Automotive differential gears are usually operating at very low speed and high load conditions and hence are usually designed to be protected against the root bending fatigue failure. Depending on application requirements and lubrication regime, surface failures may occasionally be encountered as well. Mainstream existing design procedures published by AGMA are based on analyzing one single gear pair engagement while up to four potential engagements, between two side gears and two differential pinions, exist. There are also differential designs with three or four differential pinions that increase potential number of engagements to, respectively, six and eight. Usually, the hypoid gear loading is divided by number of side gears, two, also differential pinion loads are usually assumed to be equal; this is a good estimate when no misalignments are present. When misalignments are present, load sharing between the differential pinions becomes greatly imbalanced. This study tries to come up with a simplified analytical approach to evaluate overload factor between the differential pinions as a result of misalignments realized by differential gears inside a differential case. The total indexing run-out quality of gears is also studied through treating it as a source of misalignment. This study will help designers to evaluate the effects of tolerance limits and differential case machining errors on differential gear bending lives.

References

References
1.
ANSI/AGMA Standard
,
2005
, “
Design Manual for Bevel Gears
,” American National Standard/American Gear Manufacturers Association, Alexandria, VA, Standard No.
ANSI/AGMA 2005-D03
.http://allaboutmetallurgy.com/wp/wp-content/uploads/2016/12/Design-Manual-for-Bevel-Gears.pdf
2.
Coleman
,
W.
,
1967
, “
A Scoring Formula for Bevel and Hypoid Gear Teeth
,”
J. Lubr. Technol.
,
89
(
2
), pp.
114
123
.
3.
Coleman
,
W.
,
1963
, “
Design of Bevel Gears
,”
Product Engineering
, McGraw-Hill, New York.
4.
Stadtfeld
,
H. J.
,
2007
, “
Straight Bevel Gear Cutting and Grinding on CNC Free Form Machines
,”
AGMA Fall Technical Meeting
, Detroit, MI, Standard No. 07FTM16.
5.
Hermann J
,
S.
,
2009
, “
CONIFLEX Plus Straight Bevel Gear Manufacturing
,” Company Publication, The Gleason Works, Rochester, New York.
6.
Townsend
,
D. P.
,
1991
,
Dudley's Gear Handbook
, McGraw-Hill, New York.
7.
Kolivand
,
M.
,
Ligata
,
H.
,
Steyer
,
G.
,
Benedict
,
D. K.
, and
Chen
,
J.
,
2015
, “
Actual Tooth Contact Analysis of Straight Bevel Gears
,”
ASME J. Mech. Des.
,
137
(9), p. 093302.
8.
Al-Daccak
,
M. J.
,
Angeles
,
J.
, and
González-Palacios
,
M. A.
,
1994
, “
The Modeling of Bevel Gears Using the Exact Spherical Involute
,”
ASME J. Mech. Des.
,
116
(
2
), pp.
364
368
.
9.
Figliolini
,
G.
, and
Angeles
,
J.
,
2004
, “
Algorithms for Involute and Octoidal Bevel-Gear Generation
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
664
672
.
10.
Ligata
,
H.
, and
Zhang
,
H. H.
,
2012
, “
Geometry Definition and Contact Analysis of Spherical Involute Straight Bevel Gears
,”
Int. J. Ind. Eng. Prod. Res.
,
23
(
2
), pp.
101
111
.http://ijiepr.iust.ac.ir/article-1-442-en.pdf
11.
Tsai
,
Y. C.
, and
Chin
,
P. C.
,
1987
, “
Surface Geometry of Straight and Spiral Bevel Gears
,”
J. Mech. Transm. Autom. Des.
,
109
(
4
), pp.
443
449
.
12.
Huston
,
R. L.
, and
Coy
,
J. J.
,
1981
, “
Ideal Spiral Bevel Gears—A New Approach to Surface Geometry
,”
ASME J. Mech. Des.
,
103
(
1
), pp.
127
132
.
13.
Fuentes
,
A.
,
Iserte
,
J. L.
,
Gonzalez-Perez
,
I.
, and
Sanchez-Marin
,
F. T.
,
2011
, “
Computerized Design of Advanced Straight and Skew Bevel Gears Produced by Precision Forging
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
29–32
), pp.
2363
2377
.
14.
Ligata
,
H.
,
Kahraman
,
A.
, and
Singh
,
A.
,
2007
, “
An Experimental Investigation of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Load Sharing
,”
ASME
Paper No. DETC2007-34096.
15.
Ligata
,
H.
, and
Zhang
,
H. H.
,
2011
, “
Overview and Design of Near-Net Formed Spherical Involute Straight Bevel Gears
,”
Int. J. Mod. Eng.
,
11
(
2
), pp.
47
53
.http://ijme.us/cd_11/PDF/Paper%20161%20ENG%20107.pdf
16.
Coleman
,
W.
,
1975
, “
Effect of Mounting Displacements on Bevel and Hypoid Gear Tooth Strength
,”
SAE
Paper No. 750151.
17.
Coleman
,
W.
,
1975
, “
Analysis of Mounting Deflections on Bevel and Hypoid Gears
,”
SAE
Paper No. 750152.
18.
Kolivand
,
M.
, and
Kahraman
,
A.
,
2009
, “
A Load Distribution Model for Hypoid Gears Using Ease-Off Topography and Shell Theory
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1848
1865
.
19.
Kolivand
,
M.
, and
Kahraman
,
A.
,
2010
, “
An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations
,”
ASME J. Mech. Des.
,
132
(
7
), p.
071004
.
20.
AGMA Standard
,
2009
, “
Bevel Gear Classification, Tolerances and Measuring Methods
,” American Gear Manufacturers Association, Alexandria, VA, Standard No. ANSI/AGMA 2009-B01.
21.
AGMA Standard
,
2009
, “
Bevel Gear Classification, Tolerances and Measuring Methods
,” American Gear Manufacturers Association, Alexandria, VA, Standard No. ANSI/AGMA 2009-A98.
22.
Weber
,
C.
,
1951
,
The Deformation of Loaded Gears and the Effect on Their Load Carrying Capacity (PartI)
,
Department of Scientific and Industrial Research
, UK.
You do not currently have access to this content.