Review Review on dynamics of cracked gear systems Hui Ma ⇑ , Jin Zeng, Ranjiao Feng, Xu Pang, Qibin Wang, Bangchun Wen School of Mechanical Engineering and Automation, Northeastern University, Shenyang, Liaoning 110819, PR China article info Article history: Received 5 December 2014 Received in revised form 2 June 2015 Accepted 12 June 2015 Available online 16 June 2015 Keywords: Crack propagation path Time-varying mesh stiffness (TVMS) Cracked gear systems Analytical method Finite element method abstract Dynamic characteristics of cracked gear systems, also known as cracked-gear rotor sys- tems, have received increasing interests among industry and academy in the past two dec- ades. This paper reviews published papers on the dynamics of cracked gear systems. These studies mainly focused on three topics: crack propagation prediction, time-varying mesh stiffness (TVMS) calculation and vibration response calculation; Study objects involve the spur gear, helical gear and planetary gear; Different modeling methods including ana- lytical method, finite element (FE) method, combined analytical-FE approach were adopted. More specifically, this review is composed of three related parts according to the above three topics. The first part involves the prediction of the crack propagation path based on two-dimensional (2D) or three-dimensional (3D) gear models, which provides a basis for the hypothesis of crack path in the process of TVMS calculation of cracked gear pairs. The second part summarizes the TVMS calculation methods including analytical methods, FE methods, combined analytical-FE approaches and experimental methods. The final part reviews the dynamic models for vibration analysis of cracked gear systems including lumped mass models and FE models, where the crack effects are characterized by introducing TVMS of cracked gear pairs into the system dynamic models. The well known open problems about cracked gear dynamics are finally stated, and some new research interests are also pointed out. The review will provide valuable references for future studies on dynamics of cracked gears. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Gear tooth fatigue cracks can be caused by many reasons, such as inappropriate operating conditions, material defects, manufacturing errors [1]. The crack often propagates either along the tooth root or along the rim, which depends on the gear geometry and the applied torque on the gear [2–24]. Its propagation direction may vary and it is usually determined by crack tip stress intensity factors (SIFs). The tooth crack can change mesh stiffness and therefore produce abnormal vibration responses, such as impact and high frequency noise. First of all, it is important to predict the fatigue crack propagation path with the aim of estimating the gear remaining life. Finite element (FE) method using the principles of linear elastic fracture mechanics (LEFM) are widely used to simulate the propagation path. Once the propagation path is determined, the corre- sponding time-varying mesh stiffness (TVMS) can be calculated using theoretical or experimental methods [25–64]. The changed TVMS can result in different dynamic responses, compared to the healthy gear systems. The dynamic responses of the cracked gear systems can be estimated using lumped mass models or FE models. http://dx.doi.org/10.1016/j.engfailanal.2015.06.004 1350-6307/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +86 24 83684491. E-mail address: mahui_2007@163.com (H. Ma). Engineering Failure Analysis 55 (2015) 224–245 Contents lists available at ScienceDirect Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal