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A new electromagnetic vibrational energy harvesting device for swaying cables
Applied Energy 228 (2018) 2448–2461
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A new electromagnetic vibrational energy harvesting device for swaying cables
T
⁎
Haikun Wang, Chaoming He , Siyun Lv, Haoran Sun School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
H I GH L IG H T S
device changes cable’s multi-directional vibration into unidirectional rotation. • The motion and the converted electric energy of the Y-shaped device were analyzed. • The experiment data showed an average conversion rate of 55%. • The • The regenerative energy from vibrational absorber is stored in the supercapacitors.
A R T I C LE I N FO
A B S T R A C T
Keywords: Energy harvesting Cable vibration Electromagnetic Super-capacitor
An original vibrational energy harvesting device with regard to the vibrational performance of far-end cables was designed under the condition that no power can be supplied to the far end of freight cableways in transmission and distribution projects. The device was designed to have a Y-shaped radial gear-rack structure. The random vibrations of the cable are converted into three one-way rotary motions of a Y-shaped device terminal using a Y-shaped rack unit and one-way gear-rack units. The device then harvests the electric energy through a super-capacitor and supplies power to equipment in areas out of the reach of the power supply along the cableway. An analysis and dynamic simulation of the Y-shaped rack unit and one-way gear-rack units demonstrate that the Y-shaped layout of the device adapts well to the random vibration of the cable. The device was proven to have successfully harvested the vibrational energy of the cable in several directions on its radial plane, showing good prospects in supplying power to far-end wireless surveillance equipment for freight cableways in remote mountainous areas.
1. Introduction Cableways play an important role in power transmission and distribution project construction in remote mountainous areas. With long spans and high freight transport efficiency, cableways have incomparable superiority over other means of transport and greatly reduce manpower waste. Vibrations caused by unpredictable factors in the environment, such as wind force and landslides, affect the operating safety of freight cableways, which are usually erected in remote mountainous areas. To ensure the safety of the operating cableways, the far end of cableways for power transmission and distribution construction requires a power source to supply power to the surveillance equipment at the far end of the cableway, thus supporting cableway farend equipment safety monitoring. The erection of electric wires on a mountaintop is often extremely difficult, as such areas are often out of the reach of the power supply, making it impossible to use such ⁎
equipment as wireless sensors and wireless video monitors. The constant action of wind force and freight loading and transport on a cableway in an outdoor environment causes the entire cable to sway, and these potential vibrations are considerable sources of energy to harvest. Energy harvesting from ambient vibration is a desirable solution to the power supply associated with wireless sensors for remote areas [1]. The design of an efficient, low-cost energy harvesting device that can continually supply power is critical for supplying power to cableway surveillance equipment. Vibrational energy harvesters can be divided into three main categories depending on how they operate, namely, electromagnetic induction [2–4], piezoelectricity [5] and electrostatic generation [6,7]. Among the three vibrational energy harvesters devices, the piezoelectric energy harvester has the characteristics of small, simple, and high power density [8,9], while the electrostatic energy harvester has high power conversion efficiency [10], but its energy harvesting
Corresponding author. E-mail addresses: fl[email protected], [email protected] (C. He).
https://doi.org/10.1016/j.apenergy.2018.07.059 Received 18 March 2018; Received in revised form 2 July 2018; Accepted 14 July 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.
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structures [23]. Among the aforementioned mechanisms, electromagnetic induction is a promising one that can well serve vibration control and energy harvesting functions [24–26]. The results suggest that these novel systems have been intended for energy harvesting for remote areas applications but are nevertheless inadequate such as portability and durability. The aforementioned systems have been intended to design highly efficient, portable, reliable and simple facilities, but two main challenges remain with these technologies: (i) capturing arbitrary random vibrational energy efficiently and (ii) increasing the output power so that the system is suitable for cableway equipment that requires high power. Unlike conventional vibrations, the vibrations of a cable include both vibrations in the horizontal direction under the action of wind force and those in the vertical direction caused by freight handling and unsteady traction machine operation; coupling of the two kinds of motion creates vibrations that are multi-directional and random in motion. This paper presents a novel Y-shaped energy harvesting device that can convert the multi-directional random vibrations of a cable into the one-way rotary motion of the gears, thus driving the generator to produce electricity. A super-capacitor is chosen herein as a storage capacitor based on its various advantages, such as high power density, short charging/discharging time, long cycle life and wide operating temperature range, as well as its better adaptation to electric energy with sharply varying voltage and outdoor environments with large daily temperature swings.
process an external power supply is required to generate an electrostatic field, which is contrary to the purpose of constructing an autonomous power supply system. The electromagnetic induction energy harvester has the characteristics of high power generation efficiency and large power generation [11], so it is more suitable for harvest vibration energy to supply power to wireless devices, and realize selfsupply purposes of monitoring devices in remote mountainous areas. In this study, a portable and reliable electromagnetic vibrational energy harvesting device with supercapacitors for swaying cables is investigated. Electromagnetic energy harvesting technology uses the principle of electromagnetic induction to convert vibrational energy into electric energy. Electromagnetic vibrational energy harvesting devices can be divided into two types depending on their way of motion, namely, the linear type and the rotary type. Linear electromagnetic energy harvesting technology mainly causes variation in the magnetic flux through coils wrapped around the outside of the magnets via the linear motion of the magnets. Therefore, the closed coils generate induced current. Delnavaz et al. designed a linear electromagnetic vibrational energy harvesting device to harvest energy in the course of breathing. Under a simulation of human breathing, the energy harvesting efficiency reached a maximum when the magnets fixed at the ends of the conduit; the device provided an induced voltage output of 25 mV and an output power of 3.1 μW [12]. Rotary electromagnetic energy harvesting technology converts the energy by reciprocating the linear vibrational motion into rotary motion and accomplishes power generation through the rotation of the generator in the end. This technology is mainly used to harvest vibrational energy with a low vibrational frequency and large amplitude. The University of Michigan in the US designed an electromagnetic low-frequency vibrational energy harvesting device [13]. Using frequency amplifying technology, the device converted harvested low-frequency vibrational energy into high-frequency vibrational energy and then into electric energy. S. G. Burrow et al. designed a vibrational energy harvesting device using a flux concentrator [14]. In a structure designed by the University of Southampton in the UK, a pair of Nd-Fe-B permanent magnets were placed on a horseshoe-shaped iron core; vibrations of the cantilever caused a variation in the magnetic flux to accomplish energy harvesting [15]. The electromagnetic micro-generator made in 2001 at the University of Sheffield in the UK was only 25 mm3 in size; with an operating frequency of 4 MHz, the device could provide an output power of 0.3 μW [16]. In 2009, D. Marioli, E. Sardini et al. from the University of Brescia in Italy made a coil vibration-type electromagnetic vibrational energy harvesting device using the FR4 material and printed circuit board technique [17]. Zuo et al. designed a vibrational energy harvesting device for vehicles that converted the vibrations of a vehicle into electric energy and provided a maximum output power of 68 W [18]. Zhang Zutao et al. designed an energy harvesting device for highway speed bumps that converted the up-and-down vibrations of barrier lumps on a speed bump into the rotary motion of an AC motor and provided an output voltage of up to 194 V [19]. Zhang also designed an energy harvesting device applied to the damping system of an electric car [20]. In recent years, an increasing number of studies have focused on energy harvesting and alternative energies [21]. Several energy harvesting systems have been used to the power supply problem associated with autonomous sensors. Pourghodrat et al. designed an energy harvesting system for railroads by converting the kinetic energy of the track into electricity to provide an alternative power source for remote areas [22]. Wenai Shen and Songye Zhu propose a novel system, termed electromagnetic damper cum energy harvester to bridge stay cables which is employed to fulfill both vibration damping and energy harvesting functions [1]. Palomera-Arias et al. (2008) studied linear motion EMD for the vibration control of civil
2. System design The flowchart of energy conversion using the Y-shaped energy harvesting device is shown in Fig. 1. The process consists of 4 main modules: (1) the vibrational energy input module, (2) the transmission module, (3) the energy conversion module and (4) the energy storage module. As shown in Fig. 1, the cable generated random vibrations under the action of wind load, traction and other forces, which constituted the system’s vibrational energy input module. The transmission module takes a Y-shaped radial gear-rack structure and has three oneway gear units that are evenly distributed on the circle. The transmission module converts the random vibrations of the cable into the oneway rotary motion of the three one-way gear units. The energy conversion module converts one-way rotations into electric energy via the alternator. The energy storage module stores the generated electric energy in the super-capacitor to provide far-end wireless surveillance equipment with stable electric energy input. 2.1. Vibrational energy input module Fixed at both ends, the cable is considered to be approximate to a catenary structure for analysis. The vibrational energy of the cable mainly originates from two sources. The first source is the sway of the cable under the action of wind load in an actual condition, especially the sway of cable in the horizontal direction caused by the freight on the cableway under the impact of transverse wind force. The second source is the vibration of the cable in the vertical direction that results from the freight loading and unsteady near-end machine traction operation. Coupled vibrations from the two kinds of motion become the main source of vibrational energy to be harvested, as shown in Fig. 2. 2.2. Transmission module The transmission module, the core of the energy harvesting system, can be divided into two parts: (1) one-way gear units, as shown in Figs. 3–5, and (2) a Y-shaped rack unit, as shown in Fig. 6. The
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The vibrational energy input module
The energy storage module
Cable vibration
Unsteady traction
The energy conversion module
Uniform load Freight loading
Application
Energy harvesting unit
Wind power The transmission module
One‐way bearing AC motor unidirectional rotating
Close to unit
Gear counter‐ clockwise
One‐way bearing
Away from unit
Gear clockwise
Application: light sensor
Cable vibration
Super capacitor
Fig. 1. Flowchart of energy conversion using the proposed energy harvesting device.
Unsteady traction
Uniform load (caused by the weight of cable) Wind power Freight loading 4 Fig. 2. Input of vibrational energy.
When the cable approaches a one-way gear unit, the rack moves towards the upper left, and larger gear 2 and its connecting shaft rotate clockwise, while larger gear 1 and its connecting shaft rotate counterclockwise. Since the one-way bearing cannot transfer clockwise rotations, medium gear 4 rotates clockwise, thus transferring the torque. Medium gear 3 rotates clockwise, while the corresponding smaller gear 5 rotates counterclockwise, as shown in Fig. 4. When the cable departs from a one-way gear unit, the rack moves towards the lower right, and larger gear 2 and its connecting shaft rotate counterclockwise, while larger gear 1 and its connecting shaft rotate clockwise. Medium gear 3 rotates clockwise, transferring the torque. Medium gear 4 rotates clockwise, while the corresponding smaller gear 5 rotates counterclockwise, as shown in Fig. 5. The one-way bearing guarantees that the smaller gear always
transmission module comprising the Y-shaped rack unit and one-way gear units converts the random vibrations of the cable into one-way rotations. 2.2.1. One-way gear units A one-way gear unit is a gear set comprising larger gears 1 and 2, medium gears 3 and 4 and a smaller gear 5, as shown in Fig. 4. Larger gear 2, located on the front side of the circle, meshes with one side of the rack, and medium gears 3 and 4, located on the back side of the circle, mesh with the smaller gear 5. Medium gears 3 and 4 have a builtin one-way bearing, and the larger gears, shaft and inside track of the one-way bearing are fixed together so that they have the same rotary angular speed. Smaller gear 5 in the middle is coaxial with the generator.
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Fig. 3. One-way gear unit.
Fig. 5. Cable departs from a one-way gear unit.
meshed with the racks on three parallel planes, ensuring that the three sets did not interfere with each other when they moved, as shown in Fig. 7. 2.3. Energy conversion module Making use of generator’s electromagnetic effect, the energy conversion module converts mechanical energy from the rotations of the gears into electric energy. There are three main kinds of commercially available generators: (1) AC induction motors, (2) DC brush motors and (3) DC brushless motors. DC brush motors have a short service life, as their carbon brush and commutator produce sparks and carbon dust, which are liable to cause damage to their parts when they rotate. DC brushless motors are liable to generate resonance, as there is a slight vibration when they are started at a low speed. An AC induction motor was chosen, as it is inexpensive and has a long service life; the output at a stabilized DC voltage can be achieved by alteration with an attached circuit. Fig. 4. Cable approaches a one-way gear unit.
2.4. Energy storage module maintains one-way counterclockwise rotation and finally drives the generator to run.
The vibrational energy input to the system is uncertain; vibrations may be violent if the wind load is heavy, and the voltage generated by vibration varies sharply as well. The voltage generated by the generator cannot be directly stored up, and its harvesting cannot be fulfilled until it is turned into a DC steady-state after rectification, smoothing and stabilization. Among them, the stabilizing circuit is a constant-voltage and limited-current charging circuit based on an LM317 three-terminal
2.2.2. Y-shaped rack unit The Y-shaped rack unit is shown in Fig. 6. The cable was installed to be perpendicular to the circle’s plane and pass through the circle center; the three one-way gear units were evenly distributed at an angle of 120° on the same periphery of the circle. The three sets of one-way gear units
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Fig. 6. Y-shaped rack unit.
Fig. 7. Parallel arrangement of three one-way gear units.
well to such a voltage; in addition, the capacitor has various advantages, such as a high power density, short charging/discharging time and long cycle life. The real LM317-based rectifying, smoothing, and stabilizing circuit is shown in Fig. 9.
regulator. The circuit diagram is shown in Fig. 8. A super-capacitor was chosen as the power storage capacitor, as shown in Fig. 8, because the voltage still fluctuated, although it varied less after rectification, smoothing and stabilization, and the super-capacitor can adapt very
Fig. 8. LM317-based rectifying, smoothing, stabilizing circuit. 2452
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The rotational inertia of a continuous body rotating around a specified axis can be obtained by taking the integral of the density and the radius squared with respect to volume; i.e.,
∫V ρ(r ) r 2dV
J=
(2)
ρ : density of the shafts and gears, which is a function of the radius r of the shafts and gears; V : volume of the shafts and gears. (2) Calculation of the electromagnetic damping of the generator The generator used herein was a three-phase alternator. The alternating current generated by the alternator was turned into direct current after rectification. The alternator generated a three-phase alternating voltage. There was a 120° difference between each of the phases. Fig. 9. Real LM317-based rectifying, smoothing, stabilizing circuit.
PE = Poutput + Plost =
e32 1.5 × Em2 e12 e22 + + = R e + Ri R e + Ri R e + Ri R e + Ri
(3)
Em = ke·ωg
(4)
Ce·ωg2
(5)
PE =
PE : power of the alternator; Poutput : electric power of the external load; Plost : electric power consumed by the internal resistance of the threephase winding of the alternator; e1, e2, e3 :voltage of the phases of the three-phase alternator; R e : controllable external resistor; Ri : internal resistance of each phase of the generator; Em : voltage magnitude of the phases; ke : constant of proportionality between the voltage generated by the alternator and its rotational speed; ωg : rotary angular speed of the alternator; Ce : electromagnetic damping of the alternator.
Fig. 10. Structural schematic of a one-way gear unit.
The following can be deduced from formulas (3)–(5): 3. Modeling analysis
Ce = 3.1. One-way gear unit analysis
1.5 × ke2 R e + Ri
(6)
When the vibration of the cable drove the gears and racks to move relatively, a one-way gear unit ran. A schematic of the system is shown in Fig. 10.
3.1.2. Input torque of one-way gear units When cable approaches a one-way gear unit, the meshing transmission path is gear 2- > 1-3- > 5,
3.1.1. Calculation of the damping for parts of one-way gear units
Tr =
(J1 + J2 + J3 + J4 )d2θ2 (t ) z dθ (t ) + ⎛Cr + Cm1 + 2 5 Cm5 ⎞ 2 + T3 dt 2 z 2 ⎝ ⎠ dt ⎜
(7)
(1) Calculation of the mesh damping of the gears The mesh damping between gears p and q can be obtained from
Cm = 2ξ
Tr : equivalent torque exerted by the rack on larger gear 2, the value of which is the product of the acting force Fr between the rack and the larger gear and the radius of larger gear 2; Ji : rotary inertia of gear i, i = 1, 2, 3, 4; θ2 : rotation angle of gear 2; Cr : mesh damping between the rack and gear 2; z5, z2 : number of teeth on gears 5 and 2; Cm1: mesh damping between gears 1 and 2; Cm5 : mesh damping between gears 3 and 5; T3 : torque that acts on gear 3.
kg rp rq Jp Jq rp2 Jp + rq2 Jq
⎟
(1)
ξ : damping ratio which ranges from 0.03 to 0.17, with 0.1 taken as its value herein; kg : mean value of the stiffness in the corresponding meshing pair p and q ; rp, rq : radius of the mesh gears p and q ; : rotary inertia of the mesh gears p and q .
T5 = (J5 + Je )
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d 2θ5 (t ) dθ (t ) dθ (t ) + Cm5 5 + Ce 5 dt 2 dt dt
(8)
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⎧ T3 = ⎨ θ5 = ⎩
z3 T z5 5 z3 θ z5 3
Win : mechanical energy input to the energy harvesting unit; r : radius of the reference circle of gear 2; D : displacement of contact point of gear 2 and rack.
(9)
Wout =
T5 : torque that acts on gear 5; J5 : rotary inertia of gear 5; Je : rotary inertia of the rotor of the alternator; θ3, θ5 : rotation angle of gears 3 and 5; z 3 : number of teeth on gears 3.
=
∫0
t
∫0
t
Poutput dt =
∫0
(
t
E (t )2 ηe dt = R z dθ
3 2 R e 1.5 ke z5 dt R e + Ri R e + Ri
∫0
t
2
) dt = ∫ 0
t
(
dθ
)
(
z D′
2
5 R e 1.5 ke dt dt R e + Ri R e + Ri 3 R e 1.5 ke z5 r R e + Ri R e + Ri
2
) dt (13)
2
z d 2θ2 (t ) Tr = ⎜⎛J1 + J2 + J3 + J4 + ⎛ 3 ⎞ ·(J5 + Je ) ⎞⎟ 2 z 5 ⎝ ⎠ ⎝ ⎠ dt ⎜
+ ⎜⎛Cr + Cm1 + 2Cm5 + ⎝
⎟
Wout : electric energy output from the energy harvesting unit; ηe : electrical efficiency; E (t ) : output electromotive force; R : total resistance of the generator.
2
⎛ z 3 ⎞ ·Ce ⎞⎟ dθ2 (t ) ⎝ z5 ⎠ ⎠ dt ⎜
⎟
(10)
Formula (10) can be deduced from formulas (7)–(9), and then, the units can be analyzed as a whole. When cable departs from a one-way gear unit, the meshing transmission path is gear 2-4- > 5. Due to the symmetry of structure, the equivalent torque exerted by the rack on larger gear 2 is equal to Tr .
The total efficiency of the one-way gear unit is obtained as follows:
η=
dθ2 (t ) d 2θ2 (t ) dθ2 (t ) 2 + mr · · ·r dt dt 2 dt
(11)
Pinput : power of input energy to the one-way gear units; mr : mass of the rack; r : radius of reference circle of gear 2. Win =
∫0
t
Pinput dt =
∫0
t
2
2 ⎛⎛ ⎞ d θ2 (t ) ⎛ z3 ⎞ ⎜ ⎜J1 + J2 + J3 + J4 + z 5 (J5 + Je ) ⎟ dt 2 ⎝ ⎠ ⎠ ⎝⎝ ⎜
⎟
3.1.4. Equivalent damping analysis of the one-way gear units
2
z dθ (t ) d 2θ2 (t ) 2⎞ dθ2 (t ) + ⎛⎜Cr + Cm1 + 2Cm5 + ⎛ 3 ⎞ Ce ⎞⎟ 2 r ⎟ dt + mr z dt dt 2 dt ⎝ 5⎠ ⎠ ⎝ ⎠ ⎜
=
∫0
t
Pinput = Cu·D′ 2
⎟
z3 2 ⎛⎛ ⎞ D″ ⎜ J1 + J2 + J3 + J4 + ( z 5 ) (J5 + Je ) r ⎝ ⎠ ⎝ ⎜
+ ⎛⎜Cr + Cm1 + 2Cm5 + ⎝
2
⎛ z 3 ⎞ Ce ⎞⎟ D′ + mr D″ r 2⎞ D′ dt r ⎟ r ⎝ z5 ⎠ ⎠ r ⎠
(15)
Cu : damping of the one-way gear unit. Cu denotes the overall damping of the one-way gear units, i.e., their damping to the cable. Pinput denotes the power of energy transferred by the cable to the one-way gear units.
⎟
⎜
(14)
Formulas (12) and (13) show that the independent variable D of Pinput (D) and Poutput (D) is the relative displacement between the gears and racks. Pinput and Poutput curves were obtained using MATLAB analog variable D and the functional relation between formulas (12) and (13) and D . Fig. 11a and b show two sets of Pinput and Poutput curves with simulation amplitudes of 5 cm and 10 cm, respectively, and a frequency of 3 Hz. Pinput is shown in red, and Poutput is shown in blue. The input in Fig. 11a is motion in the vertical direction with an amplitude of 5 cm and a frequency of 3 Hz. In Fig. 11b, the motion is in the vertical direction with an amplitude of 10 cm and a frequency of 3 Hz. The areas, i.e., Win and Wout , were found by integration, and the one-way gear unit’s conversion efficiency was observed using η = Win/ Wout .
3.1.3. Energy conversion of the one-way gear units
Pinput = Tr ·
Wout Win
⎟
(12)
(a) 5cm amplitude
(b) 10cm amplitude
Fig. 11. Input and output power curves of one-way gear units.
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mr ·D″·D′·r 2 + (J1 + J2 + J3 + J4 + + (Cr + Cm1 + 2Cm5 + Pinput =
z3 2 e z5
( ) C ) D′
z3 2 z5
The equivalent mass of the one-way gear units was
( ) (J + J )) D″·D′ 5
e
2
J1 + J2 + J3 + J4 + meq = mr +
(16)
r2
z3 2 z5
( ) (J + J ) 5
e
r2
(19)
Formula (17) was deduced based on formulas (15) and (16) as
mr ·D″·r 2 + ⎛J1 + J2 + J3 + J4 + ⎝ Cu =
( )
z3 2 z5
( ) (J + J ) ⎞⎠ D″ 5
e
3.1.6. Damping force simulation and analysis of the one-way gear units According to studies of the cable’s vibrational feature, most forms of motion harvested by the one-way gear units were a component motion of simple harmonic vibration, and they were also simple harmonic vibrations. Therefore, the simulation and analysis took sine wave vibrations as inputs to analyze and test the dynamic response of the one-way gear units. The variable D under the vibrational frequencies and amplitudes (2 Hz, 5 cm), (2 Hz, 10 cm), (2 Hz, 15 cm), and (4 Hz, 5 cm) ̇ were used for the simulation in Fig. 12a. The result of multiplying Dz2 z3 r 2 z1 z5 by the absolute value of variable D represents the revolving speed. See Fig. 12b. The damping force of the one-way gear units can be calculated in accordance with the formula (18) was simulated in the MATLAB programming environment, and the results are shown in Fig. 12c.
2
z + ⎛Cr + Cm1 + 2Cm5 + z3 Ce ⎞ D′ 5 ⎝ ⎠ D′·r 2
(17)
3.1.5. Damping force analysis of the one-way gear units The damping force of the one-way gear units was
mr ·D″·r 2 + ⎛J1 + J2 + J3 + J4 + ⎝ Fu = Cu·D′ =
+ ⎛Cr + Cm1 + 2Cm5 + ⎝
z3 2 z5
( ) (J + J ) ⎞⎠ D″ 5
e
2
( ) C ⎞⎠ D′ z3 z5
e
(18)
r2
(a) Rela ve displacement between gears and racks at different excita
(b) Revolving speed of the generator for conversion at different excita ons
(c) Damping force between gears and racks at different excitations Fig. 12. Dynamic response of the one-way gear units at different excitations.
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(a) One-way
(b) Right angle
(c) Y-shaped
(d) Four-way
Fig. 13. Four rack unit layouts.
Therefore, energy harvesting is largely concentrated at the position with a higher speed, or near the balance position. (2) The range of radial vibration of most cables is narrow relative to the circle in an actual condition, so the angle of the racks does not vary considerably. Since the cable was in simple harmonic vibration, the relative displacement D between the racks and gears can be deemed as approximately simple harmonic vibration.
3.2. Selection and analysis of the rack unit layout 3.2.1. Selection of the rack unit layout An appropriate rack unit layout was chosen by comparing the efficiency of several different gear-rack layouts according to the principle that fewer one-way gear units are used to achieve the maximum average energy harvested by the gear units. Considering the difficulty and cost of unit processing and fabrication, the minimum possible number of gear-rack units should be used. Four typical rack unit layouts are chosen herein, as shown in Fig. 13. The model using a single rack layout provides a low vibrational energy harvesting efficiency for the horizontal direction and a small inclination with respect to the horizontal direction; It is suitable for one-way vibrational energy harvesting but not for the condition of random cable vibration. When comparing between the right angle and four-way layouts, according to the principle of energy harvesting for the one-way gear units, the process of vibrational energy harvesting is symmetric on the two sides of the balance position when the cable vibration occurs. This symmetry occurs because the right-angle layout is on one side of the symmetric structure of the four-way layout; the vibrational energy harvested by the four-way layout is twice as much as that harvested by the right-angle layout when symmetric vibrations around the plate center occur. The four-way layout also has twice as many one-way gear units as the right-angle layout, and the one-way gear units can typically harvest the same amount of vibrational energy per unit. Comparison between the right-angle and Y-shaped layouts:
According to the above two arguments, the sum of squares of the component speeds of the racks at the balance position was selected to compare the efficiencies of the right-angle and Y-shaped layouts. The sum of squares of the component speeds of racks in the Yshaped
(V ·cos (
layout π 3
+θ
))
2
=
is
(
(V ·cos(0 + θ))2 + V ·cos
30° 45° 60°
L
L
( , y) L
90°
(0,0)
L R
( ,
)
( ,y )
R
2
+
1.5V 2 .
0° ( ,y )
π 3
The sum of squares of the component speeds of racks in the rightangle layout is (V ·cos(0 + θ))2 + (V ·sinθ)2 = V 2 . With the same vibration, energy harvested by the Y-shaped layout is 1.5 times that harvested by the right-angle layout; since the number of one-way gear units in the Y-shaped layout is 1.5 times that in the rightangle layout, the average energy harvested by the one-way gear units is identical. From the unit layout, the Y-shaped and right-angle layouts have the same energy harvesting efficiency. However, compared with the right-angle layout, the Y-shaped layout has better structural stability; thus, the Y-shaped rack unit was chosen as a result of this comprehensive consideration. The Y-shaped rack unit has a higher energy harvesting efficiency and better structural stability than traditional gears and racks. It converts the random cable vibrations into the relative motion of gears and racks and does not have an overly redundant structure. It also
(1) According to formula (13), the harvested energy is proportional to the square of the relative speed Ḋ between the gears and racks.
R
( −θ) )
120° (b) center of racks rotating: ( , y)
(a) center of racks rotating: (0,0)
Fig. 14. Motion schematic of a Y-shaped rack unit. 2456
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Rack 1
Rack 2
Rack 3
Fig. 15. Actual Y-shaped rack unit.
guarantees the efficiency and stability of the harvesting. A schematic of its motion is shown in Fig. 14, and a picture of the actual unit is shown in Fig. 15.
Fig. 16. Gear-rack balance mesh points.
(X1 , Y1) : coordinates of the center of the gear meshing with rack 1; (X2 , Y2) : coordinates of the center of the gear meshing with rack 2; (X3 , Y3) : coordinates of the center of the gear meshing with rack 3.
3.2.2. Rack unit motion analysis In a traditional energy harvesting device, the rack meshing with a gear moves up and down with only one degree of freedom; thus, only the energy of the component motion of the object in the vertical direction can be harvested when it vibrates in a direction inconsistent with that of rack motion. The displacement converted by a traditional vibrational energy harvesting device is
D = S·cosθ
In the context of MATLAB, 30°, 45°, 60°, and 90° are taken as the values of θ herein. Formulas (21)–(23) are used to simulate and obtain motion curves for conversion by the traditional device and the Y-shaped device and to analyze and compare the energy harvesting efficiencies of the two devices. Vibrational energy is harvested through its conversion into the meshed motion of gears and racks; thus, the traditional energy harvesting device and Y-shaped energy harvesting device are compared in terms of the motion of the mesh points of their gears and racks to visually reflect the conversion efficiency of the two devices. When the cable remained in a balanced state, the three racks of the Y-shaped device formed an angle of 120° with respect to each other, with the mesh points on the racks denoted as O at this point, as shown by the arrow positions in Fig. 16. Vibrations with simulative amplitude of 10 cm and θ values of 30°, 45°, 60°, and 90° were fed in, with point O as the origin of the Y axis in Fig. 17. The motion trails of the mesh points of the gears and racks of the traditional energy harvesting device were calculated using formula (21), as shown in Fig. 17-a, c, e and g, respectively. Those of the Y-shaped device relative to point O were calculated using formulas (21)–(23), as shown in Fig. 17b, d, f and h. L1, L2 and L3 in the figure are the displacements of the mesh points on racks 1, 2 and 3, respectively, in Fig. 15 relative to the balance point. For ease of comparison, motions symmetric with respect to the X axis are equivalent in terms of energy conversion because the one-way gear units can convert motions in the forward and reverse directions into motions in the same direction. To visually compare the two devices in terms of conversion efficiency, L1, L2 and L3 are superposed in the same direction every half cycle, and L4 , which reflects the motion trail of the mesh points of the equivalent gears and racks for conversion by the entire Yshaped device, is obtained.
(20)
S : vibration transmitted to the traditional vibrational energy harvesting device. θ : angle between the direction of movement and the vertical direction. In the Y-shaped energy harvesting device, the motion equation can be expressed as shown below when the direction of simple harmonic motion performed by the cable on the device plane has an inclination of θ with respect to the vertical direction, as shown in Fig. 14:
L1 = = L2 = =
L3 = =
(x −X1)2 + (y−Y1)2−r 2 −L (A·sint·sinθ−X1)2 + (A·sint·cosθ−Y1)2 −r 2 −L
(21)
(x −X2 )2 + (y−Y2)2−r 2 −L (A·sint·sinθ−X2 )2 + (A·sint·cosθ−Y2)2 −r 2 −L
(22)
(x −X3)2 + (y−Y3)2−r 2 −L (A·sint·sinθ−X3)2 + (A·sint·cosθ−Y3)2 −r 2 −L
L1: distance at which rack 1 deviates from the balance position; L2 : distance at which rack 2 deviates from the balance position; L3 : distance at which rack 3 deviates from the balance position; : distance from the mesh point to balance point balanced state of the rack; A : amplitude of the vibration.
(23) mesh point at the mesh point at the mesh point at the
3.2.3. Electric energy analysis and experimental details In the case of vibrations with an input amplitude of 15 cm, a frequency of 2 Hz and θ = 60°, the traditional layout and Y-shaped layout are compared in terms of energy harvesting efficiency, with the same
of the cable in the
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(a) The traditional device with θ =30°
(b) The Y-shaped device with θ =30°
(c) The traditional device with θ =45°
(d) The Y-shaped device with θ =45°
(f) The Y-shaped device with θ =60°
(e) The traditional device with θ = 60°
(g) The traditional device with θ =90°
(h) The Y-shaped device with θ =90°
Fig. 17. Comparison of the motion curves at the gear-rack mesh points for conversion by the traditional device and Y-shaped device.
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Table 1 Parameter values of the one-way gear units.
Table 2 Ratios of converted electric energy between the Y-shaped device and traditional energy harvesting device.
Parameter
Value
Unit
Parameter
Value
Unit
J1
0.94 × 10−4
kg m2
Ce
Nms/rad
J2
0.94 × 10−4
kg m2
mr
0.93 × 10−4 0.15
J3
0.18 × 10−4
kg m2
M
1
Z1
60
Z2 Z3 Z4
60
Z5
20
J4
0.18× 10−4
J5
0.12× 10−5
kg m2 Nms/rad
Cm1
0.75× 10−5
Nms/rad
Cm3
0.27 × 10−5
Nms/rad
Cr r
0.21 × 10−5
Nms/rad m
3× 10−2
kg
40
=
∫0
t
∫0
t
⎛Cr + Cm1 + 2Cm5 + + ⎝
(a) Tr
z3 2 e z5
( ) C ⎞⎠ (|L ′| r2
1
2
+ |L2′ |2 + |L3′ |2 ) ⎞ ⎟ dt ⎟ ⎟ ⎠
energy harves
45°
60°
90°
5 cm 10 cm 15 cm
2.04 1.99 1.91
3.06 3.02 2.96
6.13 6.08 6.15
+∞ +∞ +∞
z3 2 5 z5
30° (W)
45° (W)
60° (W)
90° (W)
5 cm 10 cm 15 cm
19.15 74.91 161.89
19.16 75.43 166.86
19.16 75.96 173.14
19.15 74.91 161.89
∫0
t
E (t )2 ηe dt = R
∫0
t
Re · R e + Ri
∫0
t
(
=
=
∫0
t
·
2
L1′ 2 r
L2′ 2 r
2
) dt L3′ 2 r
( ) ⎡⎣ ( ) + ( ) + ( ) ⎤⎦ dt
1.5· ke· z3 5
R e + Ri
z 2 1.5·R e ke· z3 5
( )
(R e + Ri
z dθ
1.5· ke· z3 dt2 Re 5 · R e + Ri R e + Ri z
)2
2
2
2
⎡ ⎛ L1′ ⎞ + ⎛ L2′ ⎞ + ⎛ L3′ ⎞ ⎤ dt ⎢ r ⎥ ⎝ r ⎠ ⎝ r ⎠⎦ ⎣⎝ ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(25)
The amount of electric energy converted by the Y-shaped device in a single cycle is shown in Table 3. The total efficiency of the Y-shaped device can be calculated in accordance with the formulas (14), (24), and (25). That of the traditional energy harvesting device can be calculated in accordance with the formulas (12), (13), (14). Based on the analysis above, calculations were performed using vibrations with amplitudes of 5, 10 and 15 cm, and θ values of 30°, 45°, 60°, and 90° simulated with MATLAB software. When θ is about 0°, the rack 1 can be considered as traditional device. The displacement of the rack 2 and the rack 3 are lower than that of the rack 1, then the electric energy harvesting efficiency of the Y-shaped device is lower than that of the traditional device with the same vibration. When θ varies from 0° to 45°, the Y-shaped device and traditional device have similar energy harvesting efficiencies. When θ varies from 45° to 90°, the Y-shaped device has a considerably higher electric energy harvesting efficiency than that of the traditional device. When θ is 90°, or when the cable is vibrating horizontally, the traditional device is unable to convert vibrational
( ) J + m ·r ⎞⎠ r
Amplitude
Wout =
Pinput dt ⎛ (|L1 |″ ·|L1 |′ + |L2 |″ ·|L2 |′ + |L3 |″ ·|L3 |′ ) ⎛J1 + J2 + J3 + J4 + ⎜ ⎝ ⎜ r2 ⎜ ⎝
30°
Table 3 Average electric power converted by the Y-shaped device.
40
one-way gear units used for motion conversion. In the context of MATLAB, the sizes of the members of the one-way gear-rack unit are assigned in Table 1, and the functional relation θ ̇ = |4Ḋ / (M·Z1)| between the angular speed of the generator and linear speed of the mesh points is used to simulate and obtain the curves of angular speed of the generator for final conversion by the traditional energy harvesting device and Y-shaped energy harvesting device, as shown in Fig. 18a and b, respectively. When direction of motion θ is equal to 60°, the motion directions of L1 and L3 are symmetric with respect to direction of the cable vibrations; thus, L1 coincides with L3 in Fig. 18b. Using MATLAB, vibrations with amplitudes of 5, 10 and 15 cm and θ values of 30°, 45°, 60°, and 90° were used as input to simulate and obtain the revolving speed curves of the generator. The energy conversion rate should be calculated by substituting the revolving speed of the generator as a dependent variable into formulas (24) and (25). Calculations yielded the ratios of converted electric energy between the Y-shaped device and traditional energy harvesting device, as shown in Table 2. Win =
Amplitude
2
(24)
device
(b) Y-shaped energy harves
de
Fig. 18. Comparison between the Y-shaped device and traditional energy harvesting device in terms of the angular speed of the generator rotary with θ = 60°. 2459
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(a) MTS test
(b) Prototype installation (Front)
(c) Prototype installation (Back)
(d) LM317
(e) External resistors
(f) Data capturing
Fig. 19. Bench tests of the proposed energy regenerative shock absorb.
′ of the Y-shaped The actual input power Pin′ and output power Pout energy harvesting device can be calculated according to formulas (26) and (27).
energy, and the ratio of the converted electric energy between the Yshaped device and the traditional device is +∞. The proposed device is better able to adapt to vibrational energy harvesting for a random cable direction. Fig. 19 shows the experimental setup for the bench test of the energy regenerative shock absorber. This test was implemented on a SANS CHT4305 material testing system from Mechanical Testing and Sensing (MTS), shown as Fig. 19a. The prototype of the proposed device was installed for the test in Fig. 19b and c. Fig. 19d shows the LM317 rectifying, smoothing, stabilizing unit which was connected to the generator. Next, three external resistors of R e = 100 Ω as shown in Fig. 19e were connected to three LM317 units respectively. Force and displacement were measured by the sensors integrated in the SANS CHT4305 testing system. The SANS PowerTest software shows the force and displacement information, and the voltage signals were recorded by the oscilloscope, shown as Fig. 19f.
Pin′ = f ·v
(26)
(U1 + U2 + U3)2 Re
′ = Pout
(27)
U1, U2, U3: measured voltages of 3 motors; f : force exerted by MTS; v : movement velocity of MTS actuator. As shown in Fig. 20a, b and c, the average values of U1, U2 and U3 is ′ ≈ 6.1 W≈ 6.1 N m/s . As 21 V, 10.0 V and 10.0 V respectively, thus Pout shown in Fig. 20c, the average values of f is 110 N, thus Pin′ = 11 N m/s .
U1 (V)
25.00
12.00
20.00
10.00
U2 (V)
8.00
15.00
6.00 10.00
4.00 2.00
t (s)
t (s) 0.80
0.90
0.60
0.70
0.50
0.40
0.30
0.10
0.20
0.00
0.00
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
1.00
5.00
(a) the measured voltage of motor 1
(b) the measured voltage of motor 2
12.00
150
U3 (V)
f (N)
10.00 8.00
100
6.00 50
t (s) 0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.00
(c) the measured voltage of motor 3
0.20
0
1.00
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.90
t (s)
0.00
0.10
2.00
(d) the force exerted by MTS
Fig. 20. Experiment data of the Y-shaped energy harvesting device. 2460
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4.00
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It can be inferred that the actual energy harvesting efficiency is
loads. Science 2005;309(5741):1725–8. [4] Mitcheson PD. Analysis and optimization of energy harvesting micro-generator systems PhD Thesis London: Imperial College London; 2005 [5] Anton SR, Sodano HA. A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 2007;16:R1–21. [6] Mitcheson PD, Miao P, Stark BH, et al. MEMS electrostatic micropower generator for low frequency operation. Sens Actuat, A 2004;115:523–9. [7] Owens BAM, Mann BP. Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting. J Sound Vib 2012;331(4):922–37. [8] Howells CA. Piezoelectric energy harvesting. Energy Convers Manage 2009;50(7):1847–50. [9] Rabinow J. The magnetic fluid clutch. Electr Eng 1948;67(12):1167. 1167-1167. [10] Erturk A. Electromechanical modeling of piezoelectric energy harvesters Dissertation of Ph. D Dept. of Engineering Mechanics, Virginia Polytechnic Institute and State University; 2009. [11] Priya S, Inman DJ. Energy harvesting technologies. New York: Springer; 2009. [12] Delnavaz A, Voix J. Electromagnetic micro-power generator for Energy harvesting from breathing. In: 38th annual conference on IEEE industrial electronics society (IECON 2012), Montreal, Canada; IEEE Industrial Electronics Society; 2012. p. 984–8. [13] Kulah H, Najafi K. Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sens J 2008;8(3):261–8. [14] Burrow SG, Clare LR. A resonant generator with non-linear compliance for energy harvesting in high vibration environments. In: IEEE International Electric-machine and Drives Conference, Antalya, Turkey; 2007. p. 715–20. [15] El-hami M, Glynne-Jones P, White NM, et al. Design and fabrication of a new vibration-based electromechanical power generator. Sens Actuat, A 2001;92(1):335–42. [16] Williams CB, Shearwood C, Harradine MA, et al. Development of an electromagnetic micro-generator. Proc Inst Elect Eng-Circuits Dev Syst 2001;148(6):337–42. [17] Marioli D, Sardini E, Serpelloni M. Electromagnetic generators employing planar inductors for autonomous sensor applications. Proc Chem 2009;1(1):469–72. [18] Li Z, Zuo L, Luhrs G, Lin L, Qin Y. Electromagnetic energy-harvesting shock absorbers: design, modeling and road tests. IEEE Trans Vehechnol 2013;62(3):1065–74. [19] Zhang Z, Zhang X, et al. Modeling and practical tests on a high-voltage kinetic energy harvesting (EH) system for a renewable road tunnel based on linear alternators. Appl Energy 2016;164:152–61. [20] Zhang Z, Zhang X, Chen W, et al. A high-efficiency energy regenerative shock absorber using supercapacitors for renewable energy applications in range extended electric vehicle. Appl Energy 2016;178:177–88. [21] Wu X, Li G, Lee D. A novel energy conversion method based on hydrogel material for self-powered sensor system applications. Appl Energy 2016;173:103–10. [22] Pourghodrat A. Energy harvesting systems design for railroad safety Master thesis University of Nebraska-Lincoln; 2011 [23] Palomera-Arias R, Connor JJ, Ochsendorf JA. Feasibility study of passive electromagnetic damping systems. J Struct Eng 2008;134:164–70. [24] Shen W, Zhu S, Xu Y. An experimental study on self-powered vibration control and monitoring system using electromagnetic TMD and wireless sensors. Sens Actuat, A 2012;180:166–76. [25] Tang X, Zuo L. Simultaneous energy harvesting and vibration control of structures with tuned mass dampers. J Intell Mater Syst Struct 2012;23(18):2117–27. [26] Zhu S, Shen W, Xu Y. Linear electromagnetic devices for vibration damping and energy harvesting: modeling and testing. Eng Struct 2012;34:198–212.
P′ η = out = 0.55 Pin′ 4. Conclusion This study presents an efficient electromagnetic energy harvesting device that stores electric energy converted from the vibrational energy of the cable. The proposed device uses a super-capacitor as a power supply to power equipment out of the reach of the power supply at the far end of the cableway. The proposed device consists of a mechanical transmission system and electric energy storage system. Due to the good adaptation to the uncertain motion direction of the cable, the Y-shaped layout can convert random vibrations on the plane of the Y-shaped mechanism into gear-rack meshed rotation. Then, the gear sets amplify vibrations from the meshed rotation and convert the two-way motion into one-way rotation through the one-way bearing, increasing the electric energy conversion efficiency. A super-capacitor was chosen for energy storage to respond to the rapidly changing transient current and to supply stable power to the external load. The device was initially evaluated via MATLAB simulation; its motion conversion efficiency was considerably higher than that of a traditional one-way energy harvesting device. This proved that the proposed electromagnetic energy harvesting system is effective and applicable in terms of acquiring renewable energy for a cableway’s far-end applications in mountainous areas. Acknowledgments Funded by National Natural Science Foundation of China (No. 51275431). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.apenergy.2018.07.059. References [1] Shen W, Zhu S. Harvesting energy via electromagnetic damper: application to bridge stay cables. J Intell Mater Syst Struct 2015;26(1):3–19. [2] Arnold DP. Review of microscale magnetic power generation. IEEE Trans Magn 2007;43:3940–51. [3] Rome LC, Flynn L, Goldman EM, Yoo TD. Generating electricity while walking with
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A new electromagnetic vibrational energy harvesting device for swaying cables
T
⁎
Haikun Wang, Chaoming He , Siyun Lv, Haoran Sun School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
H I GH L IG H T S
device changes cable’s multi-directional vibration into unidirectional rotation. • The motion and the converted electric energy of the Y-shaped device were analyzed. • The experiment data showed an average conversion rate of 55%. • The • The regenerative energy from vibrational absorber is stored in the supercapacitors.
A R T I C LE I N FO
A B S T R A C T
Keywords: Energy harvesting Cable vibration Electromagnetic Super-capacitor
An original vibrational energy harvesting device with regard to the vibrational performance of far-end cables was designed under the condition that no power can be supplied to the far end of freight cableways in transmission and distribution projects. The device was designed to have a Y-shaped radial gear-rack structure. The random vibrations of the cable are converted into three one-way rotary motions of a Y-shaped device terminal using a Y-shaped rack unit and one-way gear-rack units. The device then harvests the electric energy through a super-capacitor and supplies power to equipment in areas out of the reach of the power supply along the cableway. An analysis and dynamic simulation of the Y-shaped rack unit and one-way gear-rack units demonstrate that the Y-shaped layout of the device adapts well to the random vibration of the cable. The device was proven to have successfully harvested the vibrational energy of the cable in several directions on its radial plane, showing good prospects in supplying power to far-end wireless surveillance equipment for freight cableways in remote mountainous areas.
1. Introduction Cableways play an important role in power transmission and distribution project construction in remote mountainous areas. With long spans and high freight transport efficiency, cableways have incomparable superiority over other means of transport and greatly reduce manpower waste. Vibrations caused by unpredictable factors in the environment, such as wind force and landslides, affect the operating safety of freight cableways, which are usually erected in remote mountainous areas. To ensure the safety of the operating cableways, the far end of cableways for power transmission and distribution construction requires a power source to supply power to the surveillance equipment at the far end of the cableway, thus supporting cableway farend equipment safety monitoring. The erection of electric wires on a mountaintop is often extremely difficult, as such areas are often out of the reach of the power supply, making it impossible to use such ⁎
equipment as wireless sensors and wireless video monitors. The constant action of wind force and freight loading and transport on a cableway in an outdoor environment causes the entire cable to sway, and these potential vibrations are considerable sources of energy to harvest. Energy harvesting from ambient vibration is a desirable solution to the power supply associated with wireless sensors for remote areas [1]. The design of an efficient, low-cost energy harvesting device that can continually supply power is critical for supplying power to cableway surveillance equipment. Vibrational energy harvesters can be divided into three main categories depending on how they operate, namely, electromagnetic induction [2–4], piezoelectricity [5] and electrostatic generation [6,7]. Among the three vibrational energy harvesters devices, the piezoelectric energy harvester has the characteristics of small, simple, and high power density [8,9], while the electrostatic energy harvester has high power conversion efficiency [10], but its energy harvesting
Corresponding author. E-mail addresses: fl[email protected], [email protected] (C. He).
https://doi.org/10.1016/j.apenergy.2018.07.059 Received 18 March 2018; Received in revised form 2 July 2018; Accepted 14 July 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.
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structures [23]. Among the aforementioned mechanisms, electromagnetic induction is a promising one that can well serve vibration control and energy harvesting functions [24–26]. The results suggest that these novel systems have been intended for energy harvesting for remote areas applications but are nevertheless inadequate such as portability and durability. The aforementioned systems have been intended to design highly efficient, portable, reliable and simple facilities, but two main challenges remain with these technologies: (i) capturing arbitrary random vibrational energy efficiently and (ii) increasing the output power so that the system is suitable for cableway equipment that requires high power. Unlike conventional vibrations, the vibrations of a cable include both vibrations in the horizontal direction under the action of wind force and those in the vertical direction caused by freight handling and unsteady traction machine operation; coupling of the two kinds of motion creates vibrations that are multi-directional and random in motion. This paper presents a novel Y-shaped energy harvesting device that can convert the multi-directional random vibrations of a cable into the one-way rotary motion of the gears, thus driving the generator to produce electricity. A super-capacitor is chosen herein as a storage capacitor based on its various advantages, such as high power density, short charging/discharging time, long cycle life and wide operating temperature range, as well as its better adaptation to electric energy with sharply varying voltage and outdoor environments with large daily temperature swings.
process an external power supply is required to generate an electrostatic field, which is contrary to the purpose of constructing an autonomous power supply system. The electromagnetic induction energy harvester has the characteristics of high power generation efficiency and large power generation [11], so it is more suitable for harvest vibration energy to supply power to wireless devices, and realize selfsupply purposes of monitoring devices in remote mountainous areas. In this study, a portable and reliable electromagnetic vibrational energy harvesting device with supercapacitors for swaying cables is investigated. Electromagnetic energy harvesting technology uses the principle of electromagnetic induction to convert vibrational energy into electric energy. Electromagnetic vibrational energy harvesting devices can be divided into two types depending on their way of motion, namely, the linear type and the rotary type. Linear electromagnetic energy harvesting technology mainly causes variation in the magnetic flux through coils wrapped around the outside of the magnets via the linear motion of the magnets. Therefore, the closed coils generate induced current. Delnavaz et al. designed a linear electromagnetic vibrational energy harvesting device to harvest energy in the course of breathing. Under a simulation of human breathing, the energy harvesting efficiency reached a maximum when the magnets fixed at the ends of the conduit; the device provided an induced voltage output of 25 mV and an output power of 3.1 μW [12]. Rotary electromagnetic energy harvesting technology converts the energy by reciprocating the linear vibrational motion into rotary motion and accomplishes power generation through the rotation of the generator in the end. This technology is mainly used to harvest vibrational energy with a low vibrational frequency and large amplitude. The University of Michigan in the US designed an electromagnetic low-frequency vibrational energy harvesting device [13]. Using frequency amplifying technology, the device converted harvested low-frequency vibrational energy into high-frequency vibrational energy and then into electric energy. S. G. Burrow et al. designed a vibrational energy harvesting device using a flux concentrator [14]. In a structure designed by the University of Southampton in the UK, a pair of Nd-Fe-B permanent magnets were placed on a horseshoe-shaped iron core; vibrations of the cantilever caused a variation in the magnetic flux to accomplish energy harvesting [15]. The electromagnetic micro-generator made in 2001 at the University of Sheffield in the UK was only 25 mm3 in size; with an operating frequency of 4 MHz, the device could provide an output power of 0.3 μW [16]. In 2009, D. Marioli, E. Sardini et al. from the University of Brescia in Italy made a coil vibration-type electromagnetic vibrational energy harvesting device using the FR4 material and printed circuit board technique [17]. Zuo et al. designed a vibrational energy harvesting device for vehicles that converted the vibrations of a vehicle into electric energy and provided a maximum output power of 68 W [18]. Zhang Zutao et al. designed an energy harvesting device for highway speed bumps that converted the up-and-down vibrations of barrier lumps on a speed bump into the rotary motion of an AC motor and provided an output voltage of up to 194 V [19]. Zhang also designed an energy harvesting device applied to the damping system of an electric car [20]. In recent years, an increasing number of studies have focused on energy harvesting and alternative energies [21]. Several energy harvesting systems have been used to the power supply problem associated with autonomous sensors. Pourghodrat et al. designed an energy harvesting system for railroads by converting the kinetic energy of the track into electricity to provide an alternative power source for remote areas [22]. Wenai Shen and Songye Zhu propose a novel system, termed electromagnetic damper cum energy harvester to bridge stay cables which is employed to fulfill both vibration damping and energy harvesting functions [1]. Palomera-Arias et al. (2008) studied linear motion EMD for the vibration control of civil
2. System design The flowchart of energy conversion using the Y-shaped energy harvesting device is shown in Fig. 1. The process consists of 4 main modules: (1) the vibrational energy input module, (2) the transmission module, (3) the energy conversion module and (4) the energy storage module. As shown in Fig. 1, the cable generated random vibrations under the action of wind load, traction and other forces, which constituted the system’s vibrational energy input module. The transmission module takes a Y-shaped radial gear-rack structure and has three oneway gear units that are evenly distributed on the circle. The transmission module converts the random vibrations of the cable into the oneway rotary motion of the three one-way gear units. The energy conversion module converts one-way rotations into electric energy via the alternator. The energy storage module stores the generated electric energy in the super-capacitor to provide far-end wireless surveillance equipment with stable electric energy input. 2.1. Vibrational energy input module Fixed at both ends, the cable is considered to be approximate to a catenary structure for analysis. The vibrational energy of the cable mainly originates from two sources. The first source is the sway of the cable under the action of wind load in an actual condition, especially the sway of cable in the horizontal direction caused by the freight on the cableway under the impact of transverse wind force. The second source is the vibration of the cable in the vertical direction that results from the freight loading and unsteady near-end machine traction operation. Coupled vibrations from the two kinds of motion become the main source of vibrational energy to be harvested, as shown in Fig. 2. 2.2. Transmission module The transmission module, the core of the energy harvesting system, can be divided into two parts: (1) one-way gear units, as shown in Figs. 3–5, and (2) a Y-shaped rack unit, as shown in Fig. 6. The
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The vibrational energy input module
The energy storage module
Cable vibration
Unsteady traction
The energy conversion module
Uniform load Freight loading
Application
Energy harvesting unit
Wind power The transmission module
One‐way bearing AC motor unidirectional rotating
Close to unit
Gear counter‐ clockwise
One‐way bearing
Away from unit
Gear clockwise
Application: light sensor
Cable vibration
Super capacitor
Fig. 1. Flowchart of energy conversion using the proposed energy harvesting device.
Unsteady traction
Uniform load (caused by the weight of cable) Wind power Freight loading 4 Fig. 2. Input of vibrational energy.
When the cable approaches a one-way gear unit, the rack moves towards the upper left, and larger gear 2 and its connecting shaft rotate clockwise, while larger gear 1 and its connecting shaft rotate counterclockwise. Since the one-way bearing cannot transfer clockwise rotations, medium gear 4 rotates clockwise, thus transferring the torque. Medium gear 3 rotates clockwise, while the corresponding smaller gear 5 rotates counterclockwise, as shown in Fig. 4. When the cable departs from a one-way gear unit, the rack moves towards the lower right, and larger gear 2 and its connecting shaft rotate counterclockwise, while larger gear 1 and its connecting shaft rotate clockwise. Medium gear 3 rotates clockwise, transferring the torque. Medium gear 4 rotates clockwise, while the corresponding smaller gear 5 rotates counterclockwise, as shown in Fig. 5. The one-way bearing guarantees that the smaller gear always
transmission module comprising the Y-shaped rack unit and one-way gear units converts the random vibrations of the cable into one-way rotations. 2.2.1. One-way gear units A one-way gear unit is a gear set comprising larger gears 1 and 2, medium gears 3 and 4 and a smaller gear 5, as shown in Fig. 4. Larger gear 2, located on the front side of the circle, meshes with one side of the rack, and medium gears 3 and 4, located on the back side of the circle, mesh with the smaller gear 5. Medium gears 3 and 4 have a builtin one-way bearing, and the larger gears, shaft and inside track of the one-way bearing are fixed together so that they have the same rotary angular speed. Smaller gear 5 in the middle is coaxial with the generator.
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Fig. 3. One-way gear unit.
Fig. 5. Cable departs from a one-way gear unit.
meshed with the racks on three parallel planes, ensuring that the three sets did not interfere with each other when they moved, as shown in Fig. 7. 2.3. Energy conversion module Making use of generator’s electromagnetic effect, the energy conversion module converts mechanical energy from the rotations of the gears into electric energy. There are three main kinds of commercially available generators: (1) AC induction motors, (2) DC brush motors and (3) DC brushless motors. DC brush motors have a short service life, as their carbon brush and commutator produce sparks and carbon dust, which are liable to cause damage to their parts when they rotate. DC brushless motors are liable to generate resonance, as there is a slight vibration when they are started at a low speed. An AC induction motor was chosen, as it is inexpensive and has a long service life; the output at a stabilized DC voltage can be achieved by alteration with an attached circuit. Fig. 4. Cable approaches a one-way gear unit.
2.4. Energy storage module maintains one-way counterclockwise rotation and finally drives the generator to run.
The vibrational energy input to the system is uncertain; vibrations may be violent if the wind load is heavy, and the voltage generated by vibration varies sharply as well. The voltage generated by the generator cannot be directly stored up, and its harvesting cannot be fulfilled until it is turned into a DC steady-state after rectification, smoothing and stabilization. Among them, the stabilizing circuit is a constant-voltage and limited-current charging circuit based on an LM317 three-terminal
2.2.2. Y-shaped rack unit The Y-shaped rack unit is shown in Fig. 6. The cable was installed to be perpendicular to the circle’s plane and pass through the circle center; the three one-way gear units were evenly distributed at an angle of 120° on the same periphery of the circle. The three sets of one-way gear units
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Fig. 6. Y-shaped rack unit.
Fig. 7. Parallel arrangement of three one-way gear units.
well to such a voltage; in addition, the capacitor has various advantages, such as a high power density, short charging/discharging time and long cycle life. The real LM317-based rectifying, smoothing, and stabilizing circuit is shown in Fig. 9.
regulator. The circuit diagram is shown in Fig. 8. A super-capacitor was chosen as the power storage capacitor, as shown in Fig. 8, because the voltage still fluctuated, although it varied less after rectification, smoothing and stabilization, and the super-capacitor can adapt very
Fig. 8. LM317-based rectifying, smoothing, stabilizing circuit. 2452
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The rotational inertia of a continuous body rotating around a specified axis can be obtained by taking the integral of the density and the radius squared with respect to volume; i.e.,
∫V ρ(r ) r 2dV
J=
(2)
ρ : density of the shafts and gears, which is a function of the radius r of the shafts and gears; V : volume of the shafts and gears. (2) Calculation of the electromagnetic damping of the generator The generator used herein was a three-phase alternator. The alternating current generated by the alternator was turned into direct current after rectification. The alternator generated a three-phase alternating voltage. There was a 120° difference between each of the phases. Fig. 9. Real LM317-based rectifying, smoothing, stabilizing circuit.
PE = Poutput + Plost =
e32 1.5 × Em2 e12 e22 + + = R e + Ri R e + Ri R e + Ri R e + Ri
(3)
Em = ke·ωg
(4)
Ce·ωg2
(5)
PE =
PE : power of the alternator; Poutput : electric power of the external load; Plost : electric power consumed by the internal resistance of the threephase winding of the alternator; e1, e2, e3 :voltage of the phases of the three-phase alternator; R e : controllable external resistor; Ri : internal resistance of each phase of the generator; Em : voltage magnitude of the phases; ke : constant of proportionality between the voltage generated by the alternator and its rotational speed; ωg : rotary angular speed of the alternator; Ce : electromagnetic damping of the alternator.
Fig. 10. Structural schematic of a one-way gear unit.
The following can be deduced from formulas (3)–(5): 3. Modeling analysis
Ce = 3.1. One-way gear unit analysis
1.5 × ke2 R e + Ri
(6)
When the vibration of the cable drove the gears and racks to move relatively, a one-way gear unit ran. A schematic of the system is shown in Fig. 10.
3.1.2. Input torque of one-way gear units When cable approaches a one-way gear unit, the meshing transmission path is gear 2- > 1-3- > 5,
3.1.1. Calculation of the damping for parts of one-way gear units
Tr =
(J1 + J2 + J3 + J4 )d2θ2 (t ) z dθ (t ) + ⎛Cr + Cm1 + 2 5 Cm5 ⎞ 2 + T3 dt 2 z 2 ⎝ ⎠ dt ⎜
(7)
(1) Calculation of the mesh damping of the gears The mesh damping between gears p and q can be obtained from
Cm = 2ξ
Tr : equivalent torque exerted by the rack on larger gear 2, the value of which is the product of the acting force Fr between the rack and the larger gear and the radius of larger gear 2; Ji : rotary inertia of gear i, i = 1, 2, 3, 4; θ2 : rotation angle of gear 2; Cr : mesh damping between the rack and gear 2; z5, z2 : number of teeth on gears 5 and 2; Cm1: mesh damping between gears 1 and 2; Cm5 : mesh damping between gears 3 and 5; T3 : torque that acts on gear 3.
kg rp rq Jp Jq rp2 Jp + rq2 Jq
⎟
(1)
ξ : damping ratio which ranges from 0.03 to 0.17, with 0.1 taken as its value herein; kg : mean value of the stiffness in the corresponding meshing pair p and q ; rp, rq : radius of the mesh gears p and q ; : rotary inertia of the mesh gears p and q .
T5 = (J5 + Je )
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⎧ T3 = ⎨ θ5 = ⎩
z3 T z5 5 z3 θ z5 3
Win : mechanical energy input to the energy harvesting unit; r : radius of the reference circle of gear 2; D : displacement of contact point of gear 2 and rack.
(9)
Wout =
T5 : torque that acts on gear 5; J5 : rotary inertia of gear 5; Je : rotary inertia of the rotor of the alternator; θ3, θ5 : rotation angle of gears 3 and 5; z 3 : number of teeth on gears 3.
=
∫0
t
∫0
t
Poutput dt =
∫0
(
t
E (t )2 ηe dt = R z dθ
3 2 R e 1.5 ke z5 dt R e + Ri R e + Ri
∫0
t
2
) dt = ∫ 0
t
(
dθ
)
(
z D′
2
5 R e 1.5 ke dt dt R e + Ri R e + Ri 3 R e 1.5 ke z5 r R e + Ri R e + Ri
2
) dt (13)
2
z d 2θ2 (t ) Tr = ⎜⎛J1 + J2 + J3 + J4 + ⎛ 3 ⎞ ·(J5 + Je ) ⎞⎟ 2 z 5 ⎝ ⎠ ⎝ ⎠ dt ⎜
+ ⎜⎛Cr + Cm1 + 2Cm5 + ⎝
⎟
Wout : electric energy output from the energy harvesting unit; ηe : electrical efficiency; E (t ) : output electromotive force; R : total resistance of the generator.
2
⎛ z 3 ⎞ ·Ce ⎞⎟ dθ2 (t ) ⎝ z5 ⎠ ⎠ dt ⎜
⎟
(10)
Formula (10) can be deduced from formulas (7)–(9), and then, the units can be analyzed as a whole. When cable departs from a one-way gear unit, the meshing transmission path is gear 2-4- > 5. Due to the symmetry of structure, the equivalent torque exerted by the rack on larger gear 2 is equal to Tr .
The total efficiency of the one-way gear unit is obtained as follows:
η=
dθ2 (t ) d 2θ2 (t ) dθ2 (t ) 2 + mr · · ·r dt dt 2 dt
(11)
Pinput : power of input energy to the one-way gear units; mr : mass of the rack; r : radius of reference circle of gear 2. Win =
∫0
t
Pinput dt =
∫0
t
2
2 ⎛⎛ ⎞ d θ2 (t ) ⎛ z3 ⎞ ⎜ ⎜J1 + J2 + J3 + J4 + z 5 (J5 + Je ) ⎟ dt 2 ⎝ ⎠ ⎠ ⎝⎝ ⎜
⎟
3.1.4. Equivalent damping analysis of the one-way gear units
2
z dθ (t ) d 2θ2 (t ) 2⎞ dθ2 (t ) + ⎛⎜Cr + Cm1 + 2Cm5 + ⎛ 3 ⎞ Ce ⎞⎟ 2 r ⎟ dt + mr z dt dt 2 dt ⎝ 5⎠ ⎠ ⎝ ⎠ ⎜
=
∫0
t
Pinput = Cu·D′ 2
⎟
z3 2 ⎛⎛ ⎞ D″ ⎜ J1 + J2 + J3 + J4 + ( z 5 ) (J5 + Je ) r ⎝ ⎠ ⎝ ⎜
+ ⎛⎜Cr + Cm1 + 2Cm5 + ⎝
2
⎛ z 3 ⎞ Ce ⎞⎟ D′ + mr D″ r 2⎞ D′ dt r ⎟ r ⎝ z5 ⎠ ⎠ r ⎠
(15)
Cu : damping of the one-way gear unit. Cu denotes the overall damping of the one-way gear units, i.e., their damping to the cable. Pinput denotes the power of energy transferred by the cable to the one-way gear units.
⎟
⎜
(14)
Formulas (12) and (13) show that the independent variable D of Pinput (D) and Poutput (D) is the relative displacement between the gears and racks. Pinput and Poutput curves were obtained using MATLAB analog variable D and the functional relation between formulas (12) and (13) and D . Fig. 11a and b show two sets of Pinput and Poutput curves with simulation amplitudes of 5 cm and 10 cm, respectively, and a frequency of 3 Hz. Pinput is shown in red, and Poutput is shown in blue. The input in Fig. 11a is motion in the vertical direction with an amplitude of 5 cm and a frequency of 3 Hz. In Fig. 11b, the motion is in the vertical direction with an amplitude of 10 cm and a frequency of 3 Hz. The areas, i.e., Win and Wout , were found by integration, and the one-way gear unit’s conversion efficiency was observed using η = Win/ Wout .
3.1.3. Energy conversion of the one-way gear units
Pinput = Tr ·
Wout Win
⎟
(12)
(a) 5cm amplitude
(b) 10cm amplitude
Fig. 11. Input and output power curves of one-way gear units.
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mr ·D″·D′·r 2 + (J1 + J2 + J3 + J4 + + (Cr + Cm1 + 2Cm5 + Pinput =
z3 2 e z5
( ) C ) D′
z3 2 z5
The equivalent mass of the one-way gear units was
( ) (J + J )) D″·D′ 5
e
2
J1 + J2 + J3 + J4 + meq = mr +
(16)
r2
z3 2 z5
( ) (J + J ) 5
e
r2
(19)
Formula (17) was deduced based on formulas (15) and (16) as
mr ·D″·r 2 + ⎛J1 + J2 + J3 + J4 + ⎝ Cu =
( )
z3 2 z5
( ) (J + J ) ⎞⎠ D″ 5
e
3.1.6. Damping force simulation and analysis of the one-way gear units According to studies of the cable’s vibrational feature, most forms of motion harvested by the one-way gear units were a component motion of simple harmonic vibration, and they were also simple harmonic vibrations. Therefore, the simulation and analysis took sine wave vibrations as inputs to analyze and test the dynamic response of the one-way gear units. The variable D under the vibrational frequencies and amplitudes (2 Hz, 5 cm), (2 Hz, 10 cm), (2 Hz, 15 cm), and (4 Hz, 5 cm) ̇ were used for the simulation in Fig. 12a. The result of multiplying Dz2 z3 r 2 z1 z5 by the absolute value of variable D represents the revolving speed. See Fig. 12b. The damping force of the one-way gear units can be calculated in accordance with the formula (18) was simulated in the MATLAB programming environment, and the results are shown in Fig. 12c.
2
z + ⎛Cr + Cm1 + 2Cm5 + z3 Ce ⎞ D′ 5 ⎝ ⎠ D′·r 2
(17)
3.1.5. Damping force analysis of the one-way gear units The damping force of the one-way gear units was
mr ·D″·r 2 + ⎛J1 + J2 + J3 + J4 + ⎝ Fu = Cu·D′ =
+ ⎛Cr + Cm1 + 2Cm5 + ⎝
z3 2 z5
( ) (J + J ) ⎞⎠ D″ 5
e
2
( ) C ⎞⎠ D′ z3 z5
e
(18)
r2
(a) Rela ve displacement between gears and racks at different excita
(b) Revolving speed of the generator for conversion at different excita ons
(c) Damping force between gears and racks at different excitations Fig. 12. Dynamic response of the one-way gear units at different excitations.
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(a) One-way
(b) Right angle
(c) Y-shaped
(d) Four-way
Fig. 13. Four rack unit layouts.
Therefore, energy harvesting is largely concentrated at the position with a higher speed, or near the balance position. (2) The range of radial vibration of most cables is narrow relative to the circle in an actual condition, so the angle of the racks does not vary considerably. Since the cable was in simple harmonic vibration, the relative displacement D between the racks and gears can be deemed as approximately simple harmonic vibration.
3.2. Selection and analysis of the rack unit layout 3.2.1. Selection of the rack unit layout An appropriate rack unit layout was chosen by comparing the efficiency of several different gear-rack layouts according to the principle that fewer one-way gear units are used to achieve the maximum average energy harvested by the gear units. Considering the difficulty and cost of unit processing and fabrication, the minimum possible number of gear-rack units should be used. Four typical rack unit layouts are chosen herein, as shown in Fig. 13. The model using a single rack layout provides a low vibrational energy harvesting efficiency for the horizontal direction and a small inclination with respect to the horizontal direction; It is suitable for one-way vibrational energy harvesting but not for the condition of random cable vibration. When comparing between the right angle and four-way layouts, according to the principle of energy harvesting for the one-way gear units, the process of vibrational energy harvesting is symmetric on the two sides of the balance position when the cable vibration occurs. This symmetry occurs because the right-angle layout is on one side of the symmetric structure of the four-way layout; the vibrational energy harvested by the four-way layout is twice as much as that harvested by the right-angle layout when symmetric vibrations around the plate center occur. The four-way layout also has twice as many one-way gear units as the right-angle layout, and the one-way gear units can typically harvest the same amount of vibrational energy per unit. Comparison between the right-angle and Y-shaped layouts:
According to the above two arguments, the sum of squares of the component speeds of the racks at the balance position was selected to compare the efficiencies of the right-angle and Y-shaped layouts. The sum of squares of the component speeds of racks in the Yshaped
(V ·cos (
layout π 3
+θ
))
2
=
is
(
(V ·cos(0 + θ))2 + V ·cos
30° 45° 60°
L
L
( , y) L
90°
(0,0)
L R
( ,
)
( ,y )
R
2
+
1.5V 2 .
0° ( ,y )
π 3
The sum of squares of the component speeds of racks in the rightangle layout is (V ·cos(0 + θ))2 + (V ·sinθ)2 = V 2 . With the same vibration, energy harvested by the Y-shaped layout is 1.5 times that harvested by the right-angle layout; since the number of one-way gear units in the Y-shaped layout is 1.5 times that in the rightangle layout, the average energy harvested by the one-way gear units is identical. From the unit layout, the Y-shaped and right-angle layouts have the same energy harvesting efficiency. However, compared with the right-angle layout, the Y-shaped layout has better structural stability; thus, the Y-shaped rack unit was chosen as a result of this comprehensive consideration. The Y-shaped rack unit has a higher energy harvesting efficiency and better structural stability than traditional gears and racks. It converts the random cable vibrations into the relative motion of gears and racks and does not have an overly redundant structure. It also
(1) According to formula (13), the harvested energy is proportional to the square of the relative speed Ḋ between the gears and racks.
R
( −θ) )
120° (b) center of racks rotating: ( , y)
(a) center of racks rotating: (0,0)
Fig. 14. Motion schematic of a Y-shaped rack unit. 2456
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Rack 1
Rack 2
Rack 3
Fig. 15. Actual Y-shaped rack unit.
guarantees the efficiency and stability of the harvesting. A schematic of its motion is shown in Fig. 14, and a picture of the actual unit is shown in Fig. 15.
Fig. 16. Gear-rack balance mesh points.
(X1 , Y1) : coordinates of the center of the gear meshing with rack 1; (X2 , Y2) : coordinates of the center of the gear meshing with rack 2; (X3 , Y3) : coordinates of the center of the gear meshing with rack 3.
3.2.2. Rack unit motion analysis In a traditional energy harvesting device, the rack meshing with a gear moves up and down with only one degree of freedom; thus, only the energy of the component motion of the object in the vertical direction can be harvested when it vibrates in a direction inconsistent with that of rack motion. The displacement converted by a traditional vibrational energy harvesting device is
D = S·cosθ
In the context of MATLAB, 30°, 45°, 60°, and 90° are taken as the values of θ herein. Formulas (21)–(23) are used to simulate and obtain motion curves for conversion by the traditional device and the Y-shaped device and to analyze and compare the energy harvesting efficiencies of the two devices. Vibrational energy is harvested through its conversion into the meshed motion of gears and racks; thus, the traditional energy harvesting device and Y-shaped energy harvesting device are compared in terms of the motion of the mesh points of their gears and racks to visually reflect the conversion efficiency of the two devices. When the cable remained in a balanced state, the three racks of the Y-shaped device formed an angle of 120° with respect to each other, with the mesh points on the racks denoted as O at this point, as shown by the arrow positions in Fig. 16. Vibrations with simulative amplitude of 10 cm and θ values of 30°, 45°, 60°, and 90° were fed in, with point O as the origin of the Y axis in Fig. 17. The motion trails of the mesh points of the gears and racks of the traditional energy harvesting device were calculated using formula (21), as shown in Fig. 17-a, c, e and g, respectively. Those of the Y-shaped device relative to point O were calculated using formulas (21)–(23), as shown in Fig. 17b, d, f and h. L1, L2 and L3 in the figure are the displacements of the mesh points on racks 1, 2 and 3, respectively, in Fig. 15 relative to the balance point. For ease of comparison, motions symmetric with respect to the X axis are equivalent in terms of energy conversion because the one-way gear units can convert motions in the forward and reverse directions into motions in the same direction. To visually compare the two devices in terms of conversion efficiency, L1, L2 and L3 are superposed in the same direction every half cycle, and L4 , which reflects the motion trail of the mesh points of the equivalent gears and racks for conversion by the entire Yshaped device, is obtained.
(20)
S : vibration transmitted to the traditional vibrational energy harvesting device. θ : angle between the direction of movement and the vertical direction. In the Y-shaped energy harvesting device, the motion equation can be expressed as shown below when the direction of simple harmonic motion performed by the cable on the device plane has an inclination of θ with respect to the vertical direction, as shown in Fig. 14:
L1 = = L2 = =
L3 = =
(x −X1)2 + (y−Y1)2−r 2 −L (A·sint·sinθ−X1)2 + (A·sint·cosθ−Y1)2 −r 2 −L
(21)
(x −X2 )2 + (y−Y2)2−r 2 −L (A·sint·sinθ−X2 )2 + (A·sint·cosθ−Y2)2 −r 2 −L
(22)
(x −X3)2 + (y−Y3)2−r 2 −L (A·sint·sinθ−X3)2 + (A·sint·cosθ−Y3)2 −r 2 −L
L1: distance at which rack 1 deviates from the balance position; L2 : distance at which rack 2 deviates from the balance position; L3 : distance at which rack 3 deviates from the balance position; : distance from the mesh point to balance point balanced state of the rack; A : amplitude of the vibration.
(23) mesh point at the mesh point at the mesh point at the
3.2.3. Electric energy analysis and experimental details In the case of vibrations with an input amplitude of 15 cm, a frequency of 2 Hz and θ = 60°, the traditional layout and Y-shaped layout are compared in terms of energy harvesting efficiency, with the same
of the cable in the
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(a) The traditional device with θ =30°
(b) The Y-shaped device with θ =30°
(c) The traditional device with θ =45°
(d) The Y-shaped device with θ =45°
(f) The Y-shaped device with θ =60°
(e) The traditional device with θ = 60°
(g) The traditional device with θ =90°
(h) The Y-shaped device with θ =90°
Fig. 17. Comparison of the motion curves at the gear-rack mesh points for conversion by the traditional device and Y-shaped device.
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Table 1 Parameter values of the one-way gear units.
Table 2 Ratios of converted electric energy between the Y-shaped device and traditional energy harvesting device.
Parameter
Value
Unit
Parameter
Value
Unit
J1
0.94 × 10−4
kg m2
Ce
Nms/rad
J2
0.94 × 10−4
kg m2
mr
0.93 × 10−4 0.15
J3
0.18 × 10−4
kg m2
M
1
Z1
60
Z2 Z3 Z4
60
Z5
20
J4
0.18× 10−4
J5
0.12× 10−5
kg m2 Nms/rad
Cm1
0.75× 10−5
Nms/rad
Cm3
0.27 × 10−5
Nms/rad
Cr r
0.21 × 10−5
Nms/rad m
3× 10−2
kg
40
=
∫0
t
∫0
t
⎛Cr + Cm1 + 2Cm5 + + ⎝
(a) Tr
z3 2 e z5
( ) C ⎞⎠ (|L ′| r2
1
2
+ |L2′ |2 + |L3′ |2 ) ⎞ ⎟ dt ⎟ ⎟ ⎠
energy harves
45°
60°
90°
5 cm 10 cm 15 cm
2.04 1.99 1.91
3.06 3.02 2.96
6.13 6.08 6.15
+∞ +∞ +∞
z3 2 5 z5
30° (W)
45° (W)
60° (W)
90° (W)
5 cm 10 cm 15 cm
19.15 74.91 161.89
19.16 75.43 166.86
19.16 75.96 173.14
19.15 74.91 161.89
∫0
t
E (t )2 ηe dt = R
∫0
t
Re · R e + Ri
∫0
t
(
=
=
∫0
t
·
2
L1′ 2 r
L2′ 2 r
2
) dt L3′ 2 r
( ) ⎡⎣ ( ) + ( ) + ( ) ⎤⎦ dt
1.5· ke· z3 5
R e + Ri
z 2 1.5·R e ke· z3 5
( )
(R e + Ri
z dθ
1.5· ke· z3 dt2 Re 5 · R e + Ri R e + Ri z
)2
2
2
2
⎡ ⎛ L1′ ⎞ + ⎛ L2′ ⎞ + ⎛ L3′ ⎞ ⎤ dt ⎢ r ⎥ ⎝ r ⎠ ⎝ r ⎠⎦ ⎣⎝ ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(25)
The amount of electric energy converted by the Y-shaped device in a single cycle is shown in Table 3. The total efficiency of the Y-shaped device can be calculated in accordance with the formulas (14), (24), and (25). That of the traditional energy harvesting device can be calculated in accordance with the formulas (12), (13), (14). Based on the analysis above, calculations were performed using vibrations with amplitudes of 5, 10 and 15 cm, and θ values of 30°, 45°, 60°, and 90° simulated with MATLAB software. When θ is about 0°, the rack 1 can be considered as traditional device. The displacement of the rack 2 and the rack 3 are lower than that of the rack 1, then the electric energy harvesting efficiency of the Y-shaped device is lower than that of the traditional device with the same vibration. When θ varies from 0° to 45°, the Y-shaped device and traditional device have similar energy harvesting efficiencies. When θ varies from 45° to 90°, the Y-shaped device has a considerably higher electric energy harvesting efficiency than that of the traditional device. When θ is 90°, or when the cable is vibrating horizontally, the traditional device is unable to convert vibrational
( ) J + m ·r ⎞⎠ r
Amplitude
Wout =
Pinput dt ⎛ (|L1 |″ ·|L1 |′ + |L2 |″ ·|L2 |′ + |L3 |″ ·|L3 |′ ) ⎛J1 + J2 + J3 + J4 + ⎜ ⎝ ⎜ r2 ⎜ ⎝
30°
Table 3 Average electric power converted by the Y-shaped device.
40
one-way gear units used for motion conversion. In the context of MATLAB, the sizes of the members of the one-way gear-rack unit are assigned in Table 1, and the functional relation θ ̇ = |4Ḋ / (M·Z1)| between the angular speed of the generator and linear speed of the mesh points is used to simulate and obtain the curves of angular speed of the generator for final conversion by the traditional energy harvesting device and Y-shaped energy harvesting device, as shown in Fig. 18a and b, respectively. When direction of motion θ is equal to 60°, the motion directions of L1 and L3 are symmetric with respect to direction of the cable vibrations; thus, L1 coincides with L3 in Fig. 18b. Using MATLAB, vibrations with amplitudes of 5, 10 and 15 cm and θ values of 30°, 45°, 60°, and 90° were used as input to simulate and obtain the revolving speed curves of the generator. The energy conversion rate should be calculated by substituting the revolving speed of the generator as a dependent variable into formulas (24) and (25). Calculations yielded the ratios of converted electric energy between the Y-shaped device and traditional energy harvesting device, as shown in Table 2. Win =
Amplitude
2
(24)
device
(b) Y-shaped energy harves
de
Fig. 18. Comparison between the Y-shaped device and traditional energy harvesting device in terms of the angular speed of the generator rotary with θ = 60°. 2459
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(a) MTS test
(b) Prototype installation (Front)
(c) Prototype installation (Back)
(d) LM317
(e) External resistors
(f) Data capturing
Fig. 19. Bench tests of the proposed energy regenerative shock absorb.
′ of the Y-shaped The actual input power Pin′ and output power Pout energy harvesting device can be calculated according to formulas (26) and (27).
energy, and the ratio of the converted electric energy between the Yshaped device and the traditional device is +∞. The proposed device is better able to adapt to vibrational energy harvesting for a random cable direction. Fig. 19 shows the experimental setup for the bench test of the energy regenerative shock absorber. This test was implemented on a SANS CHT4305 material testing system from Mechanical Testing and Sensing (MTS), shown as Fig. 19a. The prototype of the proposed device was installed for the test in Fig. 19b and c. Fig. 19d shows the LM317 rectifying, smoothing, stabilizing unit which was connected to the generator. Next, three external resistors of R e = 100 Ω as shown in Fig. 19e were connected to three LM317 units respectively. Force and displacement were measured by the sensors integrated in the SANS CHT4305 testing system. The SANS PowerTest software shows the force and displacement information, and the voltage signals were recorded by the oscilloscope, shown as Fig. 19f.
Pin′ = f ·v
(26)
(U1 + U2 + U3)2 Re
′ = Pout
(27)
U1, U2, U3: measured voltages of 3 motors; f : force exerted by MTS; v : movement velocity of MTS actuator. As shown in Fig. 20a, b and c, the average values of U1, U2 and U3 is ′ ≈ 6.1 W≈ 6.1 N m/s . As 21 V, 10.0 V and 10.0 V respectively, thus Pout shown in Fig. 20c, the average values of f is 110 N, thus Pin′ = 11 N m/s .
U1 (V)
25.00
12.00
20.00
10.00
U2 (V)
8.00
15.00
6.00 10.00
4.00 2.00
t (s)
t (s) 0.80
0.90
0.60
0.70
0.50
0.40
0.30
0.10
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It can be inferred that the actual energy harvesting efficiency is
loads. Science 2005;309(5741):1725–8. [4] Mitcheson PD. Analysis and optimization of energy harvesting micro-generator systems PhD Thesis London: Imperial College London; 2005 [5] Anton SR, Sodano HA. A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 2007;16:R1–21. [6] Mitcheson PD, Miao P, Stark BH, et al. MEMS electrostatic micropower generator for low frequency operation. Sens Actuat, A 2004;115:523–9. [7] Owens BAM, Mann BP. Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting. J Sound Vib 2012;331(4):922–37. [8] Howells CA. Piezoelectric energy harvesting. Energy Convers Manage 2009;50(7):1847–50. [9] Rabinow J. The magnetic fluid clutch. Electr Eng 1948;67(12):1167. 1167-1167. [10] Erturk A. Electromechanical modeling of piezoelectric energy harvesters Dissertation of Ph. D Dept. of Engineering Mechanics, Virginia Polytechnic Institute and State University; 2009. [11] Priya S, Inman DJ. Energy harvesting technologies. New York: Springer; 2009. [12] Delnavaz A, Voix J. Electromagnetic micro-power generator for Energy harvesting from breathing. In: 38th annual conference on IEEE industrial electronics society (IECON 2012), Montreal, Canada; IEEE Industrial Electronics Society; 2012. p. 984–8. [13] Kulah H, Najafi K. Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sens J 2008;8(3):261–8. [14] Burrow SG, Clare LR. A resonant generator with non-linear compliance for energy harvesting in high vibration environments. In: IEEE International Electric-machine and Drives Conference, Antalya, Turkey; 2007. p. 715–20. [15] El-hami M, Glynne-Jones P, White NM, et al. Design and fabrication of a new vibration-based electromechanical power generator. Sens Actuat, A 2001;92(1):335–42. [16] Williams CB, Shearwood C, Harradine MA, et al. Development of an electromagnetic micro-generator. Proc Inst Elect Eng-Circuits Dev Syst 2001;148(6):337–42. [17] Marioli D, Sardini E, Serpelloni M. Electromagnetic generators employing planar inductors for autonomous sensor applications. Proc Chem 2009;1(1):469–72. [18] Li Z, Zuo L, Luhrs G, Lin L, Qin Y. Electromagnetic energy-harvesting shock absorbers: design, modeling and road tests. IEEE Trans Vehechnol 2013;62(3):1065–74. [19] Zhang Z, Zhang X, et al. Modeling and practical tests on a high-voltage kinetic energy harvesting (EH) system for a renewable road tunnel based on linear alternators. Appl Energy 2016;164:152–61. [20] Zhang Z, Zhang X, Chen W, et al. A high-efficiency energy regenerative shock absorber using supercapacitors for renewable energy applications in range extended electric vehicle. Appl Energy 2016;178:177–88. [21] Wu X, Li G, Lee D. A novel energy conversion method based on hydrogel material for self-powered sensor system applications. Appl Energy 2016;173:103–10. [22] Pourghodrat A. Energy harvesting systems design for railroad safety Master thesis University of Nebraska-Lincoln; 2011 [23] Palomera-Arias R, Connor JJ, Ochsendorf JA. Feasibility study of passive electromagnetic damping systems. J Struct Eng 2008;134:164–70. [24] Shen W, Zhu S, Xu Y. An experimental study on self-powered vibration control and monitoring system using electromagnetic TMD and wireless sensors. Sens Actuat, A 2012;180:166–76. [25] Tang X, Zuo L. Simultaneous energy harvesting and vibration control of structures with tuned mass dampers. J Intell Mater Syst Struct 2012;23(18):2117–27. [26] Zhu S, Shen W, Xu Y. Linear electromagnetic devices for vibration damping and energy harvesting: modeling and testing. Eng Struct 2012;34:198–212.
P′ η = out = 0.55 Pin′ 4. Conclusion This study presents an efficient electromagnetic energy harvesting device that stores electric energy converted from the vibrational energy of the cable. The proposed device uses a super-capacitor as a power supply to power equipment out of the reach of the power supply at the far end of the cableway. The proposed device consists of a mechanical transmission system and electric energy storage system. Due to the good adaptation to the uncertain motion direction of the cable, the Y-shaped layout can convert random vibrations on the plane of the Y-shaped mechanism into gear-rack meshed rotation. Then, the gear sets amplify vibrations from the meshed rotation and convert the two-way motion into one-way rotation through the one-way bearing, increasing the electric energy conversion efficiency. A super-capacitor was chosen for energy storage to respond to the rapidly changing transient current and to supply stable power to the external load. The device was initially evaluated via MATLAB simulation; its motion conversion efficiency was considerably higher than that of a traditional one-way energy harvesting device. This proved that the proposed electromagnetic energy harvesting system is effective and applicable in terms of acquiring renewable energy for a cableway’s far-end applications in mountainous areas. Acknowledgments Funded by National Natural Science Foundation of China (No. 51275431). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.apenergy.2018.07.059. References [1] Shen W, Zhu S. Harvesting energy via electromagnetic damper: application to bridge stay cables. J Intell Mater Syst Struct 2015;26(1):3–19. [2] Arnold DP. Review of microscale magnetic power generation. IEEE Trans Magn 2007;43:3940–51. [3] Rome LC, Flynn L, Goldman EM, Yoo TD. Generating electricity while walking with
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