Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

References

References
1.
Tangasawi
,
O.
,
Theodossiades
,
S.
, and
Rahnejat
,
H.
,
2007
, “
Lightly Loaded Lubricated Impacts: Idle Gear Rattle
,”
J. Sound Vib.
,
308
(
3
), pp.
418
430
.10.1016/j.jsv.2007.03.077
2.
Koronias
,
G.
,
Theodossiades
,
S.
,
Rahnejat
,
H.
, and
Saunders
,
T.
,
2011
, “
Axle Whine Phenomenon in Light Trucks: A Combined Numerical and Experimental Investigation
,”
Proc. Inst. Mech. Eng., Part D
,
225
(
7
), pp.
885
894
.10.1177/0954407011401302
3.
Ozguven
,
H. N.
, and
Houser
,
D. R.
,
1988
, “
Mathematical Models Used in Gear Dynamics—A Review
,”
J. Sound Vib.
,
121
(
3
), pp.
383
411
.10.1016/S0022-460X(88)80365-1
4.
Kahraman
,
A.
, and
Singh
,
R.
,
1991
, “
Interactions Between the Time Varying Mesh Stiffness and Clearance Nonlinearities in a Geared System
,”
J. Sound Vib.
,
146
(
1
), pp.
135
156
.10.1016/0022-460X(91)90527-Q
5.
Amabili
,
M.
, and
Rivola
,
A.
,
1997
, “
Dynamic Analysis of Spur Gear Pairs: Steady-State Response and Stability of the SDOF Model With Time Varying Mesh Damping
,”
Mech. Syst. Signal Process.
,
11
(3), pp.
375
390
.10.1006/mssp.1996.0072
6.
Remmers
,
E. P.
,
1971
, “
Dynamics of Automotive Rear Axle Gear Noise
,”
SAE
Paper No. 710114. 10.4271/710114
7.
Kiyono
,
S.
,
Fujii
,
Y.
, and
Suzuki
,
Y.
,
1981
, “
Analysis of Vibration of Bevel Gears
,”
Bull. Jpn. Soc. Mech. Eng.
,
24
(188), pp.
441
446
.10.1299/jsme1958.24.441
8.
Abe
,
E.
, and
Hagiwara
,
H.
,
1990
, “
Advanced Method for Reduction in Axle Gear Noise
,” Gear Design, Manufacturing and Inspection Manual,
SAE
Paper No. 750150. 10.4271/750150
9.
Hirasaka
,
N.
,
Sugita
,
H.
, and
Asai
,
M.
,
1991
, “
A Simulation Method of Rear Axle Gear Noise
,”
SAE
Paper No. 911041. 10.4271/911041
10.
Donley
,
M. G.
,
Lim
,
T. C.
, and
Steyer
,
G. C.
,
1992
, “
Dynamic Analysis of Automotive Gearing Systems
,”
SAE
Paper No. 920762. 10.4271/920762
11.
Cheng
,
Y.
, and
Lim
,
T. C.
,
1998
, “
Dynamic Analysis of High Speed Hypoid Gears With Emphasis on Automotive Axle Noise Problem
,”
ASME
Paper No. DETC98/PTG-5784.
12.
Cheng
,
Y.
, and
Lim
,
T. C.
,
2000
, “
Dynamics of Hypoid Gear Transmission With Time-Varying Mesh
,”
ASME
Paper No. DETC2000/PTG-14432.
13.
Cheng
,
Y.
, and
Lim
,
T. C.
,
2001
, “
Vibration Analysis of Hypoid Transmissions Applying an Exact Geometry-Based Gear Mesh Theory
,”
J. Sound Vib.
,
240
(3), pp.
519
543
.10.1006/jsvi.2000.3247
14.
Jiang
,
X.
,
2002
, “
Non-Linear Torsional Dynamic Analysis of Hypoid Gear Pairs
,” M.Sc. thesis, The University of Alabama, Tuscaloosa, AL.
15.
Wang
,
H.
,
2002
, “
Gear Mesh Characteristics and Dynamics of Hypoid Geared Rotor System
,” Ph.D. thesis, The University of Alabama, Tuscaloosa, AL.
16.
Wang
,
J.
,
Lim
,
T. C.
, and
Li
,
M.
,
2007
, “
Dynamics of a Hypoid Gear Pair Considering the Effects of Time-Varying Mesh Parameters and Backlash Nonlinearity
,”
J. Sound Vib.
,
229
(
2
), pp.
287
310
. 10.1016/j.jsv.2008.06.021
17.
Dareing
,
D. W.
, and
Johnson
,
K. L.
,
1975
, “
Fluid Film Damping of Rolling Contact Vibrations
,”
J. Mech. Eng. Sci.
,
17
(
4
), pp.
214
218
.10.1243/JMES_JOUR_1975_017_031_02
18.
Mehdigoli
,
H.
,
Rahnejat
,
H.
, and
Gohar
,
R.
,
1990
, “
Vibration Response of Wavy Surfaced Disc in Elastohydrodynamic Rolling Contact
,”
Wear
,
139
(
1
), pp.
1
15
.10.1016/0043-1648(90)90206-P
19.
Virlez
,
G.
,
Bruls
,
O.
,
Duysinx
,
P.
, and
Poulet
,
N.
,
2011
, “
Simulation of Differentials in Four-Wheel Drive Vehicles Using Multi-Body Dynamics
,”
ASME
Paper No. DETC2011-48313. 10.1115/DETC2011-48313
20.
Karagiannis
,
I.
, and
Theodossiades
,
S.
,
2013
, “
An Alternative Formulation of the Dynamic Transmission Error to Study the Oscillations of Automotive Hypoid Gears
,”
ASME J. Vib. Acoust.
,
136
(1), p.
011001
.10.1115/1.4025206
21.
Xu
,
H.
, and
Kahraman
,
A.
,
2007
, “
Prediction of Friction-Related Power Losses of Hypoid Gear Pairs
,”
J. Multi-Body Dyn.
,
221
(3), pp.
387
400
.10.1243/14644193JMBD48
22.
Kolivand
,
M.
,
Li
,
S.
, and
Kahraman
,
A.
,
2010
, “
Prediction of Mechanical Gear Mesh Efficiency of Hypoid Gear Pairs
,”
Mech. Mach. Theory
,
45
(11), pp.
1568
1582
.10.1016/j.mechmachtheory.2010.06.015
23.
Snidle
,
R. W.
, and
Archard
,
J. F.
,
1968
, “
Lubrication at Elliptical Contacts
,”
Proc. Inst. Mech. Eng.
,
183
(16), pp.
138
146
.10.1243/PIME_CONF_1968_183_288_02
24.
Simon
,
V.
,
1998
, “
The Influence of Misalignments on Mesh Performances of Hypoid Gears
,”
Mech. Mach. Theory
,
33
(8), pp.
1277
1291
.10.1016/S0094-114X(98)00005-6
25.
Simon
,
V.
,
2009
, “
Influence of Machine Tool Setting Parameters on EHD Lubrication in Hypoid Gears
,”
Mech. Mach. Theory
,
44
(5), pp.
923
937
.10.1016/j.mechmachtheory.2008.06.005
26.
Ito
,
N.
, and
Takahashi
,
K.
,
2000
, “
Differential Geometrical Conditions of Hypoid Gears With Conjugate Tooth Surfaces
,”
ASME J. Mech. Des.
,
122
(3), pp.
323
330
.10.1115/1.1286236
27.
Gohar
,
R.
,
1971
, “
Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact
,”
ASME J. Lub. Tech.
,
93
(3), pp.
371
382
.10.1115/1.3451598
28.
Chittenden
,
R. J.
,
Dowson
,
D.
,
Dunn
,
J. F.
, and
Taylor
,
C. M.
,
1985
, “
A Theoretical Analysis of the Isothermal Elastohydrodynamic Lubrication of Concentrated Contacts. I. Direction of Lubricant Entrainment Coincident With the Major Axis of the Hertzian Contact Ellipse
,”
Proc. R. Soc., London, Ser. A
,
397
(1813), pp.
245
269
.10.1098/rspa.1985.0014
29.
Chittenden
,
R. J.
,
Dowson
,
D.
,
Dunn
,
J. F.
, and
Taylor
,
C. M.
,
1985
, “
A Theoretical Analysis of the Isothermal Elastohydrodynamic Lubrication of Concentrated Contacts. II. General Case, With Lubricant Entrainment Along Either Principal Axis of the Hertzian Contact Ellipse or at Some Intermediate Angle
,”
Proc. R. Soc., London, Ser. A
,
397
(1813), pp.
271
294
.10.1098/rspa.1985.0015
30.
Jalali-Vahid
,
D.
,
Rahnejat
,
H.
,
Gohar
,
R.
, and
Jin
,
Z. M.
,
2000
, “
Prediction of Oil-Film Thickness and Shape in Elliptical Point Contacts Under Combined Rolling and Sliding Motion
,”
Proc. Inst. Mech. Eng., Part J
,
214
(5), pp.
427
437
.10.1243/1350650001543304
31.
Mohammadpour
,
M.
,
Theodossiades
,
S.
, and
Rahnejat
,
H.
,
2012
, “
Elastohydrodynamic Lubrication of Hypoid Gears at High Loads
,”
Proc. Inst. Mech. Eng., Part J
,
226
(
3
), pp.
183
198
.10.1177/1350650111431027
32.
De la Cruz
,
M.
,
Chong
,
W. W. F.
,
Teodorescu
,
M.
,
Theodossiades
,
S.
, and
Rahnejat
,
H.
,
2012
, “
Transient Mixed Thermo-Elastohydrodynamic Lubrication in Multi-Speed Transmissions
,”
Tribol. Int.
,
49
, pp.
17
29
.10.1016/j.triboint.2011.12.006
33.
Fujii
,
M.
,
Nagasaki
,
Y.
, and
Nohara
,
M.
,
1997
, “
Differences in Dynamic Behavior Between Straight and Skew Bevel Gears
,”
Trans. Jpn. Soc. Mech. Eng., Part C
,
63
(
613
), pp.
3229
3234
.10.1299/kikaic.63.3229
34.
Yinong
,
L.
,
Guiyan
,
L.
, and
Ling
,
Z.
,
2010
, “
Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System
,”
Math. Prob. Eng.
,
2010
, p.
124148
.10.1155/2010/124148
35.
Yang
,
J.
, and
Lim
,
T.
,
2011
, “
Dynamics of Coupled Nonlinear Hypoid Gear Mesh and Time-Varying Bearing Stiffness Systems
,”
SAE Int. J. Passeng. Cars
,
4
(2), pp.
1039
1049
.10.4271/2011-01-1548
36.
Karagiannis
,
Y.
,
Theodossiades
,
S.
, and
Rahnejat
,
H.
,
2012
, “
On the Dynamics of Lubricated Hypoid Gears
,”
Mech. Mach. Theory
,
48
, pp.
94
120
.10.1016/j.mechmachtheory.2011.08.012
37.
Theodossiades
,
S.
, and
Natsiavas
,
S.
,
2001
, “
On Geared Rotordynamic Systems With Oil Journal Bearings
,”
J. Sound Vib.
,
243
(
4
), pp.
721
745
.10.1006/jsvi.2000.3430
38.
Caughey
,
T. K.
,
1960
, “
Classical Normal Modes in Damped Linear Dynamic Systems
,”
ASME J. Appl. Mech.
,
27
(2), pp.
269
271
.10.1115/1.3643949
39.
Harris
,
T.
, and
Kotzalas
,
M. N.
,
2007
,
Advanced Concepts of Bearing Technology
,
Taylors and Francis
,
London
.
40.
Gillespie
,
T. D.
,
1992
,
Fundamentals of Vehicle Dynamics
,
Society of Automotive Engineers
,
Warrendale, PA
.
41.
Rahnejat
,
H.
,
1998
, “
Multi-Body Dynamics: Vehicles, Machines and Mechanisms
,” Professional Engineering Publishing, Bury St. Edmunds, UK.
42.
Evans
,
C. R.
, and
Johnson
,
K. L.
,
1986
, “
Regimes of Traction in Elastohydrodynamic Lubrication
,”
Proc. Inst. Mech. Eng.
,
200
(C
5
), pp.
313
324
. 10.1243/PIME_PROC_1986_200_135_02
43.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
,
1970
, “
The Contact of Two Nominally Flat Rough Surfaces
,”
Proc. Inst. Mech. Eng.
,
185
(1), pp.
625
633
.10.1243/PIME_PROC_1970_185_069_02
44.
Teodorescu
,
M.
,
Balakrishnan
,
S.
, and
Rahnejat
,
H.
,
2005
, “
Integrated Tribological Analysis Within a Multi-Physics Approach to System Dynamics
,”
Tribol. Interface Eng. Ser.
,
48
, pp.
725
737
.10.1016/S0167-8922(05)80074-4
45.
Mohammadpour
,
M.
,
Theodossiades
,
S.
,
Rahnejat
,
H.
, and
Kelly
,
P.
,
2013
, “
Transmission Efficiency and Noise, Vibration and Harshness Refinement of Differential Hypoid Gear Pairs
,”
Proc. Inst. Mech. Eng., Part K
,
228
(1), pp.
19
33
.10.1177/1464419313496559
46.
Litvin
,
F. L.
, and
Fuentes
,
A.
,
2004
, “
Gear Geometry and Applied Theory
,”
2nd ed.
,
Cambridge University Press
,
New York
.
47.
Yamada
,
T.
, and
Mitsui
,
J.
,
1979
, “
A Study on the Unstable Vibration Phenomena of a Reduction Gear System, Including the Lightly Loaded Journal Bearings, for a Marine Steam Turbine
,”
Bull. JSME
,
22
(163), pp.
98
106
.10.1299/jsme1958.22.98
48.
Kahraman
,
A.
, and
Singh
,
R.
,
1990
, “
Non-Linear Dynamics of a Spur Gear Pair
,”
J. Sound Vib.
,
142
(
1
), pp.
49
75
.10.1016/0022-460X(90)90582-K
49.
Cheng
,
Y.
, and
Lim
,
T. C.
,
2003
, “
Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
373
382
.10.1115/1.1564064
You do not currently have access to this content.