vibration energy harvesting: going beyond idealization

Sigma Xi - Student Resarch Showcase 1March, 2013

Experimental analysis of a piezoelectric energy harvesting system for harmonic, random, and sine on random vibration

Research conducted under Brian K. Hatchell (PNNL) in fulfillment of DOE Office of Science, Science Undergraduate Laboratory Internship (SULI) and to support projects contracted by the U.S. Army

Sigma Xi - Student Research Showcase 2013

JACKSON W. CRYNSB.S. Applied Mathematics, Engineering and PhysicsUniversity of Wisconsin - Madison

Sigma Xi - Student Resarch Showcase 2

Abstract

Advancements in low power electronics in the past decade allow systems to run off of progressively less energy and even eliminate the need for external power supplies completely. The key to self-sustaining electronics is the ability to harness energy from the surrounding environment and turn it into usable electrical energy, or Energy Harvesting. In many industrial applications, ambient energy is readily available in the form of mechanical vibrations. Piezoelectric ceramics provide a compact, energy dense means of transducing mechanical vibrations of the environment to electrical power. Harvesting power with a commercially available piezoelectric vibration powered generator using a full-wave rectifier conditioning circuit is experimentally compared for varying sinusoidal, random and sine on random (SOR) input vibration scenarios. Much of the available literature focuses on maximizing harvested power through theoretical predictions and power processing circuits that require accurate knowledge of generator internal electromechanical characteristics and idealization of input vibration, which cannot be assumed in general application. Characteristics of complex vibration sources significantly alter power generation and processing requirements, likely rendering idealized analysis inaccurate. Going beyond idealized steady state sinusoidal and simplified random vibration input, SOR testing allows for more accurate representation of real world ambient vibration and is an invaluable tool in harvester development.

March, 2013


Background

What is Energy Harvesting?

Application Goals

Vibration Powered Generators (Transducers)

Piezoelectric Effect

Power Conditioning

Sigma Xi - Student Resarch Showcase

What is Energy Harvesting?

• Every process dissipates waste energy to the surrounding environment

• Ambient energy comes in many usable forms

[5]

• Convert ambient energy to usable electrical energy – transducers• Small amounts of power – mW or µW (milli-Watts or micro-Watts) [3]

• Not a new idea!4March, 2013

Electromagnetic Radiation (1) Thermal Gradient (2) Potential Energy Forms (3) Vibration (Potential + Kinetic) (4)

(5) (7)(6) (8)


Application Goals

Supply power to off grid devicesRemote equipment

Monitors in hazardous environments

Wireless data logging and transmission

Reduce maintenance requirements and costs

Relieve dependence on primary batteries

Fits into national “green” initiatives

March, 2013

(9)

(10)


Vibration Powered Generators (Transducers)

Machines, moving parts and large power generators present significant vibration energy [2, 3, 8]

Three transduction mechanisms [1, 8, 10]:Electrostatic – parallel plate capacitor

Electromagnetic – magnetic induction

Piezoelectric – piezoelectric effect

Numerous studies have been conducted on power transduction [15,3,9]

Piezoelectric transducers are the most energy dense [8,12]

March, 2013

Driving and Biking Walking Numerical and Theoretical Simulations

(11) (12) (13)


Piezoelectric Effect

Electric charge accumulates in certain materials in response to applied mechanical stress [11]

This study analyzes a commercially available bimorph transducerTwo piezoelectric layers

Two electrical signals of opposite sines

March, 2013

(14) (15)


Power Conditioning

Conditioning circuitry – the components necessary to supply power from the transducer to the target electronics with specified current and voltage characteristics

This study includes the target electronics in the conditioning circuit

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Example conditioning circuit

(16)


Research Overview

Research Goals {10}

Energy Harvesting Architecture {11 – 18 }

Literature Review and Harvester Validation {19 – 36}

Expanded Vibration Testing {37 – 46}

Discussion and Design Implications {47 – 50}


Research Goals

Convince the reader that accurate experimental testing is an invaluable and essential tool in harvester development

Determine implications of complex vibration characteristics on harvester performance

Show that theoretical power harvesting predictions and numerical simulations require assumptions that cannot be made in general application:

Oversimplifying assumptions of input vibration

Exact knowledge of transducer internal electrical and mechanical characteristics

March, 2013


Energy Harvesting Architecture

12

Piezoelectric transducerV25w QuickPack® actuatorproduced by Midé [24,25]

Proof mass(for frequency tuning)

Rigid clamp(fixed-free cantilever beam)

Vibration SourceLDS V721 – 1000 L shaker

Closed loop vibration control

Power conditioning circuitryStandard circuit


March, 2013

AC signal

Exact transducer internal electrical and mechanical characteristics unknown

[17]



Mount in cantilever configurationInput vibration at base

Natural frequencyTune with proof mass to match source vibration

Modal analysis allows for accurate natural frequency determination

Bare natural frequency of 124.5 Hz

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Piezoelectric Transducer Set-Up

[18]



AC-DC conversionTransducer creates AC signal (oscillatory)

Most microelectronics require DC

Full-wave bridge rectifier

Signal smoothingA time varying signal is damagingto DC electronics

Provide power to load Microelectronics

Resistor

Secondary (rechargeable) battery

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Power Conditioning Duties

http://www.electronics-tutorials.ws/diode/diode_6.htmlhttp://www.eleinmec.com/article.asp?18

[19]

[20]



Standard (linear) InterfaceTarget electronics (load) modeled represented by resistor

Net transfer of energy through transient components is null, thus equivalent resistance is sufficient

Capacitance is constant, locate optimal impedance by varying resistanceCR = 600 µF, RL -> variable.

Non-linear processing not considered in this studyDesigned for steady sinusoidal vibration only

Dissipates extra power

Application specific designs require additional voltage controlAdditional control circuitry always dissipates extra power

Circuit used here finds the maximum available power for harvesting(except for loses in rectifier bridge and capacitor leakage)

March, 2013

Power Conditioning Circuitry [3,7,14-16,26]



Test multiple scenariosHarmonic, Random – simplified

SOR – sine and random superposition for accurate testing

Characterize and control the input vibration by acceleration

Acceleration response is the most common form of vibration measurement and characterization

Allows for subsequent validation in other experiments

Method assumes harvester does not alter input dynamics (source is much larger than harvester) [31]

Monitor force and acceleration with PCB impedance head 288D01

March, 2013

Impedance head

Shaker armature



Note that input power is NOT constant for identical acceleration amplitudes at different driving frequencies and bandwidths

Mechanical sinusoidal power is proportional to velocity amplitude

Velocity is inversely proportional to the natural frequency for a given acceleration

[20]

Similarly input power increases with bandwidth since more sine components are incorporated

Input power variations are not of concern in design, however, since ambient power is of no cost to the developer

March, 2013



Fundamental Objective:

How does power harvesting vary with input acceleration characteristics, transducer natural frequency, and load resistance?

Measure voltage and current delivered to load to find harvested power

Measure input acceleration and force to find input power, when needed

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Literature Review and Harvester Validation

General

Sinusoidal input vibration*

Flat random vibration*

*Analytical relations for purely sinusoidal and flat broadband vibration have been developed in other works for custom developed harvesters and simulations [6, 9 ,18-20]



Properly developed harvesters can harvest tens to hundreds of mW of power [1, 3, 6-9]

Vibration Energy Harvesters (VEH) require careful development for effective power conversion

Characterization of ambient source vibration

Tuning of transducer to achieve resonance

Determination of optimal impedance

Harvesting electrical power induces mechanical damping and alters the transducer vibration dynamics, creating an electromechanical system [9]

March, 2013


Conditioning circuitry designs can range from a few analog components to complex architectures controlled by firmware [3,7,14-16,26]

Non-linear power processing has been shown to significantly increase harvested power over passive (standard) power processing

Synchronized Charge Extraction (SEC)

Synchronized Switch Harvesting with Inductor (SSHI)

Additional control circuitry dissipates extra power, reducing efficiency


March, 2013

[21]



Previous research heavily focused on two idealized vibration cases:steady state sinusoidal vibration sources and flat, broadband random profiles [1, 6, 7, 9, 12, 13, 16, 17]

Analysis and modeling are simplified in these cases

Non-linear SSHI requires steady state sinusoidal

Non-linear SEC performance drops in non-sinusoidal vibration environments

Many studies omit inclusion of the significant power loss from additional control circuitry that can be on the order of hundred of μW []

No studies addressed voltage fluctuations induced by random vibration

March, 2013

[22] [23]



Few studies incorporated more complex vibrational sources [2,18]Sinusoidal and flat random vibration inputs are scarce in application

Real ambient conditions can be accurately modeled by incorporating both random and sinusoidal content

March, 2013

Acceleration Spectral Density of a typical Apache Helicopter flight is significantly more complex than sinusoidal or flat random vibration

• Peaks are accounted for by sinusoidal components superposed on top of a random profile



Experimental Sinusoidal Input Validation

Unless otherwise stated, harvester is driven at the transducer natural frequency

Sinusoidal vibrations are characterized by driving frequency and amplitude

“Amplitude” refers to acceleration amplitude, zero to peak

March, 2013



Sinusoidal – Amplitude variation

Theoretical Expectations:Displacement and voltage scale linearly with input amplitude

Power scales quadratically with voltage and thus amplitude

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Quadratic trend is clearly exhibited at two natural frequencies.



Sinusoidal – Natural Frequency VariationTheoretical Expectations:

Transducer cantilever displacement is inversely proportional to the natural frequency squaredD ~

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For identical input amplitudes: lower natural frequencies harvest more power. *

* Consequence of input power variations



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Sinusoidal – Impedance VariationTheoretical Expectations:

Resistance (impedance) effects harvested power

Optimal resistance varies with natural frequency

Optimal resistance is around 40 kΩ and 15 kΩ for 58.3Hz and 124.5 Hz respectively



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Sinusoidal – Impedance Variation (cont’d)Theoretical Expectations:

Optimal resistance is inversely proportional to the natural frequency

Ropt ~

As natural frequency increases, optimal impedance decreases and peak narrows



March, 2013

Sinusoidal –Frequency Response Function (FRF) for powerTheoretical expectations:

All mechanical vibratory systems have a frequency dependent transfer function

Deviating from natural frequency lowers the resulting transducer dynamic amplitudes and thus harvested power

Harvested power drops by approximately 50% within 1 Hz deviation from natural frequency, reinforcing the importance of accurate tuning of transducer

Implies that there is an approximate non-negligible transducer bandwidth of +/- 3 Hz in which power is generated



Experimental Random Input Validation

The terms broadband and random vibration are often used interchangeably, but random vibrations need not be broad in general

Power is averaged of 100s samples to increase repeatabilityRandom vibrations vary statistically in time [18]

Random vibrations are characterized by Power Spectral Density (PSD), or acceleration spectral density, profile in units of [g2/Hz]

Integrating the PSD over a frequency range and taking the square root results in the Root Mean Square (RMS) level of vibration in g’s for that filtered frequency range

“Amplitude” refers to spectral density near the transducer natural frequency

It is shown later that spectral densities far from the resonant frequency negligibly influence the harvester

March, 2013



Random – Amplitude VariationTheoretical Expectations:

Power scales linearly with spectral density

Power scales inversely with natural frequency, as with sinusoidal

March, 2013

As derived in [18], harvested power varies linearly with spectral density



Random – Impedance VariationTheoretical Expectations:

Random vibration has higher optimal resistance than sinusoidal vibration

Optimal impedance scales inversely with natural frequency

March, 2013

Optimal resistance is higher for random vibration than sinusoidal vibration for both frequencies, and decreases with natural frequency for each vibration type

33


Random – Bandwidth VariationTheoretical Expectations:

Power is independent of input bandwidth when significantly longer than that of transducer

Unspecified results for short bandwidths or varying spectral density profile shapes

March, 2013 Sigma Xi - Student Resarch Showcase

Except for random statistical deviations from one point the next, average harvested power is constant over all bandwidths



Random – Frequency VariationTheoretical Expectations:

Harvested power is inversely proportional to transducer natural frequency

March, 2013

For identical input amplitudes and bandwidths, higher natural frequencies produced less power



Harvester met and agreed with theoretical predictions for special casesSteady state sinusoidal vibration

Flat broadband vibration

Limitations of idealized studiesReal sources commonly consist of numerous sinusoidal peaks, complex random profiles, nonlinear and transient interactions

No found studies incorporated non-flat random profiles

No found studies incorporated multiple sinusoidal components

No found studies incorporated interactions of both sinusoidal and random content

No found studies addressed time variations in random vibrations

March, 2013


Expanded Vibration Testing

March, 2013

Short bandwidth and non-flat random profiles

Sinusoidal and random component interaction

Multiple sinusoidal component interaction


Random – Short Bandwidth VariationTest varying bandwidths with identical gRMS values

Each random profile in the left plot has a 0.1414 gRMS acceleration level (note that 50 Hz and 500 Hz expand beyond plot window)

Each scenario was supplied to the bare transducer to produce right plot

The harvester gets progressively worse at harvesting power as bandwidth increases, for identical input power and gRMS levels.



Random – Non-Flat profileTest impact of spectral density profile variations

Varying shape outside the transducer natural frequency

Identical in the bandwidth of the transducer (124.5 Hz ± 3 Hz)

March, 2013

Three profiles produced nearly identical output powers of 0.65, 0.67, and 0.71 μW respectively.

Implies harvested power depends only on the spectral density near the natural frequency, other densities do not affect harvested power.

39


March, 2013

SOR – Constant Sinusoid, Variable Spectral DensityTest the effects of noise when harvesting from sinusoidal peak

0.3 g sinusoidal peak and increasing spectral density, PSDs plotted on left

Linear superposition suggests that power should increase, above the sinusoidal power, as seen in random vibration

Harvested power increases with spectral density, however differently from the random case due to time domain variations and imperfect super position in control software



SOR – Optimal ResistanceDetermine the optimal resistance when both sinusoidal and random content is present

Sinusoidal and random cases had significantly different optimal resistances

Does SOR bridge this gap?

March, 2013

Optimal resistance increases from ~15kΩ for sinusoidal to ~45kΩ for random as spectral density increases.

In other words, as vibration dominance shifts from sinusoidal to random, so does the optimal resistance

41


SOR – Multiple Sinusoidal ComponentsTest interactions of two dominant sinusoidal components

Two tones seen within 3 Hz of each other in Apache helicopter vibration

More components increase input power in the transducer bandwidth

FRF shows that harvested power value depends of frequency separation

Test two tones of 0.3 g amplitude at 58.3 Hz natural frequency

March, 2013

As frequency separation increases, harvested power approaches that of a single sinusoid at the natural frequency.

At 0.25 Hz separation, average harvested power is 28% higherMore than 1 Hz separation, harvested power is only a few % higher



SOR – Multiple Sinusoidal Components (cont’d)Multiple sine components induce significant amplitude beating in source vibration and output voltage

With negligible random vibration levels, input vibration reaches zero (left)

Filter capacitor prevents load voltage from dropping to zero and alters the input voltage from the transducer (right)

March, 2013

43


SOR – Multiple Sinusoidal Components (cont’d)

Amplitude beating is dependent on frequency separationFRF suggests beating should decrease with separation

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As frequency separation increases, beat amplitude approaches zero

For two sinusoidal components 0.25 Hz apart, load voltage beats at nearly 100% of single sine component voltage (~8 V at 58.3 Hz and 3.5 V at 124.5 Hz)

44


SOR – Multiple Sinusoidal Components (cont’d)Inclusion of more sine components in the transducer bandwidth amplifies effects

Average harvested power and amplitude beating both increase

As number of sinusoidal components increases, responses approaches that of random vibration with high spectral density

Test three 0.3 g sine components supplied to the bare transducer

March, 2013



Voltage FluctuationsInteractions between frequencies induce fluctuations in voltage delivered to the load

DC electronics are typically, designed to utilize a constant voltage supply

Even slight voltage fluctuations cause electronic devices to drop out of regulation, affect sensor readings and damage the components

No found studies discussed implications of voltage fluctuations

Sinusoidal vibrations provide nearly constant voltage to the loadSee the left plot on slide 18 (the capacitor voltage is the voltage supplied to the load)

Random vibrations induce significant voltage supply fluctuations

SOR vibrations can result in quite complicated vibration interactions and voltage supply waveforms

March, 2013

46


Voltage Fluctuations (cont’d)Load supply voltage fluctuations scale with amplitude

Multiple sinusoidal components and random vibrations alter waveform

Input power within the transducer natural frequency scales average power (i.e. including a single sinusoidal component, as in slide 39, translates waveform vertically but does not increase fluctuation intensity)

March, 2013

Sample time responses for 500 Hz bandwidth random signals supplied to a transducer tuned to 58.3 Hz at varying spectral densitiesPeak to peak:0.36 V at 2.5e-4 g2/Hz and3.61 V at 5e-3 g2/Hz


Discussion and Design Implications



Steady state, sinusoidal vibration is the most ideal form of input vibration

Only requires design for natural frequency and optimal impedanceLower frequencies harvest more power for similar amplitudes

No significant voltage fluctuations

No time dependencies

Rarely seen application

Random vibration is the least ideal form of input vibrationOnly requires design for natural frequency and optimal impedance

Significantly less efficient than sinusoidal In order to harvest significant power spectral densities, more than 1e-3 g2/Hz are typically needed

Usually only 1e-6 to 1e-4 g2/Hz in application [2,8,32]

Overshadowed by voltage fluctuations, requires additional charge control circuitry

March, 2013



Designing a harvester for use with complex vibration sources requires acknowledgement of more characteristic factors than sinusoidal or random vibration

Sinusoidal frequencies, number of sinusoidal components, separation between sinusoidal components, random spectral density profile, determination of optimal impedance

Ignoring random content or nearby sinusoidal content gives a poor representation of harvested power and load voltage

Ignoring random content gives incorrect optimal impedance

Harvested power gains from additional random component or multiple sinusoidal components are overshadowed by induced voltage fluctuations

Improper source vibration and harvester response representation during development hurts application

Lowers power harvesting ability and efficiency

Omitting necessary voltage control and processing circuitry can bring about unexpected consequences such as inaccurate sensor readings, poor circuit functionality and possible damage to target electronics

March, 2013


Conclusion

Idealized sinusoidal and random vibration studies are NOT sufficient for general harvester development

Environments with sufficiently low noise or random vibration levels and sufficiently spread dominant frequencies may suffice

Theoretical and numerical predictions hinge upon exact knowledge of transducer mechanical and electrical properties

This cannot be assumed in general

Internal transducer electrical and mechanical properties are unknown unless custom developed by applicant

Sine on random vibration testing and experimental validation is an essential tool in harvester development

SOR testing can recreate almost any vibration environment

SOR control can provide accurate quantitative results when harvesting from complex vibrational sources

March, 2013

Acknowledgements

Brian Hatchell for mentoring me through this experimental process and providing the inspiration for the project

Emiliano Santiago-Rojas for applying electrical expertise and making this cross discipline application possible

Karen Wieda for advising and aiding my assimilating into the PNNL research environment

A special thanks to:

Department of Energy – Office of Science and the U.S. Army for making this research project possible

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vibration energy harvesting: going beyond idealization

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