Study on high-speed traction drive CVT for aircraft power generation - Gyroscopic effect of the thrust ball bearing on the CVT -

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1 Bulletin of the JSME Journal of Advanced Mechanical Design, Systems, and Manufacturing Vol.11, No.6, 217 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, , Japan matsuda_kippei@khi.co.jp ** Yokohama National University 79-5, Tokiwa-dai, Hodogaya-ku, Yokohama City, , Japan Received: 4 August 217; Revised: 18 September 217; Accepted: 17 October 217 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, 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 2, rpm with a peripheral speed of the traction contact of 7 m/s. Keywords : Aerospace equipment, Generator, Traction drive, Half toroidal CVT, Gyroscopic, Thrust ball bearing 1. Introduction An airplane is usually equipped with generators driven by an engine to supply 4 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, 28). 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 7m/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. Paper No [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 1

2 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) Fig. 1 Electrical power generating capacity of aircraft (Balaji,28) Table 1 Comparison of T-CVT specification for 9 kva T-IDG for automobile for aircraft (Tanaka et al., 1999) Max. input speed [rpm] 15, 7 2,5 Peripheral velocity [m/sec] 39 24* 51 *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 9 kva T-IDG is shown in Fig. 2. The T-IDG generates 115 V/ 4 Hz/ 3 phase AC electrical power. The T-CVT converts the variable input speed provided by an aircraft engine, from 4,5 rpm to 9,2 rpm, to a constant output speed of 24, 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 i r / r V 3 1, (1) where r 1 is the radius of rotation to a contact point of the input disc and r 3 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 F S as shown in Fig. 5. For instance, when the speed of the generator is less than 24, 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 [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 2

3 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) 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. Input Shaft (4,5 9,2 rpm variable) Traction Drive Variator r 1 A r 3 Input Disc Output Disc Generator Rotor (24, rpm const.) Output Terminal Power Roller A Thrust Ball Bearing Fig. 2 Cutaway of 9 kva T-IDG Fig. 3 Basic structure of T-CVT Contact Point Offset Drive Rotor Force Force to Tilt : F S Speed: U Disc Oil In Oil Out Driven Rotor Speed: U-U Force Shear of Oil Film Offset Servo Piston Section A-A of Fig.3 Fig. 4 Principle of traction drive Fig. 5 Ratio-changing mechanism 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., 25, Miyata et al., 29). 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., 21). 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. [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 23

4 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) 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: Kz L 7 / 3 31/ 3 V 9 /1, (2) where L is the number of stress cycles, z 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: z, (3) 1/ 3 1/ 3 F r F r 1/ 3 2 / 3, (4) 2 / 3 5 / 3 V F r, (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: L F 3 r 5.4. (6) The force is proportional to the torque T as follows: 1 F Tr. (7) The lifetime H is expressed in terms of the rotational speed N as H F r N T r N. (8) The torque T is inversely proportional to the rotational speed N and proportional to the transmitted power P as follows: 1 T PN. (9) According to the specified life design, Eq. (8) is expressed by P r N const 3. (1) As the weight W is proportional to the third power of the radius r, Eq. (1) is reduced to 15/14 5 / 7 W P N, (11) 3 where W r. [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 24

5 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) 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. Real Spinning Axis rev 2r R rot G Microslip Ideal Spinning Axis Thrust Load F T /n F Race F Spinning Axis A M F A Race F C F T /n Section A-A Fig. 6 Schematic and notation of a thrust ball bearing Assuming that a pure thrust load is applied on the bearing, the gyroscopic moment M G and friction moment M F are given by M sin, (12) G I b rot M F 2F r rev, (13) where I b is the moment of inertia of a ball, rot is the spin angular velocity, rev is 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, F is the contact force on a ball, and r is the radius of a ball. The angular velocities rot and rev can be described in terms of the rotational speed of the power roller by the following equations: cos 2sin sin rev, (14) rot R r cos, (15) 2r sin sin where R is the pitch circle radius of the bearing and is the contact angle of each ball which is given by [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 25

6 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) 2FT arctan, (16) nfc where F C is the centrifugal force of each ball, F T is the thrust force on the power-roller, and n is the number of balls. To suppress gyroscopic sliding, M G should be smaller than M F : M G M F, (17) This inequality gives the criterion AR 3 r 15F 2 1, (18) where is the mass density of the balls from which the moment of inertia I b is converted, and A is the constant given by r R cos sin sin A 1 cos. (19) 2 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. (1), the left side of Eq. (18) is related to the rotational speed N and power P as follows: AR 3 r 15F 2 r 4 N 2 F / 22/ 1/ N P N F N P F. (2) To avoid gyroscopic sliding, using small balls to reduce r 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 4% of that of the steel ball, which also relaxes the criteria of gyroscopic sliding by 4%. Additionally, preloading of the CVT is essential to increase F 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 [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 26

7 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) 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 F T is described in terms of the clamping force F C as follows: T FC cos sin 2 F, (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 roller is given by 1 k cos 2 sin, (22) out where k 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 1 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 14,2 N. On the other hand, CVT can transmit a power given by P 2 t C C 1 R F k cos 2 sin 2 out, (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 (P pre in Fig. 9) is obtained from the highest value in Fig. 1 and Eq. (22). Figure 11 shows the power transmitted by the preload as a function of the output speed out, which was analyzed by considering the effect of a size reduction using Eq. (1) 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, rpm, the preload necessary to oppose the gyroscopic moment is 14,2 N, where the load transmitted by the preload is 1 kw; therefore, this preload is the excess clamping force for the traction drive when the power is less than 1 kw. Power Roller k =e /R C R c F T out Cam Clamping Clamping Force Preload Cam Clamp e Input Disc Output Disc F C Preload Spring P pre Power Transmission Fig. 8 Schematic of the clamping system Fig. 9 Typical characteristic of clamping force [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 27

8 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) Preload should be determined by this point. Fig. 1 Necessary preload for CVT Fig. 11 Calculated effect of the output speed on the preload, the power transmitted by only the preload and the size Table 2 Analysis condition Ball Radius r mm Pitch Circle Radius R 3.8 mm Density of Balls 32 kg/m 3 Number of Balls n 9 Angle of Rotation Axis 74 degrees Friction Coefficient*.55 Cavity Radius R C 45 mm Half Cone Angle 58 degrees Aspect Ratio k.65 Tilting Angle 25 to 91 degrees Traction Coefficient* t.5 * 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 2, 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, 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 9 kva T-IDG. The maximum rotational speed is 33% [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 28

9 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) higher than the original value, where the velocity of the traction contact surface is as high as 7 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 Max Speed T-CVT for 9 kva T-IDG 4 m/s 15, rpm Protptype T-CVT 7 m/s 2, rpm Torus Diameter 11 mm mm CVT Rated Load Baseline Approx. 33% Weight Baseline Approx. 3% Gears CVT Fig. 13 Prototype of high-speed T-CVT Motor Dynamometer Inner Ring (Rotating Side) Fig. 12 Test rig Retainer Outer Ring (Fixed Side) Thermocouple Fig.14 Measurement position of temperature at power-roller bearing 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, rpm to 2, 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 11,6 N to a sufficient value of 2, 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 14,3 rpm owing to the gyroscopic sliding of the thrust bearing, while in the [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 29

10 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) case of the sufficient preload, the temperature is stable for an input speed of 15, 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 2, 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. Input Speed Output Speed Fig.15 The test result showing constant-output speed control Temperature is stable. Temperature rise due to sliding Fig.16 Measurement showing temperature increase of the power roller due to gyroscopic sliding of the thrust ball bearing above 14,3 rpm at an insufficient preload of 11.6 kn Fig.17 Measurement showing stable temperature of the power roller without gyroscopic sliding of the thrust ball bearing at a sufficient preload of 2 kn [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 1 2

11 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) Direction of raceway Direction of streaks Smear streaks Fig. 18 Photograph of the race of the power-roller bearing after gyroscopic sliding, where the smear streaks are observed OK (Not slide until maximum speed) Theoretical line where gyroscopic sliding occurs based on Eq. (18) Maximum speed of CVT Gyroscopic sliding occurred Fig. 19 Comparison between test results and the calculation of the input speed when gyroscopic sliding occurs 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 1%. 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 F C due to the frictional resistance of clamping system - Decrease in the thrust force F T due to unbalanced clamping force among four power-rollers in a CVT [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 11 2

12 Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (217) - Decrease in the contact force F 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 7 m/s. Acknowledgement We appreciate all staff at KHI Ltd. and NSK Ltd. who contributed to the development. References Balaji, S., Aircraft electrical Power Systems, Frost & Sullivan Market Insight, 24 Nov. 28 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 (21), pp (in Japanese) Hata, H., Aoyama, S. and Miyaji, T., Performance and Characteristics of Idemitsu Traction Oils, Idemitsu Tribology Review T-28-4 (25) Machida, H., Itoh, H., Imanishi, T., and Tanaka, H., Design Principle of High Power Traction Drive CVT, SAE Technical Paper (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 (29) 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 Tevaarwerk, J. L., Traction Drive Performance Prediction for the Johnson and Tevaarwerk Traction Model, NASA Technical Paper, NASA TP-153 (1979) Yamamoto, S., Study on Ball Motion of High-Speed Ball Bearings, Transactions of Japan Society of Tribologists, Vol. 13, No. 9 (1968), pp (in Japanese) [DOI: /jamdsm.217jamdsm87] 217 The Japan Society of Mechanical Engineers 12 2