Research and Development of Cone to Cone Type CVT - IFToMM

12th IFToMM World Congress, Besançon (France), June18-21, 2007
CK-xxx
Research and Development of Cone to Cone Type CVT
H. Komatsubara * T. Yamazaki † S. Kuribayashi ‡
Yamagata University Yamagata University Kuribayashi Steamship
Yamagata, Japan Yamagata, Japan Tokyo, Japan
Abstract— 1 Traction drive CVT is a low noise and a low
vibration. But most of traction drive CVT have complex structure.
One of the authors invented a new type of traction drive CVT. As
for this new CVT, the structure is simple, and transfer efficiency
is high. This new CVT is called Cone to Cone Type CVT(CTC-
CVT). The purpose of this research aimed at practical use of
CTC-CVT In this report, first the structure and the speed
changing mechanism of CTC-CVT is examined. Secondly, the
design of CTC-CVT is described. Finally, the mechanical
efficiency of power transmission is examined.
Keywords: machine element, tribology, lubrication, CVT,
traction drive, efficiency
I. Introduction
In the traction drive, mechanical power is transmitted
between two rotors via an elastohydrodynamic lubrication
(EHL) oil film. The traction oil intervening between the
rotors forms an oil film when it experiences a pressing
force, and it transmits mechanical power by the shear
force (traction force) of this oil film. The traction drive is
low vibration and low noise and has the feature of being
able to make up a continuously variable transmission
(CVT). For the traction drive type CVT, various structures
have been developed. Ring-corn type CVT [1] and kopp
type CVT [2] have been applied to industrial machine.
Half-toroidal CVT has been practically used for
automobiles [3]. Power transmission efficiency of this
CVT is over 92 [%] [4]. In addition, shaft drive CVT [5]
and full-toroidal CVT [6] have been studied. However,
the CVT of this traction drive type has a narrow range of
reduction ratio and the structure is complex.
Thus, Kuribayashi, one of the authors, devised a CVT
using cones in the traction drive type CVT, whose
structure is simple and from which a high reduction ratio
is available[7]. Figure 1 shows a schematic of the power
transmission portion of the devised CVT. Figure 2 shows
an exploded perspective view of the power transmission
portion. In this CVT, intermediate rolling elements are
placed between the input and output shafts to transmit
mechanical power. The input and output shafts have a
concave conical form, and the intermediate rolling
elements have a convex conical form. Because mechanical
power is transmitted from cone to cone, this new CVT is
called the cone-to-cone type CVT (CTC-CVT). On the
input and output shafts, gears are attached at the shaft end
as shown in Figure 2. By attaching the gears, the number
of mating parts of the input and output shafts and the
rolling elements can be increased. By increasing the
number of mating parts of the input and output shafts and
the rolling elements, high torque can be transmitted.
This study aims at practical development of CTC-CVT
which simple structure parts and power transmission
efficiency is about 90 [%]. This time, to know the basic
characteristics of the CTC-CVT, one set of input and
output shafts and rolling elements was examined without
attaching gears at the input and output shaft ends.
First the structure and speed-changing mechanism of
the CTC-CVT are described. Finally, the design and
power transmission efficiency examination of a prototype
are presented.
Fig. 1. Schematic of CTC-CVT
*E-mail: hkomatsu@yz.yamagata-u.ac.jp
† E-mail: am01137@dipfr.dip.yz.yamagata-u.ac.jp
‡ E-mail: a.kotani@kuribayashi.co.jp
Fig. 2. Exploded perspective view of CTC-CVT

12th IFToMM World Congress, Besançon (France), June18-21, 2007
CK-xxx
II. Basic Structure
A. Structure of CTC-CVT
Figure 3 shows a schematic of the power transmission
portion of the CTC-CVT. This CTC-CVT is composed of
input and output shafts and an intermediate rolling
element inscribed between them. The input and output
shafts have a concave conical form, and the intermediate
rolling element has a convex conical form. An offset of E
is given between the input and output shafts. Traction oil
intervenes between the concave cone at the end of each
shaft and the convex cone of the intermediate rolling
element, and it forms an oil film when a pressing force is
applied from the input shaft side. A traction force is
produced by the oil film, and the rotation of the input shaft
is transmitted to the output shaft via the intermediate
rolling element. Speed changes are effected by changing
the contact radius of the intermediate rolling element, and
the radius change is in turn effected by translating the
intermediate rolling element obliquely along the cone
angle.
B. Speed-changing Mechanism
The CTC-CVT changes the speed smoothly by
translating the intermediate rolling element obliquely
along the cone angle. Figure 4 shows the geometry of the
power transmission portion. Letting r 1 be the corotation
radius of the input shaft, r 2 be the corotation radius of the
convex cone on the input side, ω 1 be the angular velocity
of the input shaft, and ω 2 be the angular velocity of the
rolling element, then the following relationship is obtained
on the input side.
r
1ω1
= r2ω
2
(1)
Letting r 3 be the corotation radius of the convex cone
on the output side, r 4 be the corotation radius of the output
shaft, and ω 3 be the angular velocity of the output shaft,
then the following relationship is obtained on the output
side.
r
3ω2
= r4ω
3
(2)
The reduction ratio, e, is the ratio of the angular
velocity of the input shaft to that of the output shaft and is
given by the following equation using Equations 1 and 2.
ω1
ω1
ω2
r2
r4
e = = ⋅ = (3)
ω3
ω2
ω3
r3
r1
If the corotation radii, r 1 and r 4 , of the input and output
r 2 =2r 3 r 2 =r 3
shafts are equal, the following equation is obtained.
e = r 2
r 3
(4)
If the convex cone is translated, the corotation radii r 2
and r 3 of the intermediate rolling element at the points of
contact respectively with the input and output shafts
change. As shown in Figure 5(a), the reduction ratio is
2.0 if the length of r 2 is twice the length of r 3 . It is 1.0 if
the length of r 2 is equal to the length of r 3 (Figure 5(b)).
Likewise, the reduction ratio is 0.5 if the length of r 2 is
half the length of r 3 (Figure 5(c)). Thus, when the
corotation radii of the intermediate rolling element change,
the reduction ratio changes according to Equations 3 and 4.
Fig. 3. Schematic of power transmission portion
Fig. 4. Geometrical parameters of CTC-CVT
III. Design of CTC-CVT Prototype
To verify the operation and performance of the CTC-
CVT, a CTC-CVT prototype was designed. Figure 6
shows a sectional view of the designed CTC-CVT. Table
1 shows the specifications for the designed CTC-CVT
prototype.
As a design condition, a motor with a rated capacity of
15 [kw] and a rotational speed of 1500 [rpm] was used as
the input power source. The design was done on the
design concept of attaining a prototype with high power
transmission efficiency.
For changing the speed, a mechanism to translate the
r 2 =r 3 /2
(a) e=2.0 (b) e=1.0 (c) e=0.5
Fig. 5. Reduction ratio change mechanism of CTC-CVT

12th IFToMM World Congress, Besançon (France), June18-21, 2007
CK-xxx
intermediate rolling element along the cone angle by
turning a handle was used. Figure 7 shows a schematic of
the transmission mechanism. A case supports the
intermediate rolling element, and a slider is attached to the
case. A groove is cut in the frame at the same angle as the
convex cone. A handle is attached on the top of the case,
and turning the handle translates the case along the groove
and can effect stepless speed changes.
The pressure force necessary for the traction drive is
given by the loading cam on the input shaft side. The
loading cam is a device to produce a pressing force
according to the input torque. For the bearings on the
input and output shafts, a duplex angular bearing and
roller bearing are used. The bearings of the CTC-CVT
experience radial and thrust loads. These bearings are
used as a combination that can carry these loads and cause
little power loss at the bearings. The CVT was designed
so that the duplex angular bearing will carry radial and
thrust loads and the roller bearing will carry a large radial
load. The distance between the bearings was decided in
consideration of the allowable angle and efficiency of the
bearings.
For the lubrication of the various parts of the CVT,
forced lubrication using a CVT lubrication hydraulic unit
(pump, filter, cooler and tank) was used, and this unit is
installed separately from the CVT prototype. Labyrinth
seals are used, in consideration of the power loss by the
sealing devices.
Fig. 7. Schematic of Transmission Mechanism
Fig. 6. Schematic view of CTC-CVT
Output Torque T 2 (Nm) 95.5
Reduction ratio e 0.5 - 2.0
Input speed N 1 (min -1 ) 1500
Output speed N 2 (min -1 ) 750 - 3000
Cone angle δ (deg) 46
Contact radius r 1,r 4 (mm) 46
Offset E (mm) 13
TABLE I. Design specification of CTC-CVT
IV. Examination of Power Transmission Efficiency
Power transmission efficiency is most important as
performance of the transmission and an examination about
this was performed. The power loss by the traction drive
type CVT includes the loss by the support bearing, the
loss occurring at the contact surface of the power
transmission portion, the loss by agitation of traction oil
and the loss by oil seals and other sealing devices. The
prototype fabricated this time employs forced lubrication,
which sprays traction oil onto the CVT by the external
hydraulic unit. Thus it is thought that there is no power
loss by agitation of traction oil. Because labyrinth seals
are used for the sealing devices, it is considered that there
is no power loss by the sealing devices. Therefore, the
loss by the support bearing and the loss at the contact
surface of the power transmission portion were examined.
A. Effect of Bearing Loss
By the pressure force from the loading cam, a radial
load acts on the roller bearing on the input and output
shafts, and radial and thrust loads occur on the duplex
angular bearing. Due to these loads, a torque loss occurs
at each bearing. This torque loss is expressed as kinetic
friction torque, M t . The kinetic friction torque, M t ,
occurring at each bearing is expressed by the following
equation:
M
t
= M
l
+ M
v
(5)
where M l is the load term and M v is the velocity term.

12th IFToMM World Congress, Besançon (France), June18-21, 2007
CK-xxx
B. Effect of Spin
Around the normal to the contact surface of the power
transmission portion, relative rotary motion of the oil film
occurs in the elliptic contact area, and this motion is called
spin. The traction oil is heated by this spin, increasing the
slippage and reducing the shear force. The loss due to the
spin was theoretically found by an analytical method by
using the elastoplastic model of Johnson and Tevaarwerk
[8] and taking into account the oil’s shear force reduction
accompanying the heating.
C. Power Transmission Efficiency
The power transmission efficiency η P can be expressed
by the following equation using the speed transmission
efficiency η S and torque transmission efficiency η T .
η
P
= η
S
⋅ηT
(6)
The speed transmission efficiency represents the
relationship of the actual rotational speed to the rotational
speed of the ideal transmission free from slippage under
point contact condition. The speed transmission
efficiency can be found theoretically from the slippage
rate (creep) on the input and output sides. The creep can
be found from the traction curve as the magnitude of creep
for the set traction coefficient. The traction curve
represents the relationship between creep and traction
coefficient. The traction coefficient represents the ratio of
the traction force to the normal force, which is the normal
component of the pressure force acting on the
intermediate rolling element. Figure 8 shows the traction
curve of the CTC-CVT for the design specifications given
in Table 1. The temperature of the traction oil was taken
at 60 [°C].
The torque transmission efficiency represents the
relationship of the actually transmitted torque to the
ideally transmitted torque free from slippage under point
contact condition. The torque transmission efficiency can
be found from the loss at each bearing and the loss due to
spin. Figure 9 shows the calculated power transmission
efficiency versus input torque for reduction ratios of 2.0,
1.0 and 0.5.
The power transmission efficiency decreases as the
input torque increases. The power transmission efficiency
also decreases as the reduction ratio decreases, that is, the
output speed is increased. The torque loss at the bearings
increases as the input torque increases. When the output
speed is increased, a torque loss occurs at the bearings.
Moreover, the surface pressure in the contact area
becomes large and the slippage increases, so the power
loss becomes large. The power transmission efficiency
was 93% at a reduction ratio of 2.0 for the design
specifications given in Table 1.
V. Conclusion
(1) Aiming at practical development of a CTC-CVT
which is a continuously variable transmission using cones,
we designed a prototype and examined its power
transmission efficiency.
(2) We found the bearing loss and spin loss in the traction
area, which contribute to a reduction of power
transmission efficiency. As a result, the calculated
efficiency of the designed CTC-CVT is 93%.
The CTC-CVT designed this time is now in the process
of fabrication, and we will do a trial run to measure the
efficiency and compare it with the theoretical value.
Traction coefficient µ
Power transmission efficiency[%]
0.1
0.08
0.06
0.04
0.02
0
100
95
90
85
80
75
70
References
e=2.0
e=1.0
e=0.5
0 1 2 3 4 5 6
Creep Cr[%]
Fig. 8. Traction curve of CTC-CVT
0 10 20 30 40 50 60 70 80 90 100 110 120
Input torque[Nm]
e=2.0
e=1.0
e=0.5
Fig. 9. Power transmission efficiency of CTC-CVT
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