An original displacement-based formulation of tooth friction power losses in spur and helical gears is established, which can account for the influence of tooth profile modifications. Several analytical formulas are derived enabling friction losses to be easily estimated for a wide range of gears at the design stage. Numerous comparisons with both the classic formulas in the literature and the results of numerical simulations are presented, which confirm the accuracy of the proposed approach.

1.
Reuleaux
,
F.
, 1894,
The Constructor—A Handbook of Machine Design
,
4th ed.
,
H. H.
Suplee
, ed.,
H. H. Suplee
,
Philadelphia, PA
, pp.
127
150
(available online at KMODDL).
2.
Weisbach
,
J.
, 1894,
Principles of the Mechanics of Machinery and Engineering
,
Wiley
,
New York
, Vol.
3
, pp.
347
360
.
3.
Buckingham
,
E.
, 1949,
Analytical Mechanics of Gears
,
McGraw-Hill
,
London
, pp.
395
425
.
4.
Merritt
,
H. E.
, 1971,
Gear Engineering
,
Pitman
,
New York
pp.
345
357
.
5.
Niemann
,
G.
, and
Winter
,
H.
, 1989,
Maschinenelement
,
Springer-Verlag
,
Berlin
, Vol.
2
.
6.
Pedrero
,
J. I.
, 1999, “
Determination of the Efficiency of Cylindrical Gear Sets
,”
Fourth World Congress on Gearing and Power Transmission
, Paris, Vol.
1
, pp.
297
302
.
7.
Martin
,
K. F.
, 1981, “
The Efficiency of Involute Spur Gears
,”
ASME J. Mech. Des.
0161-8458,
103
, pp.
160
169
.
8.
Trachman
,
E. G.
, 1978, “
A Simplified Technique for Predicting Traction in Elastohydrodynamic Contacts
,”
Tribol. Trans.
1040-2004,
21
(
1
), pp.
53
62
.
9.
Anderson
,
N. E.
, and
Loewenthal
,
S. H.
, 1981, “
Effect of Geometry and Operating Conditions on Spur Gear System Power Loss
,”
ASME J. Mech. Des.
0161-8458,
103
, pp.
151
159
.
10.
Anderson
,
N. E.
, and
Loewenthal
,
S. H.
, 1982, “
Design of Spur Gears for Improved Efficiency
,”
ASME J. Mech. Des.
0161-8458,
104
, pp.
767
774
.
11.
Diab
,
Y.
,
Ville
,
F.
,
Velex
,
P.
, and
Changenet
,
C.
, 2004, “
Windage Losses in High-Speed Gears—Preliminary Experimental and Theoretical Results
,”
ASME J. Mech. Des.
0161-8458,
126
(
5
), pp.
903
908
.
12.
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
.
13.
Höhn
,
B. R.
,
Michaelis
,
K.
, and
Wimmer
,
A.
, 2005, “
Low Loss Gears
,”
AGMA Fall Technical Meeting
, Paper No. 05FTM11.
14.
Changenet
,
C.
,
Oviedo-Marlot
,
X.
, and
Velex
,
P.
, 2006, “
Power Loss Predictions in Geared Transmissions Using Thermal Networks—Applications to a 6-Speed Manual Gearbox
,”
ASME J. Mech. Des.
0161-8458,
128
(
3
), pp.
618
625
.
15.
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
(
1
), pp.
58
68
.
16.
Diab
,
Y.
,
Ville
,
F.
, and
Velex
,
P.
, 2006, “
Prediction of Power Losses Due to Tooth Friction in Gears
,”
Tribol. Trans.
1040-2004,
49
(
2
), pp.
260
270
.
17.
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
.
18.
Velex
,
P.
, and
Cahouet
,
V.
, 2000, “
Experimental and Numerical Investigations on the Influence of Tooth Friction in Spur and Helical Gear Dynamics
,”
ASME J. Mech. Des.
0161-8458,
122
(
4
), pp.
515
522
.
19.
Velex
,
P.
, and
Maatar
,
M.
, 1996, “
A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behaviour
,”
J. Sound Vib.
0022-460X,
191
(
5
), pp.
629
660
.
20.
Baud
,
S.
, and
Velex
,
P.
, 2002, “
Static and Dynamic Tooth Loading in Spur and Helical Geared Systems—Experiments and Model Validation
,”
ASME J. Mech. Des.
0161-8458,
124
(
2
), pp.
334
346
.
21.
Raclot
,
J. -P.
, and
Velex
,
P.
, 1999, “
Simulation of the Dynamic Behaviour of Single and Multi-Stage Geared Systems With Shape Deviations and Mounting Errors by Using a Spectral Method
,”
J. Sound Vib.
0022-460X,
220
(
5
), pp.
861
903
.
22.
Küçükay
,
F.
, 1984, “
Dynamic Behaviour of High Speed Gears
,”
Proceedings of the Third International Conference on Vibrations in Rotating Machinery
, Heslington, UK, pp.
81
90
.
23.
Velex
,
P.
,
Maatar
,
M.
, and
Raclot
,
J. -P.
, 1997, “
Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior—Formulation and Assessment
,”
ASME J. Mech. Des.
0161-8458,
119
, pp.
292
298
.
24.
Weber
,
C.
, and
Banaschek
,
K.
, 1953,
Formänderung und Profilrücknahme bei Gerad-und Schrägverzahnten Antriebstechnik
,
Vieweg
,
Braunschweig
, Vol.
11
.
25.
Lundberg
,
G.
, 1939, “
Elastische Berührung zweier Halbraüme
,”
Forsch. Geb. Ing.
0367-2204,
10
(
5
), pp.
201
211
.
26.
Munro
,
R. G.
, 1990, “
Optimum Profile Relief and Transmission Error in Spur Gears
,”
Proceedings of the Institution of Mechanical Engineers, First International Conference on Gearbox Noise and Vibration
, Cambridge, pp.
35
42
.
27.
Velex
,
P.
, and
Sainsot
,
P.
, 2002, “
An Analytical Study of Tooth Friction Excitations in Errorless Spur and Helical Gears
,”
Mech. Mach. Theory
0094-114X,
37
(
7
), pp.
641
658
.
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