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High-speed spinning disks on flexible threads

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A common spinning toy, called “buzzer”, consists of a perforated disk and flexible threads. Despite of its simple construction, a buzzer can effectively transfer translational motions into high-speed rotations. In the present work, we find that the disk can be spun by hand at an extremely high rotational speed, e.g., 200,000 rpm, which is much faster than the previously reported speed of any manually operated device. We explore, both experimentally and theoretically, the detailed mechanics and potential applications of such a thread–disk system. The theoretical prediction, validated by experimental measurements, can help design and optimize the system for, e.g., easier operation and faster rotation. Furthermore, we investigate the synchronized motion of multiple disks spinning on a string. Distinctly different twist waves can be realized by the multi-disk system, which could be exploited in the control of mechanical waves. Finally, we develop two types of manually-powered electric generators based on the thread–disk system. The high-speed rotation of the rotors enables a pulsed high current, which holds great promise for potential applications in, for instance, generating electricity and harvesting energy from ocean waves and other rhythmic translational motions.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
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High-speed spinning disks on
exible threads
Zi-Long Zhao1, Shiwei Zhou1, Shanqing Xu1, Xi-Qiao Feng2 & Yi Min Xie1,3
A common spinning toy, called “buzzer”, consists of a perforated disk and exible threads. Despite of its
simple construction, a buzzer can eectively transfer translational motions into high-speed rotations. In
the present work, we nd that the disk can be spun by hand at an extremely high rotational speed, e.g.,
200,000 rpm, which is much faster than the previously reported speed of any manually operated device.
We explore, both experimentally and theoretically, the detailed mechanics and potential applications
of such a thread–disk system. The theoretical prediction, validated by experimental measurements,
can help design and optimize the system for, e.g., easier operation and faster rotation. Furthermore,
we investigate the synchronized motion of multiple disks spinning on a string. Distinctly dierent twist
waves can be realized by the multi-disk system, which could be exploited in the control of mechanical
waves. Finally, we develop two types of manually-powered electric generators based on the thread–disk
system. The high-speed rotation of the rotors enables a pulsed high current, which holds great promise
for potential applications in, for instance, generating electricity and harvesting energy from ocean
waves and other rhythmic translational motions.
Buzzer or whirligig, an ancient mechanical device dating back to more than ve thousand years ago1, is usually
constructed by hanging the perforated rotator at the midpoint of the string, which is made of two exible threads
with the ends tied together (Fig.1). Aer winding the string with the ends stationed, the rotation of the disk
could be realized by alternately pulling or releasing the tension on it. e kinetic behavior of the system could
be described as two successive stages: unwinding and winding. In the unwinding process, the string is subject
to axial tensile forces at the two ends, which unwinds the threads and makes the disk spin. e rotational speed
of the disk reaches the maximum when the threads are totally unwound. In the winding process, the string is
loosened and the momentum of the whirling disk rewinds the threads. When the twist (turns per unit length) of
the string increases to the maximum, the motion of the disk comes to a momentary halt. A new rotation cycle of
unwinding/winding would start if stretching force is reapplied at this moment.
e thread–disk system is of particular interest owing to its potential applications. e principles of buzzer
prototype, featured by its simple construction, can be employed in developing novel devices and materials. For
example, one-dimensional or quasi-one-dimensional materials such as carbon nanotube ropes2,3 and articial
muscles4,5 open opportunities for preparing high-performance thread materials. Rapid development of experi-
mental techniques such as 3D printing and laser engraving enable the easy design and fabrication of the rotators.
Resorting to these advancements, many apparatuses such as chemical reactors6 and high-speed confocal micros-
copy systems79 have been developed recently based on spinning disks. e thread–disk system also shows great
potential in producing thin organic lms1013, quantitative analysis of cell adhesion14,15, high-speed compressive
image acquisition16, and centrifugation and microuidics1721.
e dynamic process of the string–disk system involves complicated coupling of dierent deformation mech-
anisms, e.g., the tension, bending, and torsion of the threads. e elasticity of the thread materials, a crucial factor
of such a system, was not considered in existing studies22,23. Experienced operators may nd that the unwind-
ing/winding performances of the system signicantly depend on, e.g., the positions of the holes on the disk
and the rhythm of applied axial forces. Motivated by the promising applications of the system, here we propose
a theoretical model to correlate its mechanical responses with the material properties, structural geometries,
and loading conditions. e model can be extended to analyze the dynamics of a wide variety of chiral materi-
als2426. Furthermore, we explore the kinetics of spinning multiple disks on a string. e temporal evolutions of
the positions and angular velocities of the disks were measured by using a high-speed camera. e inuence of the
1Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, 3001, Australia.
2AML & CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China. 3XIE Archi-
Structure Design (Shanghai) Co., Ltd, Shanghai, 200092, China. Correspondence and requests for materials should
be addressed to Y.M.X. (email: mike.xie@rmit.edu.au)
Received: 11 July 2017
Accepted: 19 September 2017
Published: xx xx xxxx
OPEN
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
structural parameters and initial conditions on their coupled motion is revealed. Distinctly dierent twist waves
can be realized by using the multi-disk system, which could be used in the control of mechanical waves and the
design of, e.g., turbine engines and rotor compressors27,28.
Due to the coupled extension and torsion of the helically twisted string29, the thread–disk system could eec-
tively transfer the translational motion to a rotational one. At a right rhythm, the disk of a buzzer could be spun
at a rotational speed as high as 200,000 rpm, which is the fastest ever experimentally observed speed of any
manually operated device (Supplementary Fig.S1), and much higher than the previous record 125,000 rpm23.
e high-speed rotational motion is of paramount importance in power generation. In 1831, Michael Faraday
developed the rst homopolar generator, also known as the Faraday disc30, which consisted of a conducting y-
wheel with one electrical contact near the axis and the other near the periphery. When the ywheel was rotated by
hand, the generator could produce a current at a low voltage. Inspired by the Faraday disc, we develop two types
of thread–disk based electric generators in the present work. Both of them are easily constructed and manually
powered. e high-speed rotation of their rotors enables a pulsed high current, which holds great promise for a
variety of technologically signicant applications in electricity generation.
Results and Discussion
Figure1 illustrates the structural parameters of the thread–disk system. Due to symmetry, we consider only the
le half of the system. For simplicity, the weight of the disk and threads is neglected in the theoretical model. e
force exerted on the string is along the x axis. e length of the string is ls0 in the absence of external loads. e
deformed string is ls in length, which consists of helically wound threads to the end and unwound threads linking
the disk. e length of the twisted string section is denoted as lst. Let rh represent the distance from the center
of the disk to the drill holes through which the threads pass. e mass density, Young’s modulus, radius, and
winding angle of the threads are denoted as ρt, Et, rt0, and ϕt, respectively. e mass, radius, thickness, moment of
inertia, and angular velocity of the disk are denoted as md, rd, hd, Jd, and ωd, respectively.
Selection of thread materials. e thread–disk device is an energy-dissipative system: in each rotation
cycle, the work of the external force is dissipated due to frictions in the threads as well as between the disk and air.
Before the system is actuated, the threads are wound up rst. e operator may hold the two ends of the string
with the disk loosely hanging in the middle and swing in circles to twist the string. Pulling the tightly twisted
string, the threads will be unwound and the disk will be twirled. Successive rotation cycles could be achieved only
if the momentum of the spinning disk is large enough to rewind the threads; otherwise, the rotation cycle would
be aborted as the maximal winding angle ϕtm of the threads is too small. In order to increase ϕtm, intuitively it is
desirable to use a disk with a larger moment of inertia Jd and threads with lower stiness in both bending and tor-
sion, i.e., larger-sized disk with greater mass density and more exible threads. For example, a lightweight small
button can hardly be used to wind threads made of relatively stier materials such as shing lines.
Figure 1. Schematic for theoretical model. Structural parameters of the thread–disk system are illustrated. e
periodic rotation of the system is divided into to two stages: unwinding (from (a) to (b)) and winding (from
(b) to (c)). e Cartesian coordinate system xoy is introduced, where the origin o is located at the clamped end
of the string, and x and y axes are along and perpendicular to its length direction, respectively. e lengths of the
string and its twisted section are denoted as ls and lst, respectively. e length of the threads is denoted as lt. e
radii of the threads and the disk are denoted as rt and rd, respectively. e distance between the center of the disk
and the holes is rh.
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Selecting appropriate materials for the threads and disk is a key step in constructing an optimized system.
Ideal materials could be easily found for making the disk because only its mass and geometry have signicant
inuence on the mechanical responses of the system. However, for threads, because of the complex coupling of
dierent physical mechanisms in the dynamic process including tension, bending, and torsion, it is rather di-
cult to select eective and ecient thread materials. During the winding process, the kinetic energy of the disk is
converted to the strain energy of the threads. For a certain amount of the total strain energy, threads with lower
stiness will have larger deformation (i.e., a larger winding angle ϕtm). For homogeneous, linearly elastic thread
materials, the bending energy Ubend and torsional energy Utorsion could be much greater than the tensile energy
Utension. Our theoretical analysis reveals that multi-lament microstructures can eectively reduce the bending
and torsional stiness of the threads, resulting in a larger winding angle ϕtm (Supplementary Information). e
larger the lament number, the smaller the normalized energies Ubend/Utension and Utorsion/Utension. When the la-
ment number of the threads is suciently large, the internal bending and torsional forces and moments could be
neglected. us we use the multi-lament cotton/nylon twine as the thread material in this study.
Unwinding dynamics. During the unwinding process, the string is subjected to coupled extensional–tor-
sional deformations. e axial tensile force Fs and torque Ms of the string depend on its axial deformation εs, while
the torque is transmitted to the disk and twirls it. e kinetic equation of the spinning disk is 2Ms + Jdd2ϕt/dt2 = 0,
where the torque Ms is correlated with the structural geometries and elastic deformation of the threads. With the
relation between Ms and ϕt determined, the winding angle ϕt and rotational speed ωd of the disk can be solved
from the governing equation. e detailed theoretical derivation is given in Supplementary Information. Here we
attempt to reveal the inuence of loading rate
ε ε=td/d
ss
on the unwinding dynamics. In the examples, we take
Et = 2 GPa, rt0 = 1 mm, ϕtm = 3600o, ls0 = 20 cm, md = 50 g, rd = 5 cm (Jd = 6.25 × 105 kg · m2), and rh = 1 mm. e
strain of the string is assumed to be
tt()/
nn
smin maxmin unwind
εεεε=+
, where tunwind is the unwinding period
and n a dimensionless exponent. e minimal
εmin
and the maximal axial strain
max
ε
of the string are determined
from Fs|t=0 s = 0 N and tunwind = 1 s.
e temporal evolutions of the axial tensile force Fs and torque Ms of the string, the winding angle ϕt of the
threads, and the angular velocity ωd of the disk are plotted in Fig.2, where we take n = 1/3, 1/2, 1, 2, and 3 for
dierent loading rates
s
ε
. e maximal axial strain of a string that makes Fs = 0 N and Ms = 0 N · m is referred to
as the critical strain:
ε
ϕϕ=− +−rrr1(2/ 2)
1
cr t0
2tt ht0
. Only when εs > εcr, can the string accelerate the
disk. As shown in Fig.2, the unwinding processes of n = 1/3, 1/2, and 1 are aborted as a result of εs < εcr, while
that of n = 2 and 3 are completed with
ϕ|=°
=
0
ttt
unwind
. In the early stage of the unwinding process, the strain rates
Figure 2. Inuence of the loading rate on the unwinding dynamics. (a) Tensile force Fs and (b) torque Ms of the
string, (c) winding angle ϕt of the threads, and (d) angular velocity ωd of the disk are plotted with time t for
dierent loading rates
, where n is set as 1/3, 1/2, 1, 2, and 3.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
s
ε
in the case of n 1 are distinctly greater than that of n > 1, which lead to a rapid decrease in the winding angle
ϕt (Fig.2c) and, in turn, increase the critical strain εcr. If the increasing εcr exceeds εs, the string is loosened and
featured by Fs = 0 N and Ms = 0 N · m (Fig.2a and b). An appropriate strain rate
εs
(e.g., n = 2 and 3) enables the
disk to be continuously accelerated to the end of the unwinding process (Fig.2d). It is worthy of mentioning that,
less than 200 N is required to twirl the disk to 10000o/s (about 1667 rpm) when n = 1/3, while nearly 400 N is
required in the case of n = 3 to make the disk spin at the similar speed (Fig.2a and d). In the former case, however,
the maximal torque Ms is much larger than that in the later (Fig.2b).
e dependence of the unwinding dynamics on the structural geometries, e.g., the length ls0 of the string, the
radius rt0 of the threads, and the distance 2rh between the drill holes, is also explored. When εs = εcr, the disk will
be spun at a constant velocity ωc and the winding angle of the threads ϕt = ϕtm ωct. With ωc and ϕt known, the
lower limit of the strain rate that keeps the disk accelerating can be determined as
td/d
cr cr
ε ε=
. e smaller the
cr
ε
, the easier the unwinding process will be. e
cr
ε
vs. t relations are plotted in Fig.3a and b, where we take
ϕtm = 3600o, ωc = 3600o/s, ls0 = 20 cm, and several representative values of
=rrl/
hhs0
and
=rrl/
t0 t0 s0
. e critical
strain rate
cr
ε
increases with increasing
rh
and
rt0
. It suggests that threads with a large slenderness (i.e.,
rlr/
t01s0 t0
=
)
and a disk with paracentral holes favor easier unwinding. However, threads with an excessively large length can-
not be easily rewound when a lightweight disk is used during the winding process. When the thread radius rt0 is
specied, using longer threads, though with a larger slenderness, may not lead to an easier operation. Excellent
performance (e.g., faster rotation and easier operation) of the system requires an adequate combination of thread
and disk materials.
e angular velocity ωd of the disk is further plotted as a function of the tensile force Fs of the string in Fig.3c
and d, where we take Et = 2 GPa, ϕtm = 3600o, ls0 = 20 cm, εs = εcr|t=0s + t3/10, Jd = 6.25 × 105 kg · m2, and several
representative
rh
and
rt0
. For a xed Fs, ωd increases with the increasing
rh
and
rt0
. is is because the torque trans-
mitted to the disk will be enlarged if
rh
and
rt0
increase. When the length ls0 of the string is specied, the disk could
be spun at a higher speed by using thicker threads, which is consistent with previous experimental observations1.
It suggests that threads with a smaller slenderness and a disk with a larger distance between drill holes are prefer-
able to achieve a high-speed rotation.
Winding dynamics. During the winding process, the momentum of the spinning disk rewinds the threads.
A mechanics model is proposed to investigate the winding dynamics and the detailed derivation is given in
Supplementary Information. Denoting the torsional stiness and the moment of inertia per unit length of the
string as Ks and Js, respectively, the wave propagation of the twist in the string can be described as
tx//
2s2s22s2
ωλω
∂∂
=∂, where λs = (2πJs/Ks)1/2 is the propagation velocity of the twist. e initial conditions
Figure 3. Parametric study of the unwinding dynamics. Critical strain rate
cr
ε
of the string is plotted with time
for dierent
rh
in (a) and
rt0
in (b). Angular velocity ωd of the disk is plotted as a function of the tensile force Fs of
the string for dierent
rh
in (c) and
rt0
in (d).
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
are assumed to be
ω ω=xxl(,0) /
mm
sdms
and ωs(x,0)/t = 0, where ωdm is the maximal rotational speed of the
disk and m is a dimensionless exponent. e following parameters are used in the examples: ρt = 1150 kg/m3,
Et = 2 GPa, rt0 = 1 mm, ls = 20 cm, εs = 2%, ωdm = 10000o/s, and Jd = 6.25 × 105 kg · m2.
e angular velocity ωs of the string and the helical angle θt of the threads are plotted with the relative position
=xxl/(2)
s
in Fig.4, where we take m = 1 in Fig.4a and b, and m = 1/2 in Fig.4c and d. e ϕt vs. t relations are
shown in the inserts of Fig.4a and c. In the case of m = 1, the angular velocity ωs increases linearly with
x
, while
decreases with time t (Fig.4a). e angular acceleration
ωs
of the string increases with t as a result of the increas-
ing twist. ωs reduces to approximately 0o/s when t = 0.25 s, suggesting that the kinetic energy of the spinning disk
has been totally converted to the elastic strain energy of the threads. Figure4b shows that the helical angle θt of
threads keeps constant along the x axis and increases with t. Figure4c shows that ωs(x, t) varies nonlinearly with
x in the case of
ω ω=
xxl(,0)
sdm1/2s1/2
. e mechanical constraint at
x0=
interferes with the propagation of the
twist wave. Aer the start of winding, the angular velocity ωs of the string has an abrupt decrease near the clamped
end. e string keeps rotating when the angular velocity ωd = ωs(ls, t) of the disk decreases to zero (t = 0.25 s),
suggesting that the kinetic energy of the disk is partly dissipated in the threads. Figure4d shows a similar θt vs. x
relation to that in Fig.4b. It can be seen from Fig.4 that the initial conditions ωs(x, 0) of the winding process may
signicantly inuence the angular velocity ωs of the string.
Experimental verication. e angular velocity ωd of the disk was measured by using a high-speed camera
(Supplementary VideoS1). e ωd vs. t relation is plotted in Fig.5a, where the inserts illustrate the congurational
evolution of the system. e string is totally untwisted (ϕt = 0o) at time t1 and t3, and the rotational speed ωd peaks
at these moments. At t2, the threads are tightly wound (ϕt = ϕtm) and the angular velocity ωd = 0o/s. e maximal
winding angle ϕtm of the threads is calculated by integrating ωd from t1 to t2. e length ls0 of the strings used in
the experiments was approximately 30 cm. e axial deformation εs of the string was captured by using a digital
camera. e parameters of the system were measured as: Et = 0.5 GPa, rt0 = 0.544 mm, md = 8.60 g, rd = 2 cm, and
hd = 6 mm.
e measured ωd vs. t relations (shown in red circles) are compared with the theoretical predictions (blue
lines) in Fig.5b–d, where the distances 2rh between the two drill holes are 5 mm, 10 mm, and 20 mm, respectively.
e loading history εs(t) is shown in the insert of each plot. e theoretical predictions of the angular velocity are
in good agreement with the experimental results for small ωd, while greater than the measurements for large ωd.
Figure 4. Parametric study of the winding dynamics. Angular velocity ωs of the string and helical angle θt of the
threads are plotted with
x
for dierent initial conditions
ω ω=xxl(,0) /
mm
sdms
, where m = 1 in (a) and (b), and
m = 1/2 in (c) and (d). Temporal evolution of the winding angle ϕt of the threads is shown in the inserts of
(a) and (c).
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
is is because the frictional eects in the system and the Poisson eect of the threads are neglected in the theo-
retical analysis. Due to the friction, the work of external forces cannot be totally converted into the kinetic energy
of the disk. e energy dissipated in the threads depends on their complicated deformation, sub-structures, and
surface frictional properties. e air drag that tends to decelerate the spinning disk is proportional to
d
2
ω
and will
increase rapidly with the increasing radius rd. Besides, the radius rt of the threads shrinks with the increasing
tensile strain εt. Due to
θ=MFr tan
sstt
, neglecting the Poisson eect will lead to an overestimate of the torque that
transmitted to the disk. erefore, the discrepancies between the theoretical predictions and experimental meas-
urements become larger as ωd goes higher.
In order to decrease the energy dissipated through the air drag, one may use a disk with a small surface area by
reducing the radius rd and the thickness hd. On the other hand, the moment of inertia Jd of the disk must be large
enough to prevent the spinning disk from stalling. It is suggested that materials with higher mass densities are
used to maintain the moment of inertia while reducing the size of the disk.
Multiple disks on a string. Another set of experiments were performed to investigate the dynamics of spinning
multiple disks on a string. e disks were initially located together in the middle of the string. Aer a few rotation
cycles, the disks would move apart from each other. ey usually went through multiple instabilities, which would
cause the string to wobble. e stability of the system was signicantly inuenced by the loading conditions (e.g., the
frequency of the external force). e dynamic process reaches a steady state only if all disks are trapped in the equilib-
rium positions; otherwise, they would keep on shiing along the string. Here we analyze the angular velocity and the
equilibrium positions of the disks. e parameters of the systems were measured as: Et = 0.5 GPa, rt0 = 0.544 mm,
ls0 = 0.3 m, md = 3.31 g, rd = 2 cm, hd = 2 mm, and rh = 2.5 mm. For each system, let
ωd
denote the angular velocity
normalized by the maximum rotational speed among all disks, and
t
the time normalized by the period of the rotation
cycle. Figure6 shows the
d
ω
vs.
t
relations, where there are two disks in Fig.6a, three disks in Fig.6b and c, and four
disks in Fig.6d–f, respectively. e sketch below each plot illustrates the equilibrium positions of the disks. Details of
the kinetic behavior of the six systems are demonstrated in Supplementary VideosS2–9,respectively.
Figure6a shows that the two disks rotate in opposite directions at the same speed
ωd
. e equilibrium posi-
tions of the disks are approximately symmetrical about the midpoint of the string (
=x1/2
), where the rotational
speed of the string is zero. is thread–disk system can be considered as two independent subsystems separated
Figure 5. Temporal evolution of the angular velocity of the disk. (a) e angular velocity ωd of the disk
was measured. e threads were wound from t1 to t2, and unwound from t2 to t3. Both the experimental
measurements (red circles) and theoretical predictions (blue lines) of the ωd vs. t relations are plotted, where
rh/rd = 1/8 in (b), 1/4 in (c), and 1/2 in (d). e loading history εs(t) was measured and given in the insert of
each plot.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
by the midpoint. By neglecting the frictional eects of the thread–disk and thread–thread interfaces, the tensile
force of the threads keeps constant along their length directions. e kinetic equilibrium requires that the string
have the same amount of twists on both sides of a disk. us the ideal equilibrium positions of the two disks
should be respectively located at
x1/4=
and 3/4, which are in good agreement with the experimental
measurements.
In Fig.6b, the disk that is trapped in the middle of the string is almost motionless (
0
d
ω
). Its inuence on the
dynamics of the system can be neglected. It is clearly seen that the other two disks exhibit similar dynamic behav-
ior to those in Fig.6a. In another scenario, as shown in Fig.6c, two of the three disks, though without glue or
constraint between them, stay together and rotate synchronously. Since
rr
ht0
1, the local torque Mlocal of the
string that is transmitted to the disk is proportional to the local twist Ts, which keeps constant along the length
direction of the string (Supplementary Information). It is known from dωd/dt = Mlocal/Jd that the angular accelera-
tion of the disk is inversely proportional to its moments of inertia Jd. us the rotational speed of the double disks
is 1/2 of that of the single disk. Besides, the node (ωs 0o/s) of the twist wave is positioned at
x1/3=
, such that
Figure 6. Spinning multiple disks on a string. Temporal evolution of the normalized angular velocity
ωd
of the
disks and their equilibrium positions were measured by using a high-speed camera, with two disks in (a), three
disks in (b) and (c), and four disks in (d)–(f), respectively. All these drawings were drawn by the rst author Zi-
Long Zhao.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
the string could have a uniform twist. us the ideal equilibrium positions of the double disks and the single disk
are
x1/6=
and 2/3, respectively, which coincide with the experimental results. It is interesting to note from
Fig.6b and c that a multi-disk system may evolve into dierent steady states. It suggests that initial conditions,
e.g., initial positions of the disks, could signicantly inuence the dynamics of the system.
Similarly, in Fig.6d, the disk trapped in the vicinity of the node
x1/3=
and featured by
ω0
d
can be
neglected in the analysis. e ideal equilibrium positions of the other three disks are
x1/6=
, 1/2, and 5/6,
respectively. e kinetic behavior of the disks in Fig.6e and f is similar to those in Fig.6b and c, respectively. e
ideal equilibrium positions of the disks are
=x1/4
, 1/2, and 3/4 in Fig.6e, and
x1/8=
and 5/8 in Fig.6f. For
each system, the whirling disks are coupled by the string: they all end up spinning at the same frequency. Using
the above analysis, one can readily predict the possible steady states of the multi-disk system when there are more
than 4 disks on a string. e synchronized motion of the disks can be easily tuned by changing, e.g., their number,
initial positions, and moments of inertia. Distinctly dierent twist waves can be realized by the multi-disk system,
which may hold potential applications in designing advanced materials and novel devices.
Electric generators. e thread–disk system enables a high-speed rotation, which has great potential for
power generation use. We developed two types of electric generators based on the system and demonstrated in
Fig.7. Both of them contain permanent magnets and coils of enameled copper wire. ey can be easily oper-
ated manually to produce alternating current. In the rst generator (Fig.7a), the stator consists of two neodym-
ium block magnets, which are placed parallel to each other (Fig.7b). e north pole of one magnet faces the
south pole of the other. e rotor is comprised of four coils of copper wire mounted on a perforated plastic disk
(Fig.7c). Each of the coils is connected to an LED bulb, forming a closed circuit.
e disk is spun in a plane perpendicular to the uniform static magnetic eld between the magnets. e mag-
netic ux through the wire loop is dened as
φ=⋅
ΣBAd
, where denotes the hypothetical surface whose
boundary is the wire loop, B the magnetic eld, and dA the innitesimal area element of . Here the magnetic
eld B is invariant and the surface varies with time. e coils rotate with the spinning disk at a high speed in the
static magnetic eld, rending a rapid change in the magnetic ux φ. According to Faraday’s law, the voltage
between the two ends of a coil is calculated as U = Ndφ/dt, where N designates the number of turns of the coil.
A higher voltage could be generated if the number of turns N, the magnetic eld B, and the rotational speed ωd of
the disk increase. When the voltage U is suciently large, the electric current owing through the circuit can light
the LED bulbs (Fig.7a and Supplementary VideoS8).
In the second electric generator (Fig.7d), the stator is the coils of wire (Fig.7e) and the rotor is made of several
neodymium disc magnets (Fig.7f). e coils are immobilized on two vertical plates and the magnets are mounted
on a spinning disk. e hypothetical surfaces of the wire loops are perpendicular to the string. During the
rotation cycle, the surface remains unchanged and the magnetic eld B varies with the whirling magnets. e
bulbs connected to the coils can be lit when the rotational speed of the disk is suciently high (Fig.7d and
Supplementary VideoS9). For example, in this electric generator, the disk is 100 mm in diameter, each coil has
360 turns, and the magnetic ux of each neodymium disc magnet is about 0.1 T. e maximal voltage of the gen-
erator can be about
14V
when the disk rotates at 1000 rpm. e voltage of the bulbs to obtain typical optical
characteristics is 1.8–3.3 V. us the bulbs can be easily lit by the generator.
Figure 7. read–disk based electric generators. e rst generator (a) is constructed by the stationary
magnets (b) and the coils of enameled copper wire (c) that are mounted on the spinning disk. e second
generator (d) is constructed by the stationary coils of wire (e) and the lightweight disc magnets (f) that are
mounted on the perforated disk. All these photographs were taken by the rst author Zi-Long Zhao.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
e thread–disk based electric generators presented here are easy-to-use and constructed by only a few simple
components. ey take advantage of the high-speed rotation of the disk. Our experiments demonstrated that
the maximal rotational speed of the disk could be as high as 200,000 rpm. Besides, the thread–disk system can
eectively transfer the translational force to a rotational motion, which could be exploited to harvest the kinetic
energy of wind and ocean waves. e endless movements of wind and water always create enormous amounts
of energy31. Hydroelectric power stations use the torrent of dammed water to spin the propeller-like turbines by
striking their angled blades. en the generators connected to the turbines convert the rotational motion into
electricity. e energy of moving wind is captured and harvested in a similar way for power generation.
When the thread–disk based electric generators are used to capture the wind power, they can be micromin-
iaturized and used in an array. e wind force32, Fw = CdPwAs, could be transmitted by tailor-made windshields
to drive the generators, where Cd, Pw, and As denote the drag coecient, wind pressure, and projected area of the
windshields, respectively. Cd is dimensionless and has the order of magnitude 1. When Pw = 300 Pa (the wind
speed is about 22 m/s) and As = 1 m2, e wind can make a rotor with Jd = 5 × 105 kg · m2 spin at approximately
2000 rpm. By optimizing the structural geometries and topologies of the system (e.g., reducing the surface area
of the rotors), the energy loss induced by, e.g., air drag, could be reduced and the eciency of energy conversion
could be further improved. e ultrahigh rotational speed of the rotors enables pulsed high currents, which can
be applied in, e.g., generating electricity and harvesting energy from ocean waves and other rhythmic transla-
tional motions.
Conclusions
In summary, we have investigated the dynamic behavior of the thread–disk system. A theoretical model is estab-
lished to examine the dependence of its unwinding and winding performance on the material properties, struc-
tural geometries, and loading conditions. e theoretical analysis, validated by experiments, can help design and
optimize the system for, e.g., easier operation and faster rotation. e synchronization phenomenon of spinning
multiple disks on a string is observed and measured. e inuence of the structural parameters, e.g., the number
and initial positions of the disks, on their synchronized motion is revealed. Distinctly dierent twist waves can
be realized by the multi-disk system, which is potentially important in designing advanced materials and novel
devices, e.g., turbine engines and rotor compressors. Finally, two types of electric generators are developed based
on the thread–disk system, which take advantage of the high-speed rotation of the spinning disk. is work has
shed light on the mechanics of the thread–disk system and demonstrated an important application in generating
electricity. e established theoretical model has paved a way towards further applications of the thread–disk
system in various elds. It is also worth mentioning that precisely evaluating the energy dissipation of the system
could help improve its eciency for the energy conversion, which deserves further research.
Methods
Measurements of the dynamics of the thread–disk system. Cotton twine and plastic laminates
(Polymethylmethacrylate, PMMA) were used for the threads and disks, respectively. e perforated disks were
fabricated by using a laser engraving machine (Rayjet-156, Trotec Laser, Austria). Stainless steel key rings were
used as handles. Each end of the string was tied to a handle, where one handle was xed on a support stand and
the other was held by hand. e slow motion analysis of the spinning disk was performed by using a high-speed
video camera (Fastcam Mini UX100, Photron, Japan). A digital camera (EOS 6D, Canon, Japan) was used to
capture the deformation of the string, where a 1000 mm steel ruler was mounted parallel to the string to measure
its length. e angular velocity of the disks and the axial tensile strain of the strings were determined through
image processing.
Measurements of mechanical properties of threads. Quasi-static uniaxial tensile tests of the threads
were performed with a crosshead speed of 2.0 mm/min at the room temperature using universal testing machine
(ESA-CU200, Shimadzu, Japan). e initial distance between clamps in the tensile tests was 0.1 m. e force–
displacement curves were recorded automatically. e thread approximately had a circular cross section, and its
diameter was measured by using a vernier caliper. e Young’s modulus of the material was determined from the
linear regime of the stress–strain curves.
Spinning the disk at 200,000 rpm. Nylon twine was here used for making the threads to provide high
tensile strength and high wear-resistance. e threads were thin and exible, which could be easily wound by a
disk with a small moment of inertia. e radius and the thickness of the disk could be reduced to decrease the
air drag. Copper sheet, featured by a high mass density, was used for the disk to maintain the moment of inertia
while reducing the surface area. e edges of the holes on the disk were polished by ne sandpaper, which eec-
tively reduced the abrasion to the threads. Pine wood was used for the handles. e parameters of the thread–
disk system were measured as: Et = 30 GPa, rt0 = 0.06 mm, ls0 = 1.5 m, md = 1.39 g, rd = 1 cm, hd = 0.56 mm, and
rh = 1.5 mm. e angular velocity of the spinning disk was measured by using a high-speed camera (Fastcam Mini
UX100, Photron, Japan), where the video-recording frame-rate and shutter speed were set as 10,000 frames per
second and 1/20,000 s, respectively. e maximum recorded rotational speed of the disk was as high as 200,000
rpm (Supplementary FigureS1).
Electric generators based on the thread–disk system. Coils of enameled copper wire and neodym-
ium magnets were used for both generators. e diameter and linear mass density of the wire are 0.25 mm and
0.44 g/m, respectively. Each of the circular coils, 4 cm in diameter, has approximately 180 turns in the rst genera-
tor (Fig.7a) and 360 turns in the second (Fig.7d). e mass, dimensions, and magnetic ux of each block magnet,
used for the rst generator, are 231 g, 50 × 50 × 12.5 mm (length × width × thickness), and 0.2598 T, respectively.
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Scientific REPORtS | 7: 13111 | DOI:10.1038/s41598-017-13137-1
e mass, diameter, thickness, and magnetic ux of each neodymium disc magnet used for the second generator
are 7 g, 25 mm, 2 mm, and 0.0995 T, respectively. e total mass and diameter of the rotors are 68.48 g and 150
mm for the rst generator and 78.29 g and 100 mm for the second. LED bulbs with dierent colors, including red,
blue, green, and yellow, were used in the experiments. e continuous forward current and voltage of the bulbs
to obtain typical optical characteristics are 20 mA and 1.8–3.3 V, respectively. White nylon cable ties (100 mm
in length and 2.5 mm in width) were used to x the coils of wire and the disc magnets on the disks. Four threads
were used to spin the disk in each of the electric generator.
Data availability. e data that support the ndings of this study are available from the corresponding
author upon request.
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Acknowledgements
e work was supported by the Australian Research Council (DP160101400), the Fundamental Research Funds
for the Central Universities (2014ZD16), the National Natural Science Foundation of China (11432008) and
Tsinghua University (20121087991). e authors wish to thank Prof. Guangming Zhang, Prof. Xuehua Zhang,
Dr. Claire Shuiqing Zhang, Ms. Haiyun Yang, Mr. Eric Xiang Gao, Mr. Shamir Bhuiyan, Mr. Anbang Chen, and
Mr. Patrick Wilkins for their help.
Author Contributions
Y.M.X. initiated and directed this study. Z.L.Z., Y.M.X, X.Q.F., and S.Z. designed the research. Z.L.Z. conducted
the theoretical analysis and performed the experiments. S.Z. contributed to the theoretical analysis. S.X.
contributed to the experiments. Z.L.Z. and Y.M.X. wrote the paper. All authors contributed to revising the
manuscript.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-017-13137-1.
Competing Interests: e authors declare that they have no competing interests.
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Through natural selection, many plant organs have evolved optimal morphologies at different length scales. However, the biomechanical strategies for different plant species to optimize their organ structures remain unclear. Here, we investigate several species of aquatic macrophytes living in the same natural environment but adopting distinctly different twisting chiral morphologies. To reveal the principle of chiral growth in these plants, we performed systematic observations and measurements of morphologies, multiscale structures, and mechanical properties of their slender emergent stalks or leaves. Theoretical modeling of pre-twisted beams in bending and buckling indicates that the different growth tactics of the plants can be strongly correlated with their biomechanical functions. It is shown that the twisting chirality of aquatic macrophytes can significantly improve their survivability against failure under both internal and external loads. The theoretical predictions for different chiral configurations are in excellent agreement with experimental measurements.
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This paper presents the liquid-liquid flow behaviour and the liquid-liquid mass transfer rates for a rotor-stator spinning disc reactor, with an axial disc spacing of 1 mm, a rotor radius of 0.066 m, and rotational disc speeds up to 1600 rpm. The liquid-liquid mass transfer rate is determined from extraction experiments of benzoic acid from n-heptane to water. For the calculation of the overall mass transfer rate the dimerization and acid dissociation equilibria are taken into account. Three flow patterns are characterized. Up to 100 rpm continuous radially inwards spiralling n-heptane patterns are observed. Between 100 rpm and 300 rpm this continuous spiral changes to spiralling n-heptane droplets. Above 300 rpm fully dispersed phase flow is observed. The overall mass transfer rate increases from 0.17 m(ORG)(3) m(R)(-3) s(-1) at 100 rpm and a water flow rate of 2.5 x 10(-6) m(AQ)(3) s(-1) (water: n-heptane = 1.1:1) to 51.47 m(ORG)(3) m(R)(-3) s(-1) at 1600 rpm and a water flow rate of 12.5 x 10(-6) m(AQ)(3) s(-1) (water: n-heptane = 5.6:1). These mass transfer rates are at least 25 times higher compared to those in packed columns, and at most 15 times higher compared to mass transfer rates in state of the art microchannels. (c) 2012 Elsevier B.V. All rights reserved.