Time-varying mesh stiffness calculation of cracked spur gears

Abstract Considering the misalignment of gear root circle and base circle and accurate transition curve, an improved mesh stiffness model for a healthy gear pair is proposed and validated by the finite element method (FEM). Based on the improved method, three mesh stiffness calculation methods (method 1: straight lines for crack path and limiting line; method 2: straight line for crack path and parabolic curve for limiting line proposed in Ref. [1] ; method 3: parabolic curves for crack path and limiting line) for cracked gear pair are presented and compared with FEM. The results show that there is a significant difference between method 1 and FEM under large crack condition and the results of methods 2 and 3 are quite close to FEM result, which also shows that the parabolic curve as a limiting line is appropriate. Mesh stiffness of method 2 is very close to that of method 3, which also shows that it is acceptable to assume the crack path to be a straight line.

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

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

[3]  Robert G. Parker,et al.  An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model , 2012 .

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

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

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

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

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

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

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

[11]  Guo Zhong,et al.  Parameterization Precise Modeling of Involutes Spur Gear Based on APDL , 2010 .

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

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

[14]  Hui Ma,et al.  Effects of tip relief on vibration responses of a geared rotor system , 2014 .

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

[16]  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 .

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

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

[19]  Zaigang Chen,et al.  Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack , 2013 .

[20]  David G. Lewicki,et al.  Gear Crack Propagation Path Studies: Guidelines for Ultra-Safe Design , 2001 .

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

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

[23]  Hengan Ou,et al.  A finite element method for 3D static and dynamic contact/impact analysis of gear drives , 2007 .