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.
Issue Section:
Design of Direct Contact Systems
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
.10.1115/1.36705543.
Cornell
, R. W.
, 1981
, “Compliance and Stress Sensitivity of Spur Gear Teeth
,” ASME J. Mech. Des.
, 103
(2
), pp. 447
–459
.10.1115/1.32549394.
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
.10.1115/1.17582528.
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
.10.1115/1.34382629.
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
.10.1115/1.343833510.
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/jsme1958.15.11611.
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)90429-412.
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
.10.1115/1.282670113.
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.2003.06.00116.
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
.10.1115/1.402437421.
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)00015-023.
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
.10.1115/1.282693324.
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
.10.1115/1.240377326.
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
.10.1115/1.291278528.
Sundaresan
, S.
, Ishii
, K.
, and Houser
, D. R.
, 1992
, “Design Optimization for Robustness Using Performance Simulation Programs
,” Eng. Optim.
, 20
(3
), pp. 163
–178
.10.1080/03052159208941278Copyright © 2015 by ASME
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