Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.

References

1.
Weber
,
C.
, and
Banaschek
,
K.
,
1953
,
Formänderung und Profilrücknahme bei Gerad-und Schrägverzahnten Antriebstechnik
, Vol.
11
,
Vieweg
,
Braunschweig
.
2.
Attia
,
A. Y.
,
1964
, “
Deflection of Spur Gear Teeth Cut in Thin Rims
,”
ASME J. Manuf. Sci. Eng.
,
86
(
4
), pp.
333
341
.10.1115/1.3670554
3.
Cornell
,
R. W.
,
1981
, “
Compliance and Stress Sensitivity of Spur Gear Teeth
,”
ASME J. Mech. Des.
,
103
(
2
), pp.
447
459
.10.1115/1.3254939
4.
Winter
,
H.
, and
Podlesnik
,
B.
,
1983
, “
Zahnfedersteifigkeit von Stirnrad-paaren, Teil 1
,”
Antriebstechnik
,
22
(
3
), pp.
39
42
.
5.
Winter
,
H.
, and
Podlesnik
,
B.
,
1983
, “
Zahnfedersteifigkeit von Stirnrad-paaren, Teil 2
,”
Antriebstechnik
,
22
(
5
), pp.
51
58
.
6.
Winter
,
H.
, and
Podlesnik
,
B.
,
1983
, “
Zahnfedersteifigkeit von Stirnrad-paaren, Teil 3
,”
Antriebstechnik
,
23
(
11
), pp.
43
49
.
7.
Sainsot
,
P.
,
Velex
,
P.
, and
Duverger
,
O.
,
2004
, “
Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
748
752
.10.1115/1.1758252
8.
Wilcox
,
L.
, and
Coleman
,
W.
,
1973
, “
Application of Finite Elements to the Analysis of Gear Tooth Stresses
,”
ASME J. Manuf. Sci. Eng.
,
95
(
4
), pp.
1139
1148
.10.1115/1.3438262
9.
Chabert
,
G.
,
Tran
,
T. D.
, and
Mathis
,
R.
,
1974
, “
An Evaluation of Stresses and Deflections of Spur Gear Teeth Under Strain
,”
ASME J. Manuf. Sci. Eng.
,
96
(
1
), pp.
85
93
.10.1115/1.3438335
10.
Umezawa
,
K.
,
1972
, “
Deflections and Moments Due to a Concentrated Load on a Rack-Shaped Cantilever Plate With Finite Width for Gears
,”
Bull. JSME
,
15
(
79
), pp.
116
130
.10.1299/jsme1958.15.116
11.
Yau
,
E.
,
Busby
,
H. R.
, and
Houser
,
D. R.
,
1994
, “
A Rayleigh-Ritz Approach to Modeling Bending and Shear Deflections of Gear Teeth
,”
Comput. Struct.
,
50
(
5
), pp.
705
713
.10.1016/0045-7949(94)90429-4
12.
Cai
,
Y.
,
1995
, “
Simulation of the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair)
,”
ASME J. Mech. Des.
,
117
(
3
), pp.
460
469
.10.1115/1.2826701
13.
Seager
,
D. L.
,
1967
, “
Some Elastic Effects in Helical Gears
,” Ph.D. thesis, Cambridge University, Cambridge, p.
209
.
14.
Schmidt
,
G. R.
,
Pinnekamp
,
W.
, and
Wunder
,
A.
,
1980
, “
Optimal Tooth Profile Correction of Helical Gears
,”
Proceedings of the Third International Power Transmissions and Gearing Conference
, San Francisco, Paper No. DET-110.
15.
Ajmi
,
M.
, and
Velex
,
P.
,
2005
, “
A Model for Simulating the Quasi-Static and Dynamic Behaviour of Solid Wide-Faced Spur and Helical Gears
,”
Mech. Mach. Theory
,
40
(
2
), pp.
173
190
.10.1016/j.mechmachtheory.2003.06.001
16.
Vedmar
,
L.
,
1981
, “
On the Design of External Involute Helical Gears
,” Ph.D. thesis, Lund Technical University, Lund, p.
100
.
17.
Steward
,
J. H.
,
1989
, “
Elastic Analysis of Load Distribution in Wide-Faced Spur Gears
,” Ph.D. thesis, University of Newcastle, Newcastle, p.
208
.
18.
Haddad
,
C. D.
,
1991
, “
The Elastic Analysis of Load Distribution in Wide-Faced Helical Gears
,” Ph.D. thesis, University of Newcastle, Newcastle, p.
470
.
19.
Smith
,
J. D.
,
2003
,
Gear Noise and Vibration
,
Marcel Dekker
,
Cambridge
, Cambridge, pp.
35
40
.
20.
Bruyère
,
J.
, and
Velex
,
P.
,
2013
, “
Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method
,”
ASME J. Mech. Des.
,
135
(
7
), p.
071009
.10.1115/1.4024374
21.
ISO∕DIS 6336-2 &3,
2004
,
Calculation of Load Capacity of Spur and Helical Gears—Parts 2 and 3
,
International Organization for Standardization
,
Geneva, Switzerland
.
22.
Velex
,
P.
, and
Sainsot
,
P.
,
2002
, “
An Analytical Study of Tooth Friction Excitations in Errorless Spur and Helical Gears
,”
Mech. Mach. Theory
,
37
(
7
), pp.
641
658
.10.1016/S0094-114X(02)00015-0
23.
Maatar
,
M.
, and
Velex
,
P.
,
1996
, “
An Analytical Expression of the Time-Varying Contact Length in Perfect Cylindrical Gears-Some Possible Applications in Gear Dynamics
,”
ASME J. Mech. Des.
,
118
(
4
), pp.
586
589
.10.1115/1.2826933
24.
Cai
,
Y.
, and
Hayashi
,
T.
,
1992
, “
The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make Its Rotational Vibration Equal Zero
,”
Proceedings of the 6th ASME International Power Transmission and Gearing Conference
, Phoenix, pp.
453
460
.
25.
Pedrero
,
J. I.
,
Vallejo
,
I. I.
, and
Pleguezuelos
,
M.
,
2007
, “
Calculation of Tooth Bending Strength and Surface Durability of High Transverse Contact Ratio Spur and Helical Gear Drives
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
69
74
.10.1115/1.2403773
26.
Houser
,
D. R.
,
Harianto
,
J.
,
Iyer
,
N.
,
Josephson
,
J.
, and
Chandrasekaren
,
B.
,
2000
, “
A Multi-Variable Approach to Determining the “Best” Gear Design
,”
Proceedings of the 8th ASME International Power Transmission and Gearing Conference
, Baltimore, Sept. 10–13.
27.
Sundaresan
,
S.
,
Ishii
,
K.
, and
Houser
,
D. R.
,
1991
, “
A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error
,”
ASME J. Mech. Des.
,
113
(
3
), pp.
318
325
.10.1115/1.2912785
28.
Sundaresan
,
S.
,
Ishii
,
K.
, and
Houser
,
D. R.
,
1992
, “
Design Optimization for Robustness Using Performance Simulation Programs
,”
Eng. Optim.
,
20
(
3
), pp.
163
178
.10.1080/03052159208941278
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