A new finite element model for stress analysis of gear drives is proposed. Tie-surface constraints are applied at each tooth of the gear model to obtain meshes that can be independently defined: a finer mesh at contact surfaces and fillet and a coarser mesh in the remaining part of the tooth. Tie-surface constraints are also applied for the connection of several teeth in the model. The model is validated by application of the Hertz's theory in a spiral bevel gear drive with localized bearing contact and by observation of convergency of contact and bending stresses. Maximum contact pressure, maximum Mises stress, maximum Tresca stress, maximum major principal stress, and loaded transmission errors are evaluated along two cycles of meshing. The effects of the boundary conditions that models with three, five, seven, and all the teeth of the gear drive provide on the above-mentioned variables are discussed. Several numerical examples are presented.

References

References
1.
Wilcox
,
L.
, and
Coleman
,
W.
,
1973
, “
Application of Finite Elements to the Analysis of Gear Tooth Stresses
,”
ASME J. Eng. Ind.
,
95
(
4
), pp.
1139
1148
.
2.
Handschuh
,
R. F.
, and
Litvin
,
F. L.
,
1991
, “
A Method for Determining Spiral-Bevel Gear Tooth Geometry for Finite Element Analysis
,” National Aeronautics and Space Administration, Washington, DC, AVSCOM Technical Report No.
91-C-020
.http://www.dtic.mil/dtic/tr/fulltext/u2/a242332.pdf
3.
Argyris
,
J. H.
,
Fuentes
,
A.
, and
Litvin
,
F. L.
,
2002
, “
Computerized Integrated Approach for Design and Stress Analysis of Spiral Bevel Gears
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
11–12
), pp.
1057
1095
.
4.
Gonzalez-Perez
,
I.
,
Roda-Casanova
,
V.
,
Fuentes
,
A.
,
Sanchez-Marin
,
F. T.
, and
Iserte
,
J. L.
,
2012
, “
A Finite Element Model for Consideration of the Torsional Effect on the Bearing Contact of Gear Drives
,”
ASME J. Mech. Des.
,
134
(
7
), p.
071007
.
5.
Li
,
S.
,
2002
, “
Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear
,”
ASME J. Mech. Des.
,
124
(
3
), pp.
511
517
.
6.
Gonzalez-Perez
,
I.
,
Fuentes
,
A.
,
Roda-Casanova
,
V.
,
Sanchez-Marin
,
F. T.
, and
Iserte
,
J. L.
,
2013
, “
A Finite Element Model for Stress Analysis of Lightweight Spur Gear Drives Based on Thin-Webbed and Thin-Rimmed Gears
,”
International Conference on Gears, VDI-Society for Product and Process Design
, Garching, Germany, Oct. 7–9, pp.
75
86
.
7.
Roda-Casanova
,
V.
,
Sanchez-Marin
,
F. T.
,
Gonzalez-Perez
,
I.
,
Iserte
,
J. L.
, and
Fuentes
,
A.
,
2013
, “
Determination of the ISO Face Load Factor in Spur Gear Drives by the Finite Element Modeling of Gears and Shafts
,”
Mech. Mach. Theory
,
65
, pp.
1
13
.
8.
Fuentes
,
A.
,
Ruiz-Orzaez
,
R.
, and
Gonzalez-Perez
,
I.
,
2016
, “
Compensation of Errors of Alignment Caused by Shaft Deflections in Spiral Bevel Gear Drives
,”
Theory and Practice of Gearing and Transmissions
(Mechanisms and Machine Science), Vol. 34, Springer, Cham, Switzerland, pp. 301–319.
9.
Vijayakar
,
S. M.
,
1987
, “
Finite Element Methods for Quasi-Prismatic Bodies With Application to Gears
,”
Ph.D. thesis
, The Ohio State University, Columbus, OH.https://etd.ohiolink.edu/pg_10?114811821050336::NO:10:P10_ETD_SUBID:138872
10.
Gonzalez-Perez
,
I.
, and
Fuentes
,
A.
,
2017
, “
Implementation of a Finite Element Model for Stress Analysis of Gear Drives Based on Multi-Point Constraints
,”
Mech. Mach. Theory
,
117
, pp.
35
47
.
11.
Mao
,
K.
,
2007
, “
Gear Tooth Contact Analysis and Its Application in the Reduction of Fatigue Wear
,”
Wear
,
262
(
11–12
), pp.
1281
1288
.
12.
Vijayakar
,
S. M.
,
1991
, “
A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem
,”
Int. J. Numer. Methods Eng.
,
31
(3), pp.
525
545
.
13.
Faggioni
,
M.
,
Samani
,
F. S.
,
Bertachi
,
G.
, and
Pellicano
,
F.
,
2011
, “
Dynamic Optimization of Spur Gears
,”
Mech. Mach. Theory
,
46
(
4
), pp.
544
557
.
14.
Wang
,
J.
,
Shen
,
W.
,
Wang
,
Z.
,
Yao
,
M.
, and
Zeng
,
X.
,
2014
, “
Multi-Objective Optimization of Drive Gears for Power Split Device Using Surrogate Models
,”
J. Mech. Sci. Technol.
,
28
(
6
), pp.
2205
2214
.
15.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
16.
Coy
,
J. J.
, and
Chao
,
C. H.
,
1981
, “
A Method of Selecting Grid Size to Account for Hertz Deformation in Finite Element Analysis of Spur Gears
,” NASA Lewis Research Center, Cleveland, OH, AVRADCOM Technical Report No.
81-C-14
.https://ntrs.nasa.gov/search.jsp?R=19810018987
17.
Gonzalez-Perez
,
I.
,
Iserte
,
J. L.
, and
Fuentes
,
A.
,
2011
, “
Implementation of Hertz Theory and Validation of a Finite Element Model for Stress Analysis of Gear Drives With Localized Bearing Contact
,”
Mech. Mach. Theory
,
46
(
6
), pp.
765
783
.
18.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
,
Gear Geometry and Applied Theory
,
Cambridge University Press
,
Cambridge, UK
.
19.
Dassault Systemes
,
2015
, “
ABAQUS/Standard Analysis User's Guide
,” Dassault Systemes, Inc., Waltham, MA.
20.
Krumme
,
W.
,
2013
,
Klingelnberg-Spiralkegelräder: Berechnung, Herstellung Und Einbau
,
Springer-Verlag
,
Berlin
.
21.
Gonzalez-Perez
,
I.
, and
Fuentes-Aznar
,
A.
,
2017
, “
Analytical Determination of Basic Machine-Tool Settings for Generation of Spiral Bevel Gears and Compensation of Errors of Alignment in the Cyclo-Palloid System
,”
Int. J. Mech. Sci.
,
120
, pp.
91
104
.
22.
Fuentes
,
A.
,
Ruiz-Orzaez
,
R.
, and
Gonzalez-Perez
,
I.
,
2014
, “
Computerized Design, Simulation of Meshing, and Finite Element Analysis of Two Types of Geometry of Curvilinear Cylindrical Gears
,”
Comput. Methods Appl. Mech. Eng.
,
272
, pp.
321
339
.
23.
Sheveleva
,
G. I.
,
Volkov
,
A. E.
, and
Medvedev
,
V. I.
,
2007
, “
Algorithms for Analysis of Meshing and Contact of Spiral Bevel Gears
,”
Mech. Mach. Theory
,
42
(
2
), pp.
198
215
.
24.
Jaluria
,
Y.
,
1996
,
Computer Methods for Engineering
,
Taylor & Francis
,
New York
.
You do not currently have access to this content.