Error Analysis on Finite Element Modeling of Involute Spur Gears

Finite element analysis can incorporate two-dimensional (2D) modeling if the geometry, load, and boundary conditions meet the requirements. For many applications, a wide range of problems are solved in 2D, due to the efficiency and costs of computation. However, care has to be taken to avoid modeling errors from significantly influencing the result. When the application area is nonlinear, such as when modeling contact problems or fracture analysis, etc, the 2D assumption must be used cautiously. In this paper, a large number of 2D and three-dimensional (3D) gear models were investigated using finite element analysis. The models included contact analysis between teeth in mesh, a gear body (disk), and teeth with and without a crack at the tooth root. The model results were compared using parameters such as the torsional (mesh) stiffness, tooth stresses and the stress intensity factors that are obtained under assumptions of plane stress, plane strain, and 3D analysis. The models considered variations of face width of the gear from 5 mm to 300 mm. This research shows that caution must be used especially where 2D assumptions are used in the modeling of solid gears.

[1]  Omer Eyercioglu,et al.  Evaluation of Gear Tooth Stresses by Finite Element Method , 1995 .

[2]  R. Muthukumar,et al.  Estimation of gear tooth deflection by the finite element method , 1987 .

[3]  Sandro Barone,et al.  Evaluation of the effect of misalignment and profile modification in face gear drive by a finite element meshing simulation , 2004 .

[4]  Rowland Richards,et al.  Principles of Solid Mechanics , 2000 .

[5]  Steven M. Lepi.  Practical Guide to Finite Elements: A Solid Mechanics Approach , 1998 .

[6]  A. Boresi,et al.  Elasticity in engineering mechanics , 1974 .

[7]  Vilmos Simon,et al.  Load Distribution in Cylindrical Worm Gears , 2000 .

[8]  P. C. Paris,et al.  Stress Analysis of Cracks , 1965 .

[9]  Michael M. Khonsari,et al.  Surface Temperature in Oscillating Sliding Interfaces , 2004 .

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

[11]  Teik C. Lim,et al.  Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics , 2003 .

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

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

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

[15]  Robert G. Parker,et al.  Mesh Phasing Relationships in Planetary and Epicyclic Gears , 2004 .

[16]  Wu Chang-hua,et al.  A Finite-Element-Based Study of the Load Distribution of a Heavily Loaded Spur Gear System With Effects of Transmission Shafts and Gear Blanks , 2003 .

[17]  Seney Sirichai,et al.  Torsional properties of spur gears in mesh using nonlinear finite element analysis. , 1999 .

[18]  Rajendra Singh,et al.  Strategies for Modeling Friction in Gear Dynamics , 2003 .

[19]  Ian Howard,et al.  THE DYNAMIC MODELLING OF A SPUR GEAR IN MESH INCLUDING FRICTION AND A CRACK , 2001 .

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