An analytical-finite-element method for calculating mesh stiffness of spur gear pairs with complicated foundation and crack

Abstract Gear weight optimization is mainly through thin-web and hole in gear foundation. In this paper, an analytical-finite-element model for calculating time-varying mesh stiffness of spur gear pairs with complicated foundation (thin-web and holes) and crack is developed. The pinion and gear foundations are simulated as cylinders and modeled by three-dimensional finite element. The tooth pair is equivalent to a spring and mesh stiffness of a tooth pair is obtained by potential energy method. The spring is rigidly coupled with the pinion and gear foundations. Then, three type examples are presented to verify the model. The first type example is three spur gear pairs with solid foundation. The second type example is gear pairs with thin-web and web holes. And the third example is a gear pair with the cracked foundation. The analysis results show that the model proposed in this paper is applicable and efficient for spur gears with complicated foundation and crack. Finally, the time-varying mesh stiffness is also studied to reveal the effects of web widths, web hole radii and crack lengths.

[1]  Ming J. Zuo,et al.  Dynamic modeling of gearbox faults: A review , 2018 .

[2]  Aizoh Kubo,et al.  Analysis of General Characteristics of Transmission Error of Gears With Convex Modification of Tooth Flank Form Considering Elastic Deformation Under Load , 2009 .

[3]  Wei Sun,et al.  Effects of flank deviation on load distributions for helical gear , 2011 .

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

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

[6]  Bangchun Wen,et al.  Effects of tooth crack on vibration responses of a profile shifted gear rotor system , 2015 .

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

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

[9]  Qibin Wang,et al.  Time-varying mesh stiffness analysis of a single-roller enveloping hourglass worm gear , 2019 .

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

[11]  Ian Howard,et al.  The torsional stiffness of involute spur gears , 2004 .

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

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

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

[15]  Yaguo Lei,et al.  A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears , 2018, Mechanical Systems and Signal Processing.

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

[17]  Anand Parey,et al.  Effect of Back-side Contact on Mesh Stiffness of Spur Gear Pair by Finite Element Method ☆ , 2017 .

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

[19]  Wanming Zhai,et al.  Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift , 2016 .

[20]  V. Simon.  Load and Stress Distributions in Spur and Helical Gears , 1988 .

[21]  Shuting Li,et al.  Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears , 2007 .

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

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

[24]  Shuting Li,et al.  Centrifugal load and its effects on bending strength and contact strength of a high speed thin-walled spur gear with offset web , 2008 .

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

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

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

[28]  A. Fernandez del Rincon,et al.  A model for the study of meshing stiffness in spur gear transmissions , 2013 .

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

[30]  Zaigang Chen,et al.  Mesh stiffness of an internal spur gear pair with ring gear rim deformation , 2013 .

[31]  Shuting Li,et al.  Effects of centrifugal load on tooth contact stresses and bending stresses of thin-rimmed spur gears with inclined webs , 2013 .

[32]  Shuting Li,et al.  Effects of misalignment error, tooth modifications and transmitted torque on tooth engagements of a pair of spur gears , 2015 .

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

[34]  Bangchun Wen,et al.  Time-varying mesh characteristics of a spur gear pair considering the tip-fillet and friction , 2017 .

[35]  Jie Zhang,et al.  Improved analytical methods for calculation of gear tooth fillet-foundation stiffness with tooth root crack , 2017 .

[36]  Bangchun Wen,et al.  An improved analytical method for calculating time-varying mesh stiffness of helical gears , 2018 .

[37]  Shuting Li.  Contact Stress and Root Stress Analyses of Thin-Rimmed Spur Gears With Inclined Webs , 2012 .

[38]  Louis Cloutier,et al.  Express Model for Load Sharing and Stress Analysis in Helical Gears , 2005 .

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

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

[41]  Zhao Bo,et al.  An improved time-varying mesh stiffness model for helical gear pairs considering axial mesh force component , 2018, Mechanical Systems and Signal Processing.

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

[43]  Shuting Li.  Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications , 2007 .

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

[45]  Yong Qin,et al.  Three new models for evaluation of standard involute spur gear mesh stiffness , 2018 .

[46]  Lixin Xu,et al.  Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears , 2017 .

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