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汽车零部件采购、销售通信录       填写你的培训需求,我们帮你找      招募汽车专业培训老师 
 
 
 
 
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— 1Traction 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(CTCCVT). 
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 
*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 
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 
Fig. 2. Exploded perspective view of CTC-CVT 
12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx 
(a) e=2.0 (b) e=1.0 (c) e=0.5 
Fig. 5. Reduction ratio change mechanism of CTC-CVT 
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 r1 be the corotation 
radius of the input shaft, r2 be the corotation radius of the 
convex cone on the input side, w1 be the angular velocity 
of the input shaft, and w2 be the angular velocity of the 
rolling element, then the following relationship is obtained 
on the input side. 
1 1 2 2 rw = rw (1) 
Letting r3 be the corotation radius of the convex cone 
on the output side, r4 be the corotation radius of the output 
shaft, and w3 be the angular velocity of the output shaft, 
then the following relationship is obtained on the output 
side. 
3 2 4 3 rw = rw (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. 
3 1 
2 4 
3 
2 
2 
1 
3 
1 
r r 
r r 
e = = × = 
w 
w 
w 
w 
w 
w 
(3) 
If the corotation radii, r1 and r4, of the input and output 
shafts are equal, the following equation is obtained. 
2 3 e = r r (4) 
If the convex cone is translated, the corotation radii r2 
and r3 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 r2 is twice the length of r3. It is 1.0 if 
the length of r2 is equal to the length of r3 (Figure 5(b)). 
Likewise, the reduction ratio is 0.5 if the length of r2 is 
half the length of r3 (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 CTCCVT, 
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 
r2=2r3 r2=r3 
r2=r3/2 
12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx 
Fig. 6. Schematic view of CTC-CVT 
int ermediate 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 
Output Torque T2 (Nm) 95.5 
Reduction ratio e 0.5 - 2.0 
Input speed N1 (min-1) 1500 
Output speed N2 (min-1) 750 - 3000 
Cone angle d (deg) 46 
Contact radius r1 
, 
r4 (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, Mt. The kinetic friction torque, Mt, 
occurring at each bearing is expressed by the following 
equation: 
t l v M = M + M (5) 
where Ml is the load term and Mv 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 hP can be expressed 
by the following equation using the speed transmission 
efficiency hS and torque transmission efficiency hT. 
P S T h =h ×h (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. 
0 
0.02 
0.04 
0.06 
0.08 
0.1 
0 1 2 3 4 5 6 
Creep Cr[%] 
Traction coefficient μ 
e=2.0 
e=1.0 
e=0.5 
Fig. 8. Traction curve of CTC-CVT 
70 
75 
80 
85 
90 
95 
100 
0 10 20 30 40 50 60 70 80 90 100 110 120 
Input torque[Nm] 
Power transmission efficiency[%] 
e=2.0 
e=1.0 
e=0.5 
Fig. 9. Power transmission efficiency of CTC-CVT 
References 
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CVT (1st Report, Design of Transmission), Trans. JSME, 
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[2] FRANK NAJLEPSZY, Traction Drives Roll up Impressive Gains, 
MACHINE DESIGN, 57-25, (1985), 68-75 
[3] Machida, Hata, Nakano and Tanaka, Half-Troidal Traction Drive 
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