A linear Finite Strip element for the analysis of rectangular and annular sector thick plates is presented to permit the deflection analysis of spur and straight bevel gear teeth, which are respectively modeled as rectangular and annular sector cantilever plates. Plate deflections are obtained by a hybrid procedure based on the minimum total potential energy theorem, which retains advantages of both the orthotropic-plate method and the Finite Element concept and is called the Finite Strip Method. The formulation accounting for transverse shear deformation is based on Mindlin’s plate theory. Since the presented Finite Strip element supports any combination of continuous thickness variations, the true shape of the tooth is used in the solution. The formulation can be easily applied to any boundary conditions and supports any type and combination of transverse loads and moments. Application of the Finite Strip Method to predict the deflection of spur and straight bevel gear teeth is demonstrated and results are compared to those obtained by the Finite Element Method.

Issue Section:
Research Papers
Topics:
Bevel gears, Deflection, Finite strip method, Plates (structures), Strips, Accounting, Boundary-value problems, Cantilevers, Finite element analysis, Finite element methods, Plate theory, Potential energy, Shapes, Shear deformation, Stress, Theorems (Mathematics)
1.
Arbabi
F.
, and
Li
F.
,
1991
, “
Macrostrip for Variable Section Plates
,”
J. Struct. Div.
, Vol.
117
, pp.
1759
–
1779
.
2.
Attia
A. Y.
,
1964
, “
Deflection of Spur Gear Teeth Cut in Thin Rims
,”
ASME Journal of Engineering for Industry
, Vol.
86
, pp.
333
–
342
.
3.
Baud
R. V.
, and
Peterson
R. E.
,
1929
, “
Load Stress Cycle in Gear Teeth
,”
J. Mech. Engr. Sci.
, Vol.
51
, pp.
653
–
662
.
4.
Burdon, R. L., and Douglas Faires, J., 1989, Numerical Analysis, 4th Ed. PWS-KENT, Boston.
5.
Cardou
A.
, and
Tordion
G. V.
,
1985
, “
Calculation of Spur Gear Tooth Flexibility by the Complex Potential Method
,”
Transactions of the ASME
, Vol.
107
, pp.
38
–
42
.
6.
Cheung
M. S.
, and
Chan
M. Y. T.
,
1981
, “
Static and Dynamic Analysis of Thin and Thick Sectorial Plates by the Finite Strip Method
,”
Comp. Struct.
, Vol.
14
, pp.
79
–
88
.
7.
Cheung
Y. K.
,
1968
, “
The Finite Strip Method in the Analysis of Elastic Plates With Two Opposite Simply Supported Ends
,”
Proc. Inst. Civ. Eng.
, Vol.
40
, pp.
1
–
7
.
8.
Cheung, Y. K., 1976, Finite Strip in Structural Analysis, 1st Ed. Pergamon Press, Oxford.
9.
Cheung, Y. K., Fan, S. C., and Wu, C. Q., 1982, “Spline Finite Strip in Structure Analysis,” Proc. Int. Conf. on Finite Element Method, Shanghai, pp. 704–709.
10.
Cornell
R. W.
,
1980
, “
Compliance and Stress Sensitivity of Spur Gear Teeth
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
103
, pp.
447
–
459
.
11.
Dhatt, G., and Touzot, G., 1981, Une Pre´sentation de la Me´thode des E´le´ments Finis, Presses de l’Universite´ Laval, Que´bec.
12.
Gagnon, P., Gosselin, C., and Cloutier, L., “A Finite Strip Element for the Analysis of Variable Thickness Rectangular Plates,” Comp. Struct., in press.
13.
Gosselin
C. J.
, and
Cloutier
L.
,
1993
, “
The Generating Space for Parabolic Motion Error Spiral Bevel Gear Cut by the Gleason Method
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
483
–
489
.
14.
Imbert, J. F., 1984, Analyse des Structures par E´le´ments Finis, 2nd Ed. Cepadues-Editions, France.
15.
Loo, Y. C., and Cusens, A. C., 1978, The Finite Strip Method in Bridge Engineering, Cement and Concrete Association.
16.
Mawenya
A. S.
, and
Davies
J. D.
,
1974
, “
Finite Strip Analysis of Plate Bending Including Transverse Shear Effects
,”
Building Science
, Vol.
9
, pp.
175
–
180
.
17.
Mindlin
R. D.
,
1945
, “
Influence of Rotary Inertia and Shear on Flexural Motions of Isotropic Elastic Plates
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
12
, pp.
69
–
77
.
18.
Mizusawa
T.
, and
Takami
K.
,
1992
, “
Vibration of Tapered Thickness Annular Sector Plates by Spline Element Method
,”
J. Sound Vibr.
, Vol.
154
, pp.
147
–
160
.
19.
Muthukumar
R.
, and
Raghavan
M. R.
,
1987
, “
Estimation of Gear Tooth Deflection by the Finite Element Method
,”
Mech. Mach. Theory
, Vol.
22
, pp.
177
–
181
.
20.
On˜ate
E.
, and
Suarez
B.
,
1983
, “
A Comparison of the Linear, Quadratic and Cubic Mindlin Strip Elements for the Analysis of Thick and Thin Plates
,”
Comp. Struct.
, Vol.
17
, pp.
427
–
439
.
21.
Powell
G. H.
, and
Ogden
D. W.
,
1969
, “
Analysis of Orthotropic Bridge Decks
,”
Am. Soc. Civ. Engrs.
, Vol.
95
, ST5, pp.
909
–
923
.
22.
Timoshenko, S. P., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill, New York.
23.
Tobe
T.
,
Kato
M.
, and
Inoue
K.
,
1978
, “
Bending of Stub Cantilever Plate and Some Applications to Strength of Gear Teeth
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
100
, pp.
374
–
381
.
24.
Uko
C. E. A.
, and
Cusens
A. R.
,
1988
, “
Application of Spline Finite Strip Analysis to Variable Depth Bridges
,”
Cummun. Appli. Numer. Meth.
, Vol.
4
, pp.
273
–
278
.
25.
Vaidyanathan
S.
,
Busby
H. R.
, and
Houser
D. R.
,
1994
, “
A Numerical Approach to the Static Analysis of an Annular Sector Mindlin Plate With Applications to Bevel Gear Design
,”
Comp. Struct.
, Vol.
51
, pp.
255
–
266
.
26.
Walker
H.
,
1938
, “
Gear Tooth Deflection and Profile Modification
,”
The Engineer
, Vol.
166
, pp.
434
–
436
.
27.
Weber, C., 1949, “The Deformation of Loaded Gears and the Effect on Their Load Carrying Capacity—Part I,” Department of Scientific and Industrial Research, London.
28.
Wellauer
E. J.
, and
Seireg
A.
,
1960
, “
Bending Strength of Gear Teeth by Cantilever-Plate Theory
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
82
, pp.
205
–
212
.
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