2. because, although energy reclaiming suspension8,9
may
be used to recover vibration energy and optimize
damping, the mechanical properties of a vehicle will be
affected due to its complicated structure.10,11
On account
of the difficulty in collecting vibration energy and the
low conversion efficiency, it is difficult to recover
vibration energy by other means.
In terms of vibration energy harvesting, there has
been a great deal of research on piezoelectric cantilever
beams. A deceleration strip based on the piezoelectric
cantilever beam for energy feedback12,13
was designed to
affect the scale of recovered energy by virtue of the length
of vibration by triggering the piezoelectric cantilever
beam 2 times in the process of shock compression and
response under different traveling speeds. By making full
use of space, a multilayer piezoelectric cantilever
structure was designed. For research on vibration energy
recovery in the event that piezoelectric devices are
installed on different parts of a vehicle, in Mouapi
et al,14
power was supplied to wireless sensor networks
by placement of a piezoelectric cantilever beam under
the passenger seat. However, the vibration displacement
was limited in this position. In another study,15
Murugan
and Chandru were more concerned with energy storage
than with actual usage. However, through modeling and
simulation, recovery of the energy generated from the
vibration of suspension equipped with a piezoelectric
device was proved to be feasible. In Viet et al,16
a rotating
mechanism and piezoelectric materials were used for the
energy harvesting of an ocean wave. The impact of the
distance between the gear and the leverage was discussed,
but the gear pitch was not fully considered. The model
offered in Manla et al17
provided an idea of harvesting
energy from rotating objects. In previous study,18
Xie
and Wang fully considered the effect of road excitation
on the energy harvesting of piezoelectric cantilever
beams, and a simulation was conducted. The relevant
filtering methods19-21
provide the basis for processing of
the filtering algorithm of vibration waveforms.
In this paper, in relation to vibration energy
harvesting in the process of electric vehicle operation, an
energy feedback mechanism was designed when vehicle
suspension remained unchanged. Vibration straight‐line
displacements were divided into small circumferential
segments by bringing in a gear structure and separately
used to continuously generate power from the
piezoelectric bending element. A virtual vibration
displacement filtering algorithm was proposed for
calculating the recovery power of the energy feedback
mechanism. The impact of gear pitch on the regeneration
power value by changing the gear pitch was discussed,
and the reasonable gear pitch value could be determined
at a fixed speed.
The remained of this paper is organized as follows.
Section 2 introduced the components of the energy
feedback mechanism and experimental platforms.
Section 3 proposed the virtual displacement filtering algo-
rithm and 2 methods of determining gear pitch and
deduced the power calculation method. Section 4 made
a comparison among different filtering algorithms and
gear pitches and their effects on the results. Section 5
drew conclusions based on the overall analyses.
2 | ENERGY FEEDBACK
MECHANISM AND EXPERIMENTAL
PLATFORM
A piezoelectric bending element–based energy feedback
mechanism is designed to make piezoelectric devices
generate electric power with the piezoelectric bending
elements arranged in the form of a cantilever beam using
the variation in the relative displacement between the
suspension and the vehicle body in the process of vehicle
operation as a driving source. The piezoelectric bending
elements in the form of a cantilever beam are subject to
materials, so only a few millimeters of displacement are
allowed at the free end, which is far exceeded by the
variation in the relative displacement between the
suspension and the vehicle body in the process of
vibration. Therefore, a change is made from linear
displacement to circular displacement, and a gear unit is
installed on the circle to divide large displacements into
small segments for repeated excitation within the range
of maximum allowable displacement of the piezoelectric
bending elements. Meanwhile, in consideration of the
output power and space utilization efficiency of the
mechanical structure, the cantilever piezoelectric bending
element–based energy feedback mechanism is designed to
be layered, and several groups are set on the circle. Light
fine rods are used to connect the elements to eliminate
phase difference and avoid voltage offset. The
piezoelectric bending element–based energy feedback
mechanism model is shown in Figure 1. The parameters
of a 1/4 vehicle are listed in Table 1.
The parameters of a single piezoelectric bending
element are shown in Table 2.
The size of the piezoelectric ceramic is
60 mm × 31 mm × 0.2 mm, and the size of the base plate
is 80 mm × 33 mm × 0.2 mm.
Supported by a cantilever, the maximum deflection is
10 mm at the free end.
Since the power of the piezoelectric bending elements
is not subject to series‐parallel connection, the ability of
the entire energy feedback mechanism to generate
maximum power depends on such ability of a single
LI ET AL. 1703
3. piezoelectric bending element. As the mechanism
achieves excitation with a gear, the gear pitch has a direct
impact on the maximum deflection at the free end of a
piezoelectric bending element in the form of a cantilever
beam. Any increase of the gear pitch has a positive effect
on a single excitation of the piezoelectric bending element
to output power. However, the excitation frequency
decreases with the increase of the gear pitch. Virtual
displacements disable excitation to produce power in the
process of the reciprocating motion arising out of
suspension vibration; thus, with the increase of the gear
pitch, the number of virtual displacements grows, and
the excitation frequency decreases greatly. Therefore, only
a reasonable gear pitch can enable the maximum output
power of a single piezoelectric bending element to be
obtained. Furthermore, in the process of determining
the gear pitch, consideration must be given to the depth
of the excitation side in the gear, as it may affect the actual
energized displacement and size of the output power.
For accuracy and convenience purposes, the power
recovered by a piezoelectric cantilever beam is measured
step‐by‐step in this paper. First, a displacement sensor
KTC‐75 mm is installed on the 1/4 vehicle body between
the vehicle body and the suspension. The sensor measures
the displacement st and sends the signal to the signal
conversion circuit. The signal conversion circuit, which
is supplied by a battery, can transform the displacement
signal into a voltage signal. The voltage signal is collected
by the DAQ card and then displayed and recorded by the
software platform. Second, the displacement st is loaded
on the energy feedback mechanism. A load is series
connected with the piezoelectric bending element. The
DAQ card and the software platform are used to measure
and record the voltage U generated by the piezoelectric
bending element. Finally, the power P recovered by the
piezoelectric cantilever beam can be calculated with the
power calculation method. The experimental platform
for measuring vehicle vibration displacement is shown in
Figure 2, and the experimental platform for measuring
the energy harvesting mechanism is shown in Figure 3.
3 | POWER CALCULATION
METHOD
As a smoothing filtering algorithm, the virtual vehicle
vibration displacement filtering algorithm aims to remove
the virtual displacements that disable the excitation of
piezoelectric bending elements to generate power in the
process of the reciprocating motion arising out of
suspension vibration. As shown in Figure 4, in the left
red frame, from 1250 to 2000 ms, the vibration
displacement frequency is high while the oscillations are
small. If the positions of the gear and piezoelectric bender
are as shown in Figure 5A, the displacement may cause
the gear to rotate in a reverse direction but not reach the
piezoelectric bender. Another situation is shown in
Figure 5B. The gear reaches the piezoelectric bender, but
the displacement may cause small deviations. In this case,
the electric power is too small and hard to calculate.
Therefore, these parts of the displacement curve need to
be filtered to determine the part that cannot generate
electricity effectively according to the gear pitch. However,
in the right red frame, from 3250 to 3500 ms, the peak of
FIGURE 1 Piezoelectric bending element–based energy feedback mechanism model. A, Sketch. B, 1/4 vehicle model. C, Mathematic model
diagram [Colour figure can be viewed at wileyonlinelibrary.com]
TABLE 1 Parameters of a 1/4 vehicle
m1, kg m2, kg k1, N/m k2, N/m
24 313 65 000 85 200
TABLE 2 Parameters of a piezoelectric bending element
Quality factor, Qm 70
Electromechanical coupling factor, Kp 0.65
Piezoelectric constant, D31 10−12
(C/N) −186
Piezoelectric constant, D33 10−12
(C/N) 670
Piezoelectric constant, D15 10−12
(C/N) 660
Dielectric constant, ε11/ε0 3130
Dielectric constant, ε33/ε0 3400
1704 LI ET AL.
4. the curve can excite the piezoelectric bending elements. It
should not be filtered. To distinguish whether a part of the
displacement vibration can generate electricity effectively
or not, as well as calculate the power accurately, it is
necessary to use the displacement filtering algorithm.
Existing filtering algorithms such as limiting filtering
and smoothing filtering22
could be used to address the
curve; however, the result may not be satisfactory. The
limiting filtering algorithm is simple and can overcome
the impulsive interference caused by accidental factors
but is unable to suppress the periodic interference. Aimed
at the filtering application in this paper, it may block parts
that satisfied the filtering condition but were filtered by
the previous effect, just as the red frame in Figure 4
shows. The 3‐point smoothing filtering algorithm can
enhance the low frequency parts but may not remove
continuous tiny vibrations, and the parts that can truly
excite the bender are not even distinguishable.
The virtual displacement filtering algorithm is
described in Table 3.
Distance d should be taken based on the required
processing accuracy and the maximum allowable
deflection of the piezoelectric bending element.
FIGURE 3 Experimental platform for energy harvesting
mechanism [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 2 Experimental platform for measuring vehicle vibration displacement [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 4 Original vibration waveform
collected by KTC‐75 mm [Colour figure
can be viewed at wileyonlinelibrary.com]
LI ET AL. 1705
5. To verify the applicability of the virtual displacement
filtering algorithm, comparison is made between the
common limit filtering algorithm, the 3‐point smoothing
filtering algorithm, and the virtual displacement filtering
algorithm in effect. Refer to Figures 6 and 7 for the
comparison in filtering effect when d = 3 mm and
d = 7 mm, respectively.
According to the principle and the filtering process,
the virtual displacement filtering algorithm is used mainly
to remove the virtual displacements and retain the
effective displacements that may energize the piezoelec-
tric bending elements as much as possible. Removing
the virtual displacements may make the average speed v
at which the gear energizes the piezoelectric bending
FIGURE 5 Comparison between 2
methods of determining gear pitch. A,
Method D. B, Method d
TABLE 3 Virtual displacement filtering algorithm
Step 0: Determine the extreme points
• Set a = 10−5
mm and i = j = 1.
• Differentiate the continuously equal points of the vibration displacement waveform. If sj + 1 = sj, then sj + 1 = sj + 1 + a.
• Determine all extreme points in the vibration waveform x1, x2, x3, ..., xn.
Step 1: Filter the virtual distance
• Define the filtering distance d.
• Take extreme points xi + 1 and xi + 2; if |xi + 1 − xi + 2| > d, proceed to step 3; otherwise, take extreme points xi, xi + 1, xi + 2, xi + 3.
• If |xi + 1 − xi + 2| > |xi + 2 − xi + 3|, then remove xi + 2, and define xi, xi + 1, xi + 4, xi + 5 as the threshold of the next iteration; otherwise,
remove xi + 1 or xi + 2, which can retain the part of the higher slope, and define xi, xi + 3, xi + 4, xi + 5 as the threshold of the next iteration.
Step 2: Complete the linear interpolation
• Linearly interpolate part of the removed extreme points.
• Go to step 1 for the next iteration.
Step 3: Reset the algorithm
• Increment i and go to step 1 for the next iteration.
FIGURE 6 Comparison in filtering
effect when d = 3 mm [Colour figure can
be viewed at wileyonlinelibrary.com]
1706 LI ET AL.
6. elements more accurate, based on which the length of
excitation by a single tooth can be calculated more
accurately. The length plays an important role in
calculating the average power of the piezoelectric bending
elements. To verify that the algorithm is more applicable
for calculating the power of the energy feedback
mechanism, a comparison is made.
As seen in Figure 4, the waveform is described by
displacement‐time. The average speed of triggering the
piezoelectric bending element can be calculated from
the path length and time.
v ¼
∫t
0 _
s
j jdt
t
: (1)
In Equation 1, s refers to the displacement of the
vibration waveform; _
s refers to the instantaneous speed;
and ∫t
0 _
s
j jdt refers to the path length during the time 0 ~ t.
When d = 3 mm, vvirtual = 57.36 mm/s,
vsmooth = 66.63 mm/s, vlimiting = 56.62 mm/s, and the
length of excitation of the piezoelectric bending element
by a single tooth td‐virtual = 52.3 ms, td‐smooth = 45.0 ms,
and td‐limiting = 53.0 ms, the error rates for the 3‐point
smoothing filtering algorithm and limit filtering
algorithm are 13.96% and 1.34%, respectively. When
d = 7 mm, vvirtual = 43.97 mm/s, vsmooth = 66.63 mm/s,
vlimiting = 32.49 mm/s, and the applicable length td‐vir-
tual = 162.90 ms, td‐smooth = 105.06 ms, and td‐limit-
ing = 215.45 ms, the error rates for the 3‐point
smoothing filtering algorithm and limit filtering
algorithm are 35.51% and 32.26%, respectively. Therefore,
the virtual displacement filtering algorithm is more
applicable to the research object than the limit filtering
algorithm, but the 3‐point smoothing filtering algorithm
does not apply due to the lack of a changeable threshold.
Refer to Figure 8 for the effect yielded by virtual
displacement filtering at different filtering distances.
Through analysis of the vibration waveform filtered,
the effective displacements are obtained, which may ener-
gize the energy feedback mechanism at different filtering
distances, and the average excitation speed v and length td
based on the effective displacements are calculated.
Refer to Table 4 for the average excitation speed v and
length td at different filtering distances, as well as the peak
voltage (2kΩ load) of single excitation at the applicable
distances.
To analyze the relationship between the maximum
peak voltage and the gear pitch, the model of the piezo-
electric cantilever beam with a single degree of freedom
is introduced in Figure 9.
The control equation for the model23
can be expressed
as follows:
M €
ω þ C _
ω þ Kω−θu ¼ f ext; (2)
wherein ω refers to displacement; u refers to voltage; M
refers to effective mass; C refers to effective damping
coefficient; K refers to stiffness coefficient; θ refers to
FIGURE 7 Comparison in filtering
effect when d = 7 mm [Colour figure can
be viewed at wileyonlinelibrary.com]
FIGURE 8 Effect of virtual
displacement filtering at different filtering
distances [Colour figure can be viewed at
wileyonlinelibrary.com]
LI ET AL. 1707
7. electromechanical coupling coefficient; and fext refers to
applied excitation.
As the displacement under single excitation by the
piezoelectric bending element is d, the first‐ and
second‐order derivatives only relate to the real
vibration at the moment of excitation. However, no
direction relation exists, and these derivatives are less
affected by the change in d; thus, they may be defined
as constants. Similarly, fext is also considered a
constant. Accordingly, the relationship between the
voltage generated by the cantilever beam of the
piezoelectric bending element and d is expressed with
the following equation:
u ¼ kd þ a; (3)
wherein k ¼
K
θ
, a ¼
M €
ω þ C _
ω−f ext
θ
, and a is constant;
there is a linear relation between u and d.
Refer to Figure 10 for the trend of the change in the
average excitation speed v with d at the driving speed of
20 km/h based on actual measurements and the filtering
algorithm.
According to line v‐d, v‐d is approximately linear. For
the convenience of calculation and analysis, set
v ¼ k′
d þ c: (4)
Then
td ¼
1
k′
þ c=d
: (5)
Refer to Figure 5 for the 2 methods that are available
to achieve the deformation of the displacement of d at
the excitation side.
In method D, the gear pitch is 2d, and the actual
displacement is D = d. After the tooth is separated from
the excitation side, damping vibration should occur for
the piezoelectric bending element, but due to the continu-
ous rotation of the gear, the piezoelectric bending element
will inevitably strike the next tooth in the process of first
spring back, following which high‐frequency vibration
arises on the basis of the original damping vibration. In
this case, due to the uncertain gear speed, it is difficult
to accurately calculate the power with a mathematical
FIGURE 9 Model of a piezoelectric cantilever beam with a single
degree of freedom FIGURE 10 Trend of the change in average excitation speed v
with d at the driving speed of 20 km/h [Colour figure can be
viewed at wileyonlinelibrary.com]
TABLE 4 Results of excitation at different filtering distances at the driving speed of 20 km/h
Filtering Distance d, mm Excitation Speed v, mm/s Excitation Time Interval td, ms Peak Voltage U0, V
1 68.613 14.575 6.66
2 62.633 31.932 8.45
3 57.361 52.300 10.27
4 51.792 77.232 12.22
5 49.420 101.175 14.04
6 46.539 128.923 15.60
7 43.971 159.195 18.46
8 41.845 191.182 19.18
1708 LI ET AL.
8. formula. Therefore, with method D, the average power
may be estimated roughly by measuring the actual voltage
and averaging the sum of the instantaneous powers of
2000 points.
p ¼
∑
2000
n¼0
Un
2
R
2000
: (6)
If the superposed vibration with a period of
approximately 3 ms is ignored and the voltage is
processed as a damping vibration waveform, the average
power may be calculated as follows:
Un ¼ U0e−βDt
cos ωDt þ ϕ0
ð Þ; (7)
p ¼
∫td
0
Un
2
R
dt
td
; (8)
wherein βD refers to the damping coefficient; ωD = 2π/TD
is the angular frequency; TD refers to the period of
damping vibration; Un refers to the voltage at each
moment; U0 refers to the initial voltage; and ϕ0 refers to
the initial phase.
The voltage generated by the piezoelectric bending
elements is similar to a waveform, as shown in
Figure 11.
In method d, the gear pitch is d, and the actual
displacement is D = d. An analysis is made on the status
of a piezoelectric bending element in the process of single
excitement as follows: first, when the gear pitch is d, the
deformation of the displacement of d occurs at the
excitement end; after the tooth is separate from the end,
damping vibration should occur for the piezoelectric
bending element, and the damping coefficient is β1.
However, at the moment of separation, the next tooth
has moved to the equilibrium position of the element.
Therefore, at the equilibrium position, complete β1
damping vibration cannot be achieved, but β2 damping
vibration occurs around the position. After the vibration
lasts T1, the second peak of β1 damping vibration arises,
and β2 damping vibration occurs again once the element
is energized, and so on.
The voltage generated by piezoelectric bending
elements is similar to the waveform shown in Figure 12.
Similarly, with method d, the average power may be
estimated roughly by averaging the sum of the
instantaneous powers. Through comparison between
method d and method D, the average power obtained
with method d is 41.36% greater than that obtained with
FIGURE 11 Excitation voltage u of the
piezoelectric bending element when gear
pitch is 2d [Colour figure can be viewed at
wileyonlinelibrary.com]
FIGURE 12 Excitation voltage u of the
piezoelectric bending element when the
gear pitch is d [Colour figure can be
viewed at wileyonlinelibrary.com]
LI ET AL. 1709
9. method D. This is because the vibration frequency of the
piezoelectric bending element is larger in method d, and
with the increase of vibration frequency, the internal
resistance reduces and the output power increases.
The average output power of d is calculated, and the
process of excitement transient is ignored. Then, the
maximum voltage is taken as the initial point to arrive
at the equation for the damping vibration of the voltage
waveform as follows:
Un ¼ U0e−β1 n−1
ð ÞT1
; (9)
U ¼ Une−β2t
cos ω2t þ ϕ0
ð Þ; (10)
wherein β1 and β2 are damping coefficients; ω2 = 2π/T2 is
the angular frequency; T1 and T2, respectively, refer to the
periods of β1 damping vibration and β2 damping
vibration; U refers to the voltage at each moment; Un
refers to the starting voltage of each β2 damping vibration;
U0 refers to the initial voltage; and ϕ0 refers to the initial
phase.
Regardless of the power generated in the process of
changing the transient excitation voltage from 0 to U0,
when t = 0, U0 = kd + a, ϕ0 = 0, and the time taken to
produce the voltage signal–based free vibration waveform
between the 2 excitations by the piezoelectric bending
element td = d/v. For this case, after load R is applied, a
discussion on the average power on R in 2 circumstances
is made.
When td < T1, the voltage signal actually produced by
gear excitation is only enough to produce β2 damping
vibration. When the next tooth comes, a new peak voltage
signal arises, beginning a new period of β2 damping
vibration. The waveform of the voltage U can be treated
as the β2 damping vibration waveform that has a period
of td. U can be expressed as U ¼ U0e−β2t
cosω2t, and the
instantaneous power can be expressed as
U2
R
. The average
power p can be calculated by integrating for time td and
dividing by time td.
p ¼
∫td
0
U0e−β2t
cosω2t
2
R
dt
td
(11)
When td T1, the voltage signal actually produced by
gear excitation is similar to the waveform shown in
Figure 11. When the next tooth comes, a new peak voltage
signal arises, beginning a new period. In this situation, the
waveform of the voltage U also has a period of td and can
be considered as a nesting of 2 damping vibrations. One is
β2 damping vibration that has a period of T1, and the peak
voltage spacing T1 can be considered as β1 damping
vibration. The voltage is expressed in Equations 9 and
10. A period of td is composed of [td/T1] periods of T1,
and an incomplete period lasts T1⋅
td
T1
−
td
T1
. It is
necessary to integrate by segments for summation and
then divide by time td to arrive at the average power.
Accordingly, the average power p is calculated as follows:
p ¼
∑n¼1 td=T1
½ ∫T1
0
Une−β2t
cosω2t
2
R
dt
td
þ
∫
T1⋅
td
T1
−
td
T1
0
U td
T1
h i
þ1
e−β2t
cosω2t
0
@
1
A
2
R
dt
td
; (12)
wherein [td/T1] refers to the value obtained by rounding
down. In Equation 12, the first half refers to the summing
power of the integral periods of T1, and the second half
refers to the power of the incomplete period that lasts
T1⋅
td
T1
−
td
T1
.
4 | RESULTS AND DISCUSSIONS
For the road of actually measured roughness
Gq(n0) = 256 × 10−6
m3
and grade C, after the parameters
measured and calculated are put into the formula, the
following relationship is obtained.
As shown in Figure 13, when the driving speed is
20 km/h, the excitation voltage peak of the piezoelectric
bending element linearly increases with d/D; as shown
in Figure 14A,C, the average excitation speed
approximately linearly reduces with d/D, and as shown
FIGURE 13 Trend of the change in u with d/D at the driving
speed of 20 km/h [Colour figure can be viewed at
wileyonlinelibrary.com]
1710 LI ET AL.
10. in Figure 14B,D, the average power first increases and
then reduces with d/D.
In method D, the accuracy of the average excitation
speed obtained with the virtual displacement filtering
algorithm is 42.56% higher than that obtained with the
limit filtering algorithm on an average basis, and with the
virtual displacement filtering algorithm, the average
power of a single piezoelectric bending element is maxi-
mum when D = 5 mm, which is 18.17% higher than the
peak power calculated with the limit filtering algorithm
when D = 4 mm. In method d, the accuracy of the average
excitation speed obtained with the virtual displacement
filtering algorithm is 19.77% higher than that obtained
with the limit filtering algorithm on an average basis. With
the virtual displacement filtering algorithm, the average
power of a single piezoelectric bending element is maxi-
mum when d = 7 mm, which is 18.36% higher than the
peak power calculated with the limit filtering algorithm
when d = 6 mm. However, through horizontal comparison
between the 2 methods, method d makes the average
power peak calculated with the virtual displacement
filtering algorithm 39.68% higher than that of method D,
and the average power peak calculated with the limit
filtering algorithm is 39.54% higher than in method D.
Therefore, at a driving speed of 20 km/h, in consider-
ation of the effect of processing accuracy and integer d,
the average power of a single piezoelectric bending
element is maximum when d = 7 mm.
To verify the algorithm is feasible, repeated
experiments are made when the driving speed is 60 km/
h. According to Figures 15 and 16, the peak voltage of a
piezoelectric bending element linearly increases with d/
D, and the average excitation speed approximately
linearly reduces with d/D. The average power is subject
to the scope of maximum deflection at the free end and
FIGURE 14 A, Average excitation speed. B, Average power in the case of a 2d gear pitch at the driving speed of 20 km/h. C, Average
excitation speed. D, Average power in the case of a d gear pitch at the driving speed of 20 km/h [Colour figure can be viewed at
wileyonlinelibrary.com]
FIGURE 15 Trend of the change in U with d/D at the driving
speed of 60 km/h [Colour figure can be viewed at
wileyonlinelibrary.com]
LI ET AL. 1711
11. increases when d/D is not more than 10 mm; however,
through simulation, regardless of the effect of maximum
deflection, the average power first increases and then
decreases with d/D.
In method D, the accuracy of the average excitation
speed obtained with the virtual displacement filtering
algorithm is 18.64% higher than that obtained with the
limit filtering algorithm on an average basis. With the vir-
tual displacement filtering algorithm, the average power
of a single piezoelectric bending element is maximum
when D = 10 mm, which is 32.46% higher than the peak
power calculated with the limit filtering algorithm when
D = 9 mm. In method d, the accuracy of the average
excitation speed obtained with the virtual displacement
filtering algorithm is 7.23% higher than that obtained with
the limit filtering algorithm on an average basis, and with
the virtual displacement filtering algorithm, the average
power of a single piezoelectric bending element is maxi-
mum when d = 10 mm, which is 14.69% higher than the
peak power calculated with the limit filtering algorithm.
However, through horizontal comparison between the 2
methods, method d makes the average power peak calcu-
lated with the virtual displacement filtering algorithm
36.41% higher than that of method D and the average
power peak calculated with the limit filtering algorithm
57.54% higher than that of method D.
Through comparison between method D and method
d and between the virtual displacement filtering
algorithm and the limit filtering algorithm, we may draw
a conclusion that at the driving speed of 60 km/h, the
average power of a single piezoelectric bending element
is maximum when d = 10 mm.
5 | CONCLUSIONS
In this paper, to address the problem of vibration energy
harvesting in a vehicle, an experimental platform is used
to measure the vibration displacement of a vehicle.
Compared with the conventional piezoelectric cantilever
systems, a gear was incorporated into the system to
improve the structure. Vibration straight‐line
displacements were divided into small circumferential
segments and separately used to continuously generate
power from the piezoelectric bending elements in the
allowable bending range. This design overcame the
limitation of the bending range and effectively increased
the output power of the piezoelectric bending elements.
A virtual vibration displacement filtering algorithm was
proposed for filtering the components of displacements
that could not effectively excite the piezoelectric bending
elements. Compared with several other filtering
FIGURE 16 A, Average excitation speed. B, Average power in the case of a 2d gear pitch at the driving speed of 20 km/h. C, Average
excitation speed. D, Average power in the case of a d gear pitch at the driving speed of 20 km/h [Colour figure can be viewed at
wileyonlinelibrary.com]
1712 LI ET AL.
12. algorithms, the proposed algorithm improved the
calculation accuracy of the average output power. In
addition, theoretical and experimental analyses were
made to discuss the impact of the gear pitch on the value
of regeneration power by changing the gear pitch. The
results showed that the maximum average power of a
single piezoelectric bending element could be obtained
by using a reasonable gear pitch when the vehicle
operated at a fixed speed.
ACKNOWLEDGEMENTS
This work was supported by the National Natural Science
Foundation of China (51477125), the Hubei Key
Laboratory of Power System Design and Test for Electrical
Vehicles (HBUASEV2017F008), the Hubei Science Fund
for Distinguished Young Scholars(2017CFA049), and the
Fundamental Research Funds for the Central Universities
(WUT: 2017II40GX).
ORCID
Changjun Xie http://orcid.org/0000-0002-9626-0813
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How to cite this article: Li Y, Xie C, Quan S, Zen
C, Li W. Vibration energy harvesting in vehicles by
gear segmentation and a virtual displacement
filtering algorithm. Int J Energy Res. 2018;42:
1702–1713. https://doi.org/10.1002/er.3975
LI ET AL. 1713
