Abstract
A computational model is proposed for the prediction of friction-related mechanical efficiency losses of parallel-axis gear pairs. The model incorporates a gear load distribution model, a friction model, and a mechanical efficiency formulation to predict the instantaneous mechanical efficiency of a gear pair under typical operating, surface, and lubrication conditions. The friction model uses a new friction coefficient formula obtained by using a validated non-Newtonian thermal elastohydrodynamic lubrication (EHL) model in conjunction with a multiple linear regression analysis. The load and friction coefficient distribution predictions are used to compute instantaneous torque/power losses and the mechanical efficiency of a gear pair at any given rotational position. Efficiency measurements from gear pairs having various gear designs and surface treatments are compared to model predictions. Mechanical efficiency predictions are shown to be within 0.1% of the measured values, indicating that the proposed efficiency model is accurate. Results of a parametric study are presented at the end to highlight the influence of key basic gear geometric parameters, tooth modifications, operating conditions, surface finish, and lubricant properties on mechanical efficiency losses.
Issue Section:
Research Papers
References
1.
Reuleaux
,
F.
,
1886, “Friction in Tooth
Gearing
,” Trans. ASME
0097-6822, VIII
, pp.
45
–85
.2.
Martin
, K.
F.
, 1978,
“A Review of Friction Predictions in Gear
Teeth
,” Wear
0043-1648, 49
,
201
–238
.3.
Yada
,
T.
,
1997, “Review of Gear
Efficiency Equation and Force Treatment
,” JSME Int.
J., Ser. C
1340-8062, 40
, pp.
1
–8
.4.
Li
,
Y.
, and
Seireg
, A.
A.
, “Predicting the Coefficient of
Friction in Sliding-Rolling Contacts
,” Tribology Conference,
K18.5.
Denny
, C.
M.
, 1998,
“Mesh Friction in Gearing
,” AGMA Fall
Technical Meeting, 98FTM2.6.
Pedrero
, J.
I.
, 1999,
“Determination of the Efficiency of Cylindrical Gear
Sets
,” 4th World Congress on Gearing and Power Transmission,
Paris, France.7.
Michlin
,
Y.
, and
Myunster
,
V.
,
2002, “Determination of
Power Losses in Gear Transmissions with Rolling and Sliding Friction
Incorporated
,” Mech. Mach. Theory
0094-114X, 37
, pp.
167
–174
.8.
Benedict
, G.
H.
, and Kelly
, B.
W.
, 1960,
“Instantaneous Coefficients of Gear Tooth
Friction
,” Transactions of ASLE, ASLE Lubrication
Conference, 57
–70
.9.
Kelley
, B.
W.
, and Lemanski
,
A. J.
,
1967–1968, “Lubrication
of Involute Gearing
,” Proc. Inst. Mech.
Eng.
0020-3483, 182
, pp.
173
–184
.10.
ISO TC 60, DTR 13989.
11.
O’Donoghue
, J.
P.
, and Cameron
,
A.
,
1966, “Friction and
Temperature in Rolling Sliding Contacts
,” ASLE
Trans.
0569-8197, 9
, pp.
186
–194
.12.
Drozdov
, Y.
N.
, and Gavrikov
,
Y. A.
, 1967,
“Friction and Scoring Under the Conditions of Simultaneous
Rolling and Sliding of Bodies
,” Wear
0043-1648, pp.
291
–302
.13.
Misharin
, Y.
A.
, 1958,
“Influence of the Friction Condition on the Magnitude of the
Friction Coefficient in the Case of Rollers With Sliding
,”
Proceedings of Int. Conference on Gearing, Inst. Mech.
Eng.
, London, pp.
159
–164
.14.
Ku
, P.
M.
, Staph
, H.
E.
, and Carper
, H.
J.
, 1978,
“Frictional and Thermal Behaviors of Sliding Rolling
Concentrated Contacts
,” ASME J. Lubr.
Technol.
0022-2305, 100
, pp.
121
–128
.15.
Naruse
,
C.
,
Haizuka
,
S.
,
Nemoto
,
R.
, and
Kurokawa
,
K.
,
1986, “Studies on
Frictional Loss, Temperature Rise and Limiting Load for Scoring of Spur
Gear
,” Bull. JSME
0021-3764, 29
, pp.
600
–608
.16.
Sasaki
,
T.
,
Okamura
,
K.
, and
Isogai
,
R.
,
1961–1963, “Fundamental
Research in Gears
,” Bull. JSME
0021-3764, 4
,
pp.382
–393
, Sasaki
,
T.
,
Okamura
,
K.
, and
Isogai
,
R.
,
1961–1963, “Fundamental
Research in Gears
,” Bull. JSME
0021-3764, 5
, pp.
561
–569
, Sasaki
,
T.
,
Okamura
,
K.
, and
Isogai
,
R.
,
1961–1963, “Fundamental
Research in Gears
,” Bull. JSME
0021-3764, 6
, pp.
364
–375
.17.
Barnes
, J.
P.
, 1997,
“Non-dimensional Characterization of Gear Geometry, Mesh Loss
and Windage
,” AGMA 97FTM11.18.
Hohn
, B.
R.
, and Steingrover
,
K.
,
1998, “Local
Coefficients of Friction in Worm Gear Contacts
,” AGMA
98FTM10.19.
Heingartner
,
P.
, and
Mba
,
D.
,
2003, “Determining Power
Losses in The Helical Gear Mesh; Case Study
,” Proceeding of
DETC’3, ASME 2003 Design Engineering Technical Conferences and Computers and
Information in Engineering Conference, Chicago, Illinois.20.
Anderson
, N.
E.
, and Loewenthal
,
S. H.
, 1986,
“Efficiency of Nonstandard and High Contact Ratio Involute
Spur Gears
,” ASME J. Mech., Transm., Autom.
Des.
0738-0666, 108
, pp.
119
–126
.21.
Anderson
, N.
E.
, and Loewenthal
,
S. H.
, 1982,
“Design of Spur Gears for Improved
Efficiency
,” ASME J. Mech. Des.
1050-0472, 104
, pp.
767
–774
.22.
Anderson
, N.
E.
, and Loewenthal
,
S. H.
, 1981,
“Effect of Geometry and Operating Conditions on Spur Gear
System Power Loss
,” ASME J. Mech. Des.
1050-0472, 103
, pp.
151
–159
.23.
Vaishya
,
M.
, and
Houser
, D.
R.
, 1999,
“Modeling and Measurement of Sliding Friction for Gear
Analysis
,” AGMA 99FTMS1, Lakewood, CO.24.
Martin
, K.
F.
, 1981,
“The Efficiency of Involute Spur Gears
,”
ASME J. Mech. Des.
1050-0472, 103
, pp.
160
–169
.25.
Dowson
,
D.
, and
Higginson
, G.
R.
, 1964,
“A Theory of Involute Gear Lubrication
,”
Proceeding of a Symposium Organized by the Mechanical Tests of
Lubricants Panel of the Institute
, Institute of
Petroleum
, Gear Lubrication, Elsevier, London,
8
–15
.26.
Simon
,
V.
,
1981, “Load Capacity and
Efficiency of Spur Ears in Regard to Thermo-End
Lubrication
,” International Symposium on Gearing and Power
Transmissions, Tokyo, Japan.27.
Wu
,
S.
, and
Cheng
, H.
S.
, 1991,
“A Friction Model of Partial-EHL Contacts and its Application
to Power Loss in Spur Gears
,” Tribol.
Trans.
1040-2004, 34
, pp.
398
–407
.28.
Mihalidis
,
A.
,
Bakolas
,
V.
,
Panagiotidis
,
K.
, and
Drivakos
,
N.
,
2002, “Prediction of the
Friction Coefficient of Spur Gear Pairs
,” VDI-Berichte, NR.
1665, pp. 705
–719
.29.
Akin
, L.
S.
, 1974,
“EHD Lubricant Film Thickness Formulae for Power Transmission
Gears
,” ASME J. Lubr. Technol.
0022-2305, 96
, pp.
426
–431
.30.
Wellauer
, E.
J.
, and Holloway
,
S. H.
, 1976,
“Application of EHD Oil Film Theory to Industrial Gear
Drives
,” ASME J. Eng. Ind.
0022-0817, Series B, 98
, pp.
626
–634
.31.
Chittenden
, R.
J.
, Dowson
,
D.
,
Dunn
, J.
F.
, and Taylor
, C.
M.
, 1985,
“A Theoretical Analysis of The Isothermal Elastohydrodynamic
Lubricant of Concentrated Contacts
,” Proc. R. Soc.
London, Ser. A
1364-5021, 397
, pp.
271
–294
.32.
Simon
,
V.
,
1988, “Thermo-EHD
Analysis of Lubrication of Helical Gears
,” ASME J.
Mech. Des.
1050-0472, 110
, pp.
330
–336
.33.
Haizuka
,
S.
,
Naruse
,
C.
, and
Yamanaka
,
T.
,
1999, “Study of
Influence of Helix Angle on Friction Characteristics of Helical
Gears
,” Tribol. Trans.
1040-2004, 42
(3
), pp.
570
–580
.34.
Khonsari
, M.
M.
, and Booser
, E.
R.
, 2001,
Applied Tribology, Bearing Design and Lubrication
,
Wiley
, New York.35.
Conry
, T.
F.
, and Seireg
,
A.
,
1973, “A Mathematical
Programming Technique for the Evaluation of Load Distribution and Optimal
Modifications for Gear Systems
,” ASME J. Eng.
Ind.
0022-0817, 95
, pp.
1115
–1122
.36.
LDP, Gear Load Distribution Program, 2003, Gear Dynamics and Gear
Noise Research Laboratory, The Ohio State University, Columbus, Ohio,
USA.
37.
Dudley
, D.
W.
, 1994,
Handbook of Practical Gear Design
,
CRC
, Cleveland.38.
Colbourne
, J.
R.
, 1987,
The Geometry of Involute Gears
,
Springer-Verlag
, New York.39.
Litvin
, F.
L.
, 1994,
Gear Geometry and Applied Theory
, Prentice
Hall
, Englewood Cliffs, New Jersey.40.
Xu
,
H.
,
2005, “Development of a
Generalized Mechanical Efficiency Prediction Methodology for Gear
Pairs
,” Ph.D. Dissertation, Ohio State University, Columbus,
Ohio.41.
Cioc
,
C.
,
Cioc
,
S.
,
Moraru
,
L.
,
Kahraman
,
A.
, and
Keith
,
T.
,
2002, “A Deterministic
Elastohydrodynamic Lubrication Model of High-Speed Rotorcraft Transmission
Components
,” Tribol. Trans.
1040-2004, 45
, pp.
556
–562
.42.
Dowson
,
D.
, and
Higginson
, G.
R.
, 1977,
Elasto-hydrodynamic Lubrication
, SI ed.,
Pergamon Press
, Oxford,
England.43.
Chase
,
D.
,
2005, “The Development
of an Efficiency Test Methodology for High-Speed Gearbox
,”
MS thesis, The Ohio State University, Columbus, Ohio.44.
Johnson
, K.
L.
, and Cameron
,
R.
,
1967–68, “Shear Behavior
of Elastohydrodynamic Oil Films at High Rolling Contact
Pressures
,” Proc. Inst. Mech. Eng.
0020-3483, 182
(14
), pp.
307
–319
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