Review on dynamics of cracked gear systems

Abstract Dynamic characteristics of cracked gear systems, also known as cracked-gear rotor systems, have received increasing interests among industry and academy in the past two decades. 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 analytical 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.

[1]  Anand Parey,et al.  Crack behavior in a high contact ratio spur gear tooth and its effect on mesh stiffness , 2013 .

[2]  Jiande Wang,et al.  Numerical and Experimental Analysis of Spur Gears in Mesh , 2003 .

[3]  Omar D. Mohammed,et al.  Improving mesh stiffness calculation of cracked gears for the purpose of vibration-based fault analysis , 2013 .

[4]  Renping Shao,et al.  Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis , 2013 .

[5]  Paul A. Wawrzynek,et al.  Consideration of Moving Tooth Load in Gear Crack Propagation Predictions , 2001 .

[6]  C. James Li,et al.  Gear fatigue crack prognosis using embedded model, gear dynamic model and fracture mechanics , 2005 .

[7]  Zhifang Zhu,et al.  Fault feature analysis of planetary gear system with tooth root crack and flexible ring gear rim , 2015 .

[8]  Christos Spitas,et al.  Experimental Evaluation of Stress Intensity Factors in Spur Gear Teeth , 2006 .

[9]  Srečko Glodež,et al.  Computational model for the analysis of bending fatigue in gears , 2002 .

[10]  Hui Ma,et al.  Effects of gear crack propagation paths on vibration responses of the perforated gear system , 2015 .

[11]  Marc Thomas,et al.  Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set , 2015 .

[12]  Hui Ma,et al.  Time-varying mesh stiffness calculation of cracked spur gears , 2014 .

[13]  Paul A. Wawrzynek,et al.  Simulating Fatigue Crack Growth in Spiral Bevel Gears , 2001 .

[14]  Anand Parey,et al.  Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect , 2006 .

[15]  Alfonso Fernández del Rincón,et al.  Effect of cracks and pitting defects on gear meshing , 2012 .

[16]  Mohamed Haddar,et al.  Three-Dimensional Analyses by Finite Element Method of a Spur Gear: Effect of Cracks in the Teeth Foot on the Mesh Stiffness , 2007 .

[17]  M. Ajmi,et al.  A Static and Dynamic Model of Geared Transmissions by Combining Substructures and Elastic Foundations—Applications to Thin-Rimmed Gears , 2007 .

[18]  Yimin Shao,et al.  Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth , 2011 .

[19]  Zhigang Tian,et al.  Uncertainty Quantification in Gear Remaining Useful Life Prediction Through an Integrated Prognostics Method , 2013, IEEE Transactions on Reliability.

[20]  Rui Ma,et al.  Research on the dynamic mechanism of the gear system with local crack and spalling failure , 2012 .

[21]  M. Kubur,et al.  Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment , 2004 .

[22]  Ming J. Zuo,et al.  Vibration signal modeling of a planetary gear set for tooth crack detection , 2015 .

[23]  Yimin Zhang,et al.  A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors , 2017 .

[24]  Mohammad Reza Forouzan,et al.  Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method , 2014 .

[25]  Omar D. Mohammed,et al.  Vibration signal analysis for gear fault diagnosis with various crack progression scenarios , 2013 .

[26]  Ming J. Zuo,et al.  Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set , 2014 .

[27]  Fakher Chaari,et al.  Study of a spur gear dynamic behavior in transient regime , 2011 .

[28]  Shaoping Xiao,et al.  Three dimensional fatigue crack initiation and propagation analysis of a gear tooth under various load conditions and fatigue life extension with boron/epoxy patches , 2015 .

[29]  Philippe Velex,et al.  A model for the simulation of the interactions between dynamic tooth loads and contact fatigue in spur gears , 2012 .

[30]  Anand Parey,et al.  Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photoelasticity technique , 2013 .

[31]  Anand Parey,et al.  Failure path based modified gear mesh stiffness for spur gear pair with tooth root crack , 2013 .

[32]  Yanyang Zi,et al.  An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack , 2014 .

[33]  Hui Ma,et al.  Fault features analysis of cracked gear considering the effects of the extended tooth contact , 2015 .

[34]  Yimin Shao,et al.  Dynamic features of planetary gear set with tooth plastic inclination deformation due to tooth root crack , 2013 .

[35]  Ian Howard,et al.  THE DYNAMIC MODELLING OF A SPUR GEAR IN MESH INCLUDING FRICTION AND A CRACK , 2001 .

[36]  Anand Parey,et al.  Spur gear dynamic models including defects: A review , 2003 .

[37]  R. B. Randall,et al.  Differential diagnosis of spall versus cracks in the gear tooth fillet region , 2004 .

[38]  Christopher G. Cooley,et al.  A Review of Planetary and Epicyclic Gear Dynamics and Vibrations Research , 2014 .

[39]  Zhifeng Liu,et al.  Study on Calculation Methods for Sampling Frequency of Acceleration Signals in Gear System , 2013 .

[40]  Omar D. Mohammed,et al.  Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis , 2015 .

[41]  Hossein Hosseini-Toudeshky,et al.  Finite element fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches , 2012 .

[42]  Roberto Ballarini,et al.  Effect of Rim Thickness on Gear Crack Propagation Path. , 1997 .

[43]  Anand Parey,et al.  Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness , 2013 .

[44]  Shuting Li,et al.  Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear , 2002 .

[45]  Robert B. Randall,et al.  Differential diagnosis of spall vs. cracks in the gear tooth fillet region: Experimental validation , 2009 .

[46]  Zhihong Man,et al.  Modeling and analysis of gear tooth crack growth under variable-amplitude loading , 2013 .

[47]  Fakher Chaari,et al.  Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness , 2009 .

[48]  D. C. H. Yang,et al.  Hertzian damping, tooth friction and bending elasticity in gear impact dynamics , 1987 .

[49]  William D. Mark,et al.  Assessing the role of plastic deformation in gear-health monitoring by precision measurement of failed gears , 2007 .

[50]  Hsiang H. Lin,et al.  Separation distance and static transmission error of involute spur gears , 1992 .

[51]  Mohamed Haddar,et al.  Following Spur Gear Crack Propagation in the Tooth Foot by Finite Element Method , 2010 .

[52]  Sukhwan Choi,et al.  Practical gear crack prognosis via gear condition index fusion, gear dynamic simulator, and fast crack growth model , 2007 .

[53]  T. Anderson,et al.  Fracture mechanics - Fundamentals and applications , 2017 .

[54]  A. Fernandez del Rincon,et al.  Defect Simulation in a Spur Gear Transmission Model , 2010 .

[55]  Ming J. Zuo,et al.  Simulation of spur gear dynamics and estimation of fault growth , 2008 .

[56]  Fakher Chaari,et al.  Dynamic behaviour modelling of a flexible gear system by the elastic foundation theory in presence of defects , 2010 .

[57]  Wennian Yu,et al.  The effects of spur gear tooth spatial crack propagation on gear mesh stiffness , 2015 .

[58]  Srečko Glodež,et al.  A computational model for determination of service life of gears , 2002 .

[59]  Grzegorz Litak,et al.  Dynamics of a Gear System with Faults in Meshing Stiffness , 2004, nlin/0405053.

[60]  An Sung Lee,et al.  Prediction of maximum unbalance responses of a gear-coupled two-shaft rotor-bearing system , 2005 .

[61]  Ian Howard,et al.  Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations , 2006 .

[62]  Bijan Mohammadi,et al.  Crack trajectory analysis of single-side repaired thin panels in mixed-mode conditions using glass/epoxy patches , 2008 .

[63]  Xiaojun Zhou,et al.  Time-Varying Meshing Stiffness Calculation and Vibration Analysis for a 16DOF Dynamic Model With Linear Crack Growth in a Pinion , 2012 .

[64]  Zaigang Chen,et al.  Dynamic Features of a Planetary Gear System With Tooth Crack Under Different Sizes and Inclination Angles , 2013 .

[65]  P. Velex,et al.  A model for simulating the quasi-static and dynamic behaviour of solid wide-faced spur and helical gears , 2005 .

[66]  Philippe Velex,et al.  Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula , 2004 .

[67]  Anand Parey,et al.  Effect of shaft misalignment and friction force on time varying mesh stiffness of spur gear pair , 2015 .

[68]  Walter Bartelmus,et al.  MATHEMATICAL MODELLING AND COMPUTER SIMULATIONS AS AN AID TO GEARBOX DIAGNOSTICS , 2001 .

[69]  Gerd Heber,et al.  Three-dimensional, parallel, finite element simulation of fatigue crack growth in a spiral bevel pinion gear , 2005 .

[70]  Hui Ma,et al.  Fault Feature Analysis of a Cracked Gear Coupled Rotor System , 2014 .

[71]  N. K. Anifantis,et al.  Finite element modeling of spur gearing fractures , 2002 .

[72]  Yimin Shao,et al.  Dynamic simulation of planetary gear with tooth root crack in ring gear , 2013 .

[73]  Kamal A. F. Moustafa,et al.  Mathematical modeling of gearbox including defects with experimental verification , 2012 .