The present work exploits the centripetal, Coriolis and Euler forces generated in a rotating windmill. The MEMS device is placed on the blade of a windmill to harvest the energy. Modal analysis is carried out to optimize the dimensions of the structure to match the desired conditions. The real time response of the structure and the voltage generated in the piezoelectric layer are evaluated using transient analysis. It was noticed that Euler and Coriolis forces have a significant contribution in the initial time when the wind turbine accelerates from rest. The later portion is dominated by the Coriolis and Euler forces, and in some instances they cancel out each other. However, there is always a steady contribution from the centripetal force which is proportional to the magnitude of angular velocity of the wind turbine

Pavan R

Shyamsundar P I

Venkatesh K P Rao

English

Vibroengineering PROCEDIA

 60 VIBROENGINEERING PROCEDIA. NOVEMBER 2019, VOLUME 29  
Analysis of vibration based windmill coupled 
micromachined energy harvester 
Pavan R1, Shyamsundar P I2, Venkatesh K P Rao3 
Department of Mechanical Engineering, Birla Institute of Technology and Science,  
Pilani, Rajasthan, 333031, India 
3Corresponding author 
E-mail: 1f2016405@pilani.bits-pilani.ac.in, 2f2016378@pilani.bits-pilani.ac.in, 
3venkateshkp.rao@pilani.bits-pilani.ac.in 
Received 1 November 2019; accepted 7 November 2019 
DOI https://doi.org/10.21595/vp.2019.21159 
Copyright © 2019 Pavan R, et al. This is an open access article distributed under the Creative Commons Attribution License, which 
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 
Abstract. The present work exploits the centripetal, Coriolis and Euler forces generated in a 
rotating windmill. The MEMS device is placed on the blade of a windmill to harvest the energy. 
Modal analysis is carried out to optimize the dimensions of the structure to match the desired 
conditions. The real time response of the structure and the voltage generated in the piezoelectric 
layer are evaluated using transient analysis. It was noticed that Euler and Coriolis forces have a 
significant contribution in the initial time when the wind turbine accelerates from rest. The later 
portion is dominated by the Coriolis and Euler forces, and in some instances they cancel out each 
other. However, there is always a steady contribution from the centripetal force which is 
proportional to the magnitude of angular velocity of the wind turbine. 
Keywords: MEMS, piezoelectric materials, energy harvesting, natural frequency, transient 
analysis. 
1. Introduction 
With the concerns over the depletion of fossil fuels as an energy source, renewable energy is 
gaining popularity. Wind energy has the potential to become a significant source of energy in the 
future. In [1], authors have given a detailed account on harnessing energy using piezoelectric 
materials. An idea of harnessing electricity using piezoelectric material through various devices 
are reported in [2-6]. This manuscript describes a new approach to increase energy production 
from a windmill using a MEMS energy harvester. The MEMS device consists of a proof mass 
coupled to four Z-shaped cantilevers. This setup is placed on the blade of a windmill. 
The idea is to exploit the centripetal, Coriolis, and Euler forces generated in a rotating  
windmill, which otherwise goes unutilized since they increase the strain energy in the blades. This 
also gets subjected to random vibration, due to the wind as well as the vibrations of the whole 
structure. The device consists of a proof mass connected to thin beams and can move in all 
directions with different stiffness. When the windmill rotates, the centripetal acceleration initiates 
the motion in a direction. As this is a rotating frame, Coriolis force gets generated, and it acts in 
the direction perpendicular to rotation vector and velocity vector. These forces are supplemented 
by Euler forces created because of angular acceleration or deceleration of the windmill. 
All these forces, along with the random vibrations, produce stresses in the beams which can 
be converted into electricity with the help of piezoelectric material, which otherwise goes 
unutilized. This can supplement the conventional wind energy produced to a reasonable extent. 
Our device aims to harvest the strain energy created in the blades of the windmill with the help 
of a MEMS device. The device consists of a proof mass supported by four arms, which is driven 
by Euler, Centripetal and Coriolis forces created due to the windmill rotation and proof mass 
movement. This motion of the proof mass is utilized to create stress in the supporting arms, and 
the points of highest stress are identified. The so-identified points are made of piezoelectric 
materials, which are used to create potential differences and hence generate power. 
Fig. 1 shows the final geometry of the energy harvester, has a uniform thickness of 5 µm. This 
ANALYSIS OF VIBRATION BASED WINDMILL COUPLED MICROMACHINED ENERGY HARVESTER.  
PAVAN R, SHYAMSUNDAR P I, VENKATESH K P RAO 
 ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 61 
is the optimum geometry with dimensions such that the beams are not too stiff, and the Coriolis 
and centripetal accelerations of the windmill rotor can cause vibrations in the proof mass, and 
stresses are generated in the beams so that energy can be harvested using a piezoelectric material. 
The material used in this study is Ga-As. Table 1 shows the geometric and material properties of 
the structure. The material GaAs has a Zinc blende structure with piezoelectric constant, 𝑑ଵସ, 
2.63 PC/N. 
Table 1. Material and geometric properties of the structure 
Property Value 
Density 5320 kg/m3 
Elastic modulus 85.5 GPa 
Poisson’s Ratio 0.31 
Length of the beam, 𝑙௕ 100 µm 
Width of the beam 5 µm 
Proof mass  500 × 500 µm2 
 
Fig. 1. The structure of the energy harvester 
2. Modelling and analysis 
The study involves geometric parameterization, modal analysis and transient structural 
analysis of windmill coupled energy harvester. As the structure is of uniform thickness, a 2-D 
model was generated in ANSYS, and modal analysis was carried out. The proof mass length, beam 
thickness, and structural thickness were taken as parameters for optimization of the natural 
frequencies 
The optimal geometry was used to analyze the stresses generated due to the action of 
centripetal, Coriolis and tangential forces. These stresses generate potential on the surface of the 
piezoelectric material. Transient structural analysis was carried out to account for the stresses 
induced due to the combined loading (centripetal, Coriolis and Euler forces) that can arise in the 
device when mounted on a rotating body such as the windmill. COMSOL Multiphysics was used 
to simulate this environment – The device is hinged at a distance of 88 meters from a rotating 
frame. This resembles the device being attached to a windmill blade, at 8 meters from the center 
of the rotor and is constrained from performing free motion in any direction except for rotation 
with respect to the center (not the proof mass). Two different profiles of angular velocity of the 
wind turbine were given as inputs to study the resultant stresses and piezo surface potentials 
generated. 
A hypothetical angular velocity profile, which shows a steep and sudden increase and decrease 
in the angular velocities, was studied. This study was done in order to qualitatively account for 
the contribution of Euler force and Coriolis force in stress generation. Whereas the realistic 
angular velocity profile [7] depicting the working of a wind turbine on any normal day was taken 
ANALYSIS OF VIBRATION BASED WINDMILL COUPLED MICROMACHINED ENERGY HARVESTER.  
PAVAN R, SHYAMSUNDAR P I, VENKATESH K P RAO 
62 VIBROENGINEERING PROCEDIA. NOVEMBER 2019, VOLUME 29  
to account for the real-life stresses produced. It represents the angular velocity profile of a wind 
turbine starting from rest and running at an almost constant angular velocity with mild periodic 
variations. 
3. Results and discussion 
3.1. Modal analysis 
3.1.1. Mode shapes 
Using the primitive geometry (Fig. 1), modal analysis was carried out to determine the mode 
shapes and the corresponding natural frequencies. The modes of interest are given in Fig. 2. The 
four ends of the beams are fixed. Since the axial stiffness in the 𝑌-direction is highest, the natural 
frequency of the 𝑌-mode is the highest, which is evident from Fig. 2. Given these results, the 
modes in which various forces act are as follows: 𝑍-direction – Euler, 𝑌 direction – Coriolis, 
𝑋 direction – Centripetal. 
 
a) 
 
b) 
 
c) 
Fig. 2. Mode shapes of interest: a) out of plane mode at 10.85 kHz,  
b) 𝑋-direction mode at 24.408 kHz, c) 𝑌-direction mode at 30.799 kHz 
Further, parametric studies were carried out to reduce the natural frequencies to the necessary 
limits and hence to reduce the force required to produce motion and stresses in every mode 
described. 
3.1.2. Geometric parameterization 
The geometrical dimensions of the structure such as the proof mass size, structure thickness, 
and beam thickness were chosen as parameters to optimize the natural frequencies of the structure. 
For this, the variation of natural frequencies with each of the aforementioned parameters is shown 
in Fig. 3. It can be noticed that the natural frequencies for all modes decrease with increase in the 
size of the proof mass, and the natural frequency for all modes increases with increase in beam 
thickness. It is also well established that the natural frequency increases with the increase in 
structure thickness. 
3.2. Transient structural analysis 
3.2.1. Hypothetical profile 
The maximum von mises stresses induced in the device were extracted from the transient 
analysis and results are as shown in Fig. 4.  
The corresponding maximum surface potentials produced is compared to the input angular 
velocity profile and is shown in Fig. 5. It can be noticed that the Euler forces and Coriolis forces 
have significant contributions in the time range 0-3 seconds. This can be seen by the higher peak 
ANALYSIS OF VIBRATION BASED WINDMILL COUPLED MICROMACHINED ENERGY HARVESTER.  
PAVAN R, SHYAMSUNDAR P I, VENKATESH K P RAO 
 ISSN PRINT 2345-0533, ISSN ONLINE 2538-8479, KAUNAS, LITHUANIA 63 
of the surface potential graph in this time range. The rest of the surface potential line follows the 
angular velocity line proportionally which implies that the centripetal force makes majority of 
contribution at other time ranges. 
 
Fig. 3. The variation of natural frequency with various geometric parameters 
 
Fig. 4. Maximum von mises stress developed a 
function of time (hypothetical profile) 
Fig. 5. Maximum surface potentials developed  
with time (hypothetical profile) 
3.2.2. Realistic profile 
The maximum von mises stresses produced in the volume of the device concerning time were 
computed, and results are as shown in Fig. 6. 
The corresponding maximum surface potentials produced is compared to the input angular 
velocity profile and is shown in Fig. 7. Euler forces and Coriolis forces have a significant 
contribution in the time range 0-5 seconds when the wind turbine accelerates from rest. After 5 
seconds, when there is a mild periodic variation in the angular velocity, in some instances the 
Coriolis force and Euler force add up (such as the time range 10-12 seconds), and in some 
instances they cancel out each other (such as the time range 7-10 seconds). However, there is 
always a steady contribution from the centripetal force which is proportional to the magnitude of 
angular velocity of the wind turbine. 
ANALYSIS OF VIBRATION BASED WINDMILL COUPLED MICROMACHINED ENERGY HARVESTER.  
PAVAN R, SHYAMSUNDAR P I, VENKATESH K P RAO 
64 VIBROENGINEERING PROCEDIA. NOVEMBER 2019, VOLUME 29  
 
Fig. 6. Maximum von mises stress developed  
with time (realistic profile) 
 
Fig. 7. Maximum surface potentials and angular 
velocity vs time (realistic profile) 
4. Conclusions 
In the present study, a new concept of harnessing wind energy is introduced. Transient analysis 
simulation was carried out and it was observed that potential difference of the order 1 mV  
develops. The mass of each device is around 10 nanograms which is negligible compared to the 
mass of the windmill blade and hence not affecting the basic windmill operations. When several 
such devices are coupled in series, significant power can be harnessed.  
Future scope of the study can include experimental verification, fatigue analysis, efficiency 
and economic viability. 
References 
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[2] Priya Shashank Piezoelectric Windmill Apparatus. U.S. Patent No. 8,294,336, 2012. 
[3] Zhu Qiang, Peng Zhangli Mode coupling and flow energy harvesting by a flapping foil. Physics of 
Fluids, Vol. 21, Issue 3, 2009, p. 033601. 
[4] Lockhart Robert, et al. A wearable system of micromachined piezoelectric cantilevers coupled to a 
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Electro Mechanical Systems, 2014. 
[5] Alper Erturk, Inman Daniel J. Piezoelectric Energy Harvesting. John Wiley and Sons, 2011. 
[6] Kim Heung Soo, Kim Joo-Hyong, Kim Jaehwan A review of piezoelectric energy harvesting based 
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Analysis of vibration based windmill coupled micromachined energy harvester

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