High-Speed 50,000 rpm Planetary Roller Reducer for Electric Vehicles: Design and Transmission Efficiency Analysis

Due to the increasing demand for reducing carbon dioxide emissions, it is expected that most conventional vehicles having combustion engines will be replaced by electric vehicles such as hybrid cars, electric cars, and fuel-cell cars in the future. For this reason, research and development of the electric powertrain are being actively conducted, and one of the most important research themes is the miniaturization of motors with the goal of reducing vehicle weight, securing passenger space, and reducing the amount of rare metals used. The torque generated by a motor depends on its dimensions, but since output is the product of torque and rotational speed, increasing the speed allows the motor to be made smaller while maintaining the output power. For example, the Toyota Prius has increased its motor rotational speed from 5000 rpm on the first release to 17,000 rpm at present and has achieved a significant reduction in size while increasing its output [1]. The European consortium DRIVEMODE is developing an electric powertrain with a maximum rotational speed of 20,000 rpm [2]. In addition, AVL has proposed a 30,000 rpm unit [3], and the Technical University of Munich is conducting design studies on a 50,000 rpm unit [4]. Although it is necessary to consider factors such as increased windage, centrifugal force, vibration, and cooling, increasing the rotational speed is a major developmental trend [5].

In order to provide a sufficient driving force to a vehicle with a high-speed motor, it is necessary to combine the motor with a reducer. Gears are often used for this purpose [6], but traction drives are also a strong candidate for high-speed rotation [7]. A traction drive is an element that transmits power by shearing an oil film formed between two rolling elements and is considered to be suitable for high-speed operation because the noise is lower than when using gears, as there is no meshing vibration [8] and oil churning resistance is generally small [9]. In particular, planetary rollers have low power loss because they do not need bearings to support the large contact force required for transmission, and because they have multiple transmission paths, the diameter of the roller can be made smaller and the circumferential speed can be reduced, making planetary rollers suitable for high-speed reducers. Thus, a great deal of research has been conducted on this subject. For example, Someya et al. conducted power transmission experiments at a maximum speed of 90,000 rpm [10], and Nasvytis operated at 480,000 rpm, although under the no-load condition and without transmitting torque [11]. Currently, MHI Hasek manufactures 14,000 rpm industrial speed reducers [12], and Seiwa Seiki sells 30,000 rpm speed spindles for machine tools [13].

Power transmission efficiency is one of the most important performance measures for automobile transmissions, and, especially when combined with a high-speed motor, it is necessary to understand the transmission efficiency of planetary rollers at high rotations. Rohn et al. measured the transmission efficiency of a Nasvytis planetary roller at 45,000 rpm using a multirow stepped pinion driven by a gas turbine [14]. However, the transmission efficiency is approximated from the temperature rise of the lubricating oil, and the accuracy is not high. Loewenthal et al. also measured the transmission efficiency of the Nasvytis planetary roller at 73,000 pm using a power circulation test machine [15]. However, the transmission efficiency of the planetary roller is calculated from the power consumption of the drive motor, and considering the accuracy of predicting motor efficiency, it cannot be said that the measurement accuracy is high. In addition, these studies measure the transmission efficiency of the planetary roller assembly, but the percentage loss in components such as the power transmission section and bearings is not known. Nakamura et al. measured the friction loss of a simple planetary roller consisting of a single row of straight pinions at 86,000 rpm without transmitting torque [16]. Furthermore, the friction loss of the sliding bearing that supports the pinion was measured separately and was found to account for the majority of the power loss, whereas the loss in the power transmission part is relatively small. However, if the high-speed pinion power transmission surface is supported by a sliding bearing, it is natural that the loss will be large, and the inherent performance of the planetary roller cannot be measured. Furthermore, the power transmission efficiency when torque is being transmitted has not been measured. Recently, Ai [17] and Wang et al. [18] attached a torque meter and a rotation sensor to the input and output shafts of planetary rollers and measured the power transmission efficiency by applying rotation and torque with an electric motor. However, no analysis of the causes of loss was performed. In addition, the experimental conditions were 10,000 rpm or lower, which is not sufficient considering that high-speed motors for electric vehicles may reach 20,000–50,000 rpm in the future [2–5]. Furthermore, all of the aforementioned studies are based on experimental measurements only, and no calculation analysis of transmission efficiency has been performed. In order to further improve performance by analyzing the loss factors for each part and design optimal specifications, it is necessary to develop a calculation method for transmission efficiency.

Therefore, in the present study, a high-speed planetary roller prototype and its testing equipment were designed and manufactured, and the transmission efficiency was measured up to 50,000 rpm. It was confirmed that high transmission efficiency could be obtained even at high rotational speeds. When designing the prototype, a planetary arrangement suitable for the target high rotational speed was selected. A loading mechanism was also selected and a design was carried out taking into account dimensional variations. In addition, a calculation method for transmission efficiency that considers losses in the power transmission portion and bearings was developed, and it was confirmed that the obtained results agreed well with the experimental results.

The maximum rotational speed of the traction motor under consideration is 50,000 rpm [4,17,19], which is the highest among traction motors developed as power trains for electric vehicles. When considering a typical configuration consisting of a traction motor, planetary rollers, final gear, and differential gear, as shown in Fig. 1, the total reduction ratio required is approximately 30, and the reduction ratio for the final gear is generally 3–4. Therefore, the reduction ratio for the planetary roller should be at most 10, so that a single-stage planet can be used.

When configuring a reducer using a single-stage planetary arrangement, there are two possible arrangements: carrier output and ring output. When the basic efficiencies are equal, the carrier output arrangement is highly efficient and a large reduction ratio can be achieved [20]. As such, a carrier-output arrangement is often used. However, when operating at extremely high speeds, as in this case, there are concerns about the feasibility of a pinion bearing that has high-speed rotation with revolution. Since the pinion bearing of the carrier-output planetary roller was damaged, Nakamura et al. changed the mechanism to one in which the pinion power transmission surface was supported by a sliding bearing [16]. There is also a concern that the contact force may decrease due to the centrifugal force acting on the pinion roller. Therefore, regarding the carrier output and ring output, the rotational speed, load, and transmission efficiency of the pinion bearing were calculated and compared using Morozumi and Kishi's method [20]. The basic efficiency of the power transmission portion and the power loss of the bearing were determined using the method presented in Sec. 4. The maximum torque of the traction motor was set to 64 Nm. This means that, compared to the motor of the Nissan Leaf, which generates 10,000 rpm and 320 Nm, the rotational speed has increased five times, and the torque has been reduced to one-fifth. The size is similar to that of a planetary gear in an automatic transmission, and the inner diameter of the ring is 108 mm. The number of pinions was 3, the designed traction coefficient (ratio of transmitted force to contact force, which was set lower than the minimum traction coefficient) was 0.08, and the axial length of the pinion roller was set so that the maximum Hertzian surface pressure was 3 GPa considering the solid transition pressure (average pressure was 0.69 GPa, i.e., maximum Hertzian pressure was 1 GPa [21]) and fatigue life. The designed traction coefficient was chosen based on previous results that, in high-speed measurements and calculations [9,19], the traction coefficient does not fall below 0.08 under the assumed driving conditions.

Figure 2 shows the calculation results for the pinion speed and the load. The ring output has a lower rotational speed than the carrier output, and since lubricating oil can be supplied from the transmission case via the stationary carrier, the ring-output arrangement is advantageous in preventing seizure of the pinion bearing. Although the load is higher with the ring output, the same strength can be obtained by making the shaft length slightly longer. Figure 3 shows the transmission efficiency and the reduction rate for the contact force due to the centrifugal force acting on the pinion with revolution. The transfer efficiency is approximately 0.2 to 0.3% higher for carrier output, but this difference is not so large. The rate of decrease in centrifugal force in the carrier output is 6–10%, which cannot be ignored. Therefore, we determined that the ring-output arrangement is suitable for the high-speed planetary roller.

A traction drive transmits power through rolling friction, and it is necessary to apply a contact force to generate a frictional force. There are two loading methods: one uses elastic deformation of the ring to apply a constant contact force regardless of the transmitted torque, and the other uses a torque cam to apply a contact force proportional to the transmitted torque. Although torque proportional pressing can improve transmission efficiency in the low-torque range [20], the torque cam may cause unstable vibrations [22,23], and vibrations occur at high rotational speeds of tens of thousands of rpm. This may cause noise. Therefore, we calculated the transmission efficiency using the method shown in Sec. 4 and compared the differences depending on the loading method. The results are shown in Fig. 4. Constant loading gives excessive contact force in the low-torque range, resulting in low transmission efficiency, but the difference is only a few percent. Whether this difference in transmission efficiency can be tolerated must be determined based on the performance when installed in a vehicle. However, in order to prioritize avoiding trouble at high rotational speeds, this prototype uses constant loading.

When applying a constant contact force using an elastic ring, care must be taken to avoid errors in the contact force due to dimensional tolerances. The traction coefficient is less than 0.1, which requires a large contact force that is more than ten times the transmitted force. In order to achieve this, the ring needs to have high rigidity. In addition, a certain ring thickness is required in order to keep bending stress below a predetermined value, resulting in higher rigidity. However, if the rigidity is high, the error in the contact force due to the dimensional error between the inner diameter of the ring and the outer diameter of the sun roller and pinion roller becomes large. In order to prevent gross slip from occurring, the contact force must be maintained at a minimum value, and therefore, excessive contact force will be applied due to dimensional errors. However, if the contact force is too large, then the transmission efficiency and fatigue life will be reduced. Therefore, considering the ring as a thick circular ring with a rectangular cross section, we calculated the stress and deformation when receiving concentrated loads at three equally distributed locations and determined the allowable dimensional error for the allowable stress and contact force error.

Figure 5 shows the transmission efficiency of the planetary roller and the ring bending stress with respect to the increase in interference due to dimensional errors for three ring thicknesses. The width of all rings is 24 mm. The designed traction coefficient when there is no error was set to 0.08. When the dimensional tolerance class is H6, the total tolerance of the sun roller, pinion roller, and ring is 0.04 mm, and, as shown in Fig. 5, the reduction in transmission efficiency is approximately 1%, which is not a very large reduction. If selective fitting is performed as in the rolling bearings, it is possible to suppress the reduction to 0.01 mm or less, as in the rolling bearings, and the drop in transmission efficiency can be minimized. The sensitivity of the ring thickness to stress is large, and the stress decreases in inverse proportion to the ring thickness from Eq. (6), but the sensitivity of the thickness to transmission efficiency is small, as shown in Fig. 5. Therefore, by increasing the outer diameter of the ring as much as the size allows, it is possible to keep the stress below the allowable limit without reducing the transmission efficiency.

It is not easy to prepare a drive motor and torque meter that rotate at 50,000 rpm. Therefore, we arranged two planetary rollers facing each other and used one of them as a speed increaser. We connected the sun rollers and used each ring as input and output. Figure 6 shows an axial cross-sectional view of the testing machine. The sun roller is supported by a carrier fixed to the case via a ceramic ball angular bearing. The pressurization of the bearing was adjusted using a web washer. The ring deforms into a triangular shape due to the contact force, but in order to prevent loss of contact force, it must be supported without interfering with the deformation and torque must be transmitted to the output shaft. Therefore, torque transmission was performed using a coupling between a pin and a hole with a slightly larger diameter than the pin, and axial support was provided using a hook. There are two systems for lubrication of the pinion bearing, which is at risk of seizure: one from the carrier and the other from the output shaft. A cage and roller bearing was used for the radial bearing of the pinion, and a PEEK sliding bearing was used for the thrust bearing. Since the maximum output of the drive motor was 15 kW, the maximum torque of the sun roller was set to 5 Nm, and the tightening allowance was set using the same calculation as shown in Fig. 5. The calculation results are shown in Fig. 7, and the transmission efficiency and bending stress sensitivity to dimensional errors are almost the same as shown in Fig. 5. The error rank for each roller is H6. Table 1 shows the specifications of the designed test machine.

Shrink fitting is often used to assemble elastic rings, but we devised a simpler method. A screw hole was cut in a thick circular ring placed on the outer diameter of the ring, and the ring was elastically deformed into a triangular shape by applying a load with three bolts placed between the pinions. The sun and pinion were assembled in the carrier. The structure is such that the assembly can be set by inserting it into the holder and loosening the bolt (Fig. 8).

Figure 9 shows the experimental setup. Two servo motors perform drive and absorption, and a torque meter measures the torque and rotational speed on the ring. The maximum torque of the servo motor is 47 Nm, and the maximum rotational speed is 6000 rpm. The oil supply temperature was measured by measuring the temperature at the absorption motor side output shaft. The sun roller was magnetized in the radial direction, and its rotational speed was measured using a magnetic sensor and a rotational pulse meter. Lubrication was by forced circulation, and, in order to prevent the planetary rollers from submersion in the oil surface and creation of drag torque, a dry sump system was used, in which the oil inside the unit was sucked in by a pump and discharged into a separate tank. An electric heater installed in the tank was controlled by a solid-state relay and a Proportional–Integral–Differential (PID) temperature controller, making it possible to set the temperature of the oil supplied to the traction portion to any value between room temperature and 120 °C. KTF-1 traction fluid was used as the lubricant, and its properties are summarized in Table 2.

The absorption motor was set to a constant rotational speed using speed control, and the drive motor was given a sweep torque of 1 Nm/s using torque control. Figure 10 shows the transmission efficiency of the reducer planetary roller on the sun roller at three rotational speeds (the horizontal axis is $Ts$ in Eq. (8) and the vertical axis is $ηd$ in Eq. (9)): 9,000, 18,000, and 50,000 rpm. At 9000 rpm, the maximum efficiency exceeded 98%, achieving a high efficiency equivalent to that of a general planetary gear. As the rotation increases, the transmission efficiency at low torque decreases slightly, but even at 50,000 rpm, the decrease is small at approximately 5%. Similar to the comparison between parallel shaft traction rollers and gears [17], the increase in the power loss for the traction roller due to the increase in rotational speed is small. We believe that this is due to the fact that the transmission surface is smooth, meaning there is little churning and windage loss.

Figure 11 shows the torque loss for the reducer planetary roller on the sun roller. Since the torque loss is almost constant with respect to the transmitted torque, it is thought that the loss is mainly due to the contact force, and the loss due to torque, as in pinion bearings, is small.

Figure 12 shows the slip ratio for the reducer planetary roller as calculated from the rotational speed of the sun roller and the rotational speed measured with an output torque meter. This is the total slip ratio between the sun and pinion, and between the pinion and ring. The designed traction coefficient is 0.08 at 5 Nm, and the slip ratio is 0.6%, with an average slip of 0.3% per location. This is equivalent to the measurement results with parallel shaft rollers [17,19], and it is thought that power is transmitted normally without spin or skew caused by pinion roller misalignment.

The transmission efficiency of the planetary roller is calculated from the rolling friction resistance of the traction portion caused by the elastic hysteresis loss due to Hertzian deformation and the rolling shear resistance of the oil film, the friction loss of the bearing, and experimentally determined losses such as churning.

Consider the sun-pinion and pinion-ring as roller pairs, and let $R′$ be the radius of the sun roller and the pinion roller, respectively. $β$ is set to 0.007 based on Kakuta's study [24].

Next, we calculate the friction loss for the angular ball bearing that supports the sun roller, the deep groove ball bearing that supports the ring, the radial needle bearing that supports the pinion, and the thrust washer.

Since the surface pressure is low, the elastic hysteresis is considered to be smaller than the rolling viscous resistance and is ignored.

Table 3 shows the specifications and conditions used in the calculation.

Table 4 shows the measured roller diameter for the prototype, the tightening margin, and the contact force calculated using Eqs. (1)–(5). The designed traction coefficient at a rated torque of 5 Nm was 0.0723.

Figure 13 shows the calculated values superimposed on the experimental values in Fig. 10, and the calculated values agree well with the experimental values regardless of torque and rotational speed. The value of $M0$ (other torque losses) is 0.02–0.03 Nm. It is almost constant regardless of the rotational speed within the range of the experimental conditions.

Since the assembly calculations were in good agreement with the experimental results, each term was considered to be predicted with good accuracy, and the loss ratio was analyzed using the calculations. Figures 14 and 15 show the loss for each element converted into torque loss on the sun roller shaft for two levels of rotational speed. The slip ratio in the traction portion was converted into torque and added to the traction portion. As shown in the figure, the loss in the traction portion is the largest at both low and high speeds, followed by other losses at a fraction and pinion bearings at a few percent, and other bearing losses are extremely small.

Using this calculation, the transmission efficiency was predicted when designing a planetary roller with a maximum torque of 64 Nm under actual vehicle conditions and compared with that for the prototype (Fig. 16). The horizontal axis shows the load factor, which is the input torque divided by the maximum torque. Bearing stirring torque and other losses do not depend on load, so the losses do not increase even if the torque increases. As a result, the transmission efficiency is improved compared to the prototype, especially at high speeds. However, under the conditions of this experiment, the torque was less than one-tenth of that for the actual vehicle, and the load term loss could not be adequately measured, so it will be necessary in the future to confirm experimentally whether the calculation can be extrapolated even with high torque.

Conventional electric vehicle reducers use gears. The authors previously compared the transmission efficiency at high rotational speed and found that traction drives were more efficient at high rotational speed and low torque, whereas gears were more efficient at low rotational speed and high torque [9]. Therefore, traction drives are suitable for the high-rotational speed, low-torque motors considered in this study. To make the most of this characteristic, it is desirable to provide a loading force proportional to the torque. However, this would require adding a mechanism, which would increase size and cost. In addition, traction oil reduces the transmission efficiency of gears [28], resulting in large losses in the final gear. For both traction drives and gears, when oil bath lubrication is used at high speeds, churning losses become extremely large. It is expected that lubrication using a pump will be necessary. The losses caused by the pump were not considered here. The magnitude of pump losses may differ between traction drives and gears due to differences in the properties of the lubrication oil. This study showed that planetary rollers have the potential to achieve high efficiency at high rotational speed. Nevertheless, further study is needed to determine whether the entire unit is superior to a gear reducer.

Planetary rollers are expected to be used as high-speed reducers for electric vehicles. In the present study, we designed and manufactured a prototype, measured the transmission efficiency, and constructed and analyzed a transmission efficiency prediction formula. We reached the following conclusions:

• As a high-speed reducer, the planetary arrangement has excellent sun input and ring output.

• High transmission efficiency of up to 98% can be obtained for a maximum torque of 5 Nm and a maximum power of 15 kW, and the rate of decrease in transmission efficiency due to speed increase is small even at high rotational speeds of 50,000 rpm.

• We developed a method to predict the transmission efficiency with high accuracy from low to high rotational speeds and clarified the contribution of each part.

• The main f power loss factor is rolling friction in the traction portion, and other factors such as bearings and oil churning resistance have a small contribution.

• It is expected that a unit with a larger torque capacity equivalent to the actual machine will further improve the transmission efficiency.

We would like to thank Oiles Industries Co., Ltd. for designing and providing the thrust washer. We would also like to thank graduate students Mr. K. Hirata and Mr. T. Nishizawa for their efforts in designing the prototype.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$a$ =

rolling perpendicular contact radius of Hertzian contact ellipse

$b$ =

rolling direction contact radius of Hertzian contact ellipse

$h$ =

ring thickness

$u$ =

deformation in x direction

$w$ =

deformation in z direction

$E$ =

Young's modulus

$G$ =

bearing geometry factor

$K$ =

constant determined by contact surface shape

$R$ =

average radius of ring

$As$ =

cross-sectional area

$Dp$ =

Pinion roller diameter

$Dr$ =

ring inner diameter

$Ds$ =

sun roller diameter

$Fc$ =

contact force

$Rp$ =

Pinion roller radius

$Rr$ =

ring inner radius

$Rs$ =

sun roller radius

$κ$ =

section modulus of the curved beam

$ν$ =

Poisson's ratio