Piezoelectric elements can be used as sensors and actuators in flexible structures. In this paper, using the most basic concepts of piezoelectric micropower generators, all useful mathematical equations for getting analytical output are discussed and derived for different piezo positions on cantilever beam and then 3D finite element modeling and simulation of generalized piezoelectric laminated beam problem with proper specifications and properties are done in ANSYS12.0. Experimental analysis is also done on the very practical problem to harvest energy (to get electric energy) by applying some deflection (mechanical energy) on piezobonded aluminum beam, that is, to harvest energy (at microlevel at least) by using vibrations of 4stroke car diesel engine with mounting of piezo cantilever beam. Here piezoelectric beam is used to measure the charge generated from the engine vibrations. The vibration amplitudes are measured with a Laser Vibrometer with considerations of maximum number of power cycles is to be covered for analysis. The vibration response data of displacement of the cantilever at free end measured from Vibrometer are considered for harmonic and analytical analyses as mean displacement amplitude of 3.98 mm at free end. The study further carried out for effect of different piezo positions and various engine speeds also. Then comparison is also done among obtained results from these three analyses to get validation of all derived mathematical equations.
Over the past decade there has been an abundant increase of interest in selfpowered devices in engineering applications such as MEMS, continuous structural health monitoring, environmental monitoring, and portable electronics. For such applications, to achieve their full potential, we must develop practical solutions for the power supply of the electronic devices. Energy harvesting from ambient sources, such as mechanical vibrations, is a very promising alternative. One of the most efficient ways of harvesting vibration energy is piezoelectric transduction [
In this paper, we proposed a case study and a model to harvest energy from the engine vibrations. As it is well known that engine vibrations are undesired phenomenon, so we propose a piezoelectric energy harvester to harvest energy from engine vibrations. Piezoelectric material is used to convert mechanical vibrations to electrical energy. Related characteristic equations are solved analytically and results are compared using finite element and experimentation. Experiments are conducted on fourstroke diesel engines with the piezomounted cantilever beam. For this energy harvesting problem, PZT5A4E is used as a piezoelectric material. The cantilever beam consists of piezoelectric bimorph mounted on one side of an aluminum beam. Piezoelectric bimorph uses in this experiment are with 0.13 mm thick substrate layer which covered by 0.19 mm piezo layers both sides. The sizes (length × width × thickness) for bimorph and beam are about 64 × 32 × 0.19. The cantilever beam sizes on which piezo bimorph mounted are 350 × 32 × 0.8 (in mm). FEA solution is obtained by ANSYS. Modal and harmonic analysis are done to find out the first natural frequency, which is obtained as 14.16 Hz at a deflection of 3.98 mm at the free end of a cantilever beam. Output power is obtained as 194.7
For a onedegree of freedom system generator, such as a piezoelectric laminated beam vibrating under single bending modal, the mechanicalelectrical coupling equations can be expressed as follows:
In general, a larger coupling coefficient gives higher conversion efficiency. Under certain external excitations, the vibration amplitude of the generated element will be affected by the external electrical load, which is driven by the electrical power induced from the piezoelectric generator. The general equation for output voltage and the charge can be expressed as follows:
Substituting (
It is easy to achieve a certain amount of stress with the “31mode” generators by bonding the piezoelectric element to a substructure undergoing bending. In comparison with “33mode” generators, this is more suitable for MEMS applications [
31 direction: force at 1direction and electrode on 3surface.
A typical 31mode power generator is a beam type piezoelectric power generator, in which a piezoelectric layer is bonded to a host element. When the host element is vibrating under the external excitation, a corresponding deformation is induced in the piezoelectric layer. A prototype of a piezoelectric laminated beam generator is shown in Figure
Prototype of the piezoelectric power generator.
Finally the estimated power equation is as follows:
This derived equation is used to calculate the analytical power for the piezoelectric power generators.
FEA, analytical, and experimental analyses with comparison are discussed for energy harvesting using 4stroke car diesel engine vibrations. Here, the particular case in which the piezoelectric patch (PZT5A) fitted on beam fixed at 282 mm from fixed end of the cantilever is considered. Experimental work is done with a piezoelectric cantilever aluminum beam mounting over the engine. Material properties and geometrical details of aluminum and piezoelectric patch (PZT5A) are given in Table
Beam geometry and material properties of aluminum and piezo PZT5A.
Properties  Aluminum  PZT5A  Substrate 

Length 



Width 

32 mm  32 mm 
Thickness 

Δ = 0.19 mm  Δ = 0.13 mm 
Density  2700 kg/m^{3}  7500 kg/m^{3}  8600 kg/m^{3} 
Relative permittivity 


Modulus of elasticity  2.1 * 
5 
9.7 
Poisson’s ratio  0.33  0.31  0.31 
The following details are also used for getting analytical and FEA solution.
Resistance [
Vibration amplitude at free end of cantilever
The distance of piezo from fix end [
The end point distance of piezo from fix end [
For energy harvesting by aluminum cantilever beam mounted on car diesel engine, the FEA model created for the same using all the necessary properties and specifications shown in Figure
FEA model of cantilever beam built in ANSYS 12.1.
After creating the model in ANSYS12.0, the first modal frequency in modal analysis is found to be 14.16 Hz. The deflection of 3.98 mm (experimentally obtained, Figure
For the purpose of harvesting energy by using the vibrations of running the engine, arrangement of piezoelectric (PZT5A), Al beam and piezoelectric circuit properly was done and then mounted this cantilever beam (with clamping) on the engine to get the voltage and current output using engine vibrations with the help of Multimeter, Laser Vibrometer, stop watch, and piezoelectric circuit. There are some figures shown below which represent the experimental setup and work analysis. Figure
Experimental setup with aluminum cantilever beam with piezo mounted at 282 mm from fix end.
Experimental maximum vibration amplitude response of displacement 3.98 mm for 6.5 seconds at free end by Laser Vibrometer at 14.16 Hz. (850 rpm).
The charge generated in terms of voltage is collected using energy harvesting kit (Piezo system Inc., USA) and output is measured in Multimeter approximately at 850 rpm engine speed. This is the crank speed of the engine. As the vibrations induced are the resultant output at this particular engine speed so in our experimentations we directly correlate the measured vibrations at particular engine speed. The energy harvesting circuit containing resistor and capacitor is connected to piezo patch. The extreme left fix end of the beam is clamped on this frame to fulfill the condition
The natural frequency of the engine measured in a FFT form (Figure
FFT response at 850 rpm engine speed.
The experimental voltage and current are observed as 2.71 volts and 0.067 mA. So the experimental power obtained at the speed of ~850 rpm is 181.57
The energy harvesting circuit containing resistor and capacitor was connected to piezo patch. The left extreme end of beam is fixed to the frame structure which is fitted in concrete foundation, which is not connected to engine body. Here the charge generated is measured up to maximum time scale of 12 minutes, keeping the engine speed constant at 850 rpm. To optimize piezo position on beam, piezo moves seven different positions across the length over beam. The seven different positions were 5 mm, 47 mm, 95 mm, 141 mm, 189 mm, 236 mm, and 282 mm from fix clamp end of beam and voltage generated was measured for these different locations.
Here simulation of piezoelectric beam is done by applying the load file to a particular model by transient analysis. Piezo patch attached moves to seven different locations along the length of beam moving it from fix end of beam to the vibrating end of beam. Figure
FEA and experimental results comparison for different piezo positions.
When piezo position moves from extreme near to fix end (5 mm) to extreme longest from fix end (283 mm) the charge generated in turn of voltage is found to be less, as shown in Figure
In previous discussion, effect of actuator position on cantilever beam has been discussed. The analysis is done by moving actuator at seven different positions on beam in which it found that maximum voltage generated is found to be at, when piezo actuator is located at extreme position towards the fix end of beam, 5 mm from fix end of beam. Considering this actuator position as maximum charge generation further study is carried out for various speeds (Figure
This analysis is carried out at seventeen different speeds (rpm) of engine which are 750, 850, 950, 1075, 1155, 1250, 1350, 1470, 1650, 1750, 1840, 1930, 2050, 2150, 2250, 2350, and 2400 rpm. Vibration amplitude response in turns of transverse displacement was captured by Laser Vibrometer for 120 seconds by varying engine speed from 750 to 2400 rpm; vibration amplitude graph in real mode is shown in Figure
Amplitude of deflection of beam free end at various speeds.
Voltage generation at various engine speeds by the end of 12 minutes.
After measuring vibration amplitude signature in a continuous form from 750 to 2400 rpm, charge generated in turn of voltage at particular speed individually was carried out. In this section engine speed kept constant for a particular time period and voltage generated by piezoelectric patch over the beam that was noted down with 5 mm distance from fix end were measured. Experimentation was carried out for 17 different speeds which mentioned as earlier. Time period for this measurement was 12 minutes. During measurement it was found that charge generated goes on increasing up to 10 minutes; after this the curve becomes constant, so data was recorded up to 12 minutes time span for every individual speed test shown in Figure
After noting down voltage values, the same experimentation was carried out for current for estimation of power as we know that power is
For the different parameters of this piezoelectric power generator (cantilever beam mounted on the engine), all analytical values are obtained with the help of all previously derived mathematical formulations. The power of 200.8
For the value of constant
Now,
And
So
Hence the power is calculated by putting all data in formula as
In order to compare the analysis results for the energy harvesting using engine vibrations, the results are summarized for a case study when piezo position is 283 mm from fix end of beam, as shown in Table
Comparison of the analysis results for the energy harvesting.
Analysis  Volt (V)  Current (mA)  Power ( 

FEA  2.82  0.069  194.6 
Experimental  2.71  0.067  181.57 
Analytical  2.83  0.0709  200.6 
Figure
Comparison of analytical power generation of piezo position over cantilever beam at 5 mm and 283 mm.
Figure
Analytical and experimental comparison when piezo position is at 5 mm from fix end of cantilever beam.
It is observed that finite element solution and analytical solution are in close match (2.7% difference). Experimental and analytical solutions are also in close match (9.5% difference). The reason for any difference between analytical and experimental results is that the vibrations of the engine do not completely transfer to cantilever beam free end. Transmission losses occur between the engine and cantilever beam.
Here the results and analyses of vibration energy harvesting by engine vibrations from 4stroke diesel car engine are presented. For the comparison of all the three analyses FEA, analytical, and experimental, we considered a special case study in which piezo is laminated at a distance of 282 mm from fix end. The comparison is done on the first natural frequency of 14.16 Hz and deflection at free end of 3.98 mm. The output power results for this case study in FEA, experimental, and analytical analyses are 194.6
The authors declare that there is no conflict of interests regarding the publication of this paper.