In this paper we detail a review of the current state of published work regarding the modeling of rolling traction drive Continuously Variable Transmissions (CVTs). An overview of CVTs operating by traction through small contact areas is performed, the layouts and kinematics of leading examples are reviewed, including the factors affecting design optimization. Properties of the traction contacts are considered in detail, with particular attention to elastohydrodynamic lubrication and asperity contact. Factors affecting the traction coefficient are reviewed and fundamental empirical predictions are contrasted with modern modeling computations. Finally measurements of the rheology of traction fluids are considered, leading to a definition of ideal properties and the development of proprietary fluids.

1.
Hewko
,
L. O.
, 1986, “
Automotive Traction Drive CVTs—An Overview
,” SAE Paper 861355.
2.
Machida
,
H.
, and
Imanishi
,
Y.
, 1995, “
Design Principle of High Power Traction Drive CVT
,” SAE Paper 950675.
3.
Machida
,
H.
,
Abe
,
T.
, and
Kokubu
,
H.
, 1994, “
A Consideration of the High Pressure, High Temperature and High Speed Contact Surface of The Traction Drive
,” Proceedings of the JSME, Kitakyushu, Nov. 1994.
4.
Tevaarwerk
,
J. L.
, 1980, “
Thermal Influence on the Traction Behavior and Elastic/Plastic Model
,” Proc. of the 7th Leeds-Lyon, pp.
302
.
5.
Carter
,
J.
, and
Miller
,
D.
, “
The Design And Analysis of an Alternative Traction Drive CVT
,” SAE Paper No. 2003-01-0970.
6.
Smithson
,
R.
,
Miller
,
D.
, and
Allen
,
D.
, “
Scalability for an Alternative Rolling Traction CVT
,” SAE Paper 2004-01-0355.
7.
Lim
,
K. H.
, “
Optimal Design of a Traction Drive Continuously Variable Transmission
,” Ph.D. thesis, Oregon State University, 1988.
8.
Loewenthal
,
S.
, and
Zaretsky
,
E.
, 1985, “
Design of Traction Drives
,” NASA Reference Publication 1154.
9.
Akehurst
,
S.
,
Brace
,
C. J.
,
Vaughan
,
N. D.
,
Milner
,
P. J.
, and
Hosoi
,
Y.
, 2001, “
Performance Investigations of a Novel Rolling Traction Drive CVT
,” SAE Paper No. 2001-01-0874.
10.
Tevaarwerk
,
J. L.
, and
Johnson
,
K. L.
, 1979, “
The Influence of Fluid Rheology on the Performance of Traction Drives
,”
ASME J. Lubr. Technol.
0022-2305,
101
, pp.
268
274
.
11.
Tevaarwerk
,
J. L.
, 1979, “
Traction Drive Performance Predictions For the Johnson and Tevaarwerk Traction Model
,” NASA Technical Paper 1530.
12.
Greenwood
,
J.
, and
Williamson
,
J.
, 1966, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
1364-5021,
295
, pp.
300
319
.
13.
Hamrock
,
B.
, and
Dowson
,
D.
, 1977, “
Isothermal Elastohydrodynamic Lubrication of Point Contact, Part IV, Starvation Results
,”
ASME J. Lubr. Technol.
0022-2305,
99
, pp.
15
23
.
14.
Hamrock
,
B.
, and
Dowson
,
D.
, 1977, “
Isothermal Elastohydrodynamic Lubrication of Point Contact, Part III, Fully Flooded Results
,”
ASME J. Lubr. Technol.
0022-2305,
99
, pp.
264
276
.
15.
Hamrock
,
B. J.
, “
Fundamentals of Fluid Film Lubrication
,” ISBN 0-07-113356-9.
16.
Nikas
,
G. K.
, 2002, “
Fatigue Life and Traction Modeling of Continuously Variable Transmissions
,”
ASME J. Tribol.
0742-4787,
124
, pp.
689
698
.
17.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
, Cambridge.
18.
Elsharkawy
,
A. A.
, and
Hamrock
,
B. J.
, 1991, “
Subsurface Stresses in Micro-EHL Line Contacts
,”
ASME J. Tribol.
0742-4787,
113
, pp.
645
656
.
19.
Ioannides
,
E.
, and
Harris
,
T. A.
, 1985, “
A New Fatigue Life Model for Rolling Bearings
,”
ASME J. Tribol.
0742-4787,
107
, pp.
367
377
.
20.
Zou
,
Q.
,
Huang
,
C.
, and
Wen
,
S.
, 1999, “
Elastohydrodynamic Film Thickness in Elliptical Contacts With Spinning and Rolling
,”
ASME J. Tribol.
0742-4787,
121
, pp.
686
692
.
21.
Chang
,
L.
, 1992, “
Traction in Thermal Elastohydrodynamic Lubrication of Rough Surfaces
,”
ASME J. Tribol.
0742-4787,
114
, pp.
186
191
.
22.
Evans
,
C. R.
, and
Johnson
,
K. L.
, 1987, “
The Influence of Surface Roughness on Elastohydrodynamic Traction
,” Proc. of the Institution of Mechanical Engineers, IMechE England, Vol.
201
, pp.
145
150
.
23.
Ai
,
X.
, 2002, “
Development of Zero-Spin Planetary Traction Drive Transmission: Part 1—Design and Principles of Performance Calculations
,”
Trans. ASME, J. Tribol.
0742-4787,
124
, pp.
386
391
.
24.
Ai
,
X.
, 2002, “
Development of Zero-Spin Planetary Traction Drive Transmission: Part 2—Performance Testing and Evaluation
,”
Trans. ASME, J. Tribol.
0742-4787,
124
, pp.
392
397
.
25.
Forti
,
A. W.
, and
Dedini
,
F. G.
, “
The Influence of Spin and Lifetime in Design of Traction Drive Continuously Variable Transmissions
,” SAE paper 2001-01-03841.
26.
Coy
,
J. J.
,
Loewenthal
,
S. H.
, and
Zaretsky
,
E. V.
, 1976, “
Fatigue Life Analysis for Traction Drives With Application to a Toroidal Type Geometry
,” Nasa Technical Note D-8362, December.
27.
Rohn
,
D. A.
,
Loewenthal
,
S. H.
, and
Coy
,
J. J.
, 1981, “
Simplified Fatigue Life Analysis for Traction Drive Contacts
,”
ASME J. Mech. Des.
0161-8458,
103
, pp.
430
439
.
28.
Raghavan
,
M.
, 2002, “
Kinematics of the Full-Toroidal Traction Drive Variator
,”
ASME J. Mech. Des.
0161-8458,
124
, pp.
448
455
.
29.
Yamamoto
,
T.
,
Matsuda
,
K.
, and
Hibi
,
T.
, 2001, “
Analysis of the Efficiency of a Half-Toroidal CVT
,” JSAE Review, Vol.
22
, pp.
565
570
.
30.
Tanaka
,
H.
, and
Kubono
,
H.
, 1990, “
Spinning Moment of a Thrust Ball Bearing in Traction Fluid
,”
Proc. Japan Society of Mechanical Engineers
, Vol.
56
, p.
947
(in Japanese with English summary).
31.
Kakuta
,
K.
, 1961, “
Friction Moment of Radial Ball Bearing under Thrust Load
,”
Proc. Japan Society of Mechanical Engineers
, Vol.
27–178
, p.
945
(in Japanese with English summary).
32.
Yamamoto
,
T.
,
Osidari
,
T.
, and
Nakano
,
M.
, 2002, “Improvement of Loading Cam Performance in a Toroidal CVT,” JSAE Review, Vol.
23
, pp.
481
487
.
33.
Zhang
,
Y.
,
Zhang
,
X.
, and
Tobler
,
W.
, 2000, “
A Systematic Model for the Analysis of Contact, Side Slip and Traction of Toroidal Drives
,”
ASME J. Mech. Des.
0161-8458,
122
, pp.
523
528
.
34.
Cretu
,
O. S.
, and
Glovnea
,
R. P.
, 2003, “
Traction Drive With Reduced Spin Losses
,”
Trans. ASME, J. Tribol.
0742-4787,
125
, pp.
507
512
.
35.
Evans
,
C. R.
, and
Johnson
,
K. L.
, 1986, “
The Rheological Properties of Elastohydrodynamic Lubricants
,”
Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci.
0263-7154,
200
, pp.
303
312
.
36.
Evans
,
C. R.
, and
Johnson
,
K. L.
, 1986, “
Regimes of Traction in Elastohydrodynamic Lubrication
,”
Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci.
0263-7154,
200
, pp.
313
323
.
37.
Bair
,
S.
, and
Winer
,
W. O.
, 1979, “
A Rheological Model for Elastohydrodynamic Contacts Based on Primary Laboratory Data
,”
ASME J. Lubr. Technol.
0022-2305,
101
, pp.
258
265
.
38.
Johnson
,
K. L.
, and
Roberts
,
A. D.
, 1974, “
Observation of Viscoelastic Behavior of an Elastohydrodynamic Film
,”
Proc. R. Soc. London, Ser. A
1364-5021,
337
, pp.
217
242
.
39.
Tanaka
,
H.
,
Machida
,
H.
,
Hata
,
H.
, and
Nakano
,
M.
, 1995, “
Half-Toroidal Traction Drive Continuously Variable Power Transmission for Automobiles (Traction Drive Materials, Transmission Design and Efficiency)
,”
JSME Int. J., Ser. C
1340-8062,
38
, pp.
772
777
.
40.
Dowson
,
D.
,
Taylor
,
C. M.
, and
Xu
,
H.
, 1991, “
Elastohydrodynamic Lubrication of Elliptical Contacts With Spin and Rolling
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
205
, pp.
170
174
.
41.
Ge
,
P.
, and
Liu
,
Z.
, 2002, “
Experimental and Computational Investigation of the Traction Coefficient of a Ball Traction Drive Device
,”
Tribol. Int.
0301-679X,
35
pp.
219
224
.
42.
Hamrock
,
B. J.
, and
Dowson
,
D.
, 1976, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts. Part I: Theoretical Formulation
,”
ASME J. Lubr. Technol.
0022-2305
98
(
2
), pp.
223
9
.
43.
Nonishi
,
T.
,
Oda
,
S.
,
Miyachika
,
K.
, and
Koide
,
T.
, 2000, “
Limit Transmissible Torque in the Traction Drive of a Concave and Convex Roller Pair
,”
Tribol. Int.
0301-679X,
33
, pp.
233
240
.
44.
Hamrock
,
B. J.
, “
Fundamentals of Fluid Film Lubrication
,” ISBN 0-07-113356-9, pp.
77
, 611, 615.
45.
Johnson
,
K. L.
, and
Tevaarwerk
,
J. L.
, 1977, “
The Shear Behavior of Elastohydrodynamic Oil Films
,”
Proc. R. Soc. London, Ser. A
1364-5021,
356
, pp.
215
236
.
46.
Sharif
,
K. L.
,
Evans
,
H. P.
,
Snidel
,
R. W.
, and
Newall
,
J. P.
, 2004, “
Modeling of Film Thickness and Traction in a Variable Ratio Traction Drive
,”
ASME J. Tribol.
0742-4787,
126
, pp.
92
104
.
47.
Newall
,
J. P.
,
Nicolson
,
D. M.
,
Lee
,
A. P.
, and
Evans
,
S. P.
, “
Development and Assessment of Traction Fluids for Use in Toroidal (IVT) Transmissions
,” SAE Paper 2002-01-0588.
48.
Bair
,
S.
, and
Winer
,
W. O.
, 2000, “
The Pressure-Viscosity Coefficient at Hertz Pressure and Its Relation to Concentrated Contact Traction
,”
Proc. 26th Leeds-Lyon Symp. on Tribology
,
Elsevier
, Amsterdam pp.
433
443
.
49.
Larsson
,
R.
,
Larsson
,
P. O.
,
Eriksson
,
E.
,
Sjöberg
,
M.
, and
Höglund
,
E.
, 2001, “
Lubricant Properties for Input to Hydrodynamic and Elastohydro-Dynamic Lubrication Analyses
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
1350-6501,
201
, pp.
17
28
.
50.
Yasutomi
,
S.
,
Bair
,
S.
, and
Winer
,
W.
, 1984, “
An Application of a Free Volume Model to Lubricant Rheology
,”
ASME J. Tribol.
0742-4787,
106
, pp.
291
303
.
51.
Sharif
,
K. J.
,
Kong
,
S.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
, 2001, “
Contact and Elastohydrodynamic Analysis of Worm Gears: Part 1 Theoretical Formulation
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
215
, pp.
817
830
.
52.
Fang
,
N.
,
Chang
,
L.
,
Webster
,
M. N.
, and
Jackson
,
A.
, 2000, “
A Non-Averaging Method of Determining the Rheological Properties of Traction Fluids
,”
Tribol. Int.
0301-679X,
33
, pp.
751
760
.
53.
Johnson
,
K. L.
,
Nayak
,
L.
, and
Moore
,
A. J.
, 1978, “
Determination of Elastic Shear Modulus of Lubricants from Disc Machine Tests
,”
Proceedings of the 5th Leeds-Lyon Symposium
,
Leeds Mechanical Engineering Publication
, pp.
204
208
.
54.
Matsuoka
,
T.
,
Ishida
,
N.
,
Komatsu
,
S.
, and
Matsuno
,
M.
, Development of Toroidal Traction Drive CVTF for Automobile, SAE Paper 2002-01-1696.
55.
Tipton
,
C. D.
,
Qureshi
,
F.
, and
Huston
,
M. E.
, “
Automotive Traction Fluids: A Shift in Direction for Transmission Fluid Technology
,” SAE Paper 2000-01-2906.
56.
Jacobson
,
B. O.
, and
VanArsdale
,
W. E.
, 1992, “
Rheology and Elastohydrodynamic Lubrication
,”
Appl. Mech. Rev.
0003-6900,
45
, p.
B22
.
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