Vibration signal modeling of a planetary gear set for tooth crack detection Xihui Liang, Ming J. Zuo ⇑ , Mohammad R. Hoseini Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada article info Article history: Received 3 May 2014 Received in revised form 20 October 2014 Accepted 17 November 2014 Available online 26 November 2014 Keywords: Signal modeling Dynamic simulation Transmission path Tooth crack Sidebands abstract In a planetary gearbox, there are multiple vibration sources, and the transmission path of vibration signals changes due to the rotation of the carrier. This study aims to model the vibration signals of a planetary gearbox and investigate the vibration properties in the healthy condition and in the cracked tooth condition. A dynamic model is developed to simulate the vibration source signals. A modified Hamming function is proposed to repre- sent the effect of the transmission path. By incorporating the effect of multiple vibration sources and the effect of transmission path, resultant vibration signals of a planetary gearbox are obtained. Through analyzing the resultant vibration signals, some vibration properties of a planetary gearbox are revealed and the fault symptoms of sun gear tooth crack are identified and located. Finally, the proposed approach is experimentally verified. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The vibration signals of a planetary gearbox are more complicated comparing with that of a fixed-shaft gearbox. For a planetary gear set, several sun-planet gear pairs and several ring-planet gear pairs mesh simultaneously. The vibration signals generated by each sun-planet gear pair are similar but with different phases [1]. Similar comments apply to the ring-planet meshes. Due to the phase differences, some of the excitations are canceled or neutralized [2] while others are augmented. In general, vibration transducers, mounted on the housing of a gearbox or the housing of a bearing, are used to acquire vibration signals. Transmission paths of the vibration signals to a transducer change due to the revolution of the carrier. Multiple vibration sources and the effect of the transmission path will cause fault symptoms hard to be distinguished. Even though many signal processing methods have been proposed to detect gear faults [1–4], the improvements of these methods are still desired. The transducer signal is comprised of many sub signals, such as the vibrations of the sun gear, pla- net gear, ring gear, bearings and shafts. Unfortunately, there are no mature signal processing methods which can effectively denoise and separate these signals [5,6]. If we can ‘‘open’’ the black box, ‘‘see’’ all the sub-signals, and understand the gen- eration mechanisms of vibration signals, effective tools can be developed to detect gear faults. Mathematical models have been used by several researchers to investigate the vibration properties of a planetary gearbox [7,8]. However, the mathematical models lack the connection with the physical parameters of a gearbox, like the mesh stiff- ness and damping. In addition, they can hardly model the process of the fault growth. Dynamic simulation is a better choice to investigate the vibration properties of a planetary gearbox. A dynamic model is more closely connected with the physical http://dx.doi.org/10.1016/j.engfailanal.2014.11.015 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 780 492 4466; fax: +1 780 492 2200. E-mail address: ming.zuo@ualberta.ca (M.J. Zuo). Engineering Failure Analysis 48 (2015) 185–200 Contents lists available at ScienceDirect Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal