A Comparison of Several Methods for the Calculation of Gear Mesh Stiffness

The time varying gear mesh stiffness is one of the main excitations that cause unwanted vibration and noise of gear transmission systems. Numerous methods for the calculation of gear mesh stiffness have been introduced by different researchers. This paper generalizes three commonly-used approaches that have been used in literature to yield gear mesh stiffness. They are based on finite element methods, analytical methods using the potential energy principle, and an approximation method based on the ISO standard. Systematic comparisons among them were made in terms of the mesh stiffness curves, corresponding order spectrum as well as the amount of time used for computation. The advantages and disadvantages of each method are summarized.

[1]  Philippe Velex,et al.  Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears , 2015 .

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

[3]  Ian Howard,et al.  Calculation of the Combined Torsional Mesh Stiffness of Spur Gears with Two- and Three-Dimensional Parametrical FE Models , 2011 .

[4]  Giorgio Bonori,et al.  Non-smooth dynamics of spur gears with manufacturing errors , 2007 .

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

[6]  Philippe Velex,et al.  Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method , 2013 .

[7]  Y. Cai,et al.  The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment) , 1994 .

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

[9]  Geng Liu,et al.  A robust model for determining the mesh stiffness of cylindrical gears , 2015 .

[10]  Bangchun Wen,et al.  Time-varying mesh stiffness calculation of spur gears with spalling defect , 2016 .

[11]  Robert G. Parker,et al.  NON-LINEAR DYNAMIC RESPONSE OF A SPUR GEAR PAIR: MODELLING AND EXPERIMENTAL COMPARISONS , 2000 .

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

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

[14]  Mohammad M. Megahed,et al.  Evaluation of spur gear mesh compliance using the finite element method , 1999 .

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

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

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

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

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

[20]  Wennian Yu,et al.  Analytical modeling of spur gear corner contact effects , 2016 .

[21]  P. Velex.  On the modelling of spur and helical gear dynamic behaviour , 2012, 1204.2636.

[22]  P. Velex,et al.  An Analytical Expression for the Time-Varying Contact Length in Perfect Cylindrical Gears: Some Possible Applications in Gear Dynamics , 1996 .

[23]  Xi Wu,et al.  A Comparison of Gear Mesh Stiffness Modeling Strategies , 2011 .

[24]  Wennian Yu,et al.  The dynamic coupling behaviour of a cylindrical geared rotor system subjected to gear eccentricities , 2017 .

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