study on high speed traction drive cvt for aircraft power

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: [email protected]

** 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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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



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 .

4



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

5



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

6



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

7



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

8



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

9



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

10



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)

11



- 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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Balaji, S., Aircraft electrical Power Systems, Frost & Sullivan Market Insight, 24 Nov. 2008

Coy, J. J., Loewenthal, S. H. and Zaretsky, E. V., Fatigue life analysis for traction drives with application to a toroidal

type geometry, NASA Technical Note, NASA TN D-8362 C.1 (1976)

Goi, T., Tanaka, H., Nakashima, K. and Watanabe, K., Study on Stability of High Speed Traction Drive CVT for

Aircraft Generator, Transactions of the Japan Society for Aeronautical and Space Science, Vol. 58, No. 678

(2010), pp. 203-209 (in Japanese)

Hata, H., Aoyama, S. and Miyaji, T., Performance and Characteristics of Idemitsu Traction Oils, Idemitsu Tribology

Review T-28-4 (2005)

Machida, H., Itoh, H., Imanishi, T., and Tanaka, H., Design Principle of High Power Traction Drive CVT, SAE

Technical Paper 950675 (1995)

Miyata, S., Höhn, B., Michaelis, K., and Kreil, O., Experimental and Numerical Investigations for Analysis of

Temperature Rise on the Traction Contact Surface of Toroidal Cvts, SAE Technical Paper 2009-01-1661 (2009)

Tanaka, H., Shiino, R., Goi, T. and Kawakami, K., Transmission efficiency of a high speed half-toroidal CVT,

Transactions of the JSME (in Japanese), Vol. 65, No.633 (1999), Paper No. 98-0869

Tevaarwerk, J. L., Traction Drive Performance Prediction for the Johnson and Tevaarwerk Traction Model, NASA

Technical Paper, NASA TP-1530 (1979)

Yamamoto, S., Study on Ball Motion of High-Speed Ball Bearings, Transactions of Japan Society of Tribologists, Vol.

13, No. 9 (1968), pp. 505-521 (in Japanese)

study on high speed traction drive cvt for aircraft power

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