A continuously variable transmission (CVT) offers a continuum of gear ratios between desired limits. The present research focuses on developing a continuous one-dimensional model of the metal V-belt CVT in order to understand the influence of pulley flexibility and friction characteristics on its dynamic performance. A metal V-belt CVT falls under the category of friction-limited drives as its performance and torque capacity rely significantly on the friction characteristic of the contact patch between the belt element and the pulley. Since the friction characteristic of the contact patch may vary in accordance with the loading and design configurations, it is important to study the influence of the friction characteristic on the performance of a CVT. Friction between the belt and the pulley sheaves is modeled using different mathematical models which account for varying loading scenarios. Simple trigonometric functions are introduced to capture the effects of pulley deformation on the thrust ratio and slip behavior of the CVT. Moreover, since a number of models mentioned in the literature neglect the inertial coupling between the belt and the pulley, a considerable amount of effort in this paper is dedicated towards modeling the inertial coupling between the belt and the pulley and studying its influence on the dynamic performance of a CVT. The results discuss the influence of friction characteristics and pulley flexibility on the dynamic performance, the axial force requirements, and the torque transmitting capacity of a metal V-belt CVT drive.

1.
Micklem
,
J. D.
,
Longmore
,
D. K.
, and
Burrows
,
C. R.
, 1994, “
Modelling of the Steel Pushing V-Belt Continuously Variable Transmission
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
208
, pp.
13
27
.
2.
Gerbert
,
G.
, 1996, “
Belt Slip-A Unified Approach
,”
ASME J. Mech. Des.
0161-8458,
118
(
3
), pp.
432
438
.
3.
Sun
,
D. C.
, 1988, “
Performance Analysis of a Variable Speed-Ratio Metal V-Belt Drive
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
110
, pp.
472
481
.
4.
Kobayashi
,
D.
,
Mabuchi
,
Y.
, and
Katoh
,
Y.
, 1998, “
A Study on the Torque Capacity of a Metal Pushing V-Belt for CVTs
,” SAE Paper No. 980822, SAE Transmission and Driveline Systems Symposium.
5.
Carbone
,
G.
,
Mangialardi
,
L.
, and
Mantriota
,
G.
, 2000, “
Theoretical Model Of Metal V-Belt Drives During Ratio Changing Speed
,”
ASME J. Mech. Des.
0161-8458,
123
(
1
), pp.
111
117
.
6.
Carbone
,
G.
,
Mangialardi
,
L.
, and
Mantriota
,
G.
, 2003, “
EHL Visco-Plastic Friction Model in CVT Shifting Behaviour
,”
Int. J. Veh. Des.
0143-3369,
32
(
3/4
), pp.
333
357
.
7.
Carbone
,
G.
,
Mangialardi
,
L.
, and
Mantriota
,
G.
, 2005, “
The Influence of Pulley Deformations on the Shifting Mechanism of Metal Belt CVT
,”
ASME J. Mech. Des.
0161-8458,
127
, pp.
103
113
.
8.
Sorge
,
F.
, 1996, “
Influence of Pulley Bending on Metal V-Belt Mechanics
,” in
Proceedings of the International Conference on Continuously Variable Power Transmission
, Japanese Society of Automotive Engineers, Paper No. 102 (9636268), pp.
9
15
, Yokohama, Japan, September 11–12, 1996.
9.
Ide
,
T.
, and
Tanaka
,
H.
, 2002, “
Contact Force Distribution Between Pulley Sheave and Metal Pushing V-Belt
,” in
Proceedings of the CVT 2002 Congress
, VDI-Berichte, Vol.
1709
, pp.
343
335
.
10.
Sattler
,
H.
, 1999, “
Efficiency of Metal Chain and V-belt CVT
,” International Congress on Continuously Variable Power Transmission CVT’ 99, pp.
99
104
, Eindhoven, The Netherlands, September 16–17.
11.
Bullinger
,
M.
,
Pfeiffer
,
F.
, and
Ulbrich
,
H.
, 2005, “
Elastic Modelling of Bodies and Contacts in Continuous Variable Transmissions
,”
Multibody Syst. Dyn.
1384-5640,
13
(
2
), pp.
175
194
.
12.
Srivastava
,
N.
, and
Haque
,
I.
, 2005, “
On the Transient Dynamics of a Metal Pushing V-Belt CVT at High Speeds
,”
Int. J. Veh. Des.
0143-3369,
37
(
1
), pp.
46
66
.
13.
Srivastava
,
N.
,
Blouin
,
V. Y.
, and
Haque
,
I. U.
, 2004, “
Using Genetic Algorithms to Identify Initial Operating Conditions for a Transient CVT Model
,” 2004 ASME International Mechanical Engineering Congress, Paper No. IMECE2004-61999, Anaheim, CA, November 13–19.
14.
Srivastava
,
N.
, and
Haque
,
I. U.
, 2004, “
On the Operating Regime of a Metal Pushing V-Belt CVT Under Steady State Microslip Conditions
,” 2004 International Continuously Variable and Hybrid Transmission Congress, Paper No. 2004-34-2851 (04CVT-11), San Francisco, CA, September 23–25.
15.
Lebrecht
,
W.
,
Pfeiffer
,
F.
, and
Ulbrich
,
H.
, 2004, “
Analysis of Self-Induced Vibrations in a Pushing V-Belt CVT
,” 2004 International Continuously Variable and Hybrid Transmission Congress, Paper No. 04CVT-32, September 23–25, San Francisco, CA.
16.
Canudas de Wit
,
C.
,
Olsson
,
H.
,
Åström
,
K. J.
, and
Lischinsky
,
P.
, 1993, “
Dynamic Friction Models and Control Design
,” in
Proceedings of the 1993 American Control Conference
, pp.
1920
1926
, San Francisco, CA.
17.
Sferra
,
D.
,
Pennestri
,
E.
,
Valentini
,
P. P.
, and
Baldascini
,
F.
, 2002, “
Dynamic Simulation of a Metal-Belt CVT Under Transient Conditions
,” in
Proceedings of the DETC02, 2002 ASME Design Engineering Technical Conference
, Paper No. DETC02/MECH-34228, Vol.
5A
, pp.
261
268
, Montreal, Canada, September 29–October 2.
18.
Fujii
,
T.
,
Kurokawa
,
T.
, and
Kanehara
,
S.
, 1993, “
A Study of a Metal Pushing V-Belt Type CVT Part 2: Compression Force Between Metal Blocks and Ring Tension
,” SAE Transactions, Paper No. 930667, pp.
1000
1009
.
19.
Kuwabara
,
S.
,
Fujii
,
T.
, and
Kanehara
,
S.
, 1998, “
Power Transmitting Mechanism of CVT Using a Metal V-Belt and Load Distribution in the Steel Ring
,” SAE Transactions, Paper No. 980824.
20.
Fushimi
,
Y.
,
Kanehara
,
S.
, and
Fujii
,
T.
, 1996, “
A Numerical Approach to Analyze the Power Transmitting Mechanisms of a Metal Pushing V-Belt Type CVT
,” SAE Transactions, Paper No. 960720, pp.
161
172
.
21.
Kitagawa
,
T.
,
Fujii
,
T.
, and
Kanehara
,
S.
, 1995, “
A Study of a Metal Pushing V-Belt Type CVT (Part 4: Forces Act on Metal Blocks When the Speed Ratio is Changing)
,” SAE Transactions, Paper No. 950671, pp.
1344
1353
.
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