation data.