August 2015 

NASA/TM–2015-218784

Performance Comparisons and Down Selection 

of Small Motors for Two-Blade Heliogyro Solar 

Sail 6U CubeSat 

Peerawan Wiwattananon 

National Institute of Aerospace, Inc., Hampton, Virginia 

Robert G. Bryant 

Langley Research Center, Hampton, Virginia 
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August 2015 

NASA/TM–2015-218784

Performance Comparisons and Down Selection 

of Small Motors for Two-Blade Heliogyro Solar 

Sail 6U CubeSat 

Peerawan Wiwattananon 

National Institute of Aerospace, Inc., Hampton, Virginia 

Robert G. Bryant 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA STI Program / Mail Stop 148 

NASA Langley Research Center 

Hampton, VA 23681-2199

Fax: 757-864-6500

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and 

Space Administration. 
Abstract

This report compiles a review of 130 commercial small scale (a volume within 3x102

cm3) piezoelectric and electric motors and almost 20

researched-grade small scale piezoelectric motors for potential use in a

two-blade Heliogyro Solar Sail 6U CubeSat. In this application, a motor and gearhead will deploy a roll of solar sail thin film (2 μm thick)

accommodated in a 2U CubeSat (100 x 200 x 100 mm). The application requirements are: space rated, output torque of 0.8 Nm, speed of

3 rpm, weight limited to 150 grams, diameter and length within 50 mm

and 40 mm, respectively. The comparisons suggest that piezoelectric

motors without a gearhead exhibit larger output torque with respect to

their volume and weight and require less input power to produce high

torque. A commercially available electric motor plus a gearhead was

chosen through a proposed selection process to meet the application’s

design requirements. A piezoelectric motor without a gearhead was not

chosen for this application due to no commercially available gearheads

for piezoelectric motors.

1 Introduction

Motors convert electric energy into mechanical output. Electric motors

use electromagnetic force to produce mechanical output, and can be classified based upon input electric current into DC and AC motors. Commercial electric motors include DC brushes, brushless and DC stepper

motors. DC motors are of interest because of their overall simplified system architecture starting from a DC source that allow for applications in

a confined space. Electric motors exhibit very high speed ranging from

several thousand to more than 105revolutions per minute, rpm [1–3].

Thus, electric motors with both low speed and high torque are usually

unfavorable for most applications because they are larger, heavier, and

more expensive [4]. In practice, a high speed motor is usually selected

for low speed applications wherein a speed reduction mechanism, such

as a gearbox (sometimes known as a gearhead) is used. However, more

space and weight allowance is required for these transmission systems.

In order to overcome this high speed mechanical reduction problem, and

allow for high torque at low speed, a direct-drive motor is a good choice.

The most common direct drive motor used are piezoelectric motors, and piezoelectric ultrasonic motors because of low speed and high

torque [5]. These devices are commonly referred to as ultrasonic motors as the resonance frequencies are typically in the ultrasonic range [6].

The principle of ultrasonic motors is to convert vibrational strain energy from the stator to mechanical rotational output at a rotor. The

working principle of ultrasonic motors is governed by three major parts,

1
a high frequency power supply, a stator and a rotor. A stator, which

is driven by a high frequency power supply, drives a rotor to produce

mechanical output. In these motors, the permanent and electromagnets, found in the electric motors are replaced by piezoelectric ceramic

elements. Here, the piezoelectric materials produce high force at low

strains 0.01% across a broad frequency bandwidth. Thus, these piezoelectric based systems must operate at or near their resonance frequency

in order to amplify their strain while limiting their power consumption.

Watson et al. [7] showed that the force produced from a scaled down

piezoelectric ultrasonic motors is larger than that produced by electric

motors. Thus, mechanical speed reducers, such as gearheads, may not

be necessary thereby simplifying their construction. For this reason, the

use of piezoelectric ultrasonic motors, where direct drive is possible, is

becoming more popular in applications ranging from medical, aeronautics, automotive, to precision positioning, etc.

This work describes the process used to select a drive system to deploy and control solar sail blades of a 6U CubeSat. Due to this specific

application, the blade reel is a cylindrical shape limited to a diameter

of approximately 80 mm, and the motors weight must be less than 150

grams. The paper then follows with a set of motor plus a gearhead selection methods to meet the requirements. Sets of motors and gearheads

were analyzed and discussed, and the best drive system available was selected. The space-rated and non-space-rated commercial small scale DC

motors presented in this paper are from Maxon Precision Motors [1], Precision Micro Drives [8], Johnson Electric [9], Crouzet [3] and AUTOM [2].

Commercial piezoelectric ultrasonic motors from FUKOKU-Shinsei [10]

and PiezoMotor [11] and Johnson Electric [9] are also reviewed in this

report. For ease of explanation, the term ’piezoelectric motor’ will be

used to represent both piezoelectric ultrasonic and piezoelectric motors.

2 Electric Motors and Piezoelectric Motors

The general aspects and characteristics of electric motors are presented

in this section. Three electric motor types discussed are brushed, brushless, and stepper motors. The presentation is followed by a discussion of

performance of commercial and state-of-the-art researched type piezoelectric motors.

Electric Motors

Conventional brushed DC motors are composed of an armature (rotor), commutator, brushes, and field windings that convert electrical

energy into mechanical power through the use of both electro and permanent magnets. Brushed DC motors provide the smoothest drive amongst

2
the three electric motor types. However, cooling of these motors is not

efficient because heat generated inside the motor cannot effectively dissipate to the surrounding environment due to windings and other parts

inside the motor frame. This excessive heat accumulates and degrades

the motor’s performance by increasing the resistance of copper wires

in the motor. Thus, more current is required to operate the motor to

compensate for the increase in wire resistance, causing an additional increase in temperature of the motor. Lastly, continuous motor operation

promotes wear at the brushes, and the resulting dust contaminates the

internal working environment, further degrading performance.

Brushless (or electric commutation) DC motors do not contain brushes

or a commutator; there is no direct contact to the rotor. Thus, less wear

and friction affords a longer life time. Here, the windings are placed in

the stator. Without brushes inside the motor, the rotational speed limit

increases. Thus, brushless motors are suitable for very high speed applications. However, the cost of these brushless motors is comparatively

expensive because of the use of rare earth magnets and complex electric

circuitry.

Stepper motors provide a unique feature in that the output shaft rotates in a series of discrete angular intervals or steps; each step is taken

as a command when an electric pulse is received. These motors are

brushless, and are good for high-torque low-speed applications. There is

little risk of overdriving a stepper motor due to large loads, or speeds;

current is still needed to produce a holding torque [12]. Thus, heat will

be generated and accumulate inside the motor at holding positions. This

will lower the motor’s efficiency and eventually shorten its life.

Piezoelectric Motors and Piezoelectric Ultrasonic Motors

Six piezoelectric motor concepts are discussed in this report: Piezo

LEGS [11], wobble motion, travelling-wave, windmill, hybrid and a Langevintype.

The general working principle of a piezoelectric ultrasonic motor is

different than the electric motors discussed earlier, in that the motion

generated from a piezoelectric ultrasonic motor is transferred through

contact points between a stator and a rotor. Therefore, the motion

relies upon friction and mechanical strain. A Piezo LEGS [11] walking

principle relies on friction between the moving piezo legs and a rotor.

When these piezo legs are electrically activated, they elongate and bend,

Figure 1. Each piezo leg pair works together, alternately. When the

first pair elongates and contacts the rotor, it pushes and displaces the

rotor, while the second pair shrinks downward, Figure 1(a). The second

pair then elongates and pushes the rotor further in another step, as the

3
first pair shrinks downward, Figure 1(b). When these pairs are activated

out-of-phase at very high frequencies, many discrete movements of the

rotor are generated appearing as smooth continuous motion.

Figure 1. Piezo LEGS walking principle. Two leg pairs are shown in (a) and (b). (a)

The first leg pair elongates upward and push the rotor to the right, while the second

pair shrinks downward. (b) The second pair extends upward and displaces the rotor

while the first pair shrink downward [11]with permission from PiezoMotor.

Another output motion of piezoelectric motor that is used by motor

developers is a wobbling motion. The wobbling motion of a stator is

generated by the rotational and bending motion, through actuation of a

stator [13–15].

Examples of a wobbling motion of a stator include Moritas work on

cylindrical tubes [16–20]. Another wobble motion motor developed by

Koc et al. [21] attached two rectangular PZT plates on the side of an elastic hollow tube to produce a wobble motion. This produced a maximum

output power of 60 mW and an efficiency of 25%. Later on, Cagatay et

al. [22] minimized the motor dimension and produced an output power

of 3.2 mW and an efficiency of 11%. Park and He [23] used a similar

concept as Koc et al. [21] but by attaching four PZT rectangular plates

on four sides of a brass tube,. The motor could generate two bending

rotational modes using one driving signal producing wobble motion. The

wobble motion from the brass stator tube forced the rotor to rotate and

this rotation in turn forced the output shaft to rotate.

Table 1 summaries rotary motors with a wobbling concept. Some of

the observations from a wobbling concept with the same materials (PZT

and a titanium tube) [16,18] show that by doubling the motor dimension,

the output speed does not double, but increases by only 17% (from 680

rpm to 800 rpm); while the output torque does not show a significant

change at all (from 0.67 μNm to 0.7 μNm). When comparing the motor

with a stator made purely of bulk PZT [17] to one with a stator made

of a mixture of bulk PZT and titanium [17], the motor with a pure bulk

PZT shows a significant increase in output torque (from 0.7 μNm to 0.22

mNm).

4
Output Design Stator Maximum Output Dimension References

Motion Concept Materials Speed Torque mm

[rpm] [Nm]

Rotary Wobbling PZT 62x10−3 φ1.6x4 Cagatay et al. [22]

Rotary Wobbling PZT/metal 572 1.8x10−3 φ2.4x10 Koc et al. [21]

Rotary Wobbling PZT 650 0.22x10−3 φ2.4x10 Morita et al. [16]Rotary Wobbling PZT/brass 1000 370x10−6 3.975x3.975x16 Park and He [23]

Rotary Wobbling PZT/titaniun 800 0.7x10−6 φ2.4x10 Morita et al. [16]

Rotary Wobbling PZT/titaniun 680 0.67x10−6 φ1.4x5 Morita et al. [18]Rotary Wobbling PZT 3850 0.025x10−6 φ2x5.9 Kanda et al. [19, 20

Table 1. Summary of wobbling type motor design concept, materials, speed, output torque and dim

5
A traveling-wave concept can be generated by superimposing two

standing waves at the stator with a 90◦ phase difference. The traveling

wave produces tangential movement at the stator and this movement

causes tangential friction at the rotor, resulting in movement of the rotor,

Figure 2. A ring-shaped stator traveling-wave type piezoelectric ultrasonic motor is used by FUKOKU-Shinsei [10] and Shinsei [24], Figure 3(a

and b). A ring-shaped piezoelectric material is bonded to an elastic material to form a stator. The elastic material is fabricated with a number

of teeth, known as projections, around the circumference. Their function

is to improve the frictional coupling condition between the stator and a

rotor. Thus, vibrations can be amplified at the vibration nodes on the

stator to the rotor [25–30]. Zhang et al. [31] developed a travelling-wave

type micro-motor using a miniature PZT-metal composite tube stator.

Rotor

Rotor traveling direction

Traveling wave direction

Elliptical motion

Stator

Frictional 

Coating 

Material

Figure 2. Traveling-wave motion principle.

Figure 3. (a) Inside of a Shinsei piezoelectric ultrasonic motor, (b) a cut-through of

a Shinsei piezoelectric ultrasonic motor [24].

A miniaturized ”Windmill” concept ultrasonic micromotor was fabricated using a 60 vol% piezoelectric material and 40 vol% thermoplastic binder. This thermoplastic body was Computer Numerical Control

(CNC-machined) to create windmill-type blades. The windmill stator

6
disk was poled in the thickness direction. With the application of an AC

field in the thickness direction, the inward blades radial displacement

generates tangential displacement to the rotor, causing the rotor to rotate [32].

Takeda et al. [33] developed a Langevin type motor with a piezoelectric ring. The motor had a diameter of 22 mm and 30.5 mm long. It

could reach up to 293 rpm with an output torque of 5.7 μNm. Kurosawa

and Ueha [34] developed a hybrid transducer type ultrasonic motor with

longitudinal and torsional output motion. The stator was comprised of a

bolted Langevin-type torsional transducer and three multilayered piezoelectric stack actuators between the rotor. The piezoelectric actuators

produced longitudinal output motion along the motor axis to control

frictional force at the rotor. A spring was used to provide a pre-load

on the rotor. The torsional vibrator generated vibration through torsional piezoelectric plates. The two components, torsional vibrator and

piezoelectric stack actuators, were independently driven by separate input electric sources. Similarly, Nakamura et al. [35] developed a hybrid

transducer with longitudinal and torsional output motion. Wajchman et

al. [36] developed a hybrid ultrasonic motor using a rectangular crosssectioned pre-twisted beam stator made from aluminum.

It can be observed from Table 2 that the hybrid motor concept with

a duralumin stator produced larger torque than the non-hybrid ones.

This is because of a combination of motor motions, such as torsional

and longitudinal that produces an output motion. These combinations

improve the motor’s output motion compared to those having only one

motion.

7
Output Design Stator Maximum Output Dimension References

Motion Concept Materials Speed Torque mm

[rpm] [Nm]

Rotary hybrid PZT/duralumin 100 0.68 φ50x82 Kurosawa and Ueha 

Rotary hybrid PZT/duralumin 0.29 φ20x83 Nakamura et al. Rotary windmill PZT 156 22x10−6 φ5.2x0.6 Yoon et al. [32

Rotary travelling wave PZT 3000 7.8x10−6 φ1x50 Zhang et al. [31

Rotary hybrid PZT/Al 840 0.17x10−6 6.5x6.5x87.5 Wajchman et al. 

Table 2. Summary of a travelling wave, windmill and hybrid motors and materials, speed, torque and 

8
3 Performance Comparisons

This section compares and discusses the performance of motors presented

in the preceding sections. The motor’s performance are compared with

volume within 3x102cm3 and are extracted from scientific and product

literature. The comparisons suggest that piezoelectric motors without a

gearhead exhibit larger output torque with respect to their volume and

weight and require less input power to produce high torque. Figure 4

to Figure 11 present commercial and research grade piezoelectric motors

and commercial electric motors available on the market. Motor performance data are extracted from motor datasheet and cited literature.

Thus, there is no gearhead affect in these data values. The output torque

is of interest for the application that will be discussed later, wherein output torque will be discussed in terms of motor geometric characteristics

in this report.

Figure 4. Output torque versus input power. Red dots represent piezoelectric

motors. Grey dots represent electric motors. Three trend lines: 1) stepper motors

trend line, 2) piezoelectric motors trend line and 3) brushed and brushless motors

trend line, show how much torque the motors can produce with respect to input

power. The two distinct trends (a trend line of brushes and brushless motors and the

trend lines of stepper and piezoelectric motors) do not exhibit any physical meaning

to the motor performance analysis. These two trends only represent available motor

data for output torque versus input power.

Torque

The steeper trend line of piezoelectric motors versus trend line of

brushed and brushless motors suggests that piezoelectric motors require

less input power to produce output torque than brushed and brushless

9
motors, Figure 4. Stepper motors show a better trend (steeper slope)

of output torque with respect to input power than other electric motors

and piezoelectric motors, Figure 4. However, when considering the trend

of torque density versus motor volume, piezoelectric motors suggest that

they produce higher output torque density than most of the electric

motors, Figure 5 and Figure 6.

Figure 5. Torque density versus volume of the motor. Red dots represent piezoelectric motors. Grey dots represent electric motors. The shaded rectangular area

includes motors that are going to be discussed further in Figure 6

At the larger motor volumes, piezoelectric ultrasonic motors show a

higher trend of increased torque density. In general, the output torque

from electric motors is in a direct relationship to the rotor volume and

hence the motor volume [4]. However, these small scale electric motors

do not seem to show the same relationship with motor volume. The

two distinct data trends (a trend line of brushed and brushless motors

and the trend lines of stepper and piezoelectric motors) in Figure 4 have

no physical meaning against each other except that these are available

motor data extracted from literature and commercial motor datasheets.

Watson et al. [7] discussed effects of output force (hence it can be considered as output torque for a rotary motion) of electric motors when

they are scaled down. They showed that the output force of miniature

electric motors does not exhibit a direct relationship to the motor’s characteristic length, but it relates to the motor’s characteristic length to the

power of four [37]. The output force of miniature piezoelectric motors

shows a direct relationship to the motor’s characteristic length (Watson

et al. [7]). The characteristic length is an input parameter in a scaling

law that influences small scale system output behavior, for example, a

10
Motor Volume x 105

[mm3]

Figure 6. Torque density versus volume of the motor enlarged area from the shaded

rectangular in Figure 5. Red dots represent piezoelectric motors. Grey dots represent

electric motors. The arrows indicate groups of common motor volumes.

piezoelectric motor geometric parameter such as dimension of a piece of

piezoelectric material inside the piezoelectric motor. From this scaling

effect, piezoelectric motors are more competitive than electric motors in

small scale applications since the smaller the motor, the lower the output

force electric motors can produce due to the fourth power of the motor’s

characteristic length.

Besides the torque-volume density, when considering the motor’s

weight, piezoelectric motors exhibit a larger trend of torque-weight density than electric motors, Figures 7 and 8. The motors’ weights presented

here are too heavy (more than 3 kg) for applications that are going to

be discussed later in the following section, thus, only motors’ weights

up to 500 grams are going to be considered here, Figure 8. When a

motor’s weight increases, the torque density of electric motor do not

show significant increase; while piezoelectric motors exhibit a significant

increase in the magnitude of torque-weight density at a higher weight

range, Figure 8.

11
Figure 7. Weight torque density versus weight of the motor. Red dots represents

piezoelectric motors. Grey dots represents electric motors. The shaded rectangular

area includes motors that are going to be discussed further in Figure 8.

When considering a motor’s length scale such as motor diameter, at a

small diameter range, piezoelectric motors produce larger torque density

than electric motors; while, at a larger diameter range, limited numbers

of piezoelectric motors are available. The larger torque density produced

from scaled down piezoelectric motors compared to electric motors was

shown and explained by Watson et al. [7]. The motor diameter to be discussed is limited to 50 mm for a cylindrical shape. The reason that the

motor’s diameter is limited to 50 mm in this paper is that if the diameter

is larger than 50 mm, the motor tends to get very heavy and use more

space on the satellite wall which will limit the amount of the payload. A

trend can be shown that the majority of electric motors produce small

scale torque density, Figures 9 and 10. When comparing between the

motors’ output torque density with respect to the motors’ density, the

piezoelectric motors exhibit larger torque density with respect to their

density within a similar density range, Figure 11. From Figure 4 to

Figure 11, it can be concluded that the motors’ geometric characteristics and input power, i.e. weight, volume, density and linear dimension,

such as a diameter, play a significant role in output torque values; and

piezoelectric motors perform better than electric motors when geometric

characteristics and input power are taken into consideration. The plots

of torque density, shown in Figure 6 to Figure 10, show common characteristics in that the groups of motors fall into the same motor volume,

motor weight and motor diameter. This is because these motors of similar volume, weight and diameter that produce various output torques

are what is offered in the marketplace.

12
Figure 8. Weight torque density versus weight of the motor enlarged area from the

shaded rectangular in Figure 7. Red dots represents piezoelectric motors. Grey dots

represents electric motors. The arrows indicate groups of common motor volumes.

Figure 9. Torque density versus diameter of the motor. Red dots represents piezoelectric motors. Grey dots represents electric motors. The shaded rectangular area

includes motors that are going to be discussed further in Figure 10.

13
Figure 10. Torque density versus diameter of the motor enlarged area from the

shaded rectangular in Figure 9. Red dots represents piezoelectric motors. Grey dots

represents electric motors. The arrows show groups of common motor volumes.

Figure 11. Torque density versus motor density. Red dots represents piezoelectric

motors. Grey dots represents electric motors.

14
4 Heliogyro-configured Solar Sail CubeSat

A 6U CubeSat is comprised of three 2U CubeSats attached along at least

one 2U face wherein the 2U CubeSat measures 100 x 200 x 100 mm. Two

rolls of solar sail blades are accommodated in two 2U outer units of the

6U CubeSat, denoted as a solar sail propulsion unit. This solar sail

propulsion unit is comprised of motor control electronics, rechargeable

batteries and anything else associated with solar sail operation. The

central 2U unit is envisioned to house the communication, on-board data

handling, Electric Power System, Attitude Determination and Control

System, experimental instrument package etc., Figure 12. Each solar sail

reel is mounted to the satellite wall via a bearing and a motor. A motor

is used to deploy and retract the solar sail blade. The motor location

that will be discussed throughout this paper is mounted in the middle

of the 2U CubeSat wall as shown in Figure 12. When the satellite door

is opened, a solar sail is deployed out as shown in Figure 13.

Figure 12. 6U CubeSat with two deployment mechanisms at the outer 2U boxes

and one electronics/control unit is in the middle.

A thin film solar sail blade (2 μm thick) is wrapped around a shaft,

and as the shaft is rotated, the blade is deployed outward or retracted

depending on the rotational direction of the shaft and reel. It is estimated

that the inner shaft diameter of the solar sail roll is 10 mm and the solar

sail outer roll is going to be approximately 80 mm as shown in Figure 14.

The pertinent solar sail material properties are shown in Table 3. It

is estimated for an ideal case that the solar sail roll is 160 mm wide

along the 2U CubeSat length. The authors used the solar sail width of

160 mm here in order to maximize the total solar sail area and to seek

motors in the market that can meet these extreme requirements as well

as being capable of delivering a high enough torque (discussed later in

the paper) to reel out the solar sail and stay within an extreme limited

space provided. If the total length of the motor plus the bearing on the

15
Figure 13. Extended solar sails with tip masses at the two ends.

opposite side, Figure 12, are greater than 4 cm, a right-angle gearhead

may be a better option to meet the specification. Moreover, a motor set

fixed at the CubeSat corner with a pulley system to rotate the solar sail

shaft may be considered for the limited space provided.

Figure 14. A solar sail roll with an outer diameter of 90 mm and an inner diameter

of 10 mm. ’D’ and ’d’ represent outer and inner diameters, respectively. The width

of the solar sail roll is 160 mm.

16
Solar Sail Material Properties (Kapton) Value

Thickness (t) 2 μm

Density 1.5 [g/cm3]

Table 3. Solar Sail Material Properties (Kapton)

The total area of the solar sail roll, area ’A’ in Figure 14, determined by subtraction of the outer diameter roll from the inner diameter

shaft, must be equal to the solar sail length multiplied by its thickness,

Equation 1.

L × t = Π(D2

4

−

d

2

4

) (1)

where, ’L’ is the solar sail length, ’t’ is the solar sail thickness, ’D’ is the

solar sail roll outer diameter and ’d’ is the solar sail roll inner diameter.

Thus, the length of the solar sail when fully deployed can be calculated

from:

L =

Π( D2

4 −

d

2

4

)

t

(2)

This total length is assumed such that the air is pumped out from

the solar sail thin film roll. Therefore, it is assumed that there is no gap

between adjacent solar sail thin film. The mass of the solar sail roll can

be calculated by:

m = ρ × V = ρ × (Π × W × (

D2

4

−

d

2

4

)) (3)

where ’m’ is the solar sail roll mass, ρ is the solar sail density, ’V’ is

the solar sail volume, ’W’ is the solar sail roll width, ’D’ is the outer

diameter of the solar sail roll and ’d’ is the inner diameter of the solar

sail roll, or it is the solar sail shaft diameter. Since a motor is used to

deploy the solar sail, it is required to calculate the torque requirement

working against the solar sail roll. Therefore, it is assumed that the solar

sail is fully deployed and the CubeSat is rotating at 2 rpm, and the drive

assembly is required to furl the solar sail blade. Looking at the top view

of the CubeSat with a fully extended solar sail, a centrifugal force from

the tip of the solar sail towards the CubeSat is calculated as shown in

Figure 15(top) with an equation

Fn = m × ω

2

(L/2) (4)

where Fn is a centrifugal force towards the CubeSat, ’m’ is total mass of

the solar sail roll, ω is angular speed of the CubeSat [rad/sec] and ’L’ is

the solar sail total extended length. A torque required to pull back the

solar sail blade is calculated from Figure 15(bottom).

τ = Fn × r = Fn × (d/2) (5)

17
From Figure 14 and Table 3, the total solar sail length, when it is

fully extended, is 2.47 kilometers (Equation 2). From Equation 3, the

solar sail mass is 1.187 kilograms. The rotational speed of the CubeSat

is 2 rpm, thus its angular speed ’ω’ is calculated to be 0.2094 [rad/sec].

From the above results, the torque required (Equation 5) from the motor

is 0.32 Nm.

Figure 15. (Top): a top view of a CubeSat with fully extended solar sail. A dashed

circle represents a rotational trajectory of the tip of the solar sail while the CubeSat

rotates. (Bottom) a side-view of a solar sail roll shaft with fully extended solar sail.

4.1 Motors and Gearheads for a Solar Sail 6U CubeSat

This section describes a method to select a small scale motor to be used

in a two-blade Heliogyro solar sail 6U CubeSat. The motor is required

to deploy and adjust the length of the solar sails at a controlled rate.

The required starting torque (at zero speed which can be considered as

a stall torque) to deploy the solar sail was calculated to be 0.32 Nm,

18
the maximum deployment speed would be 3 rpm. A safety factor taking

into account the solar sail spool weight, the motor output torque will be

degraded with mission; the required torque is approximated to be 0.8

Nm. The motors to be considered in this selection are those presented

in the preceding section. Since the small scale motors cannot provide

such a high torque up to 0.8 Nm, a gearhead is required to increase the

torque as well as to reduce the motor speed down to 3 rpm. Only an

in-line gearhead connected to the motor is considered in this document,

other viable options, such as right angle gearheads or pulley systems are

beyond the scope of this paper’s baseline analysis, as they tend to be custom made. However, not all commercial motor manufacturers provide

gearheads for their motors, especially the piezoelectric motors because

their speed is already low (but still higher than our requirement), and

they are normally used as a direct drive. However, the commercially

available piezoelectric motors still need gearheads to reduce the speed

down to meet our requirements. The gearhead selected from Maxon

Precision Motors meets the two most important parameters for this application, i.e. the reduction ratio and the available continuous torque.

The gearhead selection process with a Maxon brushless motor, Figure 16,

and a Maxon gearhead, Figure 17, is as follows.

Figure 16. Brushless Maxon motor selection example. The motor part number

267121 is selected for this example (with permission from Maxon Precision Motors

USA.)

A motor speed reduction is calculated from a reduction ratio,

19
Figure 17. Maxon gearhead part number 166960 is selected for this example. (with

permission from Maxon Precision Motors USA.)

iGear =

nM otor

nLoad

(6)

where iGear is the reduction ratio of the gearhead, nM otor is the nominal

motor speed, and nLoad is the speed that the gearhead will produce to the

load. The nominal speed is a suggested continuous speed of this motor

with load. A larger speed such as a no load speed, or the maximum

speed at which this motor can run may also be used for the calculation.

Once the desired reduction ratio is determined, it can be used to select a gearhead. As a rule, the next smaller available gearhead reduction

ratio of the selected gear type will be used if an exact reduction ratio

is not available. This is to keep the gearhead as small as possible, i.e.

fewer number of gear stages, to meet the requirements.

Next is to calculate output torque at the load by taking into account

gearhead efficiency and reduction ratio,

MLoad = MLoad × ηGear × iGear (7)

where iGear is a reduction ratio of the gearhead (determined in Equation 6), MM otor is a nominal motor torque, MLoad is a torque that the

gearhead will provide to the load when connected to this motor, and

ηGear is the gearhead efficiency.

20
After these calculations, both the MLoad value and the maximum

continuous torque of the gearhead value must be larger than the required

torque to deploy/furl the solar sail blade. As an example, a Maxon motor

part number 267121 is selected for this application because of the highest

maximum continuous torque and it provides the highest efficiency when

compared to other EC32 flat motors as shown in Figure 16. The motor

part number 267121 possesses a load speed requirement of 3 rpm and

the motor nominal speed is 2760 rpm, Figure 16. The speed reduction

ratio was calculated to be 920:1.

With a reduction ratio of 920:1, a reduction ratio of 913:1 is selected

and shown as part number 166960, Figure 17. The output torque at the

gearhead to the load is

MLoad = 25.5mNm × 0.6 × 913 = 13.968mNm = 13.97Nm (8)

21
4.2 Results of Motors and Gearheads Selection for a Solar

Sail 6U CubeSat

The term ’a motor set’ will be used throughout this document to represent a motor when attached to a gearhead. This section shows and discusses results of various motor sets, described in the preceding section,

associated with selected gearheads according to the selection procedures

described in the previous subsection. Commercially available miniature

gearheads are limited in the market. In particular, there are no miniature

gearheads produced for all piezoelectric and electric motors. Due to this

limitation, the authors selected these gearheads from Maxon Precision

Motors because Maxon Precision Motors provides a variety of gearheads

to accommodate dimensions and reduction ratios for their products. The

authors selected these gearheads as close to the motors’ diameters and

required speed reduction ratios as possible due to the limited numbers of

products available in the market. Thus, to be precise with the gearhead

selection of all non-Maxon Precision Motors, customized gearheads are

necessary for each motor. Selection criteria for choosing a motor set are:

1) the output torque at the load (produced from a gearhead when attached with a motor) must be larger than 0.8 Nm

2) the maximum continuous torque of the gearhead must be larger than

0.8 Nm

3) the motor set weight should be within 150 grams

4) the total motor set length should be within 40 mm. This motor may

not be directly connected to the solar sail shaft but it might be connected

to a right angle motion transmission system, and

5) brushed motors are not of interested for this application

The brushed motors do not fit with this application because of fine

powder that would be generated during operation contaminating the

satellite. The output torque produced from a gearhead, when attached

to a motor, indicates the maximum output torque that the motor set

can deliver when considering that the gearhead is running at its maximum efficiency. The motor set weight limitation was approximately

5-6% of the weight limitation of a 2U CubeSat. Weight limitation of a

2U CubeSat is 2.66 kg, since a 1U CubeSat’s weight limitation is 1.33 kg

(3 lbs. per U) [38]. Since 5% of 2.66 kg is 133 grams, most of the small

scale motors plus gearheads that can provide such a high torque of 0.8

Nm are expected to be quite heavy, indicating that they may not meet

this criteria. The authors decided to take approximately 5.5% of the

2U CubeSat weight limitation, which is 146 grams. Thus, a motor set

weight limitation of 150 grams is going to be used for this application.

The weight combination of a solar sail roll plus a motor set is 1.84 kg

which is approximately 70% of the allowable weight, leaving 30% for a

solar sail spool and other subsystems inside this solar sail unit such as

22
a release mechanism to open the satellite door and the satellite structure etc. By looking at the overall drive system torque-volume density,

it can be observed that piezoelectric motor sets exhibit smaller volume

than most of the electric motor sets but their torque volume density was

considerately smaller than brushed motors, Figure 18.

Figure 18. Motor + gearhead volume versus torque volume density of motor sets.

The electric motors with motor + gearhead volume less than 1 x 10−3 mm3are

brushed motors. The rest of the electric motors with total volume larger than 1 x

10−3 mm3are brushless and stepper motors.

It can be observed that most of the electric motors show a very large

percentage volume increase when a gearhead is needed to reduce the

speed and to increase the torque up to meet the operational requirements,

Figure 19. The term percentage of the total weight (or volume) increase

indicates how much of the total weight (or volume) is increased when a

gearhead is attached to the motor compared to an individual motor itself.

There are some electric motors that show a similar trend of percentage of

total weight and volume increase when compared to sets of piezoelectric

motors, but those electric motor sets are brushed motors and will not

be considered further. It can be observed that piezoelectric motor sets

show lower percentage increase of total weight and volume than the rest

of electric motor sets. From this observation, piezoelectric motors do not

require as much space and weight from the gearheads to reduce speed

and increase the torque as electric motors require. However, all of the

piezoelectric motor sets, USR-series motors, that exhibit the lower trend

of total weight and volume increase, shown in Figure 19, do not meet

length requirement and they are too heavy. The two piezoelectric motor

23
sets, PiezoLEG 30mNm and 50mNm, meet weight requirement and their

length is quite short. However, their output torque at the load are 0.146

and 0.234 Nm, with maximum continuous output torques of 0.1 and 0.75

Nm, respectively. Hence, PiezoLEG 30mNm and 50mNm do not meet

output torque requirements.

Figure 19. Percentage of total weight increase of motor sets and percentage of total

volume increase of motor sets. Group of electric motors locate nearby piezoelectric

motors are brushes motors. The number with a unit ’mm’ indicates the total length

of the motor set.

Large ranges of output torque, from motor sets, and maximum continuous torque from gearheads are shown in Figure 20. A smaller range

of these output torques are going to be considered for ease of analysis

and these are shown in Figure 21. Two torque profiles, one horizontal

line and one vertical line, show minimum torque requirements for this

application, i.e. 0.8 Nm. Any motor sets located inside these profiles,

i.e. torques below 0.8 Nm, will not qualify for this application. The

motor names, their total length, and weight are identified at each motor

set except brushes motors that have no motor set information. It can

be observed that most of piezoelectric motors and their gearheads do a

better job in producing larger output torques than electric motors plus

their gearheads. By looking at each qualified output torque, the total

length of some piezoelectric motor sets, such as USR60-S1-V-NM are too

long to be accommodated inside this 2U satellite that allow maximum

solar sail blade width. It can be observed that the length of all of electric

motor sets exceed our requirements, i.e. 40 mm. There are a number

of motor sets that are heavier than 150 grams such as USR60-S1-V-NM,

24
USR30-S1-V, EC flat Maxon, EGEHS-12 and EGEH-12-H Johnson Electric. The two electric motor sets that possess similar lengths and weights

are within 150 grams are EC32 flat Maxon and E4HS-12 Johnson Electric motors. However, the EC20 flat Maxon motor is considered to be

the best compromise when output torques are considered. Comparing

the length and weight to the E4HS-12 Johnson Electric motors, it is the

shortest drive system, with a total length of 62.4 mm, and weighs the

least, i.e. 109 grams.

Figure 20. Motors plus gearheads output torque and maximum continuous torque

produced from gearheads. The shaded rectangle includes motors that are going to be

further discussed in Figure 21.

A large range of motor set output torque values compared to the motor set total weight are shown in Figure 22. A smaller range of output

torque values compared to the total weight are shown in Figure 23. A

torque profile of 0.8 Nm, shown as a vertical line, indicates the minimum

torque requirement. A weight profile, shown as a dotted horizontal line,

indicates the boundary of acceptable weight, i.e. 150 grams. Any motor

sets that fall below the weight profile line and produces an output torque

larger than 0.8 Nm will be considered. From these requirements, it can

be observed that there are three motor sets that show a large output

torque and weigh below 150 grams, but, they are still longer than the

40 mm length requirement. These motor sets are EC-13 flat, EC-max

16 and EC-20 flat Maxon motors. By comparing all three motor sets,

the EC-13 Maxon shows a light weight of 49 grams, while its length is

approximately similar to the other two motor sets. However, this EC-13

Maxon motor does not meet the maximum continuous output torque

25
Figure 21. Small range of output torque of motor sets and maximum continuous

torque from gearheads. Two torque profile lines are used to separate motor sets that

generate lower output torque than requirement of 0.8 Nm. The number with a unit

’mm’ indicates the total length of the motor set.

from the gearhead, Figure 21, so this motor cannot be used in this application. Similarly, EC-max 16 motor set does not meet the maximum

continuous torque from its gearhead. The gearhead of the EC-max 16 flat

motor exhibits 0.6 Nm maximum continuous output torque. The gearhead of EC-20 flat motor set exhibits 2 Nm which meets the requirement.

Gearhead maximum continuous torques and motor set output torques,

when compared to total motor set lengths, are shown in Figures 24

and 25. It can be observed that no motor set falls into the acceptable region of producing larger output torque than required with a total

length within 40 mm.

26
Figure 22. Comparison between output torques of motors plus gearheads versus

their total weight. The shaded rectangle includes motors that are going to be further

discussed in Figure 23.

Figure 23. Small range of output torque derived from motor sets compared to the

total weight. A torque profile line is used to separate motor sets that generate lower

output torque than requirement of 0.8 Nm. A motor set weight profile line is used as

a boundary of maximum allowable motor sets weight of 150 gram.

27
Figure 24. Gearhead output torque compared to total length of a motor plus a

gearhead. A torque profile line is used to separate motor sets that generate lower

output torque than requirement of 0.8 Nm. A motor set length profile line is used as

a boundary of maximum allowable motor set length.

Figure 25. Motor sets output torque compared to total their lengths. A torque

profile line is used to separate motor sets that generate lower output torque than

requirement of 0.8 Nm. A motor set length profile line is used as a boundary of

maximum allowable motor set length.

28
5 Results

Commercial electric DC and piezoelectric ultrasonic motors were compared along with research-type piezoelectric ultrasonic motors. The

output torque of piezoelectric ultrasonic motors was determined to be

greater than electric motors. Moreover, piezoelectric ultrasonic motors

required less input power than electric motors to produce larger output

torque. Piezoelectric ultrasonic motors required less space and weighed

less than electric motors. However, the piezoelectric motors were not

chosen for this application because none of miniaturized piezoelectric

motors available in the market met our size and weight limitations. In

addition, the developed research-type piezoelectric motors are still immature for space-rated applications.

Since none of the small scale motors available in the market exhibit

the high required torque at low speed, a gearhead was determined to be

necessary to produce the required output parameters. A motor plus a

gearhead, the drive system, must be used to deploy a roll of solar sail.

Gearhead selection procedures are discussed in subsection 4.1. From

analysis in subsection 4.2, none of the commercial small scale motors

available in the market met all of the requirements. However, there were

some motors that met the requirements of the output torque using a

gearhead that exceeded the minimum torque requirement, and the maximum continuous output torque. There were some motors that were

lighter than the maximum weight limitation. However, none of the motor sets met the length requirement. The best compromise (low weight

and capable of deliver required output torque) set of motor plus a gearhead was the EC20 flat Maxon motor series that can deliver the required

output torque with a weight of 109 grams. The length was still too long,

i.e. 62.4 mm. The gearhead of EC-20 flat motor set exhibited 2 Nm

which meets the requirement and requires input power of 3W which was

in an acceptable range for a 6U CubeSat power. The output torque at

the load was determined to be 2.36 Nm.

An illustration of the EC20 flat Maxon motor plus a gearhead mounted

to the solar sail roll spindle is shown in Figure 26. On the opposite side

of the spindle is a bearing to allow rotation while the motor and the gearhead rotate. The whole mechanism is confined in a length of 200 mm.

It can be seen that after taking into account the motor and the gearhead length and leaving some space for two spindle discs and a bearing,

an available width for the solar sail roll is approximately 100 mm wide.

The solar sail width of 100 mm is very narrow when a large sail area is

required to compensate for the satellite weight in order to achieve large

characteristic acceleration of the solar sail satellite. The theoretical characteristic acceleration is a metric to determine the solar sail performance

at 1 AU (astronomical unit) and is highly dependent on the ratio of the

29
solar sail area to the payload mass [39]. However, this EC20 flat Maxon

motor was chosen because of the availability of the gearhead. By assuming the outer diameter of the solar sail is 80 mm, the inner diameter of

the solar sail roll is 10 mm, Figure 14, and the solar sail roll width of

100.6 mm, Figure 26, the characteristic acceleration of this 6U Solar Sail

CubeSat is 0.509 mm/s2. This characteristic acceleration is considered

to be large when compared to the IKAROS [40] solar sail spacecraft and

a NanoSail-D [41] solar sail 3U CubeSat with characteristic acceleration

of 0.0053 mm/s2 and 0.02 mm/s2, respectively.

Figure 26. EC20 Maxon motor plus a gearhead is mounted to the solar sail roll

spindle and the opposite side is a bearing. The EC20 Maxon motor plus a gearhead

was chosen for this application because it can deliver required torque and its weight

is lower than requirement. The spindle diameter is 80 mm.

To shorten the total length of the motor set, a right-angle gearhead

may be considered, for example with piezoelectric or electric motors.

However, these right-angle gearheads available in the market by the

time this report was written (March 2015) have very low reduction ratios [42–47]. Low reduction ratios mean the speed will be reduced by a

low factor. To reduce the motor speed range of thousands to more than

105revolution per minute (rpm) [1–3] down to 3 rpm for this unique

application, an in-line gearhead, usually with higher reduction ratios, is

still needed. For those off-the-shelf right angle gearheads available in the

market at the time this report was written, it may not significantly reduce the total length of the motor set with the required additional in-line

gearhead. A recommendation is to customize a right angle gearhead for

each selected motor, especially piezoelectric motors because they already

possess low speed, as a lower number of gear stages are required, when

compared to electric motors. Using a piezoelectric motor set with customized gearhead would be another good option because its total length

can be very short, and its weight can be small.

30
One of the motor selection criteria is to limit the motor diameter to 50

mm. The reason is that if the diameter is larger than 50 mm, the motor

tends to get very heavy and use more space on the satellite wall which

will limit the amount of the payload. For example, if a Maxon motor

EC 60 flat φ60 mm brushless (diameter of 60 mm) is used, the motor’s

weight (not including a gearhead to reduce its speed) is 470 grams. If a

Maxon motor EC 90 flat φ90 mm brushless (diameter of 90 mm) is used,

the motor’s weight (not including a gearhead to reduce its speed) is 600

grams. The diameter of 60 mm is very large when it is mounted on the

satellite wall with a dimension of 100 x 100 mm. Similarly, the diameter

of 90 mm is too large for a 100 x 100 mm satellite wall as there will be

no space for the flange to mount the motor.

The solar sail roll considered in this paper has outer and inner diameters of 80 and 10 mm, respectively, and a width of 100 mm. These

dimensions make this solar sail weigh 742 grams (28% of the total allowable 2U CubeSat weight of 2.66 kg). Taking only a roll of solar sail

weight into account, there are 1920 grams left for other mechanisms and

motor’s battery/controlling system and other scientific payloads. The

motors’ weight (without a gearhead) of 600 and 900 grams already takes

23% and 34% of the total allowable weight of a 2U CubeSat (2.66 kg),

respectively. While the selected motor EC20 flat Maxon plus a gearhead

weigh only 109 grams, it takes only 4% of the total 2U CubeSat allowable

weight. Thus, the motor diameter for a limited space as shown in this

application should be limited to within 50 mm.

6 Conclusions

This report compares the performance of commercial electric DC and

piezoelectric ultrasonic motors as well as research-type piezoelectric ultrasonic motors. The most critical parameters for the ongoing space

application to deploy and control a solar sail 6U CubeSat are output

torque and input power. Motor selection methods to deploy and control

a solar sail 6U CubeSat were also discussed by comparing the performance of small scale electric and piezoelectric ultrasonic motors. A small

scale range was limited to within 3x102cm3(3x105 mm3), the diameter

was limited to 50 mm for a cylindrical shape and the motors’ weight

was required to be less than 500 grams. The driving parameters were

motor’s stall torque, between 0.8 Nm, and a weight not exceeding 150

grams. None of the motors discussed here were capable of working as

a direct drive system because of the speed requirement being too low,

3 rpm, and the required load torque being as high as 0.8 Nm for such

small scale motor. Thus, a gearhead must be attached to each motor to

reduce the speed and increase the torque. A gearhead selection method

was discussed in this paper and motor sets plus selected gearheads were

31
compared. A motor plus a gearhead must meet the following five requirements 1) the output torque at the load must be at least 0.8 Nm,

2) maximum continuous torque from the gearhead must be 0.8 Nm or

greater, 3) the motor set weight should be no greater than 150 grams,

4) the total motor set length should be within 40 mm, and 5) brushed

motor configurations should not be considered due to limited lifetime,

low efficiency, and contamination issues. It was concluded that none of

the motors (piezoelectric motors and electric motors) plus gearheads met

all the five requirements. There was only one small scale electric motor

that showed the most optimized outcome (low weight and capable of deliver required output torque) but still had a total length (a motor length

plus a gearhead length) that exceeded the requirement. If a right angle

gearhead system that was built specifically for miniature piezoelectric

motors was used, then the piezoelectric motors would be a good motor

set candidate when compared to electric motors due to the lower speed

and higher torque produced from piezoelectric motors alone. The gearhead used for piezoelectric motors could have lower gear stages than that

required by electric motors, resulting in a shorter and lighter gearhead.

Thus, a customized gearhead system should be designed, rather than a

motor, as the best approach to cost effectively enable the full capabilities

of a 2U solar sail propulsion system in terms of deployed blade area and

reel control.

32
Appendix Lists of 130Commercial Motors Shown in this

Paper

Commercial Piezoelectric Motors

Piezo LEG Rotary 30mNm, 50mNm, 80mNm and Piezo LEG Wave [48]

USR60-S1, USR60-S2, USR60-NM, USR60-V, USR30-S1,

USR30-S2, USR30-NM, USR30-V, USR45-S1, USR45-S2,

USR45-NM, USR45-V [10]

Commercial DC Motors Maxon Precision Motors [1]

RE-13 Brushes, RE-max 13 Brushes, A-Max 19 DC Brushes, A-Max

22 DC Brushes, RE-max 21 Brushes, RE-max 24 Brushes, DCX- 22s

Brushes, EC 13 Brushless, EC-max 16 Brushless, EC 10 flat Brushless,

EC 9.2 flat Brushless, EC 20flat Brushless, EC 20 flat brushless, EC 32

flat brushless, EC 32 flat brushless and EC 45 flat brushless

Commercial DC Motors Precision Microdrive [8]

Model: 103-100, 104-000, 104-001, 104-003, 106-002, 107-001, 108-

103, 108-104, 108-106

Model: 110-001, 110-002, 110-003, 112-001, 112-002, 116-101

Model: 120-002, 120-100, 124-001, 124-002

Model: 132-100, 132-201, 136-201, 136-402

Commercial DC Motors Johnson Electric [9]

DF315XLG-021, DC651(2)XLLG-022, DC651(2)XLLG-023,

DC651-P-001, DC751(2)LSG-022, DC751(2)XLLG-011,

DC751(2)XLLG-021, DC751(2)XLLG-022, DC751(2)XLLG-023,

DC751(2)XLLG-024, DC751(2)XLLG-025, DC771(2)XLLG-012,

DC771(2)XLLG-022, DC771(2)XLLG-023, DC771(2)XLLG-025,

DC781(2)XLLG-021, DC971-P-001, E4EHS-12, E5EHS-12,

E5EHS-12-H, E6EHS-12, E6EHS-12-H , E7IHM-24, E8IHM-14,

E8IHM-18, E8IHM-22, E9IWS-28, E7IHL-120, E7IHL-240,

E10DE-240-001, E10DE-240-002, E10IE-240-001

Commercial DC Motors Crouzet [3]

Part number 82710001, 82720001, 82860011, 82740001, 82810017,

82810501, 82830009, 80140510, 80180505, 80180506, 80140511,

80140512, 80120301, 82910001, 82900, 829200, 829300 2 phases,

829300 4 phases, 829400 2 phases, 829400 4 phases, 82910501, 82910502

33
Commercial DC Motors AUTOM [2]

AFF-K10WD. AFF-K20WD, AFF-030PA, AFF-050SK, AFF-130SH,

AFF-180SH, AFF-K30WD, AFF-M10PA, AFF-M20PA, AFF-M30PA,

AFF-N20VA, AFF-N30VA, ARF-130CH, ARF-300CA, ARF-300CH,

ARF-330TA, ARF-370CA, ARF-370CB, ARF-500TB, ARF-1220CA, ARF1230CA

34
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39
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Performance Comparisons and Down Selection of Small Motors for 

Two-Blade Heliogyro Solar Sail 6U CubeSat 

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Wiwattananon, Peerawan; Bryant, Robert G.

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This report compiles a review of 130 commercial small scale motors (piezoelectric and electric motors) and almost 20 researched-type small scale piezoelectric 

motors for potential use in a 2 blades Heliogyro Solar Sail 6U CubeSat. In this application, a motor and gearhead (drive system) will deploy a roll of solar sail 

thin film (2 um thick)accommodated in a 2U CubeSat (100 x 200 x 100 mm) housing. The application requirements are: space rated, output torque at full 

deployment of 0.8 Nm, reel speed of 3 rpm, drive system weight limited to 150 grams, diameter limited to 50 mm, and the length not to exceed 40 mm. The 50 

mm diameter limit was imposed as motors with larger diameters would likely weigh too much and use more space on the satellite wall. This would limit the 

amount of the payload. The motors performance are compared between small scale, volume within 3x102 cm3 (3x105 mm3), commercial electric DC motors, 

commercial piezoelectric motors, and researched-type (non-commercial) piezoelectric motors extracted from scientific and product literature. The comparisons 

suggest that piezoelectric motors without a gearhead exhibit larger output torque with respect to their volume and weight and require less input power to 

produce high torque. A commercially available electric motor plus a gearhead was chosen through a proposed selection process to meet the applications design 

requirements. 

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CubeSat; Miniature motors; Solar sail

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