Amplitudes of characteristic frequencies for fault diagnosis of planetary gearbox

Abstract

Frequency contents have been widely investigated to understand the vibration behaviors of planetary gearboxes. Appearances of certain sideband peaks in the frequency spectrum may indicate the occurrence of gear fault. However, analyzing too many sidebands will create problems and uncertainty of fault diagnoses. To this end, it is of vital importance to focus on those sidebands, as well as their amplitudes, which are directly induced by the gear faults. The Sideband Energy Ratio (SER) method, which synthesize the amplitudes of characteristic frequencies and meshing frequency, has shown its effectiveness in fault diagnosis of fixed-shaft gearboxes. However, for planetary gearboxes, the effectiveness and theoretical explanation behind this method still needs to be explored. In this paper, we first explored the amplitudes of characteristic frequencies based on a phenomenological model. Our investigation demonstrated that monitoring the amplitude of a single frequency component is inadequate for fault diagnosis of planetary gearbox. Second, the theoretical explanation of SER for a planetary gearbox is explored. Finally, a modified SER, namely the Modified Sideband Energy Ratio, is proposed to deal with the problem of rotating speed fluctuation. Experimental studies are provided to demonstrate the effectiveness of the proposed method.

Introduction

Gearboxes, such as fixed-shaft gearboxes and planetary gearboxes, are widely used to transmit power and motion. With unique advantages of compactibility and high power transmission ratio, planetary gearboxes are extensively applied in various industrial applications, such as aerospace, automobiles, heavy trucks and underground coal mining equipment [[1], [2], [3], [4]]. However, due to the heavy loads and hostile working environments, the internal gears in planetary gearboxes are proven to suffer from faults, such as pitting, crack and spalling [5]. This damage will lead to undesirable dynamic behaviors, serious performance reductions and even major break-downs [6]. Condition monitoring and fault diagnosis should be employed for cost savings.

Vibration analysis [7] is one of the key methodologies that has been deemed necessary for condition monitoring and fault diagnosis. Aiming to monitor the health conditions of the internal gears in planetary gearboxes, frequency contents of the vibration behaviors have been investigated. MacFadden [8] noticed the asymmetry of the sidebands beside the gear-meshing frequency. A phenomenological model was established to predict the sidebands in the frequency spectrum. McNames [9] and Mosher [10] discussed the peaks of the dominant frequency components using the Fourier Transform based on the MacFadden's model [8]. Vicuna [11] improved the model in Ref. [8] with consideration of the internal and external gear-meshing influences and transmission path effect. Afterwards, Parra and Vicuna [12] investigated the frequency contents predicted by Vicuna's model and the lumped-parameter models in Ref. [13]. Experimental studies showed that the vibration description of the two kinds of models are in close agreement. Furthermore, Mark and Hines [14] predicted the existence of additional sidebands caused by the torque modulations of the planet carrier. These additional sidebands might potentially mask the sidebands caused by the damage in planetary gearboxes. Inalpolat and Kahraman [15] proposed a mathematical model to predict the modulation sidebands of a planetary gear set with manufacturing errors. Hong et al. [16] developed the signal models of [9,15] in which additional frequency contents caused by gear local faults were identified. However, the frequency modulation (FM) effect generated by the gear fault was missed in the mentioned models. In this regard, Feng and Zuo [17] considered the FM effect of gear faults and gave explicit expressions including fault components of the sun gear, planet gear and ring gear. They provided a thorough understanding of the spectral structure of the planetary gear system.

Traditional ways of discussing the appearances of certain sideband peaks in terms of signal model, to some extent, may indicate the occurrence of the gear faults. However, some of the analyzing sidebands were not only induced by a gear fault but also by other modulation sources, such as the planet carrier rotation frequency, shaft rotation frequency, etc. [16,17]. These modulations are not exclusive fault indications and will enhance the uncertainty in fault diagnosis. Besides, searching for these sidebands in practice requires expert knowledge and is time consuming. High resolution of the frequency spectrum is also needed to identify these sideband peaks. Under this circumstance, it is necessary to narrow the sideband types and focus on those sidebands that are directly induced by faults.

Gear-meshing frequency and the sidebands induced by gear faults are well-known features for monitoring the gear health. By using the amplitudes of these frequency contents, Hanna et al. [18] proposed the Sideband Energy Ratio (SER) to detect the gear faults for fixed-shaft gearboxes in wind turbines. A ratio between the summation amplitudes of the first six sideband peaks on both sides of the gear-meshing frequency and the peak of the meshing frequency, the SER was defined in Eq. (1.1) [18]:

$$SER=\frac{\sum _{i=1}^{6}Sidebandampitud{e}_i}{Centermeshfrequencyamplitude}$$

Hatch et al. [19] systematical summarized this method and a patent was published to monitor the health condition of a gear. Dempsey [20] used the sideband index (SI) to detect the contact fatigue damage of the gear teeth. The only difference between SI and SER is the selection number of the sidebands, namely 3 sidebands for SI and 6 sidebands for SER. Recently, Pattabiraman et al. [21] demonstrated that SER was a reliable indicator to track the defect progression of a gear in fixed-shaft gearboxes.

However, the SER has not been studied for fault diagnosis of planetary gearboxes yet. Due to the complicated mechanical structure and the dynamic motions of internal gears, selection of the sideband types for planetary gearboxes is not as straightforward as it is for the fixed-shaft gearboxes. The SER may lose its diagnostic ability if the sideband types are inappropriately selected. Besides, different from some condition indicators such as Root Mean Square (RMS) and Kurtosis [22] in which statistical meanings are given through rigorous mathematics, theoretical support behind SER needs to be further explored for planetary gear systems. As a result, this paper focuses on the following topics:

• Amplitudes of the characteristic frequency contents will be explored based on a reported phenomenological model in Ref. [17].

• A theoretical explanation of SER for planetary gear systems will be discussed. Application of the SER for planetary gear systems will be explored.

• Considering the speed fluctuations in real practice, the SER will be modified to adapt to the working condition. Different kinds of gear health scenarios will be used for testing.

The rest of this paper is organized as follows: In Section 2, the amplitudes of the characteristic frequencies are mathematically discussed in terms of the reported model in Ref. [17]. In Section 3, theoretical explanations of SER are provided for different gear types. Finally, a modified SER method is proposed. Experimental studies will be given to validate the diagnostic effects in Section 4. Finally, Section 5 concludes the whole paper.