A Study on the Drive Performance of a Magnetic Planetary Gear Device with Dual-Input Functionality (Part 2)

M. Miyazawa*, H. Oizumi*, D. Kobayashi*, H. Tota*, and K. Tsurumoto** Faculty of Eng., *Dept. of EE, **ME, Tohoku Gakuin Univ., 1-13-1 Chuo, Tagajo, Miyagi 985-8537, Japan

We created and reported the performance of a variety of magnetic gears in previous work. Magnetic gears allow the transmission of

motive force in a completely non-contact state. Their main advantages include low vibration and noise, maintenance-free operation,

and a lack of lubrication. We have recently constructed a prototype of a magnetic planetary gear apparatus and found that the most

promising practical application of such a device, particularly for accelerator versions, is in wind-powered electrical power generating

equipment. This device boasts dual-input functionality. We envision wind power as the primary input, while the secondary input may

come from sources such as hydraulic power or electrical-storage devices to drive the mechanism that controls the rotation rate. We

reported the possibility of using secondary input as a differential mechanism in a previous paper published in this journal to

compensate for variations in the input rotation rate, thus allowing the rotation rate of the sun gear to be controlled, which constitutes

the output of the device. We used our dual-input device in this research to carry out experimental investigations into a parallel-drive

scheme in which the outer ring gear on the secondary input is rotated in the same direction that the carrier is rotated. Our experiments

revealed three distinct operating regimes for our device: a regime in which the output rotation rate was lower than the input rotation

rate, a point at which the output rotation rate fell to zero, and a regime in which the output rotation rate was greater than, but in the

direction opposite to, the input rotation rate.

Key words: planetary gear, sun gear, outer ring gear, dual-input functionality, drive performance, parallel-drive, differential-drive

1. Introduction

We created and reported the performance of a variety of

magnetic gear prototypes in this journal1)–4). Magnetic gears

allow the transmission of motive force between gears in a

completely non-contact state. Their main advantages include

low vibration and noise, maintenance-free operation, and a lack

of lubrication5)–9). We have recently constructed a prototype of a

magnetic planetary differential gear apparatus and found that the

most promising practical application of such a device,

particularly for accelerator versions, is in wind-powered

electrical power generating equipment. This device is capable of

sustaining a high speed-increase ratio, while boasting dual-input

functionality, we envision wind power as the primary input,

while the secondary input may come from sources such as

hydraulic power or electrical-storage devices to drive the

mechanism that controls the rotation rate. We reported the

possibility of using secondary input as a differential mechanism

in a previous paper published in this journal10) to compensate for

variations in the input rotation rate, thus allowing the rotation

rate of the sun gear to be controlled, which constitutes the

output of the device.

We describe further experimental investigations conducted

using this dual-input magnetic planetary gear device in this

report. In contrast to earlier work4), we here consider a

parallel-drive configuration in which the primary input is taken

from the planetary gear guiding disc (the carrier), while the

outer ring gear, which provides the secondary input, is rotated in

Fig. 1 Schematic of planetary and outer ring gearing for

accelerator.

(One example of differential (diff.) and parallel (para.) drive

configuration.)

the same direction that the carrier is rotated. We report below

the results of a comparative study contrasting the performance

of this parallel-drive configuration to the performance of

differential-drive configurations studied previously.

2. Design Specifications of the Magnetic Planetary

gear Device

Figure 1 shows the configuration of the magnetic planetary

178 Journal of the Magnetics Society of Japan Vol.38, No.4, 2014

J. Magn. Soc. Jpn., <Paper>38, 178-183 (2014)

Planetary gear (a)

Outer ring gear (c)

Sun gear (b)

Carrier

Input (2)

Output

Input (1)

Fig. 2 Photographs of planetary gears, sun gear, and outer ring

gear.

Table 1 Characteristics of planetary gear, sun gear, and outer

ring gear.

Nomenclature

Module : m = 20

Tooth profile : Involute curve

Height of tooth : H = 20 mm

Center distance : L = 60 mm

Planetary gear (a)

Number of teeth : ZP = 16

Radius of pitch circle : RP = 20 mm

Diameter of outer circle : DP = 80 mm

Sun gear (b)

Number of teeth : ZS = 16

Radius of pitch circle : RS = 20 mm

Diameter of outer circle : DS = 80 mm

Outer ring gear (c)

Number of teeth : ZO = 64

Radius of pitch circle : RO = 80 mm

Diameter of outer circle : DO = 200 mm

gear device, together with a skeleton diagram of its gear

intermeshing and an indication of the motive force transmission

pathway.

This device consists of planetary gears (a), a sun gear (b), and

an outer ring gear (c).

Figure 1 shows a case in which we have four planetary gears

spaced at 90° intervals. The planetary gears are arranged on a

disc supporting the planetary gear axis (the carrier). When an

input from the primary input source (1) is applied to the carrier,

the carrier revolves and the planetary gears spin. We carry out a

comparative investigation of two distinct strategies for driving

the outer ring gear, which controls the rotation rate, as a

secondary input: a parallel-drive configuration, in which the

outer ring gear is rotated in the same direction as the primary

input rotation, and a differential-drive configuration (studied in

previous work) in which the direction of rotation of the outer

ring gear is opposite to the direction of the primary input. Note

that, in both drive configurations, the motive force output is

taken from the sun gear. The example depicted in Fig. 1

contains graphical illustrations of both the parallel-drive and

differential-drive configurations. The gear teeth are NdFeB

magnets following an involute curve with their poles in an

alternating arrangement (N, S, N, S); in this structure, the

attractive interaction between the magnets is responsible for the

transmission of motive force. The gap between the planetary

gear and the sun gear is ℊ = 2 mm.

The blue-colored regions of Fig. 1 are the primary

intermeshing regions. Shown are the internal mesh zones, at

which the planetary gears and the outer ring gear intermesh, and

the external mesh zones, at which the planetary gears and the

sun gear intermesh. In these regions, the opposing magnets are

nearly parallel to one another, and these regions are responsible

for the majority of the motive force transmission. The

red-colored regions, in which the teeth appear to cross one

another, contribute little to the force transmission.

Figure 2 is a photograph of the magnetic planetary gear

device. As shown in the photograph, this device consists of

three types of gears: planetary gears, a sun gear, and an outer

ring gear.

Table 1 details the design specifications of the magnetic gears.

The magnets used are NdFeB magnets with yoke surface flux

density of 0.53 T. Involutes were chosen as the tooth form curve.

The ratio of teeth on the planetary gears, the sun gear, and the

outer ring gear is 1:1:4.

3. Equations for Calculating the Output Rotation Rate

The following equations are used to calculate the sun gear

rotation rate NS, which constitutes the output of the magnetic

planetary gear device of Fig. 3. The clockwise direction of

Fig. 3 Magnetic planetary gear, sun gear, and outer ring gear.

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rotation when viewing the carrier head on is taken as the

positive (+) direction, and rotations in the counter-clockwise

direction are considered negative (−). We use the following

notation:

NP, ZP: Rotation rate and number of teeth of the planetary gear

NO, ZO: Rotation rate and number of teeth of the outer ring gear

NS, ZS: Rotation rate and number of teeth of the sun gear

NC: Rotation rate of the carrier

The direction of the input carrier rotation may be either

positive or negative; here we assume it is positive.

1) Differential-drive configuration

If, in Fig. 3, the carrier rotates in the positive direction while

the outer ring gear rotates in the negative direction, the

planetary gears experience a couple moment in the negative

direction; hence, the planetary gears begin to spin in the

negative direction while simultaneously revolving in the

positive direction around the outer ring. Consequently, the sun

gear rotates in the positive direction. Denoting by ε the ratio

between the speeds of the outer ring and sun gears, we have

ε = (NS − NC)/(–NO − NC) = −ZO/ZS. (1)

Thus, from equation (1), we find Ns as

NS = NC(1 + ZO/ZS)+NO(ZO/ZS). (2)

In this case, we have ZS = 16 and ZO = 64, whereupon equation

(2) becomes

NS = 5NC + 4NO. (3)

2) Parallel-drive configuration

Next consider the case in which the carrier and the outer ring

gear both rotate in the positive direction.

a) When NC > NO, the planetary gears experience the

moment of force in the negative direction; hence, the

planetary gears spin in the negative direction while

simultaneously revolving in the positive direction. Thus,

the sun gear rotates in the positive direction, and we find

ε = (NS − NC)/−(NO − NC) = ZO/ZS. (4)

Thus, from equation (4), we find NS as

NS = 5NC − 4NO. (5)

b) When NC = NO, the two force moments acting on the

planetary gears sum to zero; hence, the planetary gears do

not spin independently, but only in their revolution in the

positive direction. The sun gear accordingly rotates in the

positive direction, and NS is given by

NS = NC. (6)

c) When NC < NO, the planetary gears experience a moment

of force in the positive direction; hence, the planetary

gears spin in the positive direction while also revolving in

the positive direction, and the sun gear consequently

rotates in the negative direction. Thus we find

ε = (NS − NC )/(NO − NC ) = −ZO/ZS. (7)

Fig. 4 Schematic of test apparatus.

From equation (7), we find NS as

NS = 5NC − 4NO. (8)

Equation (8) is identical to equation (5).

d) From equation (5), we see that in the particular case NO =

(5/4)NC we have

NS = 0. (9)

4. Test Apparatus for Observing Drive Performance

Figure 4 shows a schematic diagram of the test apparatus we

used to assess drive performance. The combined planetary

gear/outer ring gear device has an outer radius of approximately

240 mm and a width of approximately 110 mm. Based on our

experimental results thus far, the transmission efficiency of this

device is 85–90 %, and its input motive force with the planetary

gears rotating a rate of 1000 min-1 is approximately 500 W.

The primary input force is supplied from the primary axis of

an input carrier connected directly with an electric induction

motor (1) labeled in the figure; it is transmitted to the output of

the sun gear via the outer ring gear in a completely non-contact

state. The outer ring gear is driven, via a pulley from an

induction motor (2), in either the same direction or the opposite

direction of the carrier input rotation.

The magnetic planetary gear device used in this experiment

has dual-input functionality; the rotation rate NC of the carrier

which provides the primary input and the rotation rate NO of the

outer ring gear which provides another input are driven by the

induction motors (1) and (2) using V-f inverters (1) and (2),

whose frequency we vary to control rotation rates. The carrier

torque TC, the outer-ring-gear torque TO, and the sun gear torque

Ts are measured by torque meters (1), (2), and (3). The carrier

rotation rate NC, the outer ring gear rotation rate NO, and the sun

gear rotation rate NS are measured by rotation detectors installed

in the torque meters.

Since we were able to apply a load to the sun gear output axis

by using an electromagnetic brake, we tested the drive

180 Journal of the Magnetics Society of Japan Vol.38, No.4, 2014

Fig. 5 Relationship between outer ring gear speed NO and NS /NC.

(NS : sun gear speed, NC : carrier speed.)

performance under loaded conditions. We define the maximal

output torque Tsmax to be the torque obtained for the load at

which the sun gear just begins to slip or idle when under excess

loading.

5. Results and Discussion of Drive Performance

Experiments

We conducted a variety of experiments using the drive

performance test apparatus of Fig. 4.

5.1 Steady-state performance

Figure 5 plots the ratio of the output rotation rate to the

primary-input rotation rate (Ns/Nc), for the case in which the

electromagnetic brake is not applied (unloaded state), for carrier

rotation rates held constant at NC = ±200 min-1, NC = ±300 min-1,

and NC = ±400 min-1, as the rotation rate of the outer ring gear is

varied from NO = −500 min-1 to +500 min-1 in steps of 50 min-1.

In this plot, the signs of the quantities NC and NO, and the sign

of the horizontal axis (the NO axis) each represent the direction

of rotation and are defined such that positive values indicate

clockwise, while negative values indicate counter-clockwise.

As is clear from Fig. 5, the drive apparatus allows four

distinct quadrants of control operation. The value of 5 on the

vertical axis corresponds to the value of Ns/Nc at which

equation (3) predicts NO = 0, and the horizontal dashed line

through this value in the figure is the boundary between the

differential-drive and parallel-drive areas; the gray shaded

region above this line is the differential-drive area, while the

unshaded portion below the dashed line is the parallel-drive area.

Equations (3), (5), (6), (8), and (9), which calculate the output

rotation rates when the carrier is rotated in the positive direction,

yield the curves plotted in Fig. 5 in the differential-drive area of

the 2nd quadrant and the parallel-drive area of the 1st and 4 th

Fig. 6 Relationship between sun gear torque Ts and carrier

torque TC.

Fig. 7 Relationship between sun gear torque TS and outer ring

gear torque To.

quadrants. Our experiments allowed us to verify the validity of

these equations. Equations for the case in which the carrier is

rotated in the negative (counter-clockwise) direction may be

found in the same way by calculating counterclockwise as

positive; a graph of the output rotation rates thus computed

would have the differential-drive area in the 1st quadrant and the

parallel-drive area in the 2nd and 3rd quadrants. The

characteristic features of Fig. 5 remain unchanged when a load

is applied by the electromagnetic brake.

Note that, in the differential-drive configuration, the output

rotation rate always corresponds to a region of increase in speed,

whereas the parallel-drive configuration exhibits three distinct

dynamical regimes: one in which the speed decreases, one in which

the motion comes to a halt, and one in which the motion reverses

direction and increases in speed.

As particular examples, Figs. 6–9 plot the results of

experiments of drive performance in the parallel-drive

configuration (and, for comparison, in the differential-drive

configuration) with both the carrier rotation rate NC and the

outer ring rotation rate NO held constant. In our experiments,

loading via electromagnetic brake was applied to vary the sun

gear torque Ts from 0 to the maximum output torque Tsmax in

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Fig. 8 Relationship between sun gear torque Ts and carrier

torque Tc.

Fig. 9 Relationship between sun gear torque TS and outer ring

gear torque To.

steps of 0.1 Nm. The value of Tsmax was approximately 0.8 Nm

in all the experiments we conducted. The labels “para.” and

“diff.” in the figures indicate the parallel-drive and

differential-drive configurations.

For a fixed carrier rotation rate of NC = +200 min-1, the

characteristics of carrier torque TC and the outer ring torque TO

are plotted in Figs. 6 and 7 for the cases of a parallel-drive

configuration with NO = +200 min-1 (in which case, we have NS

= +200 min-1) and a differential-drive configuration with NO =

–200 min-1 (in which case, we have NS = +1800 min-1),

respectively. Positive (negative) torques on the horizontal and

vertical axes correspond to clockwise (counter-clockwise)

direction of rotation. Figures 6 and 7 indicate that, in both the

parallel-drive and differential-drive configurations, TC and TO

increase linearly in proportion with Ts. In the parallel-drive case,

the planetary gears rotate only with their revolution but do not

spin independently. In the differential-drive case, the couple acts

on the planetary gears from the carrier gear side and from the

outer ring gear side, so we have NS = +1800 min-1, a high

rotation rate compared to the NS = +200 min-1 obtained in the

parallel-drive case. The torque is larger in the differential-drive

case.

Similarly, Figs. 8 and 9 plot TC and TO for the cases of a

parallel-drive configuration with NO = +300 min-1 (in which case,

we have NS = −200 min-1) and a differential-drive configuration

with NO = −300 min-1 (in which case we have NS = +2200 min-1)

respectively; again, the carrier rotation rate is fixed at NC = +200

min-1. As above, positive (negative) torques on the horizontal

and vertical axes correspond to clockwise (counter-clockwise)

direction of rotation. In the parallel-drive case, because we have

NC < NO, the planetary gears experience a force moment from

the outer ring gear side, and hence spin in the clockwise

direction while revolving in the clockwise direction. In the

differential-drive case we find a high-speed rotation in the

positive direction with NS = +2200 min-1, as in the case for NO =

−200 min-1. In both the parallel-drive and differential-drive

configurations, TC and TO increase linearly in proportion with

Ts; there is little difference between the torques in the two cases.

5.2 Transient performance

In the parallel-drive area, there are points at which the

direction of the sun gear’s rotation (the output of the device)

changes from positive to negative, or points at which the

direction changes from negative to positive. These are the

boundary between quadrants 1 and 4, and on the boundary

between quadrants 2 and 3, in Fig. 5. Here we investigate the

transient phenomenon of reversal at the boundary separating

quadrants 1 and 4. As an example, at a carrier rotation rate of NC

= +200 min-1 and an outer ring gear rotation rate of NO = +250

min-1, equation (9) predicts that the rotation rate of the sun gear

will be NS = 0 (point a in Fig. 5). Figure 10 plots the transient

response as the outer ring gear rotation rate is varied from NO =

+200 min-1 to +300 min-1 at a sun gear torque of Ts = +0.5 Nm.

Before the variation begins, we have the parameter values NC =

Fig. 10 Waveforms of transient phenomena when changing NO

from +200 min-1 to +300 min-1.

182 Journal of the Magnetics Society of Japan Vol.38, No.4, 2014

+200 min-1, TC = +2.4 Nm, NO = +200 min-1, TO = −1.3 Nm, and

Ns = +200 min-1. After the system stabilizes, we have rotation

rates NC = +200 min-1, NO = +300 min-1, and Ns = –200 min-1

and corresponding torques of TC = −2.5 Nm, TO = +2.8 Nm, and

Ts = −0.5 Nm, respectively. As is clear from a glance at the

waveforms of the transient phenomena, the direction of the

output rotation changes; this is also readily observable by visual

inspection. However, with respect to the Ns waveform after

stabilization, the torque meter we used in this case (TS-3200A,

Ono Sokki) can only output a DC voltage for either positive

output torques or negative rotation rate outputs, but not both (its

full scale is 0.0 to ±10.0V), and hence in the plot we have

separately drawn the other output using a dashed line. The time

required for the output to stabilize was approximately 2.37

seconds.

The direction of the sun gear’s rotation similarly reverses on

the boundary between quadrants 2 and 3. For example, at point

b in Fig. 5, we have NC = −200 min-1 and NO = −250 min-1,

whereupon it follows that NS = 0. We thus confirmed that the

direction of the sun gear’s rotation indeed reverses as NO is

varied around this point; we omit the details here.

Figure 11 examines, with respect to the width of the NO

variation, the time needed for Ns to stabilize after reversing sign.

As a specific example, at the value NC = +200 min-1, we have NS

= 0 at NO = +250 min-1, and so we examine the time required for

stabilization using the horizontal axis to indicate the width of

the variation in NO (centered at NO = +250 min-1), as a

percentage change to 250 min-1. (Note that Fig. 10 corresponds

to the case of 0.4% percentage variation width in NO). In Fig. 11,

transitions from positive to negative direction of rotation are

labeled “Ns (+)→Ns (−)”, while transitions from negative to

positive rotation are labeled “Ns (−) → Ns (+)”. We learned that

the time required for the output to stabilize is approximately the

same regardless of the direction of the transition and increases

in proportion to the width of the NO variation.

Fig. 11 Relationship between percentage variation width of No

and transition duration.

6. Conclusions

In this paper, we conducted experimental investigations into

the drive performance, focusing primarily on a parallel-drive

configuration, of a magnetic planetary gear device equipped

with dual-input functionality. Upon comparison to previously

reported investigations into drive performance in a

differential-drive configuration4), the following characteristics

were revealed.

(1) The parallel-drive configuration exhibits three distinct

operating regimes: a regime in which the output rotation

rate is lower than the input rotation rate, a point at which

the output rotation rate falls to zero, and a regime in which

the output rotation is rate greater than, but in the direction

opposite to, the input rotation rate. Therefore, it is

considered that the device is suitable for an application of

drive system to a robot arm or a mechanical tool having

reversible motion, etc. In contrast, in the differential-drive

configuration the device only operates as an accelerator

device; however, it is capable of producing a high output

rotation rate.

(2) In both the parallel and differential drive configurations,

the torque at the two inputs increases in proportion to the

output torque.

(3) In the parallel-drive case, we discovered that controlling

the secondary input can cause the direction of the output

rotations to reverse. The time required for the rotation to

stabilize after such a reversal increases in proportion to the

width of the variation in the secondary input.

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Received Dec. 2, 2013; Revised Feb. 27, 2014; Accepted Apr.

10, 2014

183Journal of the Magnetics Society of Japan Vol.38, No.4, 2014