Effect of Temperature and Thermal Cycles on PZT Ceramic Performance in Fuel Injector Applications

by

Sadegh Davoudi

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Department of Mechanical & Industrial Engineering University of Toronto

© Copyright by Sadegh Davoudi 2012

ii

Effect of Temperature and Thermal Cycles on PZT Ceramic

Performance in Fuel Injector Applications

Sadegh Davoudi

Master of Applied Science

Department of Mechanical and Industrial Engineering University of Toronto

2012

Abstract

This thesis presents an experimental analysis of the effect of temperature and thermal cycles on

the performance of PZT ceramics in fuel injector applications. Due to the increase in the

implementation of piezoceramics in applications such as fuel injection technology, it is

imperative to understand how temperature affects piezoceramic performance. In this project, the

fundamental piezoelectric properties ( , , ) of bulk PZT samples and high electric-field

properties of piezoelectric stack actuators were obtained with respect to temperature and thermal

cycles. The results show that increasing temperature will increase the fundamental piezoelectric

properties of bulk piezoceramics, capacitance of stack actuators, and the displacement of

piezoactuators in the absence of external load. Raising the temperature while applying a constant

preload will initially increase piezoactuator displacement, but decrease it at higher temperatures.

Temperature had a negative effect on the hysteresis in the displacement-voltage. Additionally,

thermal hysteresis decreased significantly in subsequent temperature cycles.

iii

Acknowledgements

I would like to offer my sincere gratitude to my supervisors Professor Ridha Ben Mrad,

Professor Siyuan He, Dr. Eswar Prasad, and Professor Anthony Sinclair for providing me with

guidance and support throughout this project.

I would also like to thank our collaborators at Sensor Technology Limited, especially Dr. Sailu

Nemana for his invaluable support through both technical knowledge and equipment use.

Additionally I would like to thank Professor Yu Sun and Professor Javad Mostaghimi for access

to their equipment.

Through these years my lab colleagues have created an enjoyable and comfortable working

environment. I would especially like to thank Alaeddin, Bing, Hirmand, Imran, Jalal, James,

Khalil, Mike, Mohammad Hossein, Paul, Sergey, Tae, and Vainatey for their friendship and

support.

Finally, I would like to thank my family for their continuous and unconditional support

throughout my studies.

iv

Table of Contents

Acknowledgements .......................................................................................................................... iii 

Table of Contents ............................................................................................................................. iv 

List of Tables .................................................................................................................................. vii 

List of Figures ................................................................................................................................ viii 

List of Symbols ................................................................................................................................ xi 

List of Appendices ......................................................................................................................... xiii 

Chapter 1 ........................................................................................................................................... 1 

  Introduction and literature review ................................................................................................ 1 1

1.1  Problem statement ................................................................................................................. 1 

1.2  Motivation ............................................................................................................................. 1 

1.3  Piezoelectricity basics ........................................................................................................... 2 

1.3.1  Piezoelectric physics ................................................................................................. 2 

1.3.2  Linear piezoelectric theory ....................................................................................... 4 

1.3.3  Piezoelectric ceramic types ....................................................................................... 6 

1.4  Fuel injectors and piezoelectric actuators ............................................................................. 7 

1.5  Multilayer piezoelectric stack actuators ................................................................................ 9 

1.6  Piezoelectricity and temperature ......................................................................................... 11 

1.6.1  Effect of temperature on bulk ceramics .................................................................. 11 

1.6.2  Effect of temperature on multilayer piezoelectric stack actuators .......................... 13 

1.7  Objectives and approach ..................................................................................................... 13 

1.8  Contributions ....................................................................................................................... 15 

Chapter 2 ......................................................................................................................................... 16 

  Experimental parameters ............................................................................................................ 16 2

2.1  Piezoelectric material selection ........................................................................................... 16 

v

2.2  Determination of fundamental piezoelectric properties using the resonance method ........ 16 

2.2.1  Determination of the dielectric constant ................................................................. 18 

2.2.2  Determination of the elastic and piezoelectric constants ........................................ 18 

2.3  Nonlinear piezoelectric properties ...................................................................................... 21 

2.4  Fuel injector operating conditions ...................................................................................... 23 

2.5  Monolithic and stack piezoelectric actuator selection ........................................................ 23 

2.5.1  Bulk piezoceramic selection ................................................................................... 24 

2.5.2  Multilayer piezoelectric selection ........................................................................... 25 

2.6  Experimental Configurations .............................................................................................. 26 

2.6.1  Fundamental piezoelectric constants of bulk piezoelectric ceramic ....................... 26 

2.6.2  Nonlinear piezoelectric properties of piezoelectric stack actuator ......................... 27 

Chapter 3 ......................................................................................................................................... 28 

  Experimental setup ..................................................................................................................... 28 3

3.1  Fundamental Piezoelectric Property Measurements ........................................................... 28 

3.1.1  Bulk piezoceramic sample holder ........................................................................... 28 

3.1.2  Resonance measurements test setup ....................................................................... 30 

3.2  Nonlinear piezoelectric property measurements ................................................................. 32 

3.2.1  Multilayer stack actuator test rig ............................................................................. 35 

Chapter 4 ......................................................................................................................................... 39 

  Bulk piezoceramic experimental results .................................................................................... 39 4

4.1  Effect of temperature on piezoelectric properties ............................................................... 41 

4.1.1  The piezoelectric coefficient ( 33) ........................................................................ 41 

4.1.2  The dielectric permittivity ( 33 ) .......................................................................... 42 

4.1.3  The elastic compliance coefficient ( 33 ) ............................................................. 43 

4.1.4  The coupling factor ( 33) ....................................................................................... 44 

4.2  Discussion ........................................................................................................................... 45 

vi

Chapter 5 ......................................................................................................................................... 48 

  Stack actuator experimental results ............................................................................................ 48 5

5.1  Thermal expansion coefficient ............................................................................................ 48 

5.2  Effect of temperature on piezoelectric stack actuator properties ........................................ 49 

5.2.1  Effect of temperature on piezoactuator displacement-voltage cycle ...................... 51 

5.2.2  Effect of temperature on actuator stroke at 200 V .................................................. 53 

5.2.3  Effect of temperature on displacement hysteresis .................................................. 55 

5.2.4  Effect of temperature on piezoelectric actuator impedance .................................... 56 

5.3  Discussion ........................................................................................................................... 58 

  Conclusions and future work ..................................................................................................... 64 6

6.1  Conclusions ......................................................................................................................... 64 

6.2  Future work ......................................................................................................................... 65 

References ....................................................................................................................................... 66 

Appendix A - Length Extension Resonance Calculations .............................................................. 72 

Appendix B – Mechanical Drawings of Bulk Piezoceramic Sample Holder ................................. 75 

Appendix C – Mechanical Drawings of Piezoelectric Stack Actuator Test Rig Modifications ..... 79 

vii

List of Tables

Table 1.1 - Soft and hard piezoelectric ceramic comparison .......................................................... 6 

Table 2.1 – Polarization direction, electrode surfaces, and geometries of each mode ................. 20 

Table 2.2 – Properties of the monolithic piezoelectric ceramic .................................................... 25 

Table 2.3 – Properties of stack actuator ........................................................................................ 26 

Table 4.1 – Measured properties of bulk ceramic samples at room temperature ......................... 39 

Table 5.1 - Change in hysteresis area and width as a result of temperature increase from 26 to

130 °C ........................................................................................................................................... 56 

Table 5.2 - Change in actuator Cp and Rp for temperature change of 26 to 130 °C ..................... 56 

viii

List of Figures

Figure 1.1 - Designation of axes in piezoelectric materials ............................................................ 4 

Figure 1.2 – (a) Cross-section of Delphi’s piezoelectric based fuel injector, (b) heating of fuel

injector due to proximity to the combustion chamber ................................................................... 8 

Figure 1.3 - Multilayer stack actuator schematic ........................................................................... 9 

Figure 1.4 – The effect of constant (a) and variable (b) force on actuator displacement ............. 11 

Figure 2.1 - Sample and polarization direction for (a) and (b) measurement ................... 18 

Figure 2.2 - Impedance and Phase of a sample with length extensional mode geometry ............ 19 

Figure 2.3 - Electric field-to-displacement curve of the piezoceramic actuator under study ....... 22 

Figure 2.4 - Hysteresis area and width in a typical displacement-voltage curve .......................... 22 

Figure 2.5 - Bulk piezoelectric sample (dimensions are in mm) .................................................. 24 

Figure 2.6 - Piezoelectric actuator with characteristics shown in Table 2.3 ................................. 26 

Figure 3.1 - Sample geometry and coordinates ............................................................................ 28 

Figure 3.2 - Sample holder used in resonance measurements ...................................................... 29 

Figure 3.3 – Block diagram of bulk piezoelectric ceramic tests ................................................... 31 

Figure 3.4 – Bulk piezoceramic inside the sample-holder ............................................................ 31 

Figure 3.5 - Images of test setup for fundamental piezoelectric properties .................................. 32 

Figure 3.6 - Block diagram of spring loaded tests ........................................................................ 34 

Figure 3.7 - Block diagram of free displacement test setup ......................................................... 35 

Figure 3.8 - Test rig for nonlinear piezoelectric properties .......................................................... 36 

ix

Figure 3.9 - Stack actuator setup ................................................................................................... 37 

Figure 4.1 - The impedance spectrum for the length extensional mode and change of fr and fa at

26° and 151°C ............................................................................................................................... 40 

Figure 4.2 – Effect of a temperature cycle on the piezoelectric coefficient ( )........................ 41 

Figure 4.3 – Effect of a temperature cycle on the relative dielectric permittivity ( ) measured at

1 kHz ............................................................................................................................................. 42 

Figure 4.4 – Effect of a temperature cycle on the elastic compliance ( ) of piezoceramic ...... 43 

Figure 4.5 – Effect of a temperature cycle on the coupling coefficient ( ) .............................. 44 

Figure 4.6 – Effect of 1st temperature cycle on piezoelectric coefficient ( ) of piezoelectric

sample ........................................................................................................................................... 46 

Figure 4.7 – Effect of 1st temperature cycle on dielectric permittivity ( ) of bulk piezoelectric

ceramic .......................................................................................................................................... 47 

Figure 5.1 - Thermal expansion of piezoelectric stack actuator under different preloads ............ 49 

Figure 5.2 - Monitored waveforms of (a) voltage, (b) displacement, and (c) force during a typical

experiment ..................................................................................................................................... 50 

Figure 5.3 – Displacement - voltage curves of stack actuator with no external load actuated at (a)

0.1 Hz and (b) 50 Hz ..................................................................................................................... 51 

Figure 5.4 - Displacement - voltage curves of stack actuator with 5 MPa preload actuated at (a)

0.1 Hz and (b) 50 Hz ..................................................................................................................... 52 

Figure 5.5 - Displacement - voltage curves of stack actuator with 10 MPa preload actuated at (a)

0.1 Hz and (b) 50 Hz ..................................................................................................................... 52 

Figure 5.6 - Displacement - voltage curves of stack actuator with 20 MPa preload actuated at (a)

0.1 Hz and (b) 50 Hz ..................................................................................................................... 53 

x

Figure 5.7 - Stroke of the piezoelectric actuator under a 200 Vpp oscillating wave with 100 V DC

bias at 0.1 Hz frequency ................................................................................................................ 54 

Figure 5.8 - Stroke of the piezoelectric actuator under a 200 Vpp oscillating wave with 100 V DC

bias at 50 Hz frequency ................................................................................................................. 54 

Figure 5.9 – Variation of the displacement hysteresis of piezoactuator with temperature under

200 Vpp oscillating wave with 100 V DC offset at (a) 0.1 Hz and (b) 50 Hz ............................... 55 

Figure 5.10 - Variation of the hysteresis width of a piezoactuator with temperature under 200 Vpp

oscillating wave with 100 V DC offset at (a) 0.1 Hz and (b) 50 Hz ............................................. 55 

Figure 5.11 - Electrical model of piezoelectric actuator as a parallel capacitance (Cp) and resistor

(Rp) [33] ........................................................................................................................................ 57 

Figure 5.12 - Effect of temperature on the (a) capacitance and (b) parallel resistance of

piezoelectric actuator under 1 Vpp oscillating wave at 1 kHz ....................................................... 57 

Figure 5.13 - Effect of preload on actuator stroke at 200 V for (a) 0.1 Hz and (b) 50 Hz actuation

at room temperature ...................................................................................................................... 59 

Figure 5.14 - The dynamic d33 of EC-65 (a soft PZT) as a function of applied bias stress [37] .. 60 

Figure 5.15 - Effect of temperature on stress dependence of actuator stroke ............................... 61 

Figure 5.16 – Effect of temperature cycles on stroke of the piezoelectric actuator under a 200 Vpp

oscillating wave and 100 V DC offset at 0.1 Hz ........................................................................... 62 

Figure 5.17 - Effect of temperature cycles on stroke of the piezoelectric actuator under a 200 Vpp

oscillating wave and 100 V DC offset at 50 Hz ............................................................................ 63 

xi

List of Symbols

Symbol Unit Description

Curie temperature

Electric displacement vector (electric charge per unit area)

Strain vector

Electric field vector

Stress vector

Dielectric permittivity

Piezoelectric coefficient

Compliance

Coupling factor

Voltage

(superscript) constant electric field

(superscript) constant stress

(superscript) transpose

Sample thickness

Density

xii

Symbol Unit Description

Relative permittivity ( ⁄ )

Vacuum permittivity

Spring stiffness

Displacement hysteresis (area of hysteresis curve)

xiii

List of Appendices

Appendix A – Length Extension Resonance Calculations………………………………………72

Appendix B – Mechanical Drawings of Bulk Piezoceramic Sample Holder……………………75

Appendix C – Mechanical Drawings of Piezoelectric Stack Actuator Test Rig Modifications…79

1

Chapter 1

Introduction and literature review 1

1.1 Problem statement

Piezoelectric ceramics are implemented in a wide range of applications due to their many

favorable properties such as:

fast response time

high accuracy

high stiffness

low power consumption

precision

high force generation

ability to be used both as sensors and actuators

Precision application fields such as fuel injection technology are fields in which piezoelectric

actuators are being increasingly used for the reasons mentioned above. The aim of this project is

to understand how temperature and thermal cycles affect the performance and properties of

Lead-Zirconium-Titanate piezoelectric ceramics in order to be able to maintain the accuracy and

precision typical of piezoelectric actuators [1–3].

1.2 Motivation

As exhaust gas emission standards become more severe every day, manufacturers strive for

higher fuel-efficiency in cars. The automotive industry is therefore continuously attempting to

increase the efficiency of automobile engines. An important step in the ignition cycle that has a

great impact on the efficiency is the injection of the air/fuel mixture. The ability to withstand

high pressures and to create large displacements relative to other forms of actuators alongside the

reasons mentioned in Section 1.1, have made multilayer piezoelectric stack actuators a popular

choice for operating the injection needle valve of the fuel injector and controlling the fuel

injection process [1].

2

Since fuel injectors generally operate in the vicinity of the engine and are therefore exposed to a

wide temperature range, the temperature of the piezoelectric actuator inside will change as well.

As with all materials, the properties of piezoceramics vary with temperature. Consequently, this

change in temperature will affect the properties of the actuator and have a direct effect on its

output displacement, whereas fuel injectors require precise displacements to be able to operate

the engine at maximum efficiency. The ability to compensate for these changes will allow the

engine to run optimally at all times.

Although the automotive industry is the principle motivation, the results of this project are

applicable to any application or device that uses piezoceramics which experience varying

temperatures.

1.3 Piezoelectricity basics

1.3.1 Piezoelectric physics

In 1880, Pierre and Jacques Curie discovered that by applying pressure upon certain crystals, an

electric field proportional to the applied pressure would be generated between two surfaces of the

crystal. This phenomenon was later named the direct piezoelectric effect. Less than a year later,

Gabriel Lippman theoretically predicted the inverse piezoelectric effect using thermodynamic

principles, in which a crystal would deform due to an applied electric field. Lipmann’s theory

was experimentally verified by the Curie brothers the following year.

Of the 32 crystal classes, piezoelectricity is observed in 20 of them that lack centrosymmetry1.

For 10 of the 20 crystal classes exhibiting piezoelectric properties the polarization does not

vanish in the absence of an external electric field. These groups of crystals which display

temperature dependent spontaneous polarization are called pyroelectrics. Pyroelectric materials

whose polarization can be reversed by the application of an external electric field are called

ferroelectrics. Ferroelectrics are both piezoelectric and pyroelectric below a certain temperature

called the Curie temperature ( ). At temperatures higher than , the crystal structure transitions

to a non-piezoelectric crystallographic class [4–6]. Many of the most widely used piezoelectric

1 symmetry with respect to a point

3

ceramics are ferroelectrics such as Lead Zirconate Titanate (PZT), Barium Titanate, and Lithium

Niobate.

Ferroelectric crystals generally consist of domains: regions with homogeneous spontaneous

electrical polarization. Adjacent domains only differ in the direction of polarization, and the

planes along which neighboring domains are connected are called domain walls (boundaries).

The number of polarization directions that a domain can have depends on the number of

crystallographically equivalent polar axes in the unit cell. Domain walls can be classified into

two categories: 180° walls that separate domains with opposite polarization, and non-180° walls

which separate the rest of the boundaries. In ferroelectrics with tetragonal symmetry such as

PZT, the only non-180° domain walls are 90° boundaries. Both the 180° and non-180° walls are

ferroelectric. However, only the non-180° boundaries are affected by mechanical stress [7], [8].

Upon manufacturing, the domains in most piezoelectric materials are randomly-oriented [9].

Therefore the material has a net polarization of zero and exhibits little or no piezoelectric

activity. The most common method used to orient the crystal domains is through poling, i.e.,

polarizing the ceramic by applying a strong, static electric field at a temperature just below .

As a result of polarization, the ceramic exhibits an enhanced piezoelectric effect. The

recommended operating temperature of a piezoelectric ceramic is usually up to 50% of its ,

above which the ceramic begins to lose its polarization.

Polarized piezoelectrics are anisotropic materials. Their properties are tensor quantities that

depend on the direction of polarization, electric field, and mechanical stress. The convention is to

define the poling axis as the 3rd axis, and the shear planes by 4, 5, and 6 which are perpendicular

to the 1, 2, and 3 (X, Y, and Z) axes, respectively.

4

Figure 1.1 - Designation of axes in piezoelectric materials

1.3.2 Linear piezoelectric theory

A linear constitutive relationship is generally used to relate the electrical and mechanical

properties of piezoceramics to each other. It is assumed that all electrical and mechanical losses

can be neglected. The equations mostly used in applications that use piezoceramics as actuators

are:

( 1.1)

or

, , … , , , … , ( 1.2)

In the equations above, the superscript T stands for constant stress conditions (usually taken as

unclamped), and the superscript E stands for constant electric field conditions (usually achieved

by short-circuiting electrodes) [10].

The piezoelectric charge constant ( ) in the case of inverse piezoelectric effect refers to

mechanical strain produced in the direction per one unit of electric field applied in the direction

5

1 (X)

2 (Y)

3 (Z)

4

6

Polarization

5

of . For the direct piezoelectric effect, is the electric polarization2 generated in the material

as a result of a unit of mechanical stress. The subscript is the direction of polarization generated

and refers to the direction of the applied stress.

The dielectric constant ( ) is characterized as the amount of dielectric displacement (or charge

generated per unit area) in the direction per unit electric field applied in the direction of .

and are the electric field strength and electric charge density displacement (electric

displacement) in the direction, respectively.

The coupling factor ( ) is a constant which is not used in the previous equations but is a measure

of the effectiveness with which the piezoceramic converts electrical to mechanical energy, and

vice versa. It is defined as a specific function of piezoelectric crystal constants under any

particular boundary conditions.

( 1.3)

In the case of a long slender bar3 in which both the electrical field and the mechanical strain are

along the 3 axis, the relationship between the coupling factor and other constants can be seen

below:

( 1.4)

Other parameters such as strain ( ), compliance ( ), and stress ( ) are similar to conventional

solid mechanics notations.

It is noteworthy to mention that the reported piezoelectric properties are usually obtained for

specific material geometries under specific conditions such as low electric fields and no external

loading. Therefore, the value of the coefficients will not be exact for many practical devices.

2 In dielectric materials, the surface charge density is related to the polarization by: ∙

3 The mode of vibration will be length extensional and is discussed more thoroughly in section 2.2

6

Also, the equations used to describe piezoceramic behavior are an approximation of the actual

ceramic behavior and cannot capture the exhibited nonlinearities.

1.3.3 Piezoelectric ceramic types

Piezoelectric ceramics can be categorized into two main groups: hard and soft piezoceramics.

Soft and hard refer to the mobility of the domains and the polarization/depolarization behavior.

A comparison of hard and soft piezoelectric materials is presented in Table 1.1.

Table 1.1 - Soft and hard piezoelectric ceramic comparison

Characteristic

Piezoelectric type

Soft Hard

Domain wall mobility High Low

Piezoelectric coefficients High Low

Electromechanical coupling factors High Low

Mechanical quality factor Low High

Dielectric permittivity High Low

Dielectric losses High Low

Curie temperature Low High

Linearity Low High

Due to their characteristics, soft piezoceramics such as PZT5 are used in applications that require

large displacements and wide signal band widths. They also exhibit greater hysteresis, and are

more susceptible to depolarization. The higher domain mobility in soft piezoelectrics causes

them to be more vulnerable to temperature change and electric field magnitude compared to hard

piezoelectrics. Hard piezoceramic properties are opposite those of a soft piezoelectric ceramic

making them suitable for applications requiring high mechanical load or applied electric field.

PZT4 is a commonly used hard piezoceramic.

7

It is important to note that a soft piezoelectric ceramic might exhibit properties similar to those of

a hard piezoceramic and vice-versa. Therefore, when choosing a ceramic for a particular

application, it is practical to look beyond the nominal categorization and to the specific

characteristics of the material.

1.4 Fuel injectors and piezoelectric actuators

Modern diesel and many gas engines operate based on direct fuel injection principles, in which

fuel is injected directly into the engine as opposed to being mixed with air prior to injection. In

direct injection technology, pressurized fuel is pumped inside the injector which is then injected

inside the engine. The fuel is sprayed into the engine by opening and closing a nozzle using a

needle valve.

Previously, the needle valve was operated using solenoid technology. When the solenoid is

deactivated a spring closes the valve by forcing the needle into the nozzle passage.

Activating the solenoid will lift the needle off its seat, and fuel is injected inside the engine [1].

Due to the advances in piezoelectric actuator technology in recent years, the automotive industry

has moved towards piezoelectric based fuel injectors. A common method is using a piezoelectric

multilayer stack actuator to drive the nozzle to a sealed or open position. Piezoelectric actuators

used in engines with novel fuel injectors have optimized the injection system because of

characteristics such as fast response time, large force generation, and high accuracy and

precision. Replacing solenoid actuators with piezoelectric actuators has improved engine

performance by reducing fuel consumption by up to 15 percent, reducing emissions, and creating

quieter, more economical, and powerful engines [11], [12].

Piezoelectric ceramic actuators are being increasingly used in the automotive industry. Although

simply using piezoactuators in fuel injectors has increased the fuel-efficiency of cars, in order to

further improve engine efficiency it is important to possess a thorough understanding of the

thermo-electro-mechanical performance of piezoelectric actuators, especially in conditions

similar to the operating conditions of a fuel injection system.

Direct acting fuel injectors, are in the proximity of the engine and experience high pressures.

This will bring their temperatures close to the engine’s temperature, which will in turn change

8

the temperature of the piezoelectric actuator inside the fuel injector. As with all materials, the

properties of the piezoelectric actuator are temperature-dependent. It is therefore important to not

only understand how piezoelectric actuators respond to temperature change, but also compensate

for the observed changes. By adjusting for the changes, the automobile engine and high-

precision applications using piezoelectric actuators undergoing temperature change will operate

at their optimum.

Figure 1.2 – (a) Cross-section of Delphi’s piezoelectric based fuel injector [13], (b) heating

of fuel injector due to proximity to the combustion chamber [14]

The piezoelectric actuators used in fuel injector applications are expected to provide a relatively

large amount of displacement. Soft piezoceramics have a larger piezoelectric coefficient

compared to hard piezoelectrics and are able to provide a larger stroke. Therefore multilayer

actuators built from soft piezoelectric ceramics are used more frequently in fuel injector

applications and will be the subject of focus in this project.

Fuel injector

Combustion chamber

Fuel injector

Piezoelectric stack actuator

Injection needle

Nozzle opening

Fuel

Engine

(a) (b)

9

1.5 Multilayer piezoelectric stack actuators

A common method to use piezoelectric ceramics in actuation purposes, are multilayer

piezoelectric stack actuators. A piezoelectric stack actuator is an actuator that is made up of a

stack of thin ceramic discs ( discs), each of which has the opposite polarization from its two

adjacent discs. The discs are separated from each other by thin metallic electrodes and the same

voltage is applied to all discs. The final displacement is obtained by equation ( 1.5) in which N is

the number of piezoelectric discs used in the manufacturing of the stack.

. ( 1.5)

Figure 1.3 - Multilayer stack actuator schematic [15]

Stack actuators are capable of withstanding high pressures, creating large displacements, and

have high stiffness compared to other piezo actuators. One of the advantages of using a stack

actuator over a monolithic4 ceramic is that as a result of using thin ceramic layers the same

electric field can be applied to the ceramic by exposing the electrodes to a lower voltage. While

stack actuators have the ability to operate under high pressures, they are vulnerable and sensitive

to pulling forces and should always operate under compression.

The piezoceramics used in manufacturing multilayer piezoelectric stack actuators are used along

their poling axis. Therefore, from equation ( 1.2) the displacement along the 3rd axis from each

disc will be as follows:

4 bulk

10

( 1.6)

Since in the application of stack actuators no stress is applied to the stack along the planes

perpendicular to the 3rd axis ( 0), equation ( 1.6) is reduced to:

( 1.7)

The simplified equation reveals that the output strain of the piezoelectric stack actuator depends

mainly on two properties of the piezoelectric stack: the piezoelectric coefficient ( ) and

compliance along the poling axis ( ).

Two basic situations must be considered when operating a piezoelectric actuator against an

external force: operation against a constant or varying force. Figure 1.4 displays the effect of

different types of external forces on piezoelectric actuator strain. The strain of a piezoelectric

actuator in the absence of external loading is assumed to be .

If the load remains constant during the actuation process as a result of a constant mass or

preloading of a soft spring, the actuator will be initially compressed by ∆ 5. However, aside

from this initial offset, its capability to produce displacements will remain roughly unaffected

and full displacement will be obtained at full operating voltage. The amount of compression can

be obtained by equation ( 1.8). In this equation,∆ is the compression of a piezoelectric

actuator with stiffness due to , a constant load placed on the actuator.

∆ ( 1.8)

5 ∆ : compression due to a constant force

11

In the case where the load on the actuator changes significantly during the actuation process such

as when acting against a stiff spring, the final displacement will be less than the free

displacement of the actuator ( ). Assuming the actuator will be opposing a spring with a

constant of , the final displacement will be 6 and can be calculated via equation ( 1.9).

. ( 1.9)

(a) (b)

Figure 1.4 – The effect of constant (a) and variable (b) force on actuator displacement

1.6 Piezoelectricity and temperature

Multilayer piezoelectric actuators are made from several sections such as piezoelectric ceramic

discs, electrodes, and bonding epoxy. The changes observed in the actuator properties and

performance due to temperature can be categorized into 2 groups: changes in the piezoelectric

material itself, and changes in the piezoelectric actuator as a multi-component unit due to

changes in all components such as the bonding epoxy and metal electrodes, as well as the

ceramic.

1.6.1 Effect of temperature on bulk ceramics

Several studies have been performed on the effect of temperature on piezoceramic properties.

Previous research has determined different relationships between the piezoelectric coefficient

and temperature. Fotinich et al. and Hooker separately obtained an approximately linear

6 : maximum strain under a varying external force

12

relationship between and temperature, whereas Sherrit et al. determined a quadratic relation

between the piezoelectric coefficient and temperature [16–18]. On the other hand, no particular

trend can be detected in Sabat et al.’s results [19]. There is a consensus however that appears

to increase with temperature up to , at which it drops to zero due to depolarization. The data

shows that the dielectric coefficients ( ) increases approximately linearly up to a certain

temperature at which their rate of increase rises very rapidly. This usually occurs at a

temperature higher than 2 which is above the recommended operating temperatures. Therefore

it is reasonable to assume that the terms vary linearly with temperature within conventional

temperature ranges. Similar to , once the temperature approaches the dielectric coefficient

drops suddenly as well. The elastic compliance in the polarization direction ( ) in soft

piezoceramics seems to decrease as temperature increases from room temperature. However, it

was also reported that as the ambient temperature rises from subzero values, a broad peak occurs

between 0°C and room temperature [16], [17], [19], [20].

Several models have attempted to capture the temperature dependence of the ceramic properties.

Wang et al. developed a new equation for the strain and dielectric charge by incorporating higher

order terms in the Taylor series expansion [16]. Since both and vary approximately

linearly with temperature, they could be extrapolated to other temperature regimes. The models

were successful at low electric fields but digressed from the experimental results at higher

values. Another approach by Sherrit et al. was to express the piezoceramic properties as

polynomial curves with respect to temperature [18].

Although several studies have determined the effect of temperature on piezoceramics, few have

taken thermal hysteresis and its effect on piezoelectric properties into account. This will be an

important issue since a piezoelectric actuator used in a fuel injector will encounter thermal

hysteresis frequently. Sabat et al. include the effects of thermal hysteresis from one temperature

cycle in their experiments. However, their results show large variations from expected trends and

cannot be used to derive definitive conclusions [19].

13

1.6.2 Effect of temperature on multilayer piezoelectric stack actuators

Many studies have been performed on the dynamic and quasi-static behavior of piezoelectric

stack actuators, and modeling the stack behavior. The developed models have successfully

managed to address the nonlinearities observed in these multilayer stack actuators at room

temperatures [21–23]. However, relatively few in-depth studies exist on the effect of

temperature on stack actuator performance.

Li et al. studied the quasi-static thermo-electro-mechanical behavior of a multi-layer

piezoelectric stack up to 125°C. Their results show a bilinear stroke-temperature curve with a

nonlinear transition zone in between at around 40°C. They also attempt modeling the behavior of

the stack with respect to temperature. However, their model is only successful at very low and

high electric fields [24]. Senousy et al. determined the thermo-electro-mechanical performance

of a custom made soft PZT stack actuator under dynamic actuation for a maximum temperature

of 80°C. They report a linear increase in the dynamic stroke of the multilayer piezoelectric stack

actuator under test. Changing the ambient temperature from 23°C to 80°C, they recorded a 30%

increase for a driving field of 2 kV/mm at 100 Hz [25]. Heinzmann et al.’s experiments however,

show only a 3% increase in the dynamic stroke at 200 Hz and 1.67 kV/mm as a result of

temperature change from 25 to 75 °C [26].

In all of the experiments above, soft springs have been used to apply the required preload on the

piezoelectric actuator. By using a soft spring, it can be assumed that the actuator is experiencing

a constant force during its operation, whereas depending on the design, an actuator used in a fuel

injector might be experiencing a large change in force as it expands [1]. Also similar to research

on bulk piezoelectric ceramics, thermal hysteresis is neglected in studies involving multilayer

piezoelectric actuators.

1.7 Objectives and approach

Based on the literature and previous research in this field, capturing and modeling the effects of

temperature on piezoelectric materials is needed, especially in the case of multilayer stack

piezoelectric actuators. This thesis pursues the following objectives:

14

Investigate the temperature dependence of the fundamental properties ( , , , and

) of a bulk PZT ceramic in conditions similar to piezoceramics used in fuel injector

applications

Investigate the effect of thermal cycles on the fundamental properties of bulk PZT

ceramics

Experimentally determine the effect of temperature on the performance (displacement-

voltage curve, maximum stroke, hysteresis area and width, capacitance) of a multilayer

PZT stack actuator used in fuel injectors

Determine the effect of thermal cycles on the nonlinear properties of the PZT stack

actuator

The first step in solving this problem is determining the properties and performance of a

common monolithic (bulk) PZT ceramic and multilayer PZT stack actuator. This will ensure that

the results of the project are applicable to applications which use either a stack actuator or a bulk

ceramic. However, since the main motivation of the project is the fuel injector in an automobile

engine, the test parameters and settings will be chosen based on automobile engine conditions.

The objectives will be obtained by the following steps:

1. Design and assemble the experimental setup to measure the effect of temperature and

thermal cycles on the fundamental piezoelectric properties. This will be achieved by

measuring the , , , and of a bulk PZT ceramic.

2. Design and assemble the experimental setup to capture the temperature dependence of

multilayer PZT stack actuator performance. Stack actuator performance can be evaluated

by measuring the displacement-voltage curve, maximum stroke, hysteresis area and

width, and capacitance of the actuator under no external load and constant force

conditions and different actuation frequencies.

3. Determining and analyzing trends observed in bulk and multilayer stack actuator

ceramics.

15

1.8 Contributions

The goal of this thesis was to understand how temperature affects PZT ceramic performance.

The relationship between fundamental piezoelectric properties ( , , , and ) of a PZT

ceramic was experimentally measured. The temperature dependence of multilayer PZT stack

actuators was also assessed. This was achieved through understanding the effect of temperature

and thermal cycles on the displacement-voltage curve, maximum stroke, hysteresis area and

width, and capacitance of the actuator in various conditions. The objectives were achieved and a

list of significant contributions is summarized below.

The dynamic and quasi-static properties of multilayer piezoelectric stack actuators

were obtained at temperatures up to 130 °C. The maximum temperatures of most of

the previous studies on multilayer PZT stack actuators were limited to 80 °C. By

increasing the maximum temperature of the experiments to at least 130°C, piezoelectric

properties and performance are determined in conditions that occur in fuel injector

applications.

The effect of thermal cycles on multilayer PZT stack actuator performance was

assessed. Current studies do not take into account how subsequent temperature cycles

would affect multilayer PZT stack actuator performance.

The effects of preload magnitude on PZT stack actuator performance at high

temperatures were determined.

Hysteresis area and width area have an inverse relation with temperature.

16

Chapter 2

Experimental parameters 2

In this chapter, the experiments required to fully understand the effects of temperature on the

piezoelectric ceramic are explained. The process of selecting the suitable piezoelectric ceramic

test specimens based on the experiment requirements and piezoelectric properties under

investigation are discussed as well.

2.1 Piezoelectric material selection

A major factor when choosing a piezoelectric multilayer stack actuator for fuel injector

applications is its ability to provide the required force and displacement simultaneously. Based

on the discussion presented in subsection 1.3.3, soft piezoelectric materials can provide higher

strain levels compared to hard piezoelectric materials. On the other hand, soft piezoceramics

have a lower Curie temperature which reduces the maximum operating temperature of the stack

actuator. The maximum temperature a piezoelectric actuator implemented in a fuel injector will

reach is 150°C [24], [25]. Therefore, a suitable piezoelectric material will have the capability of

providing large displacements, but at the same time tolerate high temperatures up to 150 °C.

Lead Zirconium Titanate (PZT) piezoelectric ceramics are soft piezoelectric ceramics with Curie

temperatures above 300°C. Multilayer stack actuators made from PZT can provide a strain

equivalent to 0.1% of its length and tolerate temperatures up to 150°C, making them potentially

suitable choices for fuel injection applications.

2.2 Determination of fundamental piezoelectric properties using the resonance method

In subsection 1.3.2, it was explained that piezoelectric behavior can be modeled using the

fundamental piezoelectric properties: the piezoelectric ( ), compliance ( ), and the dielectric

permittivity ( ) coefficients. A general representation of the linear constitutive equations used

to predict piezoelectric behavior provided in equation ( 1.1) is presented below.

17

( 2.1)

Depending on the crystal structure of the piezoelectric ceramic, many elements of the above

matrix will be zero or dependent on other elements. PZT ceramics, which are one the most

widely used ceramics and also the subject of focus in this project, belong to the crystal

class. The symmetry reduced matrix of equation ( 2.1) for this crystal class has two independent

free dielectric permittivities ( , ), three independent piezoelectric constants

( , , ), and five independent elastic constants under short circuit boundary

conditions ( , , , , , 2 ) and is

displayed in equation ( 2.2). Under small stresses and electric fields, these constants can be used

to predict the behavior of a piezoelectric material [10], [27].

( 2.2)

The determination of the elastic, piezoelectric, and dielectric constants requires a series of

experiments on samples of different geometries. The quantities measured should be related to the

fundamental elastic, piezoelectric, and dielectric properties through theoretically sound equations

and methods. The techniques used for measuring these constants are explained in the following

sections.

18

2.2.1 Determination of the dielectric constant

The dielectric constants of a crystal can be obtained by measuring the capacitance of a sample

with electrodes covering the surfaces perpendicular to the direction of interest. Measurements

performed at frequencies lower than 1% of the lowest resonance frequency will provide the free

or constant stress dielectric permittivity constants ( ) which are used in the constitutive

equations. To obtain the and constants in PZT materials, plates cut normal to the 1 or 2

(X or Y) and 3 (Z) axes are required as depicted in Figure 2.1 in which the shaded areas are

electrodes and the polarization direction is parallel to the arrow [10].

Figure 2.1 - Sample and polarization direction for (a) and (b) measurement

Once the capacitance of the sample is measured, the dielectric constant can be calculated from

the thickness ( ) and cross-sectional area ( ) of the ceramic using equation ( 2.3)

.→

. ( 2.3)

Measurements conducted at frequencies much higher than the principal natural frequencies of the

specimen will yield the clamped or constant strain dielectric permittivities ( ). The dielectric

permittivities at constant strain and constant stress can be related together through other

piezoelectric constants. However, is often measured since it can be obtained with higher

accuracy than [10].

2.2.2 Determination of the elastic and piezoelectric constants

It can be deduced from the linear constitutive equations that by applying an electric field with a

frequency , a stress wave with the same frequency can be generated inside a piezoelectric

ceramic. Therefore, an electrically driven mechanical resonance can be induced in the ceramic

depending on the geometry and boundary conditions of the sample. Since the electromechanical

behavior of a piezoelectric material is dependent on the elastic, piezoelectric, and dielectric

(a) (b)

19

constants of the piezoceramic, the values of these constants can be determined by measuring the

performance of resonators with specific geometric shapes and orientations.

Basically, this method entails choosing a sample with geometric conditions so that a specific

resonance mode can be excited, for which the boundary conditions and vibrational mode shape

are known. The sample is then excited with a low-amplitude alternating field (0.5 – 1 VAC), and

the electrical impedance of the sample is measured as a function of frequency. The frequencies

of maximum admittance and maximum impedance are known as the resonance ( ) and

antiresonance ( ) frequencies, respectively [10]. Figure 2.2 depicts the impedance-frequency

curve of a PZT sample. The values of , , and of a sample can then be used to determine

the material constants involved in that vibration mode.

Figure 2.2 - Impedance and Phase of a sample with length extensional mode geometry

Table 2.1 displays the common geometries used to characterize piezoelectric materials. Details

regarding the poling direction, electrode surfaces, recommended aspect ratios of each geometry,

and the material constants that can be obtained from each mode are also included in the table.

‐100

‐75

‐50

‐25

0

25

50

75

100

9

90

900

9000

80 110 140 170 200 230 260

Phase (°)

Impedan

ce (kΩ

)

Frequency (kHz)

Impedance Phase

fa

fr

20

Table 2.1 – Polarization direction, electrode surfaces, and geometries of each mode [27]

Resonance Mode Geometry

Constants that

can be

determined

Length Extensional

5 , 5

(rod with 5 )

, , ,

, ,

Thickness Mode for plate

10 , 10

, ,

Radial

20

, , , ,

,

Thickness Shear

10

, , ,

, ,

Length Thickness

10 , 3 , 3

, , ,

w1

w2

l

t

w1

w2

t

D

t

w1

w2

t

l

w

21

As mentioned in Section 1.5, the piezoelectric properties along the 3rd axis are of particular

interest in this project. Recording the impedance as a function of frequency of a sample with the

recommended aspect ratios of the length extensional mode will provide the required data for

calculating the properties in the direction of polarization. The relations between the resonance

and antiresonance frequencies of the length extensional mode and the material constants that can

be derived from this mode can be seen in Equations ( 2.4) - ( 2.7). The derivation of these

equations using principles from Mason’s “Physical Acoustics” is available in Appendix A [28].

Aside from the geometric constraints, the important boundary condition is no-stress on the

ceramic surfaces, i.e., free vibration conditions.

( 2.4)

( 2.5)

( 2.6)

( 2.7)

2.3 Nonlinear piezoelectric properties

Many practical applications of piezoelectric materials which require large forces and

displacements, such as the fuel injection process, involve exposing the piezoelectric ceramic to

large electric-fields. As it was explained in previous sections, although linear piezoelectric theory

is a simple method of modeling a piezoelectric actuator’s performance, it is most accurate for

low electric fields and strains and is not suitable for high precision applications. A typical

electric field-displacement curve in a multilayer piezoelectric actuator can be seen in Figure 2.3.

The electric field-displacement curve of a piezoelectric actuator is dependent on the frequency,

maximum electric field, and other parameters.

22

Figure 2.3 - Electric field-to-displacement curve of the piezoceramic actuator under study

Figure 2.4 - Hysteresis area and width in a typical displacement-voltage curve

‐5

0

5

10

15

20

25

30

‐50 0 50 100 150 200 250

Displacement (µm)

Voltage (V)

0.1 Hz30 Hz50 Hz

23

An important issue when using piezoelectric actuators is the existence of hysteresis during their

cyclic actuation. This phenomenon has a major contribution in the nonlinearity of piezoelectric

ceramics at high electric fields. It is therefore important when considering the effects of

temperature on piezoelectric ceramics to determine how this nonlinear property is affected by

temperature. Hysteresis loss can be considered by two methods: the area of the hysteresis loop

which is defined as the loss of the sample per electric charge per driving field (also called

displacement hysteresis, ), or the maximum width of the hysteresis loop [29]. Both these

parameters are visible in Figure 2.4. The width of the hysteresis (displacement-voltage) curve at

low frequencies can be as high as 15% of the maximum piezoelectric actuator’s expansion [21].

The displacement-voltage curve, maximum expansion of the piezoelectric actuator, hysteresis

width and area, and stack capacitance for different actuation signals with different electric field

amplitudes and frequencies are all parameters that are of concern when dealing with

piezoactuators and practical applications.

2.4 Fuel injector operating conditions

Since piezoelectric actuators are being increasingly used in fuel injector applications, it is

important that their thermo-electro-mechanical performance be investigated in conditions similar

to an actual fuel injector. These conditions include an electric field magnitude higher than 1.5

kV.mm-1, frequency range of up to 100 Hz, and operating temperature of at least 125 °C [24],

[29]. The test specimens and experiments should be chosen and designed so that conditions close

to actual fuel injector applications can be simulated.

2.5 Monolithic and stack piezoelectric actuator selection

In order to be able to perform the experiments described in Sections 2.2 and 2.3 under conditions

explained in Section 2.4 and characterize the performance of a piezoelectric actuator with respect

to temperature, suitable samples must be selected. Ideally, the bulk ceramic and multilayer

actuator would be made up of the same material. However, due to manufacturing limitations of

piezoelectric ceramic manufacturers and their specialization in specific types of actuators or

geometries, this was not possible. Therefore, the monolithic and stack actuator ceramic were

chosen from similar but not identical materials.

24

2.5.1 Bulk piezoceramic selection

A piezoelectric sample with the appropriate geometry for producing the length extensional

resonance mode from subsection 2.2.2 is used to obtain all the piezoelectric properties in the Z

axis. An image of the geometric sample can be seen in Figure 2.5.

Figure 2.5 - Bulk piezoelectric sample (dimensions are in mm)

The required geometry for the length extensional mode is an uncommon geometry, especially

since it is a slender rod with a length to diameter ratio of 5:1. The resonance measurements are

performed at low electric fields and voltages (0.5-1 VAC) and the sample length should be

reduced as much as possible to minimize the losses. Therefore, the most suitable and practical

sample would have a length and diameter (or width) of 10 and 2 mm, respectively. Additionally,

as it was explained in subsection 1.3.1, the Curie temperature of the ceramic should be higher

than 300°C so that during the tests, the ceramic’s temperature remains below 0.5 .

Manufacturers typically do not manufacture ceramics with this aspect ratio. The sole company

that could make this sample was Sensor Tech Ltd7. The manufacturer-reported specifications of

the 2 samples from Sensor Tech Ltd. are given in Table 2.2.

7 Sensor Technology Limited: 20 Stewart Road, Collingwood, ON, Canada, L9Y 4K1. Tel.: (705) 444-1440

25

Table 2.2 – Properties of the monolithic piezoelectric ceramic

Manufacturer Sensor Tech. Ltd. Ceramic property (1) (2) Material BM500 Length (mm) 10.07 10.12 Diameter (mm) 2.03 Cross-sectional area (mm2) 3.2365 Density (kg/m3) 7762 7724 Capacitance (pF) 6.11 6.1 Dissipation 0.019 0.002 Electrodes Ag

2.5.2 Multilayer piezoelectric selection

Similar temperature and material restrictions to the bulk piezoceramic exist for the multilayer

piezoelectric stack actuator. However, in this case not only should the actuator be made of

material similar to the bulk piezoceramic sample (BM500) and have a Tc higher than 300°C, the

operating temperature of the stack as a whole should be at least 150°C as well. The best choice

for the stack actuator was the SCMAP series actuators from Noliac Group Ltd8 which is made

from NCE57 material and is the material most similar to BM500. Among the commercially

available piezoelectric stack actuators, it is also the actuator with the highest operating

temperature that can still provide large displacements. Most piezoelectric stack actuators have a

recommended operating temperature below 100°C. The specifications of the stack actuators are

given in Table 2.3 and the stack itself can be seen in Figure 2.6.

8 Noliac North America Inc.: 12600 Deerfield Parkway, Suite 100, Alpharetta, GA 30004, USA Tel: (404) 835-

1795

26

Table 2.3 – Properties of stack actuator

Manufacturer Noliac Group Material NCE57 Actuator cross section (mm×mm) 7×7 Actuator length (mm) 20 Layer thickness (mm) 0.067 Maximum operation voltage (V) 200 Capacitance (µF) 1.9 +/- 15% Blocking force (N) 1960 +/- 20% Material Curie temperature (°C) 350 Maximum operating temperature (°C) 150 External Electrodes Ag/Pd

Figure 2.6 - Piezoelectric actuator with characteristics shown in Table 2.3

2.6 Experimental Configurations

The experimental configurations for each of the tests are explained in the following subsections.

2.6.1 Fundamental piezoelectric constants of bulk piezoelectric ceramic

In order to determine the effect of temperature on the fundamental piezoelectric properties, the

values of , , and of the sample described in subsection 2.5.1 must be obtained for the

desired temperature range. Thermal hysteresis should be investigated as well. For these tests, the

impedance of the sample as a function of frequency, and its capacitance are recorded for a

27

temperature change from 25°C (room temperature) to 150°C and during the cooling down

process. A minimum of one subsequent cycle should be performed as well to see the effect of

consecutive heating cycles on the properties and their dependence on temperature.

2.6.2 Nonlinear piezoelectric properties of piezoelectric stack actuator

Initially the maximum temperature for this set of experiments was chosen to be 180°C. The

maximum manufacturer recommended temperature for the stack actuators was 150°C. However,

during the first series of tests the actuator was damaged at a temperature of 150°C. Therefore the

maximum temperature for the tests was changed to 125°C. The properties of a piezoelectric stack

actuator such as thermal expansion, maximum expansion, displacement-voltage curves,

hysteresis width and area, and capacitance are monitored and recorded under conditions of zero

external load and constant external load at different frequencies and electric fields using the

experimental setup described in Section 3.2. Similar to the experiments on bulk piezoelectric

ceramics, the effect of thermal hysteresis on multilayer piezoelectric stack actuators is of interest.

28

Chapter 3

Experimental setup 3

This chapter reviews the experimental setup for each set of experiments. The experiments

include resonance measurements for obtaining the fundamental properties of piezoceramics with

respect to temperature, and determining the nonlinear behavior of piezoelectric stack actuators as

explained in Chapter 2.

3.1 Fundamental Piezoelectric Property Measurements

3.1.1 Bulk piezoceramic sample holder

During the resonance measurements, it is imperative that free-free boundary conditions exist at

the two ends of the rod in Figure 3.1.

Figure 3.1 - Sample geometry and coordinates

The test setup used in this series of tests must have the following properties for accurate

measurements [18], [19], [30], [31]:

Contact resistance must be minimized: contact resistance causes additional error. Contact

electrodes should always be clean and hold sample firmly in place.

Does not bind the surface: in order to achieve the 0 boundary condition at both ends

of the ceramic, the sample holder should exert minimum possible force on the sample

Ability to withstand high temperatures up to 180°C

Stress relief from thermal strain: Due to thermal expansion of both the setup and the

sample, a soft spring is used to maintain contact while preventing excessive force on the

sample

0 1

32

Polarization

29

Electrical contacts can be opened and shortened: open and short compensation of the test

device (hp 4294a impedance analyzer) will easily reduce test fixture’s residuals by

eliminating the parallel and series impedance of the sample holder from the measured

values.

Sample holder has a low impedance compared to the piezoelectric sample and its

electrodes

Figure 3.2 displays a custom-designed sample holder that was designed and built to meet the

requirements listed above. The bottom and top plates are made from Teflon that provides

electrical insulation between the top and bottom electric contacts and surrounding environment

while withstanding temperatures up to 260°C. Both electrical contacts are made from copper,

with the lower electrical connection being a copper sheet and the top connection being a flexible

copper contact which acts like a soft spring. Both electrical connections are held in place by bolts

that are connected to the electrical inputs of the measurement device. The technical drawings of

the sample holder are available in Appendix B.

Figure 3.2 - Sample holder used in resonance measurements

Top and bottom Teflon plates

Copper electric contacts

Piezoelectric sample

30

3.1.2 Resonance measurements test setup

The properties of the samples used in these experiments are displayed in Table 2.2. The

piezoelectric samples were connected to an Agilent9 4294a Precision Impedance Analyzer via a

custom-made sample holder described in detail in subsection 3.1.1. The impedance analyzer

measured the capacitance of the sample as well as its impedance as a function of frequency using

its built-in functions. In order to minimize external noise, coaxial cables were used up to the

oven opening to keep the wires shielded for as long as possible. The impedance analyzer data

was then transferred to a PC using a custom-written National Instruments (NI)10 Labview 2010

program. A Thermo Fisher11 model f6018 furnace was used to manually control the temperature

of the piezoelectric ceramic and sample holder. The temperature of the ceramic was controlled

up to 0.1°C. Two type K thermocouples were used to monitor the temperature of the

piezoelectric ceramic and test setup. A bead-type thermocouple was placed as close to the

ceramic as possible without contacting it, and a surface-type thermocouple was attached to the

bottom Teflon plate next to the bottom electrode. The signals of the thermocouples were sent to

an 8 channel Omega12 TC-08 Data Acquisition Module. The output of the TC-08 DAQ module

was recorded using the Omega Logging Software on the PC. A block diagram of the

experimental setup used for determining the fundamental piezoelectric properties of the PZT

ceramic can be seen in Figure 3.3. Figure 3.4 and Figure 3.5 are images of the sample holder and

test setup.

9 Agilent Technologies Inc.: 5301 Stevens Creek Blvd, Santa Clara, CA 95051, USA, Tel: (408) 345-8886

10 National Instruments Corporation: 11500 N Mopac Expwy, Austin, TX 78759, USA, Tel: (800) 531-5066

11 Thermo Fisher Scientific: 81 Wyman Street, Waltham, MA 02454, USA, Tel: (781) 622-1000

12 OMEGA Engineering, Inc.: One Omega Drive, Stamford, CT 06907, USA, Tel: (203) 359-1660

31

Figure 3.3 – Block diagram of bulk piezoelectric ceramic tests

Figure 3.4 – Bulk piezoceramic inside the sample-holder

Omega TC-08 Thermocouple DAQ Module

Agilent 4294a Precision Impedance

Analyzer

HI

HV

LV

LI

Thermo Fisher f6018 Furnace

Omega Logging Software

PC

BNC connectors

Coaxial cable

SMA connection

Type K thermocouples

Piezoelectric Sample

Surface type thermocouple

Bead type thermocouple

Leads to Impedance Analyzer

32

Figure 3.5 - Images of test setup for fundamental piezoelectric properties

3.2 Nonlinear piezoelectric property measurements

Block diagrams of the experimental setups used for these tests are shown in Figure 3.6 and

Figure 3.7. All test data was recorded experimentally using the SCMAP08 stack. The

manufacturer reported properties were listed in Table 2.3. Experimental data was obtained by

exciting the piezoelectric actuator using a signal created in a custom-written NI Labview 2010

(SP 1) program and generated via a National Instruments (NI) PXI-5412 arbitrary waveform

generator. The output of the NI PXI-5412 waveform generator was amplified by a dsm13 VF-

500-30150 Linear Piezo Amplifier with a maximum output voltage of 200 V and 1 A peak

current. The displacement of the piezoelectric actuator was measured using a capacitive

13

Dynamic Structures & Materials, LLC: 114 SE Parkway CT, Franklin, TN 37064, USA, Tel: (615) 595-6665

Agilent 4294a Precision Impedance Analyzer

Thermo fisher f6018 furnace

Sample holder

Omega TC-08 Thermocouple DAQ module

33

displacement sensor from MTI Instruments Inc.14. This was achieved by converting the signal of

an MTI ASP-20-CTA Accumeasure probe with 25 nm resolution via an MTI Accumeasure 9000

High Precision Single Channel Amplifier System. When required, the load on the stack actuator

was determined by acquiring the signal of a Kistler15 9001A Quartz Load Washer with a Kistler

5010B Dual Mode Charge Amplifier. The actual voltage applied to the actuator was

independently measured using a voltage divider in parallel to the actuator that was comprised of

9.99 kΩ and 1.003 MΩ resistors to scale down the voltage by a factor of 100.4. The current

passing through the actuator was measured by recording the voltage over a 2.3 Ω resistor in

series with the actuator. The voltage across the resistors and outputs of the load and displacement

sensors were acquired using an NI PXIe-6356 simultaneous data acquisition module. Both the NI

PXI-5412 arbitrary waveform generator and the NI PXIe-6356 data acquisition module were

embedded on an NI PXIe-1065 chassis and controlled via an NI PXIe-8133 real-time express

controller. A separate data acquisition program was written to acquire and process the data using

the NI PXIe-6356 data acquisition module. A low pass filter was implemented in the data

acquisition program to reduce signal noise. The temperature of the piezoelectric actuator and test

rig were controlled using a manually operated Thermo Fisher model f6018 furnace. The

temperature of the ceramic was controlled up to 0.1°C accuracy. The temperature of the actuator

and test rig inside the oven was monitored via 4 type K thermocouples, where the signals were

acquired by an 8 channel Omega TC-08 Data Acquisition Module. The output of the TC-08

DAQ module was recorded by the Omega Logging Software.

14

MTI Instruments Inc.: 325 Washington Avenue Extension, Albany, NY 12205, USA, Tel: (518) 218-2550

15 Kistler Instrumente AG: Eulachstrasse 22, Postfach, CH-8408 Winterhur, Switzerland, Tel: +41 (52) 224-1111

34

Figure 3.6 - Block diagram of spring loaded tests

MTI ASP-20-CTACapacitive sensing probe

Piezoelectric stack actuator

Type K thermocouples

Kistler 9001A Quart Load Washer

Accumeasure 9000 Capacitive Sensor

Amplifier

Electrical Circuits

NI PXIe-6356 DAQ card

NI PXI-5412Arbitrary waveform

Generator

dsm VF-500Linear Piezo Amplifier

Omega TC-08 Thermocouple Data Acquisition Module

Kistler 5010B Dual Mode Charge

Amplifier

NI PXIe-1065 chassis

NI PXIe-8133 Controller

Thermo Fisher f6018 furnace

Springs

Labview 2010 (SP 1)

PC

35

Figure 3.7 - Block diagram of free displacement test setup

3.2.1 Multilayer stack actuator test rig

For the multilayer stack experiments, a test rig used previously for piezoelectric studies was

modified [22], [32], [33]. Changes were made so that both free piezoelectric measurements and

spring loaded measurements would be possible. The technical drawings of the modified parts are

available in Appendix C. The modified setup needed to endure temperatures up to 180°C. Since

the thermal expansion of the piezoelectric ceramic is also of interest, the thermal expansion of

the setup must be measurable.

MTI ASP-20-CTA Capacitive sensing probe

Piezoelectric stack actuator

Type K Thermocouples

Accumeasure 9000 Capacitive Sensor

Amplifier

Electrical Circuits

NI PXIe-6356 DAQ card

NI PXIe-1065 chassis

NI PXIe-8133 Controller NI PXI-5412

Arbitrary waveform Generator

dsm VF-500 Linear Piezo Amplifier

Omega TC-08 Thermocouple Data Acquisition Module

PC

Labview 2010 (SP 1)

Thermo Fisher f6018 furnace

36

Figure 3.8 - Test rig for nonlinear piezoelectric properties

The test rig and sensors were all chosen or modified to be able to operate at the temperatures

required in the experiments. The entire test rig (except the copper collars), was machined from

AISI Type 304 stainless steel. SFB12-ASSBBLS linear bearings from Thomson16 are also made

of stainless steel and can tolerate temperatures up to 260°C. Both the Kistler load washer and the

MTI capacitive sensing probe and their cables and connectors have a maximum operating

temperature of 200°C.

16

Thomson: 203A West Rock Road, Radford, VA 24141, USA, Tel: (540) 633-3549

MTI ASP-20-CTACapacitive sensing probe

Kistler 9001A Quartz Load Washer

Type K thermocouples

Piezoelectric stack actuator (or steel block)

High temperature bearings

Springs

Copper collars

Top bar

37

Two identical soft springs with a combined stiffness of 280 / were used to apply preload to

the stack actuator. In order to apply the preload, the top bar visible in Figure 3.8 was lowered as

the force sensor output was monitored. Once the desired preload was reached, the bolts on the

ends of the top bar were tightened to keep the springs in a compressed position. Soft springs

were used to apply the preload to maintain a constant force condition on the actuator, similar to

Figure 1.4 (a).

Figure 3.9 - Stack actuator setup

As can be seen in Figure 3.9, the stack actuator is placed between two stainless steel blocks. The

bottom block is screwed onto the test rig and holds the piezoelectric actuator in place. The top

block has two functions: force distribution and capacitive displacement sensor target. Stack

actuators require that the force applied to them be uniform across the end faces to avoid local

overload of the actuator area. For homogeneous force distribution, it is recommended to apply

the force to a piezoelectric stack actuator indirectly via a steel block with a thickness of at least

half of the stack actuator width. Additionally, the capacitive displacement sensor requires its

target to be grounded. By connecting a grounding wire to the steel block on top of the

piezoelectric actuator, the grounded target necessary for accurate displacement measurements

will be provided. The actuator is attached to the top and bottom stainless steel plates using

Type K thermocouple

Piezoelectric stack actuator

Top stainless steel block

Bottom stainless steel block

38

Aremco-Bond 86017, a thermally conductive and electrically insulating aluminum nitride high

temperature epoxy.

In order to compensate for the thermal expansion of the test setup on the displacement

measurements, a steel block with the same dimension as the piezoelectric stack actuator was

placed in the test rig. Everything including the sensors was setup to the positions and settings of

the actual tests. The output of the displacement sensor at different temperatures was recorded.

The thermal expansion of the steel block was also measured separately. The thermal expansion

of the setup was then extracted from the two sets of data.

17

Aremco Products Inc.: 707 Executive Blvd., Valley Cottage, NY 10989, USA, Tel: (845) 268-0039

39

Chapter 4

Bulk piezoceramic experimental results 4

In this chapter, the results of the experiments on bulk piezoceramics are presented. The

fundamental piezoelectric properties of two bulk piezoelectric samples along the poling direction

are determined as a function of temperature and the observed trends are analyzed.

The temperature was raised in steps from room temperature up to 150°C and back down to 26 °C

to investigate the effect of thermal hysteresis. The effects of multiple temperature cycles on the

piezoelectric properties were also investigated. Each step which included changing the

temperature, allowing the test rig and bulk piezoceramic to stabilize with respect to temperature,

and data acquisition took a minimum of 1.5 hours.

The properties investigated in this set of experiments are the piezoelectric ( ), elastic ( ),

and dielectric ( ) coefficients along with the coupling factor ( ) and were obtained using the

experimental setup described in Section 3.1. was measured by recording the capacitance of

the samples. The piezoelectric ( ) and elastic ( ) coefficients and coupling factor ( ) were

determined by finding the electrical resonance ( ) and antiresonance ( ) frequencies of the

samples at each temperature and placing them in equations ( 2.4) - ( 2.7). Figure 4.1 shows the

change of the impedance-frequency curves and the values of and of the sample for two

different temperatures. The initial measured properties of both samples at room temperature

(26°C) are presented in Table 4.1.

Table 4.1 – Measured properties of bulk ceramic samples at room temperature

Property (unit) Measured value at room temperature (1) (2)

⁄ 344.32 360.52 ⁄ 18574.7 16723.53 10 ⁄ 15.62 16.72

0.639 0.682

40

The measured properties of the piezoelectric samples differ from the manufacturer reported

values by a maximum value of 11%. The possible reasons for this difference could be ageing of

the piezoelectric ceramics, the different experimental conditions such as different measuring

equipment and sample holders, microscopically rough boundary conditions and inconsistency in

the electrical contacts of the piezoceramic and the sample holder [19].

Figure 4.1 - The impedance spectrum for the length extensional mode and change of fr and

fa at 26° and 151°C

1.00E+04

1.00E+05

1.00E+06

1.00E+07

8.00E+04 1.25E+05 1.70E+05 2.15E+05 2.60E+05

Impedan

ce (Ω)

Frequency (Hz)

T = 26°C T = 151°C

41

4.1 Effect of temperature on piezoelectric properties

The effects of temperature on the fundamental piezoelectric properties of sample #1 were

measured experimentally 3 times, i.e. three temperature cycles were applied to the sample. The

data from the 3rd temperature cycle appears to be the most consistent and is presented in

subsections 4.1.1 - 4.1.4.

4.1.1 The piezoelectric coefficient ( )

Figure 4.2 – Effect of a temperature cycle on the piezoelectric coefficient ( )

As it can be seen in Figure 4.2, the piezoelectric coefficient ( ) of the sample increases and

decreases with temperature. It was explained in subsection 2.5.1 that the signals used in

resonance measurements have low amplitudes (0.5–1 VAC) and since the piezoelectric sample is

relatively thick (10 mm length) it is important that the electrical connections are solid to

minimize losses. The fluctuations are therefore most likely due to inconsistency in the electrical

contacts as a result of thermal strains. An approximately bilinear relation between and

temperature can be seen as temperature is rising with a transition zone around 80°C.

Increasing the temperature from 26°C to 151°C raised the sample’s coefficient by 14.9%

(from 348 to 399.9 ⁄ ). Upon lowering the temperature back to the initial temperature, the

value of returned to 339.4 ⁄ , a 17.8% decrease.

330

340

350

360

370

380

390

400

410

0 20 40 60 80 100 120 140 160

d33(pC/N

)

Temperature (°C)

Temperature increase Temperature decrease

42

Considering the trend of the recorded data and disregarding the irregularities and fluctuations as

a result of measurement errors, it seems as though upon decreasing the temperature from 151°C,

the values of the piezoelectric coefficient are lower than when the temperature is rising. This is

indicative of thermal hysteresis which is generally expected in ferroelectric materials.

Nevertheless, the thermal hysteresis observed during these experiments appears to be weaker

than reported by other researchers [18], [19]. This could be as a result of the sample undergoing

three consecutive heating cycles.

4.1.2 The dielectric permittivity ( )

Figure 4.3 – Effect of a temperature cycle on the relative dielectric permittivity ( )

measured at 1 kHz

The existence of thermal hysteresis is more obvious in Figure 4.3, in which the effects of a

temperature cycle on the dielectric permittivity of a soft piezoceramic are displayed. The values

of are higher as the temperature decreases compared to when temperature rises. The

maximum difference between values at the same temperature occurs at 26°C with a 5.5%

difference in the values.

The dielectric permittivity changed approximately linearly with temperature in both directions.

The slope of the - was 6.07 and 5.15 for increasing and decreasing temperatures,

1800

2000

2200

2400

2600

2800

3000

0 20 40 60 80 100 120 140 160

ε r(ε

33/ε

0)

Temperature (°C)

Temperature increase Temperature decrease

43

respectively. Raising the temperature from 26 to 151 °C increased the dielectric permittivity by

37.5% (from 2099.4 to 2886). decreased by 30.2% once the temperature of the sample

returned to 26°C.

is usually measured at a frequency of 1 kHz and the frequency dispersion of the dielectric

permittivity is ignored. As mentioned in subsection 2.2.1, the free dielectric permittivity constant

is used in the constitutive equations and is measured at frequencies lower than 1% of the lowest

resonance frequency. 1 kHz is usually used for these measurements because at lower frequencies

the measurement accuracy is lower.

4.1.3 The elastic compliance coefficient ( )

Figure 4.4 – Effect of a temperature cycle on the elastic compliance ( ) of piezoceramic

The elastic compliance coefficient of the piezoelectric sample did not vary considerably with

temperature during these tests. The change in the value of as a result of a 125°C increase in

temperature is less than 1%. Inconsistency in the electrical contacts while decreasing the

temperature of the test setup could be the main reason for the large fluctuations observed in the

second portion of the graph.

15.2

15.4

15.6

15.8

16

16.2

16.4

16.6

0 20 40 60 80 100 120 140 160

s 33x10‐12(m

2/N

)

Temperature (°C)

Temperature increase Temperature decrease

44

Thermal hysteresis is not clearly visible in the experiment results. Similar to the piezoelectric

coefficient, this is most likely due to the heat treatment of the ceramic after three temperature

cycles.

4.1.4 The coupling factor ( )

Figure 4.5 – Effect of a temperature cycle on the coupling coefficient ( )

The coupling coefficient is an indicator of the efficiency with which mechanical energy is

converted to electrical energy by the piezoceramic and vice versa. Although it is not an

independent coefficient of piezoelectric materials, it is a theoretical value used in assessing and

comparing various piezoelectric elements. Therefore knowledge of the effect of temperature on

this constant would be useful for design purposes.

From Figure 4.5 it can be seen that temperature does not have a large effect on the coupling

factor of the BM500 material. The coupling factor changes by -1.67% as the temperature

increases from 26 to 151°C and once again decreases 3.57% as the temperature is brought down

to 26°C. Thermal hysteresis is also observed in these measurements. The value of the coupling

factor is less when the temperature is being lowered than when temperature is increasing.

0.55

0.57

0.59

0.61

0.63

0.65

0.67

0 20 40 60 80 100 120 140 160

k 33

Temperature (°C)

Temeprature increase Temperature decrease

45

4.2 Discussion

The properties of a piezoelectric material are a combination of 2 mechanisms: the intrinsic and

extrinsic contributions. The material properties originating from a single domain are called

intrinsic properties of the material or volume contribution of the ceramic. However the properties

resulting from the other parts of the material such as domain wall movements are called extrinsic

contribution of the piezoceramic. Soft piezoelectrics such as PZT have higher domain mobility

compared to hard piezoelectric ceramics and therefore increased extrinsic contribution resulting

in higher piezoelectric and dielectric coefficients.

Haun et al. theoretically calculated that the single domain (intrinsic) properties of PZT ceramics

would increase with temperature [34]. However, experimental data from Zhang et al. show this

increase to be very small compared to extrinsic contributions [20]. As the ceramic’s temperature

increases, the domain walls become more mobile. By increasing the temperature, the ceramic’s

thermal energy is increased, and the domains will require lower activation energy to reach a new

equilibrium. Structural defects and impurities of the piezoceramic will cause the domains to be

pinned down. Heating the piezoelectric will have a depinning effect on the domains by allowing

structural changes which will increase domain wall mobility [19]. Piezoelectric ceramics are

manufactured and poled at temperatures close to or higher than . The internal stresses and

cracks between domains resulting from different thermal expansion coefficients of the domains

during cooling down will also be relieved by increasing the temperature of the ceramic [16].

Therefore, increased extrinsic response and domain wall mobility is responsible for the increase

observed in piezoelectric properties, such as and , with temperature.

Compared to other piezoelectric properties, the dielectric permittivity is relatively sensitive to

temperature (37.5% change for compared to 14.9% of ). The reason lies in the different

types of domain walls. In subsection 1.3.1 the domain walls of a piezoceramic were grouped into

180° and non-180° walls. Zhang et al. determined that 180° walls do not affect the piezoelectric

coefficient whereas non-180° affect both the dielectric permittivity and piezoelectric coefficients

[20]. Therefore at higher temperatures while increased non-180° domain wall mobility will

increase both the dielectric permittivity and piezoelectric coefficients, the increased mobility of

180° domains will cause the dielectric permittivity to increase even more.

46

However small, thermal hysteresis which is expected in ferroelectric materials was observed in

all of the experimental results. The reason for thermal hysteresis is the irreversible domain wall

motions occurring while heating the ceramic [18], [19], [26], [35]. The internal stress as a result

of thermal expansion will cause both the 180° and non-180° domains to irreversibly rearrange

themselves to a state with minimum energy and create a net irreversible strain and polarization.

The hysteresis in subsequent temperature cycles will be significantly reduced since there will be

less contribution from irreversible domain switches. This can be readily observed in the data

displayed in Figure 4.6 and Figure 4.7. The graphs show the first temperature cycle applied to

the second piezoelectric sample. Thermal hysteresis is clearly visible for both the piezoelectric

coefficient and the dielectric permittivity.

Figure 4.6 – Effect of 1st temperature cycle on piezoelectric coefficient ( ) of piezoelectric

sample

350

360

370

380

390

400

410

420

430

440

0 20 40 60 80 100 120 140 160

d33(pC/N

)

Temperature (°C)

Temperature increase Temperature decrease

47

Figure 4.7 – Effect of 1st temperature cycle on dielectric permittivity ( ) of bulk

piezoelectric ceramic

1800

1900

2000

2100

2200

2300

2400

2500

2600

2700

0 20 40 60 80 100 120 140 160

ε r(ε

33/ε

0)

Temperature (°C)

Temperature increase Temperature decrease

48

Chapter 5

Stack actuator experimental results 5

In this chapter, the results of the experiments on the multilayer stack actuators are presented and

the observed trends are analyzed. The stack performance and properties such as thermal

expansion, maximum stroke, hysteresis width and area, and capacitance are measured as

functions of temperature using the experimental setup described in Section 0 3.2. The temperature

was increased in steps from 25 to 130 °C and brought back down to room temperature. The

effect of multiple cycles is also investigated and included in the results. Each step which

included changing the temperature, allowing the test rig and piezoelectric actuator to stabilize

with respect to temperature, and data acquisition took a minimum of 4 and 5 hours for increasing

and decreasing the temperature, respectively.

5.1 Thermal expansion coefficient

The first step in obtaining the thermal expansion of a multilayer stack actuator was to determine

the test rig’s thermal expansion. The thermal expansion of a 7 7 10 stainless steel block

was measured to be 18.99 10 . The expansion of the test setup while the steel block was

placed in the position of the stack actuator was determined to be 0.3536 . . The expansion

of the test setup is then determined by subtracting the two:

Setup expansion 0.3536 . 18.991 10 0.01 10 .

0.1637 .

Subtracting this value from the outputs of the displacement sensor while the piezostacks is

placed in the test rig, will reveal the thermal expansion of the stack actuator. The thermal

expansion of the stack actuator under free (no external load), 10 MPa, and 20 MPa preload are

displayed in Figure 5.1. The results suggest that preload and thermal expansion have an inverse

relationship. The highest thermal expansion coefficient18 of the actuator corresponds to the case

18

The thermal expansion coefficient of the stack actuator is obtained by dividing the actuator’s thermal expansion rate ( . ) by the actuator length ( )

49

of zero external load, with a value of 10.4 10 , followed by 6.55 10 and 6.15

10 for external loads of 10 and 20 MPa, respectively. This can be explained as a result of

softening of the piezoelectric actuator components, i.e. the piezoelectric material, bonding epoxy,

and electrodes.

Figure 5.1 - Thermal expansion of piezoelectric stack actuator under different preloads

5.2 Effect of temperature on piezoelectric stack actuator properties

The properties of the multilayer piezoelectric stack actuator under various preloads were

measured experimentally for different temperatures and frequencies. The temperature was

increased in steps from room temperature (26 °C) to 130 °C, and then brought down back to

room temperature. The maximum temperature was chosen to be 130°C due to piezoelectric stack

limitations. The experiments were repeated under different preloads (no external load, 5 MPa, 10

MPa, 20 MPa). In the following sections, the effects of temperature on the displacement–voltage

cycles, maximum stroke, hysteresis width and area, and capacitance are reported.

The minimum and maximum operating voltages of the piezoelectric actuator were 0 and 200 V,

respectively. The piezoelectric stack was actuated via a 200 Vpp oscillating wave with 100 V DC

y = 0.208x ‐ 5.884

y = 0.131x ‐ 2.942

y = 0.123x ‐ 3.193

0

5

10

15

20

25

30

20 40 60 80 100 120 140 160

Therm

al Strain (µm)

Temperature (°C)

0 MPa 9.5 MPa 20.2 MPa

50

offset. The electric field applied to the ceramic layers at 200 V is equivalent to 2985 kV/mm.

The signal was applied under quasi-static (0.1 Hz) and dynamic (50 Hz) conditions. Figure 5.2

displays the waveforms of monitored voltage, displacement, and force during one of the tests.

The voltage, displacement, and force signals were measured via the electrical circuit, MTI

capacitive sensing probe, and Kistler load washer, respectively. The configuration of these

sensors on the test setup is available in Figure 3.6. The signal applied to the actuator at room

temperature was a 200 Vpp oscillating wave with 100 V DC offset at 50 Hz. A 470N preload was

applied to the actuator. As it can be seen in Figure 5.2 (c), the force does not change

considerably during the actuation. The variation in force from its initial setting is less than 2%.

Therefore, it is reasonable to assume that the PZT actuator is operating under constant force

conditions.

(a)

(b) (c)

Figure 5.2 - Monitored waveforms of (a) voltage, (b) displacement, and (c) force during a

typical experiment

0

50

100

150

200

250

0 0.005 0.01 0.015 0.02

Voltage (V)

Time (s)

0

5

10

15

20

25

30

0 0.005 0.01 0.015 0.02

Displacement (µm)

Time (s)

462

464

466

468

470

472

474

0 0.005 0.01 0.015 0.02 0.025

Force (N)

Time (s)

51

5.2.1 Effect of temperature on piezoactuator displacement-voltage cycle

The displacement-voltage cycles at different temperatures of the multilayer piezoelectric stack

actuator are displayed for different preloads under quasi-static (0.1 Hz) and dynamic (50 Hz)

actuation in Figure 5.3 to Figure 5.6. From the curves it is seen that as temperature increases the

area within the hysteresis loop becomes smaller. The Figures also display the effect of

temperature on the overall displacement of the actuator.

(a) (b)

Figure 5.3 – Displacement - voltage curves of stack actuator with no external load actuated

at (a) 0.1 Hz and (b) 50 Hz

In Figure 5.3 the increase in displacement as temperature increases is easily visible in both quasi-

static and dynamic actuations. Figure 5.4 to Figure 5.6 show that the displacement decreases at

higher temperature, during quasi-static actuation under preload of the piezoelectric actuator.

Although there are changes in the amount of displacement during dynamic actuation of the

actuator, they are not as significant as in the quasi-static conditions. This effect can be observed

more easily in subsection 5.2.2, where the variation of the actuator stroke at 200 V is displayed

as a function of temperature.

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

52

(a) (b)

Figure 5.4 - Displacement - voltage curves of stack actuator with 5 MPa preload actuated at

(a) 0.1 Hz and (b) 50 Hz

(a) (b)

Figure 5.5 - Displacement - voltage curves of stack actuator with 10 MPa preload actuated

at (a) 0.1 Hz and (b) 50 Hz

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

53

(a) (b)

Figure 5.6 - Displacement - voltage curves of stack actuator with 20 MPa preload actuated

at (a) 0.1 Hz and (b) 50 Hz

5.2.2 Effect of temperature on actuator stroke at 200 V

The variation of the maximum displacement (stroke) of the multilayer stack actuator when

subject to 200 V is measured for increasing temperatures under various preloads. The results are

displayed in Figure 5.7 and Figure 5.8. The actuator stroke appears to be increasing with

temperature when there are no external loads on the piezoelectric actuator. This is true of both

dynamic (50 Hz) and quasi-static (0.1 Hz) actuation of the actuator. In the presence of an

external load the output displacement initially increases as the temperature increases, similar to

no load conditions. Depending on the magnitude of the external load however, the stroke of the

actuator begins to decrease after a certain temperature. The temperature at which the output

displacement begins to decrease has an inverse relationship with preload, i.e., the higher the

preload the stroke begins to decrease at a lower temperature. This can be observed in both quasi-

static actuation and dynamic frequencies although the effect is less severe during dynamic

actuation of the actuator. It is also observed as expected that for similar loading conditions, the

magnitude of the stroke is higher during quasi-static actuation compared to dynamic actuation.

Other researchers studying the effect of temperature on piezoactuator stroke have obtained

various results. Results presented by Li et al. and Senousy et al. show a bilinear relationship

between actuator stroke and temperature in the range of -30 to 80 °C under a constant 5 MPa

load [24], [25]. Heinzmann et al.’s results however, do not show a significant change in the

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

0

5

10

15

20

25

30

0 50 100 150 200

Displacement (µm)

Voltage (V)

54

stroke at 150 V for a temperature change of 25 to 75 °C [26]. This variation in the results could

be due to the different piezoelectric material of the multilayer actuators investigated in each

study. Additionally, the maximum temperature at which the actuators were experimented upon in

these studies is considerably lower than 130°C.

Figure 5.7 - Stroke of the piezoelectric actuator under a 200 Vpp oscillating wave with 100 V

DC bias at 0.1 Hz frequency

Figure 5.8 - Stroke of the piezoelectric actuator under a 200 Vpp oscillating wave with 100 V

DC bias at 50 Hz frequency

26.5

27

27.5

28

28.5

29

29.5

0 20 40 60 80 100 120 140

Actuator displacement (µm)

Temperature (°C)

No External Load 5 MPa 10 MPa 20 MPa

24

24.5

25

25.5

26

26.5

27

27.5

28

0 20 40 60 80 100 120 140

Actuator displacement (µm)

Temperature (°C)

No External Load 5 MPa 10 MPa 20 MPa

55

5.2.3 Effect of temperature on displacement hysteresis

The effect of temperature on the displacement-voltage curve and hysteresis loop can be seen in

Figure 5.9 and Figure 5.10.

(a) (b)

Figure 5.9 – Variation of the displacement hysteresis of piezoactuator with temperature

under 200 Vpp oscillating wave with 100 V DC offset at (a) 0.1 Hz and (b) 50 Hz

(a) (b)

Figure 5.10 - Variation of the hysteresis width of a piezoactuator with temperature under

200 Vpp oscillating wave with 100 V DC offset at (a) 0.1 Hz and (b) 50 Hz

6

6.5

7

7.5

8

8.5

9

9.5

10

20 50 80 110 140

Df(J/C)

Temperature (°C)

7

8

9

10

11

12

13

14

20 50 80 110 140

Df(J/C)

Temeprature (°C)

3

3.5

4

4.5

5

20 50 80 110 140

Hysteresis width (µm)

Temperature (°C)

3.5

4

4.5

5

5.5

6

6.5

20 50 80 110 140

Hysteresis width (µm)

Temperature (°C)

56

Displacement hysteresis and hysteresis width display similar trends with respect to varying

temperatures. Both hysteresis area and width generally decrease with temperature. This occurs

regardless of the actuation frequency and preload. The decrease in hysteresis width and area as

temperature changes from 26 to 130 °C can be seen in Table 5.1.

Table 5.1 - Change in hysteresis area and width as a result of temperature increase from 26

to 130 °C

Preload 0 MPa 5 MPa 10 MPa 20 MPa

Hysteresis area

0.1 Hz -12.1% -19.2% -10.6% -16.3%

50 Hz -16.5% -20.1% -8.9% -15.7%

Hysteresis width

0.1 Hz -15.9% -20.0% -15.2% -18.3%

50 Hz -16.5% -20.4% -12.4% -16.6%

An interesting observation is that in the dynamic actuation, depending on the preload the amount

of stroke initially increases as temperature rises from room temperature to 40 – 50 °C. This is

true for quasistatic actuation as well, with the exception of the case with 20 MPa preload which

the stroke remains relatively constant. It would be expected that because of the increased stroke,

the amount of displacement hysteresis ( ) would increase as well. However, except for the case

of 10 MPa preload in the dynamic actuation, both hysteresis area and width begin decreasing

from the beginning of the temperature increase.

5.2.4 Effect of temperature on piezoelectric actuator impedance

A piezoelectric ceramic is a nonlinear dielectric and therefore cannot be simply modeled as a

capacitance. Many electrical models have been suggested for piezoelectric materials such as the

Butterworth-Van Dyke (BVD) model used in the 1987 IEEE standard on piezoelectricity, and the

models described by Cady and Mason [10], [22], [36]. However, most of these models are too

non-physical and complicated to utilize in control applications. A simple electrical model for a

PZT ceramic is a capacitance and resistance in parallel [22].

Table 5.2 - Change in actuator Cp and Rp for temperature change of 26 to 130 °C

Preload 5 MPa 10 MPa 20 MPa Cp 26.3% 37.0% 23.6% Rp -32.9% -14.1% -29.2%

57

Figure 5.11 - Electrical model of piezoelectric actuator as a parallel capacitance (Cp) and

resistor (Rp) [33]

(a) (b)

Figure 5.12 - Effect of temperature on the (a) capacitance and (b) parallel resistance of

piezoelectric actuator under 1 Vpp oscillating wave at 1 kHz

Similar to the results obtained in section 4.1.2 for , the capacitance (dielectric permittivity)

which is displayed in Figure 5.12 (a), increases approximately linearly with temperature. This

occurs independently of the preload on the actuator. The parallel resistance (Rp) however

decreases with temperature but does not seem to follow a particular trend. The changes in the

parallel capacitance and resistance of the actuator are available in Table 5.2.

1.4

1.6

1.8

2

2.2

20 50 80 110 140

Cp(µF)

Temperature (°C)

300

400

500

600

700

800

900

20 50 80 110 140

Rp(Ω)

Temperature (°C)

V Cp Rp

I

58

5.3 Discussion

It was expected that similar to the results obtained for the piezoelectric coefficient ( of the

bulk piezoelectric ceramic in Chapter 4, the displacement and stroke of the multilayer

piezoelectric actuator would increase with temperature as well. The reason for the increase in

was the increased extrinsic response and domain mobility of the piezoelectric ceramics at

elevated temperatures. A detailed explanation of the effect of temperature on the intrinsic and

extrinsic responses is given in Section 4.2.

The increase in the actuator displacement at elevated temperatures was observed in the case

when no external load was applied onto the actuator in Figure 5.7 and Figure 5.8. However, once

a constant preload was applied to the actuator, depending on the amount of the load, the actuator

displacement would begin to decrease after a certain temperature. It can be concluded from the

results that the temperature at which the actuator’s stroke would decrease had an inverse relation

with the amount of preload on the actuator, i.e., as the preload on the actuator was increased, the

stroke began to decrease at a lower temperature. It is therefore necessary to understand the effect

of load on the actuator displacement to be able to explain this observation.

Figure 5.13 displays the effect of preload on actuator stroke at 200 V at room temperature. A soft

spring was used to apply preload onto the actuator as explained in subsection 3.2.1, and therefore

it can be assumed that the actuator is operating under constant force conditions19. It is important

to take into account that the force on the actuator is a constant force, not an increasing force and

it is expected to have the effect seen in Figure 1.4 (a). Based on these tests, as the force on the

actuator is increased the displacement of the actuator at 200 V increases approximately linearly.

This is true for both quasistatic and dynamic actuation.

The experimental results displayed in Figure 5.13 are similar to the results published by other

researchers [37–41]. Figure 5.14 shows the results obtained by Yang et al. regarding the effect of

preload on the dynamic piezoelectric coefficient of a soft PZT ceramic [37]. The graph shows

that as preload was increased initially increased as well. It then reached a maximum and

decreased significantly as the preload was increased further.

19

Refer to section 1.5 for more information on effect of different types of loading on actuator operation.

59

(a) (b)

Figure 5.13 - Effect of preload on actuator stroke at 200 V for (a) 0.1 Hz and (b) 50 Hz

actuation at room temperature

The main contribution to the piezoelectric expansion in soft PZTs is by the extrinsic response of

the material [20]. As an external load is applied along the poling direction, it will cause an

increase in the extrinsic contribution. The added stress will create new non-180° domain walls

which are the main contributors to the extrinsic response of and actuator displacement. The

stress will also have a de-aging effect on the ceramics and increase the extrinsic response [37],

[40], [41].

Despite its positive effects on domain mobility, stress also has a negative clamping effect on

domain mobility as well. The domain walls will be partially and progressively clamped by the

stress, which will reduce the extrinsic response of the PZT ceramic and result in lower

(displacement). Another reason for the significant decrease in in Figure 5.14 is because of

the depolarization of the ceramic due to stress. However, this issue can be overcome by exposing

the ceramic to an electric field and re-poling the piezoelectric material which is the case during

the actuation of the piezoactuator in these experiments [41].

To summarize, the effect of stress on the piezoelectric displacement ( ) is a balance between

increasing it through higher extrinsic contribution of the ceramic (positive effect) and decreasing

it by clamping the domain walls (negative effect). The maximum displacement of a piezoelectric

ceramic occurs under an optimum stress level. At stress levels below the optimum stress, the

higher extrinsic contribution overcomes the clamping of the domain walls, whereas at higher

27.6

27.8

28

28.2

28.4

28.6

28.8

4.00 8.00 12.00 16.00 20.00

Stroke

 (µm)

Preload (MPa)

25.6

25.8

26

26.2

26.4

26.6

4.00 8.00 12.00 16.00 20.00

Stroke

 (µm)

Preload (MPa)

60

stresses than the optimum stress, the clamping effect is dominant. At the optimum stress, the

positive and negative effects of stress have an equal contribution to the ceramic displacement.

Figure 5.14 - The dynamic d33 of EC-65 (a soft PZT) as a function of applied bias stress [37]

At room temperature, the multilayer piezoelectric actuator is in the rising half of the curve in

Figure 5.14, i.e., increasing the stress to 20 MPa increases the displacement of the actuator. This

is verified through the results in Figure 5.7, Figure 5.8, and Figure 5.13 and especially

Figure 5.15 - Effect of temperature on stress dependence of actuator stroke. When no external

load is present, the output displacement of the actuator increases steadily as temperature rises.

However, in the presence of preload, the output displacement displays a different trend with

temperature. Instead of a steady increase as temperature was raised, the stroke initially increased,

reached a maximum, and then began to decrease. The higher the preload on the actuator, the

decline in the stroke began at a lower temperature. An explanation for these results could be that

the optimum stress value, i.e., the stress value for which the maximum output displacement of an

actuator occurs, is different at each temperature and decreases as temperature increases. From

Figure 5.7 and Figure 5.8 it seems that 5, 10, and 20 MPa are the optimum stress values at

temperatures of approximately 60, 50, and 40 °C, respectively.

61

Figure 5.15 - Effect of temperature on stress dependence of actuator stroke

Piezoelectric actuators have a tendency to heat up quickly during dynamic actuation. Self-

heating in these actuators is as a result of mechanical and dielectric losses. Dielectric losses are

the main contributors to the self-heating phenomenon which is due to the ferroelectric losses of

the ceramic. As it was explained in section 2.3, the piezoelectric losses can be characterized

through displacement hysteresis ( ) and hysteresis width. From Figure 5.9 and Figure 5.10 it

can be concluded that both displacement hysteresis and hysteresis width decrease as temperature

increases. Piezoelectric losses are a result of domain wall motion, lattice distortion, and

microstructural evolution [29]. It was explained in section 4.2 that increasing the ceramic

temperature will increase the thermal energy of the ceramic and the domain mobility will

increase and require less energy. Additionally, higher temperatures will facilitate structural

changes in the crystal lattice and repair any microstructural distortions which occurred during the

cooling down of the ceramic after it was poled. The experiments also displayed higher losses at

higher frequencies as expected.

The effect of temperature on the capacitance of the piezoelectric stack actuator was similar to the

results obtained for in the bulk piezoceramic measurements. It was explained in the

discussion in section 4.2 that in addition to the non-180° domain walls, 180° walls also have a

role in the dielectric properties of piezoelectric actuators. Contrary to non-180° walls, 180°

domain walls are not affected by mechanical stress [7], [8]. As a result, the pinning of the non-

24

24.5

25

25.5

26

26.5

27

0 5 10

Actuator stroke

 (µm)

Stress (MPa)

T=25°C T=50° T=75°C T=100°C T=130°C

62

180° walls at higher temperatures due to the external load does not have a significant effect on

the dielectric properties as it did on piezoactuator expansion.

Thermal hysteresis was also investigated in piezoelectric actuators. Unlike the results of the bulk

piezoelectric ceramic experiments, thermal hysteresis was clearly visible in the stack actuators.

The first temperature cycle was performed under 10 MPa preload, followed by the second cycle

at 20 MPa. The third temperature cycle was performed at 5 MPa. As discussed in section 4.2,

thermal hysteresis occurs due to the irreversible domain wall motions caused by heating the

piezoelectric material; thermal hysteresis decreases with subsequent temperature cycles [18],

[19], [26], [35]. The reduction of hysteresis in subsequent cycles can be observed in Figure 5.16

and Figure 5.17. The temperature cycle with 10 MPa preload has the widest hysteresis, followed

by 20 MPa which is the second cycle. Thermal hysteresis becomes very small in the third

temperature cycle with 5 MPa preload since most of the irreversible domain switches have

already occurred. This is true for both quasi-static and dynamic actuation.

Figure 5.16 – Effect of temperature cycles on stroke of the piezoelectric actuator under a

200 Vpp oscillating wave and 100 V DC offset at 0.1 Hz

26.5

27

27.5

28

28.5

29

29.5

30

20 40 60 80 100 120 140

Actuator displacement (µm)

Temperature (°C)

5 MPa 10 MPa 20 MPa

63

Figure 5.17 - Effect of temperature cycles on stroke of the piezoelectric actuator under a

200 Vpp oscillating wave and 100 V DC offset at 50 Hz

It can also be seen in Table 5.1 and Table 5.2 that as the temperature is changed from room

temperature to 130°C, the change in Cp, Df, and hysteresis width under 20 and 5 MPa preloads

(the second and third thermal cycles), are more similar to each other compared to the changes

under 10 MPa preload (the first temperature cycle). This is also due to the irreversible domain

motions that occur during the first temperature cycle and are absent in the subsequent cycles.

[42–56]

24.5

25

25.5

26

26.5

27

27.5

28

28.5

20 40 60 80 100 120 140

Actuator displacement (µm)

Temperature (°C)

5 MPa 10 MPa 20 MPa

64

Conclusions and future work 6

6.1 Conclusions

The effect of temperature and thermal cycles on piezoelectric ceramics was studied in this

project. Temperature dependence of the fundamental piezoelectric properties ( , , , )

of a bulk piezoelectric ceramic and the nonlinear properties of a multilayer stack actuator were

investigated in operating conditions similar to the operating conditions of piezoelectric ceramics

used in fuel injectors.

The objectives achieved in this project were:

Investigate the effects of temperature on the fundamental properties of a piezoelectric

ceramic used in fuel injector applications.

Investigate the effect of thermal cycles on the fundamental properties of bulk

piezoelectric ceramics

Experimentally determine the temperature dependence of the characteristics of a stack

actuator used in fuel injectors.

Determine the effect of thermal cycles on the nonlinear properties of a piezoelectric stack

actuator

Based on the results of the experiments described in previous chapters, the piezoelectric

coefficient ( ) and dielectric permittivity ( ) of piezoelectric ceramics increases with

temperature. The displacement of the multilayer PZT stack actuator in the absence of an external

loading and its capacitance (under all preloads) also displayed similar behavior with temperature.

Increased extrinsic contribution was the main reason for the observed increase in these

properties.

In the presence of a constant external load however, the actuator stroke initially increased,

reached a maximum, and began to decrease as the temperature continued to rise. The higher the

preload, the actuator displacement reached its maximum at a lower temperature. This occurred

due to the increased clamping of the domain walls by the external load at increased temperatures.

Temperature elevation also had a negative effect on the piezoelectric losses observed in

multilayer stack actuators. The displacement hysteresis (hysteresis area) was reduced between 9

65

– 20% as the temperature increased from room temperature to ~125 °C. The width of the

displacement-voltage curve also underwent a 12 – 20% decrease for the same temperature range.

Thermal hysteresis was also investigated for the properties of bulk piezoceramics and multilayer

piezoelectric stack actuators. The samples used for the bulk piezoelectric measurements did not

display significant thermal hysteresis. On the other hand, the properties of the stack actuator

displayed significant thermal hysteresis. For both the bulk piezoelectric ceramic and stack

actuator, thermal hysteresis decreased significantly in subsequent temperature cycles. It can be

therefore concluded that prior exposure of piezoelectric ceramic actuators to be used in fuel

injectors to several heat cycles will significantly decrease the nonlinearity resulting from thermal

hysteresis.

6.2 Future work

The results obtained in this project regarding the dielectric permittivity ( ) of bulk

piezoceramics and capacitance of stack actuators (Cp) are in agreement with other studies. It is

the same case with the piezoelectric coefficient ( ) of the bulk piezoelectric ceramic.

However, a definitive behavior cannot be predicted with regards to the temperature dependence

of the output displacement and hysteresis area of multilayer piezoelectric stack actuators.

The results of this project display a strong correlation between the preload on the actuator and

the output displacement of the actuator. It is therefore recommended that in order to fully model

the effect of temperature on piezoelectric actuators especially for fuel injector applications,

several studies be performed. First, the effect of preload on piezoelectric actuator performance at

higher temperatures should be determined. As it was observed in the results, preload had an

adverse effect on the actuator output after a certain temperature. This is an important matter since

piezoelectric actuators are used with preload in most applications. Second, the effect of

temperature on piezoelectric actuators acting against a stiff spring should also be investigated. In

certain applications, the force on the actuator might increase significantly as the piezoactuator is

strained. It is therefore important to determine how a piezoelectric actuator’s performance

against an increasing force changes as temperature rises. This also shows the importance of fully

understanding the effect of a constant load on piezoelectric performance at elevated

temperatures. And third, the effect of multiple thermal cycles can be obtained with greater

accuracy if the amount of preload was the same for all temperature cycles.

66

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72

Appendix A - Length Extension Resonance Calculations

The polarization is in the 3 direction. Shaded areas are electrodes.

Figure A.1 – Sample geometry and coordinates for length extensional resonance

experiments

Boundary conditions and assumptions:

≫ , → → 0, 0  →

→ 0, 0 

 

:1

→

→ 1

→

1→

1

& → 1

→

sin cos

1

x 0 x l 1

3 2

Polarization

73

→ cos sin

The boundary conditions are now used to solve for and in equation : at 0 ,

0.

& . 0: →

& . : cos sin

→ cos 1

sin→ tan

2

& → sin tan2

cos

sin tan2

cos

→ →

→2

tan2

& → 1 2

tan2

At the electrical anti-resonant frequency, impedance is maximum ( ∞). Therefore:

tan2

∞ → 2 2

→ 2

→ 1

4

74

At resonant frequency, the impedance is minimum ( 0). As a result we shall have:

2tan

20 →

2tan

2

1

The equations relating the resonance and anti-resonance frequencies to the piezoelectric and

elastic properties of the ceramic are:

2

tan2

1

41

75

Appendix B – Mechanical Drawings of Bulk Piezoceramic Sample Holder

2550

7550

BB

714

6

46

0.032"

0.5"

0.5"

SECTION B-B

23 6

7

1

8

5

4

ITEM NO. PART NUMBER QTY.1 Base (Teflon) 12 M6 - 60mm (SS316) 13 M6 - Hex nut (SS316) 34 Top Support (Teflon) 15 Top contact (copper) 16 M4 - 25mm (SS316) 17 M4 - Hex nut (SS316) 48 Bottom Contact (copper) 19 M4 - 14 mm (SS316) 1

Sample HolderA4

SHEET 1 OF 1SCALE:1:1

DWG NO.

TITLE:

REVISIONDO NOT SCALE DRAWING

25

15

75

50

14

6

AA

5.70

0 7

SEC

TION

A-A

B C D

12

A

32

14

BA

56

Mat

eria

l

SCA

LE:1

:1SH

EET 1

OF

1

A4

C

Teflo

n

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p Ba

se

1RE

VISI

ON

DO

NO

T SC

ALE

DRA

WIN

G

Qua

ntity

:

25

50

46

1025

15

B C D

12

A

32

14

BA

56

Mat

eria

l

SCA

LE:2

:1SH

EET 1

OF

1

A4

C

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n

Top

Supp

ort

1RE

VISI

ON

DO

NO

T SC

ALE

DRA

WIN

G

Qua

ntity

:

79

Appendix C – Mechanical Drawings of Piezoelectric Stack Actuator Test Rig Modifications

10

10

M5x

0.8

5

5

AA2.

500

5

SEC

TION

A-A

Grin

d 0.00

1A

A

The

botto

m p

lane

shou

ld b

e gr

ound

and

as s

moo

th a

s pos

sible

.

B C D

12

A

32

14

BA

56

Mat

eria

l:

SCA

LE:5

:1SH

EET 1

OF

1

A4

C

Piez

o Bo

ttom

Pla

teSS

304

2D

imen

sions

: mm

Sade

gh D

avou

di

DW

G N

O.

Qua

ntity

:

86

4

M2x

0.4

2

28

2

2.50

03.

500

0.00

1A

A

The

top

plat

e sh

ould

be

grou

nd a

nd a

s sm

ooth

as p

ossib

le.

B C D

12

A

32

14

BA

56

Mat

eria

l:

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:1SH

EET 1

OF

1

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C

Piez

o To

p Pl

ate

SS 3

042D

imen

sions

: mm

Sade

gh D

avou

di

DW

G N

O.

Qua

ntity

:

10

10

33.0

20

37.0

2040

.020

40.5

25

R25

4h6G

78

B C D

12

A

32

14

BA

56

Mat

eria

l:

SCA

LE:2

:1SH

EET 1

OF

1

A4

C

Forc

e Tr

ansf

er S

haft

1018

Ste

elYi

eld

Stre

ngth

: 500

MPa

1D

imen

sions

: mm

Sade

gh D

avou

di

Title

:

Qua

ntity

:

4h6G

7A A

7.50

0

2.75

0

M3x

0.5

6

12

2.75

05

7.50

0

SEC

TION

A-A

B C D

12

A

32

14

BA

56

Mat

eria

l:

SCA

LE:5

:1SH

EET 1

OF

1

A4

C

Sens

or T

arge

t10

18 S

teel

Yiel

d St

reng

th: 5

00M

Pa

1D

imen

sions

: mm

Sade

gh D

avou

di

DW

G N

O.

Qua

ntity

:

R.25

0

R.07

0.5

88

.963

.050

.050

.450

.767

.817

1.13

4

1.58

4

only

one

hol

e is

thre

aded

1.10

0

5.5m

m

.250

.200

1.65

0

.200

.250

1.50

4

M5x

0.8

.500

1.58

4

.500

1.10

0.2

42

2x

.203

.250

.242

A sp

lit b

ushi

ng w

ith 0

.437

" ID

and

0.5"

OD

is re

quire

d.

The

1.1"

dist

ance

bet

wee

n th

e tw

o 0.

203"

hol

es m

ust b

e ex

act,

and

the

0.5"

hol

e m

ust b

e in

the

mid

dle

of t

he 1

.1".

B C D

12

A

32

14

BA

56

Mat

eria

l:

SCA

LE:1

:1SH

EET 1

OF

1

A4

C

Cap

aciti

ve S

enso

r Hol

der

SS 3

04

1D

imen

sions

: inc

hes u

nles

s st

ated

oth

erw

iseSa

degh

Dav

oudi

Title

Qua

ntity

:

100

34M8x1.25

1080

17

20 2060

99.500

2xR9

10

10

120

C

2 31 4

B

A

D

E

SS 304

1

WEIGHT:

A4

SHEET 1 OF 1SCALE:1:2

Material:

TITLE:

Dimensions: mmSadegh Davoudi

U

Quantity:

30

M4x

0.7

6 216

5

B C D

12

A

32

14

BA

56

Mat

eria

l:

SCA

LE:2

:1SH

EET 1

OF

1

A4

C

Sprin

g A

ligne

r (1)

SS 3

041D

imen

sion:

mm

Sade

gh D

avou

di

DW

G N

O.

Qua

ntity

: