An innovative semi-analytical determination approach to numerical loaded tooth contact analysis (NLTCA) for spiral bevel and hypoid gears

Abstract Loaded tooth contact analysis (LTCA) has always been a significant contact mechanical performance optimization technique for spiral bevel and hypoid gears. To distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) based on economical software package, numerical loaded tooth contact analysis (NLTCA) and its innovative semi-analytical determination approach is developed. In full consideration of tooth flank flexural behavior characteristic, double-curved shell finite element modeling is performed and then improved tooth contact analysis (TCA) is applied for data-driven determination of loaded tooth contact points. Then, in additional to the global boundary condition, the accurate local boundary conditions is also investigated. In particular, local Rayleigh-Ritz method is used to get new semi-analytically tooth compliance determination by considering computational accuracy and efficiency. Furthermore, NLTCA model is established in considerations of the accurate contact point matching, compatibility and equilibrium conditions. Finally, the main NLTCA evaluations including load distribution, loaded contact pattern, loaded contact pressure and distribution, and loaded transmission error in consideration of time-varying meshing characteristics, respectively. The provided numerical instance can verify the proposed methodology.

[1]  Han Ding,et al.  A data-driven programming of the human-computer interactions for modeling a collaborative manufacturing system of hypoid gears by considering both geometric and physical performances , 2018, Robotics and Computer-Integrated Manufacturing.

[2]  Erasmo Carrera,et al.  Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core , 2014 .

[3]  Zhenyu Zhou,et al.  A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears , 2016 .

[4]  Ahmet Kahraman,et al.  A load distribution model for hypoid gears using ease-off topography and shell theory , 2009 .

[5]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[6]  Qi Fan.  Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process , 2006 .

[7]  Donald R. Houser,et al.  A rayleigh-ritz approach to modeling bending and shear deflections of gear teeth , 1994 .

[8]  Massimo Guiggiani,et al.  Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments , 2010 .

[9]  Masaki Kameyama,et al.  Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters , 2007 .

[10]  Han Ding,et al.  An accurate model of high-performance manufacturing spiral bevel and hypoid gears based on machine setting modification , 2016 .

[11]  Han Ding,et al.  A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears , 2017 .

[12]  Faydor L. Litvin,et al.  Identification and Minimization of Deviations of Real Gear Tooth Surfaces , 1991 .

[13]  Han Ding,et al.  Automatic data-driven operation and optimization of uncertain misalignment by considering mechanical power transmission performances of spiral bevel and hypoid gears , 2019, Appl. Soft Comput..

[14]  Vilmos Simon,et al.  FEM stress analysis in hypoid gears , 2000 .

[15]  Han Ding,et al.  A data-driven optimization model to collaborative manufacturing system considering geometric and physical performances for hypoid gear product , 2018, Robotics and Computer-Integrated Manufacturing.

[16]  Han Ding,et al.  Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears , 2016 .

[17]  Donald R. Houser,et al.  A numerical approach to the static analysis of an annular sector mindlin plate with applications to bevel gear design , 1994 .

[18]  Alessandro De Rosis,et al.  Ground-induced lift enhancement in a tandem of symmetric flapping wings , 2015 .

[19]  A. Alexeev,et al.  Resonance of flexible flapping wings at low Reynolds number. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Faydor L. Litvin,et al.  Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears , 2006 .

[21]  Theodore J. Krenzer.  Tooth Contact Analysis of Spiral Bevel and Hypoid Gears Under Load , 1981 .

[22]  Jose L. Iserte,et al.  Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact , 2011 .

[23]  Faydor L. Litvin,et al.  Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears , 2002 .

[24]  Aizoh Kubo,et al.  Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces , 1998 .

[25]  J. Chróścielewski,et al.  Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory , 2016 .

[26]  Massimo Guiggiani,et al.  Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification , 2009 .

[27]  Nicholas Fantuzzi,et al.  Generalized Differential Quadrature Finite Element Method for vibration analysis of arbitrarily shaped membranes , 2014 .

[28]  Han Ding,et al.  Six sigma robust multi-objective optimization modification of machine-tool settings for hypoid gears by considering both geometric and physical performances , 2018, Appl. Soft Comput..

[29]  F. Litvin,et al.  Gear geometry and applied theory , 1994 .

[30]  Han Ding,et al.  A novel collaborative manufacturing model requiring both geometric and physical evaluations of spiral bevel gears by design for six sigma , 2019, Mechanism and Machine Theory.

[31]  Han Ding,et al.  Accurate numerical computation of loaded tooth surface contact pressure and stress distributions for spiral bevel gears by considering time-varying meshing characteristics , 2019, Adv. Eng. Softw..

[32]  Faydor L. Litvin,et al.  Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry , 1998 .

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

[34]  Chung-Biau Tsay,et al.  Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques , 2001 .

[35]  H. Ding,et al.  An innovative determination approach to tooth compliance for spiral bevel and hypoid gears by using double-curved shell model and Rayleigh–Ritz approach , 2018, Mechanism and Machine Theory.

[36]  A. Ferreira,et al.  MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells , 2016 .

[37]  Massimo Guiggiani,et al.  Multi-objective ease-off optimization of hypoid gears for their efficiency, noise, and durability performances , 2011 .

[38]  Robert G. Parker,et al.  Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems , 2002 .

[39]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[40]  N. Rogacheva.  The Theory of Piezoelectric Shells and Plates , 1994 .

[41]  Wang Qi,et al.  Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a kriging model , 2018 .

[42]  Vilmos Simon,et al.  Load Distribution in Hypoid Gears , 2000 .

[43]  Nicholas Fantuzzi,et al.  The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach , 2016 .

[44]  F. Tornabene,et al.  The local GDQ method for the natural frequencies of doubly-curved shells with variable thickness: A general formulation , 2016 .

[45]  H. Ding,et al.  Numerical determination to loaded tooth contact performances in consideration of misalignment for the spiral bevel gears , 2019, International Journal of Mechanical Sciences.

[46]  Yi-Pei Shih,et al.  Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography , 2007 .

[47]  Ahmet Kahraman,et al.  An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears , 2010 .

[48]  Zhang-Hua Fong,et al.  Numerical tooth contact analysis of a bevel gear set by using measured tooth geometry data , 2015 .

[49]  Massimo Guiggiani,et al.  Nonlinear identification of machine settings for flank form modifications in hypoid gears , 2008 .

[50]  Louis Cloutier,et al.  Accurate tooth stiffness of spiral bevel gear teeth by the Finite Strip method , 1998 .

[51]  Romesh C. Batra,et al.  Local slamming impact of sandwich composite hulls , 2009 .

[52]  Song He,et al.  Effect of Sliding Friction on Spur and Helical Gear Dynamics and Vibro-Acoustics , 2008 .

[53]  H. Ding,et al.  New determination to loaded transmission error of the spiral bevel gear considering multiple elastic deformation evaluations under different bearing supports , 2019, Mechanism and Machine Theory.

[54]  Louis Cloutier,et al.  A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears , 1995 .

[55]  D. Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals , 2003 .