This document describes a design for a piezoelectric shock absorber that can generate electricity from vehicle vibrations. It discusses two initial designs - electromagnetic and hydraulic - and proposes using a piezoelectric crystal installed within the shock absorber. When compressed, the crystal generates electric energy from the force. The design aims to limit the force on the crystal for safety while still producing optimal voltage. Analysis shows the design could generate over 25V from manual impacts. The piezoelectric shock absorber could increase fuel efficiency in hybrids or power accessories in other vehicles.

1. PIEZO ELECTRIC POWER GENERATING SCHOCK ABSORBER
ABSTRACT:
When used in a vehicle or hybrid electric vehicle the electricity generated by the shock absorber
can be stored in the battery to be used later. In non-electric vehicles the electricity can be used to
power accessories such as air conditioner. The two designs that we had considered for conserving
energy from shock absorber are:
1) Electromagnetic
2) Hydraulic
3.1 ELECTROMAGNETIC
The design consists of two tube-like components - a hollow copper coil assembly and a magnet
that uses vibration of the vehicle’s suspension to move up and down inside it. When the vehicle is
in motion, the vibration in the suspension causes the coil to move relative to the magnet. As the
copper coil moves inside this magnetic field, a voltage is generated.
But this design is not much efficient due to the losses. The power is lost in the form of eddy
current loss and hysteresis loss. Also the system tends to be bulky and cannot be successfully
implemented in smaller shock absorbers of two wheelers.
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2. 3.2 HYDRAULIC
This design consists of a hydraulic system that forces fluid through a tiny turbine attached to a
dynamo. Each time the shock absorber compresses, the fluid is forced through the turbine causing
it to rotate. Thus energy is generated in the coupled dynamo. The main disadvantage of this
method is that it can be used only in heavy vehicles.
3.3 OUR CONCEPT
In our design, the energy is regenerated using a piezoelectric crystal. A piezoelectric crystal is
installed within the shock absorber. When the shock absorber is compressed, force is transmitted
to the piezoelectric crystal. Thus electric energy is obtained from the shock absorber. The force
transmitted to the piezoelectric crystal is limited to the safe range of the material by using suitable
damping mechanism. The design considerations of the piezoelectric shock absorber are explained
in the next chapter.
The piezoelectric regenerative shock absorber can be used in any vehicle, irrespective of size
ranging from two wheelers to trucks. Piezoelectric crystal of appropriate size is fixed on the
shock absorber. By recovering the vehicle’s energy lost in vibration, the piezoelectric
regenerative system will be able to increase fuel efficiency in a hybrid or electric powered
vehicles. In other vehicles the pulsating voltage obtained from the shock absorber can be rectified
by using a rectifying circuit and can be used to charge the battery. This can be used to power
other accessories in the vehicle.

3. CHAPTER-4
DESIGN AND ANALYSIS
4.1 DESIGN
A cylindrical shaped piezoelectric material (PZC), made of Lead Zirconate Titanate Ceramic,
commercially known as DCPL-5 is fixed within the shock absorber, with suitable damping so
that only a part of the total force generated while shock absorber compression is transmitted to
the PZC, sufficient enough to generate the optimum voltage, with a constraint on the maximum
endurance strength of the material. Ceramic PZCs usually have high compressive yield stress.
The rough arrangement of components will be as shown-
Fig 4.1. Proposed design of the shock absorber
(The outer spring is omitted in the diagram to show the inner components)
PZC
Bush
Spring

4. 4.1.1 DCPL-5
It is a modified Lead Zirconate Titanate Ceramic, providing transducer elements with high electro
mechanical coupling coefficient and high charge sensitivity and curie temp of 350 º C, used for
sensing applications like ultrasonic flaw detection, under water echo sounding, pressure gauges,
strain gauges, accelerometers, medical Instruments, flow meters, NDT systems, Level gauges and
many other devices. Our model was developed using this crystal, which was sent to us by Mr.
Sunil Kapoor, Doon Ceratronics Pvt. Ltd, Dehradun, on request.
The properties of the PZC is tabulated as-
Properties Symbol DCPL-5
Piezoelectric Coupling Coefficients Kp .60
K33 .70
K31 .32
Piezoelectric Charge Coefficients(x 10-12
C/N) d33 425
d31
-170
Piezoelectric Voltage Constants (x 10-3
Vm/N) g33 25
g31
-11
Dielectric Constant at 1Khz KT33 1750
Dissipation Factor .02
Mechanical Quality Factor Qm 75
Density (Kg/m3
) 7650
Curie Temperature (Tc) °C 350
Frequency Constants(Hz-M) Np 1950

5. Important factors governing performance are the shape of the PZC transducer, the manner in
which the transducer is mounted and, of course, the nature of the electrical load. A PZC disk for
example, compressed between two metal surfaces will never be able to expand in the radial
direction as readily as would a long, thin cylinder, which is only constrained at its ends and
assumes a barrel shape on radial expansion. So the way in which the material is mounted will
directly affect the energy conversion per unit volume. The general rule therefore is to allow the
PZC body some freedom to expand radially since charge generation is directly coupled to
deformation.
4.2 ANALYSIS
Assuming the force on the PZC to be static, the following analysis is carried out
Consider a PZC cylinder of height h, polarized in the axial direction and with electrodes on its
end faces. If an axial stress T3 is applied, it will deform and hence charge will displace toward the
electrodes. Under open circuit conditions (D = 0) the voltage U3 is given by:
U 3 = - g33hT3 -- (1)
A compressive stress (negative sign) will therefore generate a positive voltage across the
transducer. To get an idea of the order of magnitude of the voltage to be expected, a 10 mm Lead
zirconatetitanate cube (g33 = 22 x 10-3
Vm/N) subjected to a force of 5kN will generate a voltage
about 11 kV. The total energy WD fed into a PZC element by a mechanical source can be split up
as follows: (no losses, open circuit)
W D = Wm + We -- (2)
Where: Wm = mechanical deformation energy.

6. We = energy stored in the electrical field in the ceramic.
The latter may be withdrawn from the element as electrical energy.
The energy WD can be simply expressed in terms of compliance SD and the mechanical stress T
by:
In which V is the volume of the PZC element. We and Wm are given in terms of the coupling
coefficient k33 by:
These equations show that for given material properties only V and T govern the energy
conversion. If, therefore, in a particular application the force that can be applied is limited, the
electrical energy generated can be increased by choosing a smaller surface area (equal volume).
For example one can use a long thin cylinder instead of a short thick one.
PZC-elements under compressive stress in open circuit conditions do not suffer from
depolarization. The induced field has the same direction as the poling field during polarization
and the voltage increases almost linearly with the stress even up to very high load levels.
=
=
=

7. Fig 4.2. Charge density on PZT5A discs as a function of compressive load. The discs (h = 5 to 16
mm) were clamped between two steel plates.
The PZC, springs and bushes are fixed on the shock absorber in such a way that the total stiffness
and hence the performance of the shock absorber as a whole is not affected.
A typical shock absorber can be shown by the following line diagram:-
Fig 4.3. Line diagram of the system

8. Where K is the stiffness of the outer spring and c is the damping coefficient of the dashpot (air
chamber).
Suppose we have an impressed oscillating force F=F0sinωt, causing a displacement x1 which is a
function of time, t.
Inertia force = mẍ
Damping force = cẋ
Spring force = kx
Thus equation of motion will be-
mẍ + cẋ + kx - F0sinωt = 0
Or mẍ + cẋ + kx = F0sinωt
The complete solution of the equation consists of two parts, the complementary function (CF)
and the particular integral (PI).
CF = Xe-ξωnt
sin (ωdt+Φ1)
Where,
X and Φ1 are determined from the initial conditions, ξ is the damping factor, ωn is the natural
frequency of the system, ωd is the damping frequency which is related to ωn as :-
ωd = 𝜔 𝑛√1 − 𝜉2

9. To obtain the PI, let c/m=a, k/m=b and F0/m =d
Then using the operator D, the equation becomes,
(D2
+aD+b)x =d sinωt
PI =
𝑑 𝑠𝑖𝑛𝜔𝑡
𝐷2+𝑎𝐷+𝑏
PI =
𝑑 𝑠𝑖𝑛𝜔𝑡
−𝜔2+𝑎𝐷+𝑏
=
1
(𝑏−𝜔2)+𝑎𝐷
×
(𝑏−𝜔2)−𝑎𝐷
(𝑏−𝜔2)−𝑎𝐷
𝑑𝑠𝑖𝑛𝜔𝑡
= 𝑑 [
𝑠𝑖𝑛𝜔𝑡(𝑏−𝜔2)−𝑎𝐷𝑠𝑖𝑛𝜔𝑡
(𝑏−𝜔2)2+ (𝑎𝜔)2
]
Taking ( 𝑏 − 𝜔2)=RcosΦ and aω =RsinΦ, on further simplification yields :-
PI =
𝐹0
√(𝑘−𝑚𝜔)2+(𝑐𝜔)2
sin(𝜔𝑡 − 𝛷)
x = CF + PI
x = Xe-ξω
n
t
sin(ωdt+Φ1) +
𝐹0
√(𝑘−𝑚𝜔)2+(𝑐𝜔)2
sin(𝜔𝑡 − 𝛷) -- (1)

10. This is the equation of displacement of an unmodified shock absorber.
Now we introduce the new components within the shock absorber to incorporate the PZC.
Let the collective stiffness of the PZC, the two bushes and the two springs be Ke
1
𝐾 𝑒
=
1
𝐾 𝑝
+
2
𝐾 𝑏
+
2
𝐾𝑠
where,
Kp is the stiffness of the PZC
Kb is the stiffness of the bushes
Ks is the stiffness of the spring.
The modified line diagram will be as :-
Fig 4.4. Line diagram of the modified system
K
1
Ke

11. Suppose we have the same impressed oscillating force F = F0sinωt, causing a displacement x1
which is a function of time, t.
Inertia force = mẍ1
Damping force = cẋ1
Spring force = K1x1
Force due to the new system = Kex1
Thus equation of motion will be-
mẍ1 + cẋ1 + (K1+Ke)x1 - F0sinωt = 0
or mẍ1 + cẋ1 + (K1+Ke)x1 = F0sinωt
The complete solution of the equation consists of two parts, The complementary function (CF)
and the particular integral (PI).
CF = X1e
-ξ1ω
n1
t
sin(ωd1t+Φ1)
Where,
X1 and Φ1 are determined from the initial conditions, ξ1 is the damping factor, ωn1is the natural
frequency of the system, and ωd1 is the damping frequency which is related to ωn as :-
ωd1 = 𝜔 𝑛√1 − 𝜉1
2
To obtain the PI, let c/m=a, k/m=b and F0/m =d

12. Then using the operator D, the equation becomes,
(D2
+aD+b)x = d sinωt
PI =
𝑑 𝑠𝑖𝑛𝜔𝑡
𝐷2+𝑎𝐷+𝑏
PI =
𝑑 𝑠𝑖𝑛𝜔𝑡
−𝜔2+𝑎𝐷+𝑏
=
1
(𝑏−𝜔2)+𝑎𝐷
×
(𝑏−𝜔2)−𝑎𝐷
(𝑏−𝜔2)−𝑎𝐷
𝑑𝑠𝑖𝑛𝜔𝑡
= 𝑑 [
𝑠𝑖𝑛𝜔𝑡(𝑏−𝜔2)−𝑎𝐷𝑠𝑖𝑛𝜔𝑡
(𝑏−𝜔2)2+ (𝑎𝜔)2
]
Taking ( 𝑏 − 𝜔2)=RcosΦ and aω =RsinΦ, on further simplification yields :-
PI =
𝐹0
√((K1+Ke)−𝑚𝜔)2+(𝑐𝜔)2
sin(𝜔𝑡 − 𝛷)
x1 = CF + PI
x1 = Xe-ξ1ω
n1
t
sin(ωd1t+Φ1) +
𝐹0
√((K1+Ke)−𝑚𝜔)2+(𝑐𝜔)2
sin(𝜔𝑡 − 𝛷)
--- (2)
The spring displacements in the two cases should be the same. Hence (1) = (2), which implies,

13. K = K1 + Ke
K1 = K - Ke
By measured data we have,
Stiffness of Original the outer spring, K = 12.80 N/mm
Combined stiffness of the inner springs, bushes plates and PZC, Ke = 2.25N/mm
We design a new outer spring of stiffness K1 = K – Ke. The length and diameter of the spring
remains unchanged.
Number of turns of the original spring = 17
Number of turns n =
𝐺×𝑑4
8𝐷3 𝐾1
G = 8 × 104
N/𝑚𝑚2
d = 7mm
D= 28mm
K1 = 12.8 – 2.25 = 10.55N/mm
On solving we get, n =18.197
n’
= n+2 = 21 turns (for squared and ground ends)
Thus the outer spring, currently in use is replaced by another spring of the same material and
dimensions with a slight change in the number of turns.

14. 4.3 RESULT
The present model was tested with a CRO to find out the output. Screenshots of the CRO are as-
Fig 4.5. Screenshots from the CRO
The X- axis shows time in milliseconds and Y- axis shows voltage in volts. The energy
generation is limited to a few fraction of a second, when the impact loading takes place.
The graphs show a peak generated voltage of up to 25 V, when subjected to shock manually. The
voltage generated depends on the force applied.

15. CHAPTER 5
CONCLUSION
The use of piezoelectric crystal in the shock absorber is a new method for power generation. By
using PZCs, power could be generated more effectively than that compared to electromagnetic
and hydraulic type generation. The piezoelectric regenerative shock absorber can be
commercialized for the use in vehicles. Also the cost involved is very low which makes it
economically efficient. This technology can be efficiently implemented in conventional vehicles
as well as electric and hybrid vehicles, which will be the future of automobile industry.
The energy regenerated by the shock absorber by this method can be found out by calculating the
current being produced. In order to calculate current, the Voltage vs. Time curve needs to be a
continuous curve, for which a continuous load has to be applied without damaging any of the
components designed in the shock absorber, especially the piezoelectric material. A special
mechanism will have to be designed for applying this load which is well beyond the scope of
mini project.
The damping system can also be further improved by providing the optimum stress for
maximum energy generation within the safe range of the ultimate stress of piezoelectric crystal.
There is still room for a lot of improvement with this concept. It can be used in all vehicles to
conserve the energy that goes waste, which though small, will be precious in the years to come,
thus turning potholes into energy advantage.

16. ANNEXURE - I
We have used bulk ceramic (commercially known as DCPL- 5) for our model. This is cheap and
has high compressive strength. But the output is not very high.
Fig AI.1 DCPL-5 bulk ceramic
AI.1 MULTILAYER GENERATORS
The technique developed to make multilayer capacitors can also be used for piezoelectric
ceramics. Thin layers of so called green ceramic are interleaved with silver-palladium electrodes,
compacted, cut to size and then sintered. With these devices, the large total surface area per unit
volume means that the generated charge is high whereas the voltage is rather low. These types of
generator are ideal for use as a solid state battery for modern electronic circuits.

17. Fig AI.2. Multilayer piezoelectric material
Fig AI.3. Output voltage as a function of compressive load
These multilayer piezoelectric crystals can be used in place of bulk ceramic for higher energy
generation.

18. ANNEXURE II
COMPARISON OF SHOCKS
These notes identify the high force that can result from and impact and the show the reduction in
force by use of a spring and a compensating hydraulic shock absorber. The example is provides
as a general illustration and is very much simplified.
Force resulting from impact with no shock absorber included
Considering a very simple duty of dropping a 1 kg load through 1m onto a machine element
represented by a short steel column 0.1m dia by 0.2m long made form steel.
Fig AII.1.

19. The stiffness of the column k = AE / l.
A = 0.00784m2
E = 21x1010
Pa (N/m2)
l = 0.2m
The stiffness of the column k is the Load /unit deflection is calculated as:-
k = 0.0784 × 21 × 1010
/0.2 = 8.25 × 1010
N/m
To calculate the maximum force resulting from the dropped load assuming conservation of
energy.
The strain energy absorbed by the column = the Potential energy absorbed from the dropped load.
The potential energy of the load = E 1
E 1=Mgh = 4.905 Nm.
This equals the strain energy absorbed by the load at impact
The strain energy absorbed = Pmaxδmax /2 = Pmax
2
/ 2 k
Therefore to calculate the maximum force developed Pmax
Pmax = Sqrt (2.E1.k) = Sqrt (4.905×8.25×1010
) = 899kN
Maximum force Resulting From Use of Spring
If a spring with a stroke of 0.1m is located on the top surface as shown below

20. Fig AII.2
The resulting maximum force is determined as follows.
Energy to be absorbed = E1 = Mgh. = 4.905 Nm
Strain energy of spring = Fδspring /2
Therefore Maximum force = 2Mgh/δspring = 98.1N
Use of the spring has reduced the maximum force by a factor of 10. However the spring is now
exerting an upwrd force which will cause the load to rebound upwards. Detailed analysis of the
system response is required to arrive at the total motion history of this event
Maximum force resulting from the use of a compensating Hydraulic Shock absorber
If a Shock absorber with a stroke of 0.1m is located on the top surface as shown below -

21. Fig AII.3
It is assumed that the shock absorber is designed to provide a constant deceleration force
throughout its stroke..
The resulting maximum force is determined as follows.
Energy to be absorbed = E1 = Mgh. = 4.905 Nm
Energy to be dissipated in the shock absorber = Fδsh_ab
Therefore Maximum force = Mgh/δsh_ab = 49.05 N
The energy has been dissipated in heating up the hydraulic fluid in the shock absorber. When the
load has come to rest the system is in a stable state. The maximum force transmitted to the
column during impact is 1/20 that experienced by without the shock absorber.

22. REFERENCES
1. en.wikipedia.org/wiki/Shock_absorber
2. www.piezomaterials.com
3. en.wikipedia.org/wiki/Piezoelectricity
4. www.doonceratronics.com
5. Theory of machines – S.S Rattan
6. Machine Design – S. Md. Jalaludeen
7. Design data book of engineers – PSG College of technology, Coimbatore