Post on 24-Mar-2022
Bulletin of the JSME
Journal of Advanced Mechanical Design, Systems, and ManufacturingVol.11, No.6, 2017
Paper No.17-00390© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Study on high-speed traction drive CVT for aircraft power
generation
- Gyroscopic effect of the thrust ball bearing on the CVT -
Kippei MATSUDA*, Tatsuhiko GOI*, Kenichiro TANAKA*, Hideyuki IMAI*, Hirohisa TANAKA** and
Yasukazu SATO** * Kawasaki Heavy Industries, Ltd.
1-1, Kawasaki-cho, Akashi City, 673-8666, Japan
E-mail: matsuda_kippei@khi.co.jp
** Yokohama National University
79-5, Tokiwa-dai, Hodogaya-ku, Yokohama City, 240-8501, Japan
1. Introduction
An airplane is usually equipped with generators driven by an engine to supply 400 Hz AC power. To maintain a
constant frequency, the generators have CVT units, which enable to change the speed ratio between an engine and a
generator freely, called integrated drive generator (IDG).
The traction drive - integrated drive generator (T-IDG®) is an innovative IDG featuring by a traction-drive CVT
instead of a current hydrostatic transmission.
In recent years, there has been a trend to replace pneumatic and hydraulic systems with electric systems to reduce
maintenance and operating costs, and increase reliability and operational efficiency. Figure 1 shows the increasing
demand for the electrical power capacity of aircraft (Balaji, 2008). To meet this demand, IDGs are becoming larger,
while there is a strong demand for weight reduction. It is well known that the higher the speed, the lighter the weight;
however, the behavior of the T-CVT has not been investigated above a velocity of 51 m/sec as shown in Table 1, and a
design method for a high-speed traction-drive CVT (T-CVT) that can operate up to 70m/sec of a peripheral speed has
not been established.
This paper reports the gyroscopic effect of a thrust ball bearing at a high rotation speed on the T-CVT, with the test
results shown for the temperature increase with or without gyroscopic sliding.
1
Received: 4 August 2017; Revised: 18 September 2017; Accepted: 17 October 2017
Abstract The traction drive - integrated drive generator (T-IDG®) has been developed since 1999 to replace current hydrostatic transmission drive generators mounted on Japanese military aircrafts. The T-IDG® consists of a generator and a half-toroidal traction-drive continuously variable transmission (CVT), which maintains a constant output speed of 24,000 rpm. In terms of coping with recent trends of high-power electric drive aircraft (MEA) and the need for weight reduction, a high-speed traction-drive CVT is advantageous over current hydro-static drive transmissions. The high-speed half-toroidal CVT has a fundamental issue regarding the thrust ball bearing, which must support a large loading force at a high rotational speed. The gyroscopic effect of the thrust ball bearing causes a serious slip called gyroscopic sliding at the insufficient preload and it damages the bearing. This paper describes the theoretical criteria and the design method for suppressing gyroscopic sliding. The test to validate the theory is also conducted with a prototype T-CVT up to 20,000 rpm with a peripheral speed of the traction contact of 70 m/s.
Keywords : Aerospace equipment, Generator, Traction drive, Half toroidal CVT, Gyroscopic, Thrust ball bearing
2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
Table 1 Comparison of T-CVT specification
*estimated by the authors, from the specifications shown by Machida et al. (1995).
2. Principle of T-IDG
2.1 Basic structure of T-IDG
The basic structure of the 90 kVA T-IDG® is shown in Fig. 2. The T-IDG® generates 115 V/ 400 Hz/ 3 phase AC
electrical power. The T-CVT converts the variable input speed provided by an aircraft engine, from 4,500 rpm to 9,200
rpm, to a constant output speed of 24,000 rpm for the AC generator. The derived type of this T-IDG has been adopted
as the main generator in Japanese military aircraft.
2.2 Outline of traction-drive CVT
Figure 3 shows the basic structure of the half-toroidal traction-drive CVT. It is mainly composed of three parts: an
input disc, an output disc, and power rollers. The power of the engine is transmitted from the input disc through the
power rollers to the output disc by a traction drive, which is the power-transmission mechanism in the toroidal CVT.
The torque into the CVT is transmitted through thin oil films existing between the discs and power rollers. As
shown in Fig. 4, a minute slippage between two rotational parts induces high shear resistance because the oil films are
very viscous owing to high contact forces.
The CVT changes its speed ratio continuously by changing the tilting angles of the power rollers as shown in Fig.
3. The contact points between the discs change as a result, and the speed reduction ratio of the CVT is given by
13 / rriV , (1)
where r1 is the radius of rotation to a contact point of the input disc and r3 is that of the output disc. The swing of each
power roller is controlled by the offset between the disc and the power roller which induces a tilting force FS as shown
in Fig. 5. For instance, when the speed of the generator is less than 24,000 rpm, the IDG controls a servo valve to
provide the offset of the power rollers, and then the power rollers start to swing. After finishing the ratio change, the
IDG controls the servo valve to cancel the offset to stop it. Note that the sensitivity of the swing motion of a power
for 90 kVA T-IDG for automobile
for aircraft
(Tanaka et al., 1999)
Max. input speed [rpm] 15,000 7000 20,500
Peripheral velocity [m/sec] 39 24* 51
Fig. 1 Electrical power generating capacity of aircraft (Balaji,2008)
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
roller is generally proportional to the rotational speed. Hence, instability due to sensitive speed control can be an
important issue in the high-speed T-CVT.
3. Analysis of weight reduction by high-speed T-CVT
Weight reduction is one of the main difficulties in designing aircraft components. In the T-IDG, the CVT accounts
for a substantial part of the total weight; therefore, we focus on reducing the weight of the CVT. A higher rotational
speed is a simple and effective way of reducing the weight while maintaining the following performances:
1) Traction performance at high velocity
2) Stability of speed-changing system
3) Gyroscopic effect of the power-roller bearing
First, a steady traction performance is important to achieve a high-speed CVT because the heat generated at the contact
surface causes a temperature rise, which deteriorates the traction coefficient (Hata et al., 2005, Miyata et al., 2009).
Second, the stability of the speed-changing system needs to be considered carefully, because the high sensitivity of the
speed-changing system may induce the unstable vibration (Goi et al., 2010). Third, the gyroscopic moment causes
serious sliding at the power-roller bearings in Fig.3, which is focused on in this paper. In the following sections, the
effects of the high-speed CVT on weight reduction and the theory of the gyroscopic sliding are described.
Fig. 2 Cutaway of 90 kVA T-IDG®
Traction Drive Variator Input Shaft
(4,500—9,200 rpm variable)
Generator Rotor
(24,000 rpm const.)
Output Terminal
Output Disc Input Disc
Thrust
Ball Bearing
r1 r3
A
A
Fig. 3 Basic structure of T-CVT
Power Roller
Offset
Servo Piston
Disc
Contact
Point
FS
Force
to Tilt :
Fig. 5 Ratio-changing mechanism
Offset
Section A-A of Fig.3
Drive Rotor
Driven Rotor Shear of Oil Film
Oil Out Oil In
Fig. 4 Principle of traction drive
Force
Force
Speed: U-U
Speed: U
3
2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
3.1 Effect of high-speed on weight reduction
A major factor determining the size of the T-CVT is the required fatigue life. In particular, the durability at traction
contact surface is a dominant factor, where the repeated high contact force and shear force cause peeling. Therefore, the
transmission of a heavy load due to a high electric load from the generator shortens the life of the CVT. In order to
avoid this, the CVT needs to be made larger to suppress the increase in contact stress; otherwise the torque into the
CVT needs to be reduced by increasing the rotational speed. This section discusses the effect of increasing the speed of
the CVT on the weight reduction.
To estimate the fatigue life of the T-CVT, Lundberg—Palmgren theory is applied (Coy et al., 1976). The number of
stress cycles endured before failure occurs is given by the following equation:
10/9
3/31
0
3/7
0
V
KzL
, (2)
where L is the number of stress cycles, z0 is the depth where the critical stress occurs, is the magnitude of the critical
stress, V is the amount of the volume stressed, and K is a constant. These variables are related to torque and size as
follows:
3/13/1
0 rFz , (3)
3/23/1
0
rF , (4)
3/53/2 rFV , (5)
where F is a representative force and r is a representative radius. Substituting Eq. (3) to (5) into Eq. (2), the following
equation can be obtained:
4.53rFL . (6)
The force is proportional to the torque T as follows:
1TrF . (7)
The lifetime H is expressed in terms of the rotational speed N as
14.8314.53 NrTNrFH . (8)
The torque T is inversely proportional to the rotational speed N and proportional to the transmitted power P as follows:
1 PNT . (9)
According to the specified life design, Eq. (8) is expressed by
constNrP 24.83 . (10)
As the weight W is proportional to the third power of the radius r, Eq. (10) is reduced to
7/514/15 NPW , (11)
where 3rW .
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
According to Eq. (11), a higher rotational speed N reduces the weight W. For instance, if the rotational speed is doubled,
the weight is reduced by 39%. Therefore, increasing the speed of the CVT is an effective way of reducing the weight of
the T-CVT.
3.2 Gyroscopic sliding of thrust ball bearing
In a high-speed T-CVT, the gyroscopic moment of a thrust ball bearing in a power roller cannot be neglected. Since
the thrust ball bearing of the power roller rotates at a high speed, it slides seriously when the gyroscopic moment is
larger than the resisting moment (Yamamoto, 1968). Figure 6 shows a schematic of a thrust ball bearing. To maintain
the rotation axis of each ball, it is necessary to oppose the gyroscopic moment; otherwise, the rotation axis inclines to
the direction of the raceway. A counter moment is generated by the friction of the micro slip caused by the minute
inclination of the rotation axis. Therefore, if the gyroscopic moment is larger than the maximum friction moment, this
slip rate increases rapidly with abnormal heat generation.
Assuming that a pure thrust load is applied on the bearing, the gyroscopic moment MG and friction moment MF are
given by
sinrevrotbG IM , (12)
002 rFM F , (13)
where Ib is the moment of inertia of a ball, rotis the spin angular velocity, revis the orbital angular velocity, is the
angle of the rotation axis due to the spinning moment, is the friction coefficient between the ball and the race, F0 is
the contact force on a ball, and r0 is the radius of a ball. The angular velocitiesrotand revcan be described in terms of
the rotational speed of the power roller 0 by the following equations:
0
sinsin2
cos
rev , (14)
0
0
00
sinsin2
cos
r
rRrot
, (15)
where R0 is the pitch circle radius of the bearing and is the contact angle of each ball which is given by
rot
F0
F0
Race
rev
Ideal Spinning Axis
Race
Real Spinning Axis
G
MF
A A
Section A-A
2r0
R0
Microslip
FC
FT/n
FT/n
Fig. 6 Schematic and notation of a thrust ball bearing
Spinning Axis
Thrust Load
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
C
T
nF
F2arctan , (16)
where FC is the centrifugal force of each ball, FT is the thrust force on the power-roller, and n is the number of balls. To
suppress gyroscopic sliding, MG should be smaller than MF:
FG MM , (17)
This inequality gives the criterion
115 0
2
0
3
00 F
rRA
, (18)
where is the mass density of the balls from which the moment of inertia Ib is converted, and A is the constant given
by
20
0
sinsin
coscos1
R
rA . (19)
From Eq. (18), a high rotational speed rapidly increases the risk of gyroscopic sliding. If the power transmission and
fatigue life are designed to be constant, from Eq. (10), the left side of Eq. (18) is related to the rotational speed N and
power P as follows:
17/1021/22124.8/432124
0
2
0
3
00
15
FPNFNPNFNrF
rRA
. (20)
To avoid gyroscopic sliding, using small balls to reduce r0 is most effective; however, it shortens the life of T-CVT
as shown in Eq. (6). Therefore, ceramic ball bearings are applied to the T-CVT as shown in Fig. 7. The density of the
ceramic ball is approximately 40% of that of the steel ball, which also relaxes the criteria of gyroscopic sliding by 40%.
Additionally, preloading of the CVT is essential to increase F0 in Eq. (18), but a too high preload deteriorates the
transmission efficiency and durability of the T-CVT. Therefore, an appropriate preload needs to be set as described in
the next section.
Fig. 7 Photograph of ceramic ball bearing supporting the power roller
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
3.3 Necessary preload of high-speed CVT
Generally, the preload of the toroidal CVT is determined by the lowest contact pressure (> 1 GPa) that must be
applied at the traction surface to generate the traction drive. A schematic of the clamping system is shown in Fig.8 and
the relationship between the power transmission and the clamping force is shown in Fig. 9. The cam clamping system
generates a clamping force proportional to the torque; however, where the cam clamping force is lower than the preload,
the clamping force is given by the preload. As mentioned in section 3.2., for a high-speed T-CVT, a large preload needs
to be applied to prevent gyroscopic sliding rather than for the traction drive. This is why the efficiency and durability of
the CVT deteriorate at too high preload. Thus, this section refers to the clamping force necessary to prevent both
gyroscopic sliding and performance deterioration.
The thrust on a power roller FT is described in terms of the clamping force FC as follows:
2sin
cosCT
FF , (21)
where is the half cone angle and is the tilting angle of the power roller. If the output speed out is constant, the
rotational speed of the power roller0 is given by
out
k
sin
2cos1 00
, (22)
where k0 is the aspect ratio of the CVT. From Eq. (18), (21), and (22), the necessary clamping force is obtained as a
function of the tilting angle. Figure 10 shows the clamping force necessary to prevent the gyroscopic sliding for the
conditions in Table 2. In this case, the preload is set to the maximum necessary force of 14,200 N.
On the other hand, CVT can transmit a power given by
out
CCt kFRP
2sin
2cos12 0, (23)
where t is the traction coefficient at the traction contact surface. Therefore, the power that can be transmitted by the
CVT only with the preload (Ppre in Fig. 9) is obtained from the highest value in Fig. 10 and Eq. (22). Figure 11 shows
the power transmitted by the preload as a function of the output speedout, which was analyzed by considering the
effect of a size reduction using Eq. (10) under the condition of constant power. This result indicates that an excess
speed leads to an excess preload, which lowers the efficiency and durability under a low load; therefore, the rotational
speed should be limited to a certain value considering the operating conditions of the CVT. For instance, if the output
speed is 9,000 rpm, the preload necessary to oppose the gyroscopic moment is 14,200 N, where the load transmitted by
the preload is 100 kW; therefore, this preload is the excess clamping force for the traction drive when the power is less
than 100 kW.
Fig. 8 Schematic of the clamping system
Output
Disc
Rc
e0
Power Roller
Input
Disc
k0=e0/RC
FC
FT out Cam
Clamping
Preload Spring
Clamping
Force
Power Transmission
Fig. 9 Typical characteristic of clamping force
Preload
Cam Clamp
Ppre
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
Table 2 Analysis condition
Ball Radius r0 8.334 mm
Pitch Circle Radius R0 30.8 mm
Density of Balls 3200 kg/m3
Number of Balls n 9
Angle of Rotation Axis 74 degrees
Friction Coefficient* 0.055
Cavity Radius RC 45 mm
Half Cone Angle 58 degrees
Aspect Ratio k0 0.65
Tilting Angle 25 to 91 degrees
Traction Coefficient* t 0.05
* Can be estimated using elastoplastic theory (Tevaarwerk, 1979).
4. Test Results of Prototype T-CVT
The performance of the high-speed T-CVT was verified using a prototype CVT.
4.1 Configuration of test rig
Figure 12 shows the test rig for the high-speed T-CVT. The rotational speed of the motor is increased using gears
up to 20,000 rpm at the CVT input discs. The CVT changes the input speed to a constant value of 8,944 rpm at the
output discs. Then the output discs drive the eddy current dynamometer where the load is applied. In the actual use of
T-CVT in T-IDG® system, the output speed of the CVT is increased to 24,000 rpm by gears, and then it drives the
generator. The load of dynamometer substitutes for the electrical load of the generator in T-IDG®.
The inside of the T-CVT is shown in Fig. 13 and its specifications are given in Table 3. The rated power capacity of
the prototype T-CVT is designed more than three times that of a 90 kVA T-IDG. The maximum rotational speed is 33%
Fig. 10 Necessary preload for CVT
Preload should be
determined by this point.
Fig. 11 Calculated effect of the output speed on the preload,
the power transmitted by only the preload and the size
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
higher than the original value, where the velocity of the traction contact surface is as high as 70 m/s. The weight is
approximately three times the original weight which is almost the same as the weight ratio of 293% estimated from Eq.
(11). If it was designed without an increase in speed, the weight of the CVT would be 363% that of the original.
Though the increase in the CVT rated load make it heavier, the rate of increase in weight is significantly suppressed by
the increase in speed.
The temperature of the power-roller is measured by thermocouple attached on the side of the outer race of the
bearing as shown in Fig. 14 in order to observe a temperature rise caused by gyroscopic sliding.
Table 3 CVT specifications
T-CVT for
90 kVA T-IDG
Protptype
T-CVT
Max Speed 40 m/s
15,000 rpm
70 m/s
20,000 rpm
Torus Diameter 110 mm 148.5 mm
CVT Rated Load Baseline Approx. 330%
Weight Baseline Approx. 300%
4.2 Test Results
Figure 15 shows a test result showing constant-output speed control. We can see that the CVT maintains output
speed of 8944 rpm while the input speed is changed from 4,000 rpm to 20,000 rpm.
Next, the effect of gyroscopic sliding on the temperature increase of the power roller is also measured while
changing the preload from an insufficient value of 11,600 N to a sufficient value of 20,000 N. The specifications of the
thrust bearing are given in Table 2. We can see in Fig.16 that at the insufficient preload, the power-roller temperature
increases suddenly at an input speed of 14,300 rpm owing to the gyroscopic sliding of the thrust bearing, while in the
Fig. 12 Test rig
Fig. 13 Prototype of high-speed T-CVT
CVT Gears
Dynamometer
Motor
Fig.14 Measurement position of temperature at power-roller bearing
Outer Ring
(Fixed Side)
Retainer
Inner Ring
(Rotating Side)
Thermocouple
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
case of the sufficient preload, the temperature is stable for an input speed of 15,000 rpm as shown in Fig.17.
Figure 18 shows the outer ring of the power-roller bearing after gyroscopic sliding. Diagonal streaks can be
observed on the raceway. It verifies that the rotation axis of the balls of the bearing inclined to the direction of the
raceway as shown in section 3.2 and Fig. 6.
Tests for the gyroscopic sliding were continued with the different preload and ball diameter of the bearing, in
order to verify the criterion of gyroscopic sliding given by Eq. (18). The relationship between the estimated input speed
where gyroscopic sliding occurs and the input speed achieved in the test is shown in Fig. 19. Gyroscopic sliding
occurred in three out of five cases, and it did not occur until maximum speed of 20,000 rpm in the rest cases.
Comparing with the dotted line in Fig. 19, which shows the criterion given by Eq. (18), we found that test results are in
good agreement with the theory.
Fig.15 The test result showing constant-output speed control
Output Speed
Input Speed
Temperature rise
due to sliding
Temperature is stable.
Fig.17 Measurement showing stable temperature of
the power roller without gyroscopic sliding of the
thrust ball bearing at a sufficient preload of 20 kN
Fig.16 Measurement showing temperature increase of the
power roller due to gyroscopic sliding of the thrust ball bearing
above 14,300 rpm at an insufficient preload of 11.6 kN
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
5. Discussions
The power-roller bearing at a high rotation speed causes gyroscopic sliding at an insufficient preload as mentioned
in section 3.2 and 3.3. Test results validate the mechanism and criterion of gyroscopic sliding, but there still remains a
small deviation between the theory and test result as shown in Fig. 19. The input speeds when gyroscopic sliding
occurred are slower than the calculated speeds by approximately 5 to 10%.
Reasons for this deviation are as follows:
- Decrease in the friction coefficient due to the temperature-rise at the power-roller bearing
- Decrease in the clamping force FC due to the frictional resistance of clamping system
- Decrease in the thrust force FT due to unbalanced clamping force among four power-rollers in a CVT
Fig. 18 Photograph of the race of the power-roller bearing after gyroscopic sliding, where the smear streaks are observed
Direction
of raceway
Direction
of streaks
Smear
streaks
Maximum speed of CVT
OK (Not slide until maximum speed)
Gyroscopic sliding occurred
Fig. 19 Comparison between test results and the calculation of the input speed when gyroscopic sliding occurs
Theoretical line where gyroscopic
sliding occurs based on Eq. (18)
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2© 2017 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2017jamdsm0087]
Matsuda, Goi, Kenichiro Tanaka, Imai, Hirohisa Tanaka and Sato,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017)
- Decrease in the contact force F0 due to unbalanced thrust force among balls in a bearing
- Increase in the half cone angle due to the deformation of discs and power-rollers
For further accurate estimation for gyroscopic sliding in T-CVT, items above need to be considered precisely.
6. Conclusions
The study of a high-speed T-CVT was performed forward meeting the demand for weight reduction. Increasing the
rotational speed is an effective way of reducing the weight of a CVT because the weight is roughly in inverse
proportion to the rotational speed. However, there are some issues regarding the thrust ball bearing in the high-speed
rotation of the T-CVT. This paper shows the effect of gyroscopic sliding of the thrust ball bearing.
The rapid rotation of the power-roller bearing causes gyroscopic sliding under an insufficient thrust load. In order
to avoid this, a high clamping preload is necessary, but too high preload deteriorates the efficiency and lifetime of the
CVT. Therefore, we have analyzed the mechanism of gyroscopic sliding and calculated theoretical minimum preload
for suppressing it. The theory and criterion of gyroscopic sliding is validated in the test in which the peripheral speed of
the traction contact surface is operated up to 70 m/s.
Acknowledgement
We appreciate all staff at KHI Ltd. and NSK Ltd. who contributed to the development.
References
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