Improved analytical methods for calculation of gear tooth fillet-foundation stiffness with tooth root crack

Abstract Two improved analytical calculation models of gear tooth fillet-foundation stiffness are proposed for spur gears with tooth root crack. The proposed two models are capable of taking tooth root crack into account in the calculation of gear tooth fillet-foundation stiffness. For Model-1, the reduction of gear tooth fillet-foundation stiffness is assumed to be the production of the stiffness under healthy condition and the ratio of the crack length to the tooth thickness along the potential crack path. While in Model-2, the stiffness of the gear tooth fillet-foundation is calculated by updating related geometrical parameters in the traditional calculation formulas for the healthy gears according to the variation of the load carrying zone due to tooth root crack. The two calculation models for calculating the tooth fillet-foundation stiffness of cracked gears are verified by the finite element method (FEM). The results show that model-1 has a relatively poor accuracy for large crack cases when the position of applied force is close to the tooth root, while model-2 has a higher accuracy for both small and large crack length. The proposed models can be employed to improve the accuracy of gear mesh stiffness calculation and assist gear faults detection and diagnosis.

[1]  Wanming Zhai,et al.  Dynamic investigation of a locomotive with effect of gear transmissions under tractive conditions , 2017 .

[2]  R. Cornell.  Compliance and Stress Sensitivity of Spur Gear Teeth , 1981 .

[3]  Kaiyun Wang,et al.  Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack , 2016 .

[4]  Yimin Shao,et al.  Dynamic simulation of planetary gear set with flexible spur ring gear , 2013 .

[5]  Hui Ma,et al.  Review on dynamics of cracked gear systems , 2015 .

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

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

[8]  Hui Ma,et al.  Improved time-varying mesh stiffness model of cracked spur gears , 2015 .

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

[10]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

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

[12]  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 .

[13]  Roberto Ballarini,et al.  Gear crack propagation investigations , 1998 .

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

[15]  C. James Li,et al.  ESTIMATING SIZE OF GEAR TOOTH ROOT CRACK USING EMBEDDED MODELLING , 2002 .

[16]  Jin Zeng,et al.  An improved analytical method for mesh stiffness calculation of spur gears with tip relief , 2016 .

[17]  Bangchun Wen,et al.  Evaluation of optimum profile modification curves of profile shifted spur gears based on vibration responses , 2016 .

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

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

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

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

[22]  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 .

[23]  Wanming Zhai,et al.  A locomotive–track coupled vertical dynamics model with gear transmissions , 2017 .

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

[25]  R.B. Randall.  The use of simulation models to generate data corresponding to faults in machines , 2009, 2009 8th International Conference on Reliability, Maintainability and Safety.

[26]  Yimin Shao,et al.  Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges , 2017 .

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