A physics-based fluid mechanics model is proposed to predict spin power losses of gear pairs due to oil churning and windage. While the model is intended to simulate oil churning losses in dip-lubricated conditions, certain components of it apply to air windage losses as well. The total spin power loss is defined as the sum of (i) power losses associated with the interactions of individual gears with the fluid, and (ii) power losses due to pumping of the oil at the gear mesh. The power losses in the first group are modeled through individual formulations for drag forces induced by the fluid on a rotating gear body along its periphery and faces, as well as for eddies formed in the cavities between adjacent teeth. Gear mesh pumping losses will be predicted analytically as the power loss due to squeezing of the lubricant, as a consequence of volume contraction of the mesh space between mating gears as they rotate. The model is applied to a unity-ratio spur gear pair to quantify the individual contributions of each power loss component to the total spin power loss. The influence of operating conditions, gear geometry parameters, and lubricant properties on spin power loss are also quantified at the end. A companion paper (Seetharaman et al., 2009, “Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation,” ASME J. Tribol., 131, p. 022202) provides comparisons to experiments for validation of the proposed model.

1.
Xu
,
H.
,
Kahraman
,
A.
,
Anderson
,
N. E.
, and
Maddock
,
D. G.
, 2007, “
Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs
,”
ASME J. Mech. Des.
0161-8458,
129
, pp.
58
68
.
2.
Martin
,
K. F.
, 1978, “
A Review of Friction Predictions in Gear Teeth
,”
Wear
0043-1648,
49
, pp.
201
238
.
3.
Daily
,
J. W.
, and
Nece
,
R. E.
, 1960, “
Chamber Dimensional Effects on Induced Flow and Frictional Resistance of Enclosed Rotating Disks
,”
ASME J. Basic Eng.
0021-9223,
82
, pp.
217
232
.
4.
Mann
,
R. W.
, and
Marston
,
C. H.
, 1961, “
Friction Drag on Bladed Disks in Housings as a Function of Reynolds Number, Axial and Radial Clearance and Blade Aspect Ratio and Solidity
,”
ASME J. Basic Eng.
0021-9223,
83
(
4
), pp.
719
723
.
5.
Bones
,
R. J.
, 1989, “
Churning Losses of Discs and Gears Running Partially Submerged in Oil
,”
Proceedings of the ASME Fifth International Power Transmission and Gearing Conference
, Chicago, IL, pp.
355
359
.
6.
von Karman
,
T.
, 1921, “
On Laminar and Turbulent Friction
,”
Z. Angew. Math. Mech.
,
1
, pp.
235
236
. 0044-2267
7.
Terekhov
,
A. S.
, 1991, “
Basic Problems of Heat Calculation of Gear Reducers
,”
JSME International Conference on Motion and Power Transmissions
, pp.
490
495
.
8.
Luke
,
P.
, and
Olver
,
A.
, 1999, “
A Study of Churning Losses in Dip-Lubricated Spur Gears
,”
J. Aerosp. Eng.
,
213
, pp.
337
346
. 0893-1321
9.
Ariura
,
Y.
,
Ueno
,
T.
, and
Sunamoto
,
S.
, 1973, “
The Lubricant Churning Loss in Spur Gear Systems
,”
Bull. JSME
,
16
, pp.
881
890
. 0021-3764
10.
Akin
,
L. S.
, and
Mross
,
J. J.
, 1975, “
Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears
,”
ASME J. Eng. Ind.
0022-0817,
97
, pp.
1266
1273
.
11.
Akin
,
L. S.
,
Townsend
,
J. P.
, and
Mross
,
J. J.
, 1975, “
Study of Lubricant Jet Flow Phenomenon in Spur Gears
,”
ASME J. Lubr. Technol.
0022-2305,
97
, pp.
288
295
.
12.
Pechersky
,
M. J.
, and
Wittbrodt
,
M. J.
, 1989, “
An Analysis of Fluid Flow Between Meshing Spur Gear Teeth
,”
Proceedings of the ASME Fifth International Power Transmission and Gearing Conference
, Chicago, IL, pp.
335
342
.
13.
Diab
,
Y.
,
Ville
,
F.
,
Houjoh
,
H.
,
Sainsot
,
P.
, and
Velex
,
P.
, 2005, “
Experimental and Numerical Investigations on the Air-Pumping Phenomenon in High-Speed Spur and Helical Gears
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
219
, pp.
785
800
.
14.
Changenet
,
C.
, and
Velex
,
P.
, 2007, “
A Model for the Prediction of Churning Losses in Geared Transmissions—Preliminary Results
,”
ASME J. Mech. Des.
0161-8458,
129
(
1
), pp.
128
133
.
15.
Höhn
,
B. R.
,
Michaelis
,
K.
, and
Völlmer
,
T.
, 1996, “
Thermal Rating of Gear Drives: Balance Between Power Loss and Heat Dissipation
,”
AGMA, Fall Technical Meeting
, pp.
1
12
, Paper No. 96FTM8.
16.
Dawson
,
P. H.
, 1984, “
Windage Losses in Larger High-Speed Gears
,”
Proceedings of the Institution of Mechanical Engineers
,
Part A: Power and Process Engineering
,
198
(
1
), pp.
51
59
. 0161-8458
17.
Diab
,
Y.
,
Ville
,
F.
, and
Velex
,
P.
, 2006, “
Investigations on Power Losses in High Speed Gears
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
1350-6501,
220
, pp.
191
298
.
18.
Eastwick
,
C. N.
, and
Johnson
,
G.
, 2008, “
Gear Windage: A Review
,”
ASME J. Mech. Des.
0161-8458,
130
(
3
), p.
034001
.
19.
Wild
,
P. M.
,
Dijlali
,
N.
, and
Vickers
,
G. W.
, 1996, “
Experimental and Computational Assessment of Windage Losses in Rotating Machinery
,”
ASME Trans. J. Fluids Eng.
0098-2202,
118
, pp.
116
122
.
20.
Al-Shibl
,
K.
,
Simmons
,
K.
, and
Eastwick
,
C. N.
, 2007, “
Modeling Gear Windage Power Loss From an Enclosed Spur Gears
,”
Proc. Inst. Mech. Eng., Part A
0957-6509,
221
(
3
), pp.
331
341
.
21.
Seetharaman
,
S.
,
Kahraman
,
A.
,
Moorhead
,
M. D.
, and
Petry-Johnson
,
T. T.
, 2009, “
Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation
,”
ASME J. Tribol.
,
131
, p.
022202
. 0161-8458
22.
Changenet
,
C.
, and
Velex
,
P.
, 2008, “
Housing Influences on Churning Losses in Geared Transmissions
,”
ASME J. Mech. Des.
0161-8458,
130
(
6
), p.
062603
.
23.
Streeter
,
L. V.
, and
Wylie
,
E. B.
, 1985,
Fluid Mechanics
,
8th ed.
,
McGraw-Hill
,
New York
.
24.
Schlichting
,
H.
, 1955,
Boundary-Layer Theory
,
McGraw-Hill
,
New York
.
25.
Petry-Johnson
,
T. T.
,
Kahraman
,
A.
,
Anderson
,
N. E.
, and
Chase
,
D. R.
, 2008, “
An Experimental Investigation of Spur Gear Efficiency
,”
ASME J. Mech. Des.
0161-8458,
130
(
6
), p.
062601
.
26.
Moorhead
,
M.
, 2007, “
Experimental Investigation of Spur Gear Efficiency and the Development of a Helical Gear Efficiency Test Machine
,” MS thesis, Ohio State University, Columbus, OH.
You do not currently have access to this content.