harmful emissions. Novel fuel injection technologies can assist in meeting such
demands. ...... Figure 2.5: a) Schematic of macroscopic spray characteristics .
Design and Development of a Direct-Acting Piezoelectric Fuel Injector
by
Hirmand Nouraei
A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Mechanical and Industrial Engineering University of Toronto
©Copyright by Hirmand Nouraei 2012
Design and Development of a Direct-Acting Piezoelectric Fuel Injector Hirmand Nouraei Masters of Applied Science Department of Mechanical and Industrial Engineering University of Toronto 2012
Abstract Manufacturers face the challenge of enhancing fuel efficiency, engine performance, and reducing harmful emissions. Novel fuel injection technologies can assist in meeting such demands. This dissertation summarizes the stages in the design, prototyping and experimental analysis of a direct-acting piezoelectric fuel injector concept. In the proposed design, a piezoelectric stack actuator is used to directly control the injection of fuel in order to enhance the injection characteristics by utilizing the fast response time of the actuator. The direct-acting concept was implemented by developing a motion inverter in the form of a disc that reverses the direction of the input and allows the actuator to directly control injections. Tests with input signals similar to those used in diesel engines confirmed the theoretical calculations and verified the prototype’s performance. This design can control the quantity of injected fuel more precisely than currently available commercial injectors.
ii
Acknowledgement I would like to thank the following. My supervisors and collaborators that provided me with valuable guidance and advice throughout the duration of this project: Dr. Ridha Ben Mrad (University of Toronto) Dr. Anthony Sinclair (University of Toronto) Dr. Siyuan He (Ryerson University) Dr. Eswar Prasad (Sensor Technology) Dr. Paul Chiarot (State University of New York) Dr. Ming Zheng (University of Windsor) I would also like to thank the staff at University of Toronto’s Machine Shop and my colleagues at the MMDL laboratory for their help and support. Finally, I would like to thank my family for encouraging me throughout the period of my Masters.
iii
Table of Contents Abstract ........................................................................................................................................... ii Acknowledgement ......................................................................................................................... iii Table of Contents ........................................................................................................................... iv List of Tables ............................................................................................................................... viii List of Figures ................................................................................................................................ ix List of Symbols ............................................................................................................................ xiv List of Appendices .........................................................................................................................xv Chapter 1 ..........................................................................................................................................1 1 Introduction .................................................................................................................................1 1.1 Problem Statement ...............................................................................................................1 1.2 Motivation ............................................................................................................................1 1.3 Objectives ............................................................................................................................2 1.4 Thesis Outline ......................................................................................................................2 Chapter 2 ..........................................................................................................................................3 2 Background and Theory ..............................................................................................................3 2.1 Diesel Engines .....................................................................................................................3 2.1.1
Basic Principles........................................................................................................3
2.1.2
Direct Injection ........................................................................................................4
2.1.3
Common-Rail System ..............................................................................................5
2.1.4
Electronic Diesel Control (EDC) .............................................................................6
2.1.5
Diesel Fuel Injection ................................................................................................6
2.1.6
Nozzle ......................................................................................................................7
2.1.7
Spray Characteristics ...............................................................................................7
iv
2.2 Commercial Fuel Injector Technology ................................................................................8 2.3 Piezoelectricity...................................................................................................................10 2.3.1
Governing Principles .............................................................................................10
2.3.2
Material Properties .................................................................................................11
2.3.3
Performance Parameters ........................................................................................11
2.3.4
Multi-Layered Piezoelectric Stack Actuators ........................................................12
2.3.5
Feasibility of Using Piezoelectric Material............................................................13
2.4 Piezoelectric Based Fuel Injectors .....................................................................................13 2.4.1
Servo-Circuit Based Injectors ................................................................................14
2.4.2
Injector Developed by Denso.................................................................................14
2.4.3
Injector Developed by Delphi ................................................................................15
2.4.4
Injector Developed by Midé ..................................................................................17
Chapter 3 ........................................................................................................................................19 3 Fuel Injector Prototype Design .................................................................................................19 3.1 Prototype Requirements .....................................................................................................19 3.2 Piezoelectric Stack Actuator ..............................................................................................20 3.3 Preload Mechanism for the Actuator .................................................................................23 3.4 Motion Inverter ..................................................................................................................25 3.5 Housing of the Fuel Injector ..............................................................................................33 3.5.1
Fuel Path and Adapter ............................................................................................33
3.5.2
End Cap ..................................................................................................................33
3.5.3
Motion Inverter Housing........................................................................................35
3.6 Alignment of Axial Forces.................................................................................................36 Chapter 4 ........................................................................................................................................39 4 Finite Element Analysis of Prototype Components ..................................................................39 v
4.1 Material Model...................................................................................................................39 4.2 Meshing..............................................................................................................................40 4.3 Failure Criteria ...................................................................................................................41 4.4 Motion Inverter ..................................................................................................................42 4.5 Actuator Housing ...............................................................................................................44 4.6 Motion Inverter Housing....................................................................................................46 4.7 Upper Interface ..................................................................................................................48 4.8 Summary ............................................................................................................................49 Chapter 5 ........................................................................................................................................50 5 Experiment Results and Discussion for Prototype ....................................................................50 5.1 Experimental Equipment ...................................................................................................50 5.1.1
Capacitive Sensor...................................................................................................52
5.1.2
High-Speed Camera ...............................................................................................52
5.1.3
Power Amplifier.....................................................................................................55
5.2 Experimental Procedure .....................................................................................................55 5.3 Experiment Results and Analysis ......................................................................................58 5.3.1
Static Performance .................................................................................................59
5.3.2
Dynamic Performance ...........................................................................................61
5.4 Discussion of Static and Dynamic Tests ............................................................................67 5.4.1
Analysis of Results ................................................................................................67
5.4.2
Potential Sources for Discrepancies.......................................................................69
5.4.3
Applicability of Concept ........................................................................................69
5.5 Recommendations for Future Work...................................................................................70 Bibliography ..................................................................................................................................72 Appendices.....................................................................................................................................76 vi
Appendix A: Engineering Drawings and Pictures of Components ...........................................76
vii
List of Tables Table 2.1: Components of a Typical Solenoid Fuel Injector .......................................................... 8 Table 3.1: Characteristics of Selected Actuator ............................................................................ 23 Table 4.1: Material properties of Grade 5 Titanium alloy [1] ...................................................... 39 Table 4.2: Material properties of High-Carbon Steel alloy [1]..................................................... 40 Table 5.1: Modules used to perform experiments [38] ................................................................. 51 Table 5.2: Calibration of camera .................................................................................................. 53 Table 5.3: Percent difference of the measurements ...................................................................... 54 Table 5.4: Summary of results of dynamic tests ........................................................................... 61
viii
List of Figures Figure 2.1: Operating cycle of a four-stroke diesel engine [7] ....................................................... 4 Figure 2.2: Direct injection fuel chamber [7] ................................................................................. 5 Figure 2.3: Schematic of the fuel rail system ................................................................................. 5 Figure 2.4: Cross-section of hole-type nozzle ............................................................................... 7 Figure 2.5: a) Schematic of macroscopic spray characteristics ...................................................... 8 Figure 2.6: Solenoid injector in operation [7] ................................................................................. 9 Figure 2.7: Typical axes of piezoelectric material ........................................................................ 10 Figure 2.8: Schematic of a piezoelectric stack actuator ................................................................ 12 Figure 2.9: Piezoelectric Fuel Injector from Denso [35] .............................................................. 15 Figure 2.10: Direct-acting piezoelectric fuel injector from Delphi [17] ....................................... 16 Figure 2.11: Configuration of flexure mechanism [29] ................................................................ 17 Figure 2.12: Mide's piezoelectric fuel injector [42] ...................................................................... 18 Figure 3.1: Schematic of fuel injector prototype .......................................................................... 20 Figure 3.2: Characteristic Curve of Selected Actuator ................................................................. 21 Figure 3.3: Piezoelectric stack actuator ........................................................................................ 23 Figure 3.4: Schematic of the disc spring used .............................................................................. 24 Figure 3.5: Displacement of piezoelectric actuator under spring load ......................................... 25 Figure 3.6: Bridge displacement amplifier ................................................................................... 26 Figure 3.7: Schematic of the disc motion inverter in top view and cross-section ........................ 27 ix
Figure 3.8: Equilibrium problem .................................................................................................. 28 Figure 3.9: Disc problem boundary conditions............................................................................. 30 Figure 3.10: Optimization Plot for the Disc Motion Inverter ....................................................... 31 Figure 3.11: Optimization results for the disc motion inverter with a 1mm thickness ................. 32 Figure 3.12: Cross-section of the assembled motion inverter....................................................... 32 Figure 3.13: Preloading problem .................................................................................................. 34 Figure 3.14: Motion inverter housing ........................................................................................... 36 Figure 3.15: Isometric and cross-sectional views of the upper interface assembly ...................... 37 Figure 3.16: Lower interface......................................................................................................... 38 Figure 4.1: Solid92 element [3] .................................................................................................... 40 Figure 4.2: Disc motion inverter model in ANSYS ...................................................................... 42 Figure 4.3: Disc deflection in the y-direction ............................................................................... 43 Figure 4.4: Von Mises stresses of disc.......................................................................................... 43 Figure 4.5: Model of the injector housing .................................................................................... 44 Figure 4.6: Von Mises stress for the injector housing .................................................................. 45 Figure 4.7: Deflection of the injector housing .............................................................................. 46 Figure 4.8: Y-component of deflection ......................................................................................... 47 Figure 4.9: Von Mises Stress ........................................................................................................ 47 Figure 4.10: Deflection of the upper interface component ........................................................... 48 Figure 4.11: Von Mises stress of the upper interface component................................................. 49 x
Figure 5.1: Flowchart of equipment.............................................................................................. 50 Figure 5.2: Setup ........................................................................................................................... 51 Figure 5.3: CAT 1400 Precision scale at 5x magnification .......................................................... 53 Figure 5.4: Calibration Curve of the Camera, Auxiliary Lens and 5x Objective Lens ................ 54 Figure 5.5: Camera and sensor correlation test ............................................................................. 55 Figure 5.6a) Isometric view of the prototype b) cross-section view of prototype ........................ 56 Figure 5.7: Cross-section of assembled prototype ........................................................................ 57 Figure 5.8: Lower section of prototype......................................................................................... 58 Figure 5.9: Sample input voltage signal ....................................................................................... 59 Figure 5.10: Input voltage signal for static tests ........................................................................... 59 Figure 5.11: Output deflection vs. input voltage for static performance ...................................... 60 Figure 5.12: a) Initial and b) final positions of the edge of the disc motion inverter at 5x magnification ................................................................................................................................ 61 Figure 5.13: Input voltage and recorded deflection at 10Hz ........................................................ 63 Figure 5.14: Zoomed input voltage and recorded deflection at 10Hz .......................................... 63 Figure 5.15: Input voltage and recorded deflection at 50Hz ........................................................ 64 Figure 5.16: Zoomed input voltage and recorded deflection at 50Hz .......................................... 64 Figure 5.17: Input voltage and recorded deflection at 100Hz ...................................................... 65 Figure 5.18: Zoomed input voltage and recorded deflection at 100Hz ........................................ 65 Figure 5.19: Input voltage and recorded deflection at 150Hz ...................................................... 66
xi
Figure 5.20: Zoomed input voltage and recorded deflection at 150Hz ........................................ 66 Figure A.1: Prototype assembly and bill of material .................................................................... 76 Figure A.2: Actuator Housing....................................................................................................... 77 Figure A.3: Actuator Housing....................................................................................................... 77 Figure A.4: Adapter for connecting high-pressure fuel line ......................................................... 78 Figure A.5: Upper Interface a) bottom View b) top View ............................................................ 78 Figure A.6: Upper interface assembly .......................................................................................... 79 Figure A.7: Upper interface part1 ................................................................................................. 80 Figure A.8: Upper interface part2 ................................................................................................. 81 Figure A.9: Lower Interface pin ................................................................................................... 82 Figure A.10: Lower interface pin.................................................................................................. 82 Figure A.11: Lower Interface cap ................................................................................................. 83 Figure A.12: Lower interface cap ................................................................................................. 83 Figure A.13: Clamp ...................................................................................................................... 84 Figure A.14: Clamp ...................................................................................................................... 84 Figure A.15: End Cap ................................................................................................................... 85 Figure A.16: End cap .................................................................................................................... 85 Figure A.17: Motion inverter housing .......................................................................................... 86 Figure A.18: Motion inverter assembly ........................................................................................ 87 Figure A.19: Titanium disc motion inverter ................................................................................. 88 xii
Figure A.20: Disc fulcrum ............................................................................................................ 89 Figure A.21: Disc fulcrum ............................................................................................................ 89 Figure A.22: Disc fork .................................................................................................................. 90 Figure A.23: Disc fork .................................................................................................................. 90
xiii
List of Symbols Symbol d33 E ε33T ε0 Fpreload
Unit [C/N] [GPa] [F/m] [F/m]
Description Piezoelectric strain constants in the 33 direction Young’s modulus Relative Dielectric Constant Vacuum Permittivity
[N]
Preload force applied to the actuator
K springs
[N/m]
Stiffness of disc springs
Fdisc
[N]
Applied force on the disc
FMax
[N]
Blocking force of the piezoelectric actuator
K actuator
[N/m]
Stiffness of the piezoelectric actuator
x M Q D
[µm] [Nm] [N] [GPa m3] [Rad]
Output displacement of the actuator Bending moment Shear force Flexural rigidity of the plate Rotation
Sy
[MPa]
Yield strength
u
[MPa] n/a [Kg/m3]
Ultimate strength Poisson’s ratio Density
von
[MPa]
Von Mises Stress
n f F d De Di l0 t h0 tL P V I N C
n/a [Hz] [N] [µm] [mm] [mm] [mm] [mm] [mm] [m] [W] [V] [A] n/a [µF]
Safety factor Input signal frequency Generated force by actuator Achieved output displacement External disc spring diameter Internal disc spring diameter Free disc spring height Disc spring thickness Disc spring free cone height Thickness of each layer of the piezoelectric stack actuator
Power Voltage Current Number of layers of the piezoelectric stack actuator Capacitance xiv
List of Appendices A1: Engineering Drawings and Pictures of Components………………………………….72
xv
1
Chapter 1
1
Introduction
1.1 Problem Statement The aim of this project is to design and develop a novel concept for piezoelectric driven fuel injectors used in injection systems of diesel engines. A piezoelectric actuator provides high force generation and fast response time; thus, it can be a great asset to the fuel injector if implemented properly. Commercial piezoelectric fuel injectors, in general, do not use the full potential offered by piezoelectric actuators and often impede the actuator’s performance with other less efficient components. Rate of fuel injection, response time of the injector and complexity of the injector design all contribute to the efficiency of the system. Using the piezoelectric actuator, the Electronic Diesel Control unit can manage a high number of multiple injections within a combustion cycle allowing very efficient combustion to occur. An increase in combustion efficiency leads to cleaner exhaust, lower noise level, and higher power output, which are all critical demands for the automotive industry [6].
1.2 Motivation The main motivation for this project is to contribute to the automotive industry by implementing a piezoelectric actuator into the fuel injector to take full advantage of the actuator’s force and response time characteristics. To fulfill this idea, the piezoelectric stack actuator should be directly performing the injection operations and the use of intermediate components is minimized. The simplicity that the use of this actuator can bring to fuel injector designs will in turn reduce fabrication and maintenance costs and challenges. Furthermore, emission regulations are getting stricter every year, thus, feasible but more advanced solutions are required to address the demand for better performing fuel injectors. The motivation for targeting the widely used common rail injection system of diesel engines comes from its increasing use in the automotive industry as well as its potential for performance improvement due to high fuel pressure values of up to 200MPa associated with the injection process. The common rail system has also been increasingly used in the European markets and is quickly catching up in the North American market.
2
1.3 Objectives The main objective of this project is to design, build, and test a fuel injector that uses a piezoelectric stack actuator to directly control the process of fuel injection in diesel engines. The fuel injector has to be compatible with commercially available diesel engines and high pressure common-rail systems. The prototype must be modular in the sense that design modifications can be made to each module without affecting the others. Additional features of the prototype include off-power holding of the injection nozzle and improved response time, compared to that of commercial injectors. Off-power holding refers to the action of the piezoelectric actuator in keeping the injection nozzle closed during its de-energized state. The actuator remains in the off-power state for the majority of an engine’s combustion cycle and is only energized for about 1% of the injection cycle. Experiments will be conducted to test the various aspects of the prototype. Detailed analysis of the experimental results will be provided in order to fully characterize the performance of the fuel injector.
1.4 Thesis Outline A summary of the chapters that make up the thesis is provided in this section. Chapter 2 contains background information focused on diesel engines principals and the role of fuel injectors in establishing the efficiency and performance of the engine. Piezoelectric actuators and some of their characteristics are also presented in Chapter 2. Chapter 3 outlines the requirements of the prototype, the design process and the methods used for designing various components of the prototype. The motion inverter design and optimization as well as the preloading mechanism are also described in detail in Chapter 3. Chapter 4 provides a summary of the Finite Element Analysis (FEA) of the critical components of the injector including the motion inverter, housing and intermediate components. FEA results are provided to validate the design process undertaken in Chapter 3. Chapter 5 elaborates on the experiments conducted, provides the results, as well as an analysis of the overall characteristics of the injector prototype. Several recommendations regarding future tasks are also provided. Miscellaneous details, such as engineering drawings for fabricated components, are provided in the appendices.
3
Chapter 2
2
Background and Theory
This section contains background information regarding design of piezoelectric fuel injectors for diesel engines. The topics covered in this section include principles of diesel engine operations, high pressure common-rail systems, and commercial fuel injector technologies. Furthermore, an introduction to the theory of piezoelectricity, piezoelectric materials and piezoelectric stack actuators is also provided. Finally, novel designs of piezoelectric based fuel injectors are presented.
2.1 Diesel Engines The world’s first diesel engine was produced in 1897 with 20hp at 175RPM by Rudolf Diesel. Diesel engines, today, are the most widely used combustion engines due to their relatively higher efficiency. They are used in a variety of applications from cars and light commercial vehicles to railway locomotives and ships. The wide range of applications of diesel engines is due to their attractive characteristics such as engine power, safety, costs, and reliability. In light commercial vehicles and passenger type vehicles, Electronic Diesel Control units have been implemented to improve torque and smoothness of engine operation. Additionally, the automotive industry is constantly pursuing lower engine emission levels, more efficient fuel economy, and faster vehicle response time [7].
2.1.1
Basic Principles
The diesel engine operates by compressing the air required for combustion to generate high temperatures. This is followed by injection of the diesel fuel, which spontaneously ignites after injection. Figure 2.1 shows the operating cycle of a four-stroke diesel engine. Step a) shows the induction stroke in which the piston moves downwards from the Top Dead Center (TDC) position while at the same time, the inlet valve opens and air is drawn into the cylinder. Next in step b), the inlet and exhaust valves are closed and the piston moves upwards to compress the air trapped in the cylinder. In car engines, the compression ratio is about 24:1, which causes the air to heat up to about 900oC. Fuel is injected when the compression stroke is almost complete.
4
Ignition occurs as shown in step c), after which an increase in the cylinder pressure forces the piston downwards. The kinetic energy transferred to the piston is converted to torque by the crankshaft. Finally, in step d), the exhaust stroke completes the cycle by forcing the exhaust gases out of the combustion chamber using the exhaust valve. On completion of the exhaust stroke, the crankshaft has completed two revolutions [7].
Figure 2.1: Operating cycle of a four-stroke diesel engine [7]
2.1.2
Direct Injection
The shape of the combustion chamber controls the exhaust characteristics of a diesel engine to some degree as it can allow for better mixing of air and fuel. There are two types of combustion chambers: divided and undivided. The undivided combustion chamber used in direct injection (DI) engines is the preferred choice as it reduces fuel consumption and noise level compared to the indirect injection engines, which use the divided combustion chamber. Figure 2.2 shows a schematic of the undivided combustion chamber. As shown in the figure, the fuel is directly injected into the combustion chamber and mixed with air. This technology creates good air turbulence and ensures that fuel is evenly distributed inside the combustion chamber. However, it requires significantly high injection pressures of up to 2000 bars.
5
Legend 1. Multi-hole injector 2. Chamber. 3. Glow plug
Figure 2.2: Direct injection fuel chamber [7]
2.1.3
Common-Rail System
To meet the demand for high injection pressures mentioned in the previous section, the pressure generation system has been separated from the fuel-injection system using a common-rail pressure unit, illustrated in Figure 2.3. The common-rail pressure unit uses a high pressure pump to increase fuel pressure and accumulate this pressure in the fuel rail. From the fuel rail, high pressure fuel is supplied to each fuel injector via a high pressure delivery line. The common-rail system is usually controlled by the Electronic Diesel Control (EDC) unit that allows flexible control of actuating mechanisms and other sub-systems to produce optimized combustion [7]. Fuel sent to injectors based on command from EDC
Fuel return to fuel tank
Fuel pumped by the high-pressure pump
High-pressure fuel rail Figure 2.3: Schematic of the fuel rail system
This was first introduced into the automotive sector in 1997, which brought many breakthroughs in meeting stringent emission level and power output standards [31]. The advantage of using the common-rail system lies in its ability to vary injection pressure and timing over a broad range. Furthermore, the generated pressure is kept constant by the pump throughout the entire combustion cycle and, thus, the quantity of injected fuel is proportional to the length of time that
6
the injection valve is open and independent of the pump speed. High-pressure injection promotes a very fine spray atomization resulting in emission reduction [17]. Since the development of the common-rail system, a heavy emphasis has been placed on the fuel injector especially on its responsiveness because it directly affects the overall performance of the engine.
2.1.4
Electronic Diesel Control (EDC)
Electronic Diesel Control (EDC) collects information such as camshaft speed, fuel rail pressure, and road speed of vehicle. EDC uses this information to send proper control signals for injection of fuel. Fast switching times are demanded from the nozzles to inject fuel at the precise moment. It enables fuel injectors to spray fuel into the combustion chamber multiple times within one combustion cycle. Without the multi-injection feature, fuel is sprayed all at once into the combustion chamber causing a rapid and high pressure rise. However, in the case of multiinjection engines, pilot injections allow for more efficient mixing of fuel and compressed air. Furthermore, post injections reduce the soot particles by burning them with small amounts of fuel. The injection duration is between 1 to 2 milliseconds. The amount of fuel injected in the pilot injection of a car engine is about 1mm3, and 50mm3 for full-load delivery. For commercial vehicles, pilot injection is about 3mm3 and full load delivery is about 350mm3 [7].
2.1.5
Diesel Fuel Injection
A number of variables affect the performance of fuel injectors: start of injection, injection duration and pressure, direction and number of injection jets. Start of injection is the point at which injection of fuel into the combustion chamber starts. Proper timing of this point is important and is done in degrees of crankshaft rotation relative to the crankshaft Top Dead Center (TDC). This point directly affects emission generation. For instance the NOx and hydrocarbon emissions are lowest when the start of injection is closest to the Top Dead Center [7]. The start-of-delivery parameter indicates the delivery of fuel from the fuel injection pump to the fuel injector. Injection lag is defined as the time from start of fuel delivery to start of injection, and ignition lag is the time from start of injection to start of ignition. The injection lag and ignition lag are delays that the fuel injection system has to compensate for by adjusting start of delivery and start of injection in response to engine speed, load and temperature [7].
7
2.1.6
Nozzle
The nozzle injects fuel into the combustion chamber of the engine and has the role of proper atomization and distribution of fuel in the combustion chamber as well as sealing off the combustion chamber from the injection system. Direct injection engines use hole-type nozzles with home diameters on the order of 0.12mm. A nozzle needle is used to seal the holes. Figure 2.4 shows the cross-section of a typical hole-type nozzle.
Nozzle
Dead volume
Needle
Fuel path
Injection orifice
Figure 2.4: Cross-section of hole-type nozzle
2.1.7
Spray Characteristics
Optical diagnostic techniques have been used to study the processes of spray formation and atomization. The spray tip penetration is the length between the tip of the nozzle and the spray tip. The spray angle is the angle between the two lines of the best fitting of the boundary points from the nozzle tip to 60% of the spray penetration. Figure 2.5a) shows the schematic of a typical spray jet. As the liquid jet leaves the nozzle, it becomes turbulent and the outer surface of the jet breaks up into droplets. The mass of air within the spray increases near the spray tip, its velocity decreases, and its width increases [45]. The overall shape of the injection jet for car engines is long and narrow, whereas, in commercial vehicles, the jet tends to be wider and shorter.
8
Nozzle tip
Spray cone angle Spray tip penetration
Figure 2.5: a) Schematic of macroscopic spray characteristics
2.2 Commercial Fuel Injector Technology In this section the operating principles of a typical solenoid fuel injector with a hydraulic servocircuit that works with the common-rail system are described. Figure 2.6 shows the three operation stages of this injector: a) sealed, b) lifting, and c) closing. The components of the fuel injector are listed in Table 2.1. Table 2.1: Components of a Typical Solenoid Fuel Injector 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Fuel return line Solenoid coil Overstroke spring Solenoid actuator Valve ball Valve-control chamber Nozzle spring Pressure shoulder of nozzle needle Injection chamber Injection orifice (nozzle) Solenoid valve spring Outlet restrictor High pressure fuel line Inlet restrictor Valve plunger Nozzle needle
The principal of operation relies on the pressurized fuel volume accumulated in the valve-control chamber (component #6) and injection chamber (component #9). In stage a), the nozzle
9
(component #10) remains closed as the fuel pressure in both chambers balance each other. In stage b), the needle (component #16) moves up and the nozzle (component #10) opens to generate the fuel spray. This is done by moving the valve ball (component #5) upwards using the solenoid actuator (component #4). Next, the valve-control chamber (component #6) is depressurized as the fuel volume escapes from the outlet restrictor (component #12). In stage c), the solenoid actuator (component #4) is de-energized; the valve-control chamber (component #6) is filled with pressurized fuel. As a result, the needle (component #16) moves down and closes the nozzle (component #10) with the assistance of the nozzle spring (component #7).
Figure 2.6: Solenoid injector in operation [7] In this particular injector, the factors that contribute to the injection lag are the response time of the solenoid actuator and the fuel flow rate through the two restrictors (components #12 and #14). The delay from pressurizing and depressurizing the valve-control chamber is a big contributor to the injection lag. In more advanced fuel injectors, piezoelectric actuators have replaced solenoid actuators due to their faster response time.
10
2.3 Piezoelectricity 2.3.1
Governing Principles
Piezoelectric materials show two types of effects. When subjected to a mechanical force, the crystals become electrically polarized, the direct effect. Also, when an electric field is applied to the material, strains result – the indirect effect. Ceramics manufactured from formulations of lead zirconate / lead titanate exhibit significant sensitivity and high operating temperatures, relative to ceramics of other compositions. Piezoceramics are anisotropic materials; therefore, their properties are tensor quantities which depend on the direction of polarization, electric field, and mechanical stress. Figure 2.7 shows the convention used to define the poling direction (axis 3), and the shear planes (axes 4, 5, and 6). 3, poling axis 6 5 2
4 1
Figure 2.7: Typical axes of piezoelectric material A linear constitutive relationship, as shown below, is used to relate the electrical and mechanical properties of piezoceramics to each other.
𝐷𝑚=𝜀𝑚𝑘𝑇𝐸𝑘+𝑑𝑚𝑖𝑇𝑖
(2.1)
𝑆𝑖=𝑑𝑖𝑚𝐸𝑚+𝑠𝑖𝑗𝐸𝑇𝑗
(2.2)
where 𝑖, j = 1,…,6 𝑎𝑛𝑑 𝑘, 𝑚 = 1,…,3. Summation is assumed over repeated indices; D is the electric displacement vector (C/m2), S is the strain vector, E is the electric field vector (V/m), T is the stress vector (N/m2), 𝜀 is the dielectric permittivity matrix (F/m), d is the piezoelectric matrix (C/N), and s is the compliance matrix (m2/N). The superscript T stands for constant stress conditions (usually taken as unclamped), and the superscript E stands for constant electric field conditions (usually taken as short-circuited electrodes). Exceeding the maximum voltage may cause dielectric breakdown and irreversible damage to the piezo actuator [44].
11
2.3.2
Material Properties
There are two basic classes of piezo ceramic materials: hard and soft. Each class of material has been developed and dedicated to a separate set of applications. Hard PZT materials provide the highest possible stability. They can be subjected to high electrical and mechanical stresses while their properties change very little under these conditions. Hard PZT materials are used in highpower and precise frequency filter applications. This class of material is developed by the addition of dopants such as potassium K+1 or iron Fe+3 to the typical PZT elements (lead zirconate or lead titanate) [19]. Soft PZT materials have high domain mobility and a relatively large piezoelectric charge coefficient, moderate permittivity and high coupling factors. Soft PZT materials provide the highest possible piezoelectric properties for actuator and ultrasonic applications. They are used for the purpose of multilayer stack actuators due to their higher piezoelectric properties, such as higher d33.Soft materials, however, have higher mechanical and electrical losses compared to hard materials and are not as stable. This class of material is doped with elements such as lanthanum (La), niobium (Nb), or antimony (Sb) [19]. For most actuator applications, the composition of piezoelectric ceramics has been the PZT (lead zirconate titanate) material. An important consideration is the ferroelectric phase transition temperature (Curie temperature). For diesel injection application, an actuator has to operate without de-poling at temperatures up to 150oC. Therefore, ferroelectric transitions with Curie Temperatures higher than 350oC are suggested [40].
2.3.3
Performance Parameters
Several important piezoelectric constants are described in this section in order to provide the necessary background information. The piezoelectric charge constant, d, is the polarization generated per unit of mechanical stress applied to a piezoelectric material. The first subscript of this constant indicates the direction of polarization generated in the material when the electric field is zero. The second subscript is the direction of the applied stress.
12
The piezoelectric charge constant can also be defined as the mechanical strain experienced by a piezoelectric material per unit of applied electric field. The first subscript in this definition is the direction of the applied electric field, and the second subscript is the direction of induced strain [44]. Elastic compliance, s, is the strain produced in a piezoelectric material per unit of stress applied and, for the 11 and 33 directions, is the reciprocal of the modulus of elasticity (Young's modulus, Y). SD is the compliance under a constant electric displacement; sE is the compliance under a constant electric field. The first subscript indicates the direction of strain; the second is the direction of stress [44]. The electromechanical coupling factor, k, is an indicator of the effectiveness with which a piezoelectric material converts electrical energy into mechanical energy, or converts mechanical energy into electrical energy. The first subscript to k denotes the direction along which the electrodes are applied; the second denotes the direction along which the mechanical energy is applied, or developed [44].
2.3.4
Multi-Layered Piezoelectric Stack Actuators
A piezoelectric stack actuator, is an actuator which consists of a stack of ceramic discs (N discs) as shown in Figure 2.8, in which each disc has an opposite polarization direction from its adjacent discs. The discs are separated from each other by thin metallic electrodes. The same voltage is applied to all discs and the final displacement is obtained from the relationship below:
Δ𝑙𝑡𝑜t𝑎𝑙=(𝑁)(Δ𝑙𝑠𝑖𝑛𝑔𝑙e 𝑑𝑖𝑠𝑐) Polarization direction + _ _
Figure 2.8: Schematic of a piezoelectric stack actuator
(2.3)
13
Stack actuators are capable of withstanding high compressional forces along their axis, creating large displacements, and have high stiffness compared to other piezoelectric actuators. While stack actuators have the ability to operate under high pressures, they are vulnerable and sensitive to pulling forces, and no pulling force should be applied to piezoelectric stacks without preload. A monolithic multilayer d33 actuator provides the highest mechanical work density and highest actuator efficiency compared to other piezoelectric devices. The actuator efficiency is defined as the ratio of mechanical power to the sum of mechanical and reactive electrical power [33]. Among the different types of piezoelectric based actuators, such as bending, tubular, stack, multilayer stack actuators are chosen as the suitable type for fuel injector applications. Even though other types of piezoelectric actuators work with lower electrical capacitance, their performance in terms of the stiffness and actuator force is always inferior compared to that of stack actuators [9]. Modern multilayer actuators consist of alternating layers of electrodes and ceramic plates, which are co-fired during the sintering process. Ceramic layers in such actuators are typically 50 to 100µm thick and the d33 constant is in the range of 425 to 670x10-12C/N [44].
2.3.5
Feasibility of Using Piezoelectric Material
Piezoelectric materials have been used in automobiles for purposes of both sensing and actuation. Piezoelectric actuators have been used in valve actuation and fuel injectors [7]. Piezoelectric sensors have been also used for acceleration and vibration sensing [25]. Piezoelectric actuators generally provide large forces but with limited stroke. Thus, they provide high control force densities per unit stroke compared to other types of actuators, such as hydraulic or pneumatic. Control force density per unit stroke is the mean control force for one stroke of the actuator relative to the unit volume of the actuator [6]. Piezoelectric actuators are, therefore, suitable for applications requiring large amounts of energy over a short period of time. The high response time of the piezoelectric actuators makes them good candidates for use in fuel injectors [25].
2.4 Piezoelectric Based Fuel Injectors This section covers recent and novel designs of piezoelectric based fuel injectors. Some of the following concepts have made their way into commercial products while others have not been so successful.
14
2.4.1
Servo-Circuit Based Injectors
Piezoelectric based fuel injectors that use a servo-circuit configuration operate very similarly in principal to the solenoid injector illustrated in Figure 2.6 with the exception that the actuator is piezoelectric based rather than solenoid based. According to a study done by Suh et al. in 2007 on the comparison of spray characteristics of piezoelectric versus solenoid based fuel injectors, the piezo-driven injection system has a few advantages [45]. The injection delay of the piezodriven type injector was shorter than that of solenoid-driven type injector by about 0.1ms. Additionally, the analysis revealed that the fuel atomization of the piezo-driven system was better, due to a faster response time and a higher injection rate [45].
2.4.2
Injector Developed by Denso1
The piezoelectric fuel injector from Denso is capable of achieving up to 5 injections per combustion cycle. This injector is part of a common-rail system capable of functioning with pressures up to 180MPa and uses a hydraulic servo-circuit configuration. As shown in Figure 2.9, the fuel pressure inside the Nozzle Back Pressure Chamber pushes the Nozzle Needle down. When the actuator is energized, the pressure in this chamber is reduced by allowing the fuel to exit through the Fuel Return path. As a result, the Nozzle Needle is pushed up by the fuel pressure accumulating beneath it. The delay from the start of electronic activation to the start of mechanical response is reduced from 0.4ms, as in the case of solenoid actuators, to 0.1ms in this case [35].
1
Denso Contact Information: Regional Headquarters, North America, 24777 Denso Dr., Southfield, MI 48033, Tel: (248) 350-7500, E-mail:
[email protected]
15
Fuel Return Fuel Inlet Piezo stack Amplifier piston Amplifier chamber Valve piston Control valve Nozzle
Valve Seat Upper Valve Seat Lower Valve Sliding Nozzle Back Pressure Chamber Nozzle Needle
Figure 2.9: Piezoelectric Fuel Injector from Denso [35] Faster response time allows for more injections with smaller quantity and closer intervals. The lifting speed of the needle is about 1.2m/s in this injector. Engine performance was improved in emission level and maximum power and torque output. Power increased from 110kW to 130 kW. Torque increased from 310Nm to 400Nm. Because of the smaller delay achieved by the piezoelectric injector, a larger number of multi-injections relative to the solenoid counterpart could be potentially achieved [35]. However, the injector’s performance is reduced because of the lag in accumulation of fuel in the amplifier chamber of the injector. This delay is seen in other servo-circuit based injectors as well. As a result, if the reliance on fuel accumulation were to be reduced, the performance of the injector could be further improved.
2.4.3
Injector Developed by Delphi2
A direct acting piezoelectric fuel injector, as shown in Figure 2.10, was developed by Delphi. This injector uses a piezoelectric stack actuator to drive the nozzle needle to sealed or opened
2
Delphi Contact Information: Troy Offices & Customer Center, 5725 Delphi Drive, Troy, Michigan 48098-2815,
USA, Tel: (248)-81-2000
16
positions directly. A hydraulic amplifier increases the output stroke of the actuator by using the area difference from the input and output pistons. The output force is as result reduced by the same amplification factor that increases the output stroke. This fuel injector was designed to be used as a part of the common-rail system showing that it is possible to use the force generated by the piezoelectric actuator to overcome the force from the high pressure fuel. The main purpose of using direct actuation is to enhance the response time of the injector compared to piezoelectric servo-circuit injectors. The achieved maximum needle speed for this injector was 3 m/s [17]. To utilize the actuator force to its full potential, Delphi’s fuel injector used “de-energize to inject” configuration as opposed to “energize to inject”. In Delphi’s configuration, the nozzle needle is lifted and fuel is injected when the actuator is de-energized, which means that the piezoelectric actuator is energized for almost 95% of the injector’s service life to seal the injector [14]. By keeping the actuator energized, relatively high positive voltages are applied to the actuator for long durations, which will result in high power drainage from the system and reduced actuator lifetime.
Figure 2.10: Direct-acting piezoelectric fuel injector from Delphi [17]
17
2.4.4
Injector Developed by Midé3
Midé has developed a piezoelectric actuator system for fuel injection control. The actuator, as shown in Figure 2.11, uses two piezoelectric stack actuators, which are 5mm x 5mm in crosssection and 50mm in length. Additionally, a flexure mechanism moves the spool that controls the fuel inlet and outlet. The left image shows a schematic of the actuator with no applied voltage. The right image shows the same actuator when voltage is applied and the two piezoelectric actuators have extended in length. The stroke of the actuator has also been labeled on the image. As the two piezoelectric actuators extend, the moving frame undergoes a rigid body rotation that results in the output stroke. Actuator Stroke Piezoelectric elements
Rigid Housing Moving frame Flexure element
No Voltage
Applied Voltage
Figure 2.11: Configuration of flexure mechanism [29] The flexure mechanism is capable of increasing the output displacement by a factor of 5.3. However, it reduces the output force from 1000N to 66N. Using the flexure element, the moving frame and the rigid housing, four pivot points are created and the linear output displacement of the stacks is converted to a purely linear motion perpendicular to the axis of the stacks [29]. Figure 2.12 shows the assembly of the actuator on a fuel injector unit. Due to its size and direction of output motion, the actuator has to be placed at 90o with respect to the body of the
3
Mide Contact Information: Mide Technology Corporation, 200 Boston Avenue, Suite 1000, Medford, MA 02155,
Tel: (781)306-0609
18
injector [29]. The Xframe Piezo actuator as labeled in Figure 2.12 shows the location and orientation of Mide’s actuator. The reduced output force and the size and orientation of this actuator limit its applicability. Although the actuator is successful in controlling injections, it cannot be readily implemented in diesel engines. Furthermore, the piezoelectric actuator does not control the injections directly, which contributes to potential lags in the injection process. Piezoelectric Actuator
Spool Inlet
Outlet
Intensifier Injection Needle
Figure 2.12: Mide's piezoelectric fuel injector [42]
19
Chapter 3
3
Fuel Injector Prototype Design
This chapter describes the motivation and detailed objectives for developing the fuel injector prototype. Description of each of the components as well as justification for the design and selection of the key features are provided.
3.1 Prototype Requirements Figure 3.1 shows a labeled schematic of the fuel injector prototype. The prototype has to provide a framework for testing different variations of the fuel injector design. It has to follow a set of design constraints, such as dimensional and fabrication related constraints. Furthermore, to allow for variations in the components and mechanisms, the prototype has to be modular in the sense that its assembly consists of several modules put together. This facilitates the replacement of one module with another to test a variety of designs without the need for building a new prototype from scratch. The requirements for each component of the prototype follow in the next few sections of this chapter. The Finite Element Analysis for the prototype components is presented in Chapter 4. A safety factor of, n = 2, has been chosen since the prototype will be tested in a laboratory environment and the loading conditions, such as preload on the piezoelectric stack and force generated by the stack, are known quantities [34]. The prototype illustrated in Figure 3.1 is designed to allow for application of preload to the actuator and to direct the output force and displacement of the actuator to a mechanical motion inverter. The main design requirements are to ensure that the actuator can be safely operated and motion inversion can be achieved. The disc springs, upper interface, lower interface, and end cap components are involved in the preloading aspect. The fork, disc motion inverter and fulcrum are the components of the motion inverter. Additionally, a fuel path and a fuel inlet have been implemented in the injector housing for later development of the servo-circuit of fuel injector prototype.
20
End cap Thrust bearing
End cap for electrical wires
Upper interface
Actuator Housing Adapter for fuel line
Lower interface cap Disc spring
Motion inverter housing
Thread engagement
Plastic tube Actuator
Lower interface pin
Fork Disc motion inverter
Opening for camera Fulcrum Opening for capacitive sensor Figure 3.1: Schematic of fuel injector prototype
3.2 Piezoelectric Stack Actuator The actuator provides the input of the system. Several commercial piezoelectric actuators were 4
studied and the Noliac NAC2022-H100 stack actuator was selected as the most appropriate. This actuator provides a blocking force of 4000N and a free displacement of 149µm. The stack has a length of 10cm and a cross-section of 1cm by 1cm, which fit within the dimensional constraints of the prototype. Compared to other piezoelectric actuators of the same length, it provides a higher stroke and output force. The maximum recommended operating voltage for this actuator is 200V, which is also typical of other commercial piezoelectric actuators currently used in fuel injectors. The free displacement is the maximum displacement that the actuator can
4
Noliac A/S, Hejreskovvej 18, DK-3490 Kvistgaard, Denmark, Phone: +45 4912 5030, Email:
[email protected]
21
generate without any opposing force at the free end. It can be evaluated using the following expression:
L Vd33
(3.1)
L0 t
where V is the operational voltage in V, d33 is the piezoelectric charge constant in m/V, L0 is the overall length of the actuator in m, and t is the thickness of the piezoelectric layers in m. The blocking force is the maximum force generated by the actuator when no displacement is generated. Using the overall length of the actuator and the free displacement, the blocking force is estimated using this expression: FB
(3.2)
EA L L0
where E is the elastic modulus in N/m2, A is the cross-sectional area of the actuator in m2. A characteristic plot describing the force and displacement relationship of a piezoelectric stack actuator at four different input voltages is shown in Figure 3.2. This curve is based on the values of blocking force and free displacement provided by the actuator’s manufacturer. The values for the points on the graph have been also confirmed using the developed prototype. 5000 200V 150V
4000
100V
Force (N)
3000
50V
2000 1000 0 0
25
50
75 100 Stroke (µm)
125
150
Figure 3.2: Characteristic Curve of Selected Actuator
175
22
The piezoelectric stack actuator has a stiffness of 27N/µm as calculated using the blocking force and free displacement values provided by the manufacturer. The blocking force is the maximum force generated at the zero displacement point (y-intercept) and the free displacement occurs at the point where there is no external force (x-intercept) acting on it. A general expression describing this linear relationship can be expressed as:
F FB
FB d L
(3.3)
where F is the generated force and d is the accompanying displacement. To select a suitable power supply to drive the actuator, it is necessary first to determine its power requirements. The capacitance of the stack is calculated using the following equation. Next, the current requirements are found. Last, the power relationship is presented.
C
T N 33 0 A tL
(3.4)
where C is the total capacitance in Farad, ε0 is the vacuum permittivity, ε33T is the relative dielectric constant, N is the total number of layers in the stack actuator, and tL is the thickness of each layer. I max 2Vmax Cf
(3.5)
where Imax is the maximum required current in Amperes and f is the frequency of operation in Hertz.
Pmax Vmax I max
(3.6)
where Pmax is the maximum power and Vmax is the maximum voltage in Volts. The electrical impedance, X in ohms, can also be calculated using: X = (1/2π f C)
(3.7)
23
Table 3.1 below shows some of the parameters related to the selected actuator. Table 3.1: Characteristics of Selected Actuator Height (mm)
Max Voltage (V)
Max Force (N)
Free Stroke (µm)
Capacitance C (µF)
Operating Frequency, f (Hz)
Operating Freq. ω (rad/s)
Impedance X (Ω)
Power P (W)
100
200
4000
149
20.5
200
1256.6
38.8
1030
The relatively high power consumption is due to the high capacitance of the actuator. This high capacitance is a result of the relatively large number of 20µm thin layers of the stack actuator. Despite the significant power requirements, current laboratory power amplifiers such as Noliac NDR6880 are capable of providing the required voltage and current. Furthermore, power amplifiers such as the IPoD piezoelectric driving module, which is used for testing fuel injectors, can also provide the power requirements. Figure 3.3 shows a photo of the piezoelectric stack actuator used. Since only gauge 28 wires could be soldered to the actuator, 9 sets of wires were soldered to each side of the actuator in order to distribute the input current between the wires. The black dots indicate the positive electrodes, which are connected to the red wires. The top and bottom layers of the stack are inactive PZT layers with a fine surface finish. These two layers are used to interface the stack with the other mechanical components. Negative electrodes
Positive electrodes
Inactive PZT layer
Active PZT layers
Figure 3.3: Piezoelectric stack actuator
3.3 Preload Mechanism for the Actuator Preloading the actuator is an essential part of the prototype design. Preload is necessary for safely operating the actuator and it also affects the performance of the device significantly. Piezoelectric material is much better at sustaining compressive load than tensile load, so a
24
general rule in using the actuator is to keep the working range within compression. Furthermore, a preload of about 10MPa is required for the actuator under dynamic conditions. Since the input current is proportional to the speed of motion, sudden changes in current cause significant acceleration of the actuator. Thus, to prevent damage, the stack has to be put under higher compressive load to ensure that tension on the layers is prevented. It is, thus, important to use an accurate and repeatable method to provide the preload for different experiments. One typical way of compressing the actuator can be facilitated using a disc spring. The performance of the actuator can be affected if the spring’s stiffness is comparable to that of the actuator. In such a case, the output deflection of the actuator can be reduced significantly. Due to size constraints, the only viable option for providing the necessary preload of 1000N, equivalent to 10MPa, was a disc spring. The basic idea is to place the disc spring on one end of the actuator and use a threaded end cap on the other end. The end cap is tightened using a torque wrench, which provides a repeatable method for applying a certain preload. This way, the disc springs and the piezoelectric stack are members that undergo compression. Using their stiffness values, a set of disc springs capable of generating the 1000N preload were selected. Figure 3.4 shows an illustration of the disc springs used. The parameters displayed in the figure are external disc diameter De, internal disc diameter Di, free disc height l0, disc thickness t, and free cone height, h0.
Figure 3.4: Schematic of the disc spring used The ratio of the free cone height, h0, to the disc thickness, t, has to be equal to or lower than 0.4 in order for the disc spring to have a constant stiffness and linear force displacement curve. The selected disc spring has a stiffness of 6.34 N/µm. Two of these springs are placed in parallel, providing a total stiffness of 12.68N/µm. The displacement of the stack is well within the traveling range of the disc spring combination and the required preload of 1000N can be applied
25
as well. Due to the relatively high stiffness of the disc springs, the output displacement of the piezoelectric actuator will be altered as shown in Figure 3.5. When the actuator is countered with a spring of appreciable stiffness, the maximum stroke of the actuator decreases significantly, case B. However, if the stiffness of the springs is much lower compared to that of the actuator, the output displacement loss will be negligible meaning that the actuator can provide an output displacement close to its maximum free displacement.
Spring stiffness, K
Displacement, ΔL
Piezoelectric stack actuator Case A Lost stroke
L0
Case A: Free displacement
Case B: Forced displacement
Case B
Applied Voltage, V
Figure 3.5: Displacement of piezoelectric actuator under spring load
3.4 Motion Inverter The motion inverter is a mechanism designed to reverse the direction of the output displacement provided by the stack actuator. This mechanism is required because in order for fuel to be sprayed out upon actuation, the needle of the nozzle has to be pulled up. However, the stack provides an output displacement in the opposite direction. It would be beneficial if the same mechanism provides an amplification factor to improve the stroke of the piezoelectric stack. Data available on needle stroke in fuel injectors is mostly gathered for purposes of numerical modeling of the injector and are rarely provided as a method for evaluating the performance of the fuel injector. Nonetheless, needle stroke values of 300µm to 500µm have been reported [18]. The performance of an injector, however, is mainly judged by the quantity of injected fuel and response time of the injector [7]. In this project, since the motion inverter has to be designed and
26
tested, it is important to evaluate its performance by its ability to reverse the direction of motion and potentially magnify the output motion. A hydraulic motion inverter and amplifier have been reported in the past [12]. However, assembly of the hydraulic unit as well as removal of cavities due to air dissolved in the hydraulic fluid caused the design to be of very low efficiency and low repeatability. As a result, a mechanical approach is pursued in this project. Previous mechanical components coupled with piezoelectric actuators mostly fall under the category of compliant mechanisms. Mechanisms, such as flexure hinges, are typically used to amplify the low displacement of the piezoelectric actuator. However, they are of relatively low stiffness and cannot be used to transfer large forces. Another issue with the existing methods is that the direction of the output motion is normally perpendicular to that of the input displacement [36]. Although such mechanisms can provide displacements of up to 1mm, they cannot be readily implemented in the fuel injector prototype. Furthermore, Figure 3.6 shows a bridge displacement amplifier made of a combination of flexure hinges, bars, and pivot points. As the two piezoelectric actuators extend, the bars are forced to rotate about the pivot points and generated and upward output motion. The hinges in these components are essential to providing the output motion. However, they are also locations of stress concentrations and sources of complexity in design and fabrication of the displacement amplifiers [47].
Flexure hinge Piezoelectric actuator
Output
Bar Piezoelectric actuator
Figure 3.6: Bridge displacement amplifier In order to minimize the number of components in the motion inverter and ease the fabrication and assembly process, a relatively simple idea was pursued. The idea is to apply the output force of the actuator on the outer edge of a disc that is resting on a fulcrum, as shown in Figure 3.7. As
27
the outside edges are forced downwards, the center moves in the upward direction, thus, inverting the motion. Applied force on edge of the disc, P0 Disc thickness, h Fulcrum location, a
Circular fulcrum
Figure 3.7: Schematic of the disc motion inverter in top view and cross-section Steel, Titanium and Aluminum were evaluated as three material choices for the fabrication of the disc motion inverter. Steel, AISI1045, provides the largest Young’s Modulus among the three options, 190-210MPa, and a yield strength of 505MPa. High strength Aluminum, Al7075, provides the smallest Young’s Modulus of about 70-80MPa, and a yield strength of 455MPa. However, Grade 5 Titanium, Ti-6Al-4V, was selected as the most suitable of the three options with a Young’s Modulus of 110MPa, and a yield strength of 900MPa. The higher yield strength of Titanium and its relatively low Young’s Modulus make it the better choice. Furthermore, the higher hardness of Titanium lowers the possibility of indentation of the motion inverter disc during application of the load. Through some preliminary tests, it was deduced that a disc of constant thickness provides reasonable stability and can be loaded uniformly. Plate theory was used to determine the effects of bending moment and shear on the disc to characterize the disc. The problem was formulated as follows. First, the equation of force equilibrium between the piezoelectric actuator, the disc springs, and the disc motion inverter is set up.
28
Fpreload K springs x Fdisc FMax K actuator x
(3.8)
where Fpreload is the preload force applied to the actuator, K springs is the stiffness of the disc springs, Fdisc is the applied force on the disc motion inverter, FMax is the blocking force of the piezoelectric actuator, K actuator is the stiffness of the piezoelectric actuator and x is the output displacement of the actuator, which is the same as the deflection of the disc motion inverter and disc springs. It is assumed that the disc motion inverter behaves similarly to a spring and has a constant stiffness. The schematic in Figure 3.8 shows the equilibrium problem.
Piezoelectric stack actuator
Disc springs
Disc motion inverter
Figure 3.8: Equilibrium problem The disc related parameters constitute the unknowns of the design. Thus, the deflection of the disc is calculated parametrically using plate theory under the assumptions of linear loading on the edge of the disc, axisymmetric boundary conditions, and consideration that the shear effects are significant. The disc was divided to two segments, a solid segment and an annular segment. Since the effects of both shear and bending have to be investigated and it is also desirable to isolate the deflection of the disc in terms of the geometrical parameters, the analytical method developed by Lee in 1989 has been used [24]. In this method, the effects of bending moment and shear forces have been decoupled so that the deflection due to each can be calculated separately. Then the total deflection can be found using the following equations. Equation (3.9) states that
29
the total deflection is equal to the sum of the deflection due to pure bending and the four fifth of the deflection due to shear [24].
4 w1 w1k w1s 5
(3.9)
w1k C31r12 C41
(3.10)
w1s C11I 0 (k11 ) C41
(3.11)
R k1 420(1 v) 1 h1
(3.12)
where w1 is the total deflection of the solid disc, w1k is the deflection due to bending for the solid axisymmetric disc segment, and w1s is the deflection due to shear in the solid axisymmetric disc segment. I0 is the modified Bessel function of the first kind.
4 w2 w2k w2s 5
(3.13)
w2K C12 ln(r2 ) C22 r22 ln(r2 ) C32 r12 C42
(3.14)
w2s C12 I 0 (k2 2 ) C22 K0 (k2 2 ) C32 ln( 2 ) C42
(3.15)
where:
(3.16) R k2 420(1 v) 2 h2 w2 is the total deflection of the annular disc, w2k is the deflection due to bending and w2s is the deflection due to shear in the axisymmetric annular disc segment. I0 and K0 are the modified Bessel functions of the first and second kind, respectively. Boundary conditions are defined to satisfy conditions of simple support and line loading, as shown in Figure 3.9.
w1k 0 and w1s 0 w1 0 r1 R1 1 2 1k 2k and 1s 2s M M k k s s 2 1 M 1 M 2 and M 1 M 2
30
w2k 0 and w2s 0 w2 0 r2 R1 1 2 1k 2k and 1s 2s M M k k s s 2 1 M 1 M 2 and M 1 M 2
M 2k 0 and M 2s 0 M 2 0 r2 R2 P0 2 k P0 2 420(1 v) s 105 P0 )w Q2 2 R r ( w ) 2 R D and r ( h2 2 R2 D 2 2 where M is the bending moment, Q is the shear force, D is flexural rigidity of the plate, and is the rotation. The equation for D is:
D
(3.17)
Eh3 12(1 v 2 ) R2
P0 h
+Z-axis a
R1
r1 r2
Figure 3.9: Disc problem boundary conditions Once the deflection of the center of the disc is found in terms of the geometrical parameters, which include the diameter and thickness of the disc as well as the location of the fulcrum, the force applied on the disc and the edge deflection can also be found. The largest possible radius was selected for the disc based on the size constraints for the fuel injector prototype. The thickness and fulcrum location were the two parameters varied in the optimization process. Figure 3.11 shows the results for edge and center deflections at different fulcrum locations for a disc with a thickness of 1mm. The inputs provided to the optimization program included the preload, 1000N, the Young’s modulus of Titanium, 114GPa, the diameter of the disc, 31.75mm, and stiffness of the disc springs. The optimization code calculated the deflections at the center and edge of the plate, the load exerted on the plate and the total load generated by the piezoelectric actuator. Two parameters were varied during the optimization process. The
31
thickness of the plate was varied from 0.5mm to 5mm in 0.1mm increments. The location of the fulcrum from the edge of the plate was the second variable parameter, from 0mm to 10mm in 1mm increments. Figure 3.10 shows the optimization curve for the output deflection of the motion inverter.
Figure 3.10: Optimization Plot for the Disc Motion Inverter After careful consideration of the optimization results, a plate thickness of 1mm was selected. This thickness allows a relatively large diameter to thickness ratio, which minimizes the effects of shear forces on deflection. Additionally, a support location of 4mm away from the edge of the disc was chosen to ensure that the outside segment of the plate has the necessary stiffness.
32
200 Edge deflection
180
Center deflection
Deflection (µm)
160 140 120 100 80 60 40 20 0 0.0
2.0 4.0 6.0 8.0 10.0 Distance of fulcrum from edge of disc, a (mm)
12.0
Figure 3.11: Optimization results for the disc motion inverter with a 1mm thickness From the optimization results, a thickness of 1mm and a fulcrum-edge distance of 4mm were selected. The theoretical edge displacement for this case is 65µm and the center displacement is 88µm. The theoretical amplification factor is, thus, 1.35. A load of 2252N is needed from the piezoelectric actuator and, of this force, 425N will be transferred to the disc as the input force on the disc. Furthermore, Finite Element Analysis, shown in Chapter 4, was used to verify the deflection and failure criteria for the fabricated disc. Figure 3.12 shows a cross-section of the assembled motion inverter unit. The interface between the fork, which transfers the force of the actuator to the disc, is an edge of width of 0.5mm.
Set screw location
Fork Disc
R=2.2mm
Fulcrum Fulcrum screws
Figure 3.12: Cross-section of the assembled motion inverter
33
The contact between the fulcrum and the disc is tangential to replicate simple support conditions. A fillet radius of 2.20mm was selected based on some preliminary tests to reduce the local stresses as much as possible. The fulcrum is fixed to the housing component using two screws and the fork is connected to other intermediate components using a set of set screws at the top.
3.5 Housing of the Fuel Injector The prototype housing consists of the housing for the piezoelectric stack actuator and the housing for the motion inverter. The housing of the actuator contains several important features as described below.
3.5.1
Fuel Path and Adapter
The adapter for the high-pressure fuel line is labeled in Figure 3.1. The fitting is machined as an additional piece, press-fitted into the housing of the injector, and then welded in place. The housing is then stress relieved before fine machining is done. The adapter has external M12 threads and a tip that fits the high-pressure fuel line. The tip of the adapter provides the necessary sealing of the end of the fuel line. Figure A.4 shows an engineering drawing of the adapter. The path for the fuel is created using wire Electrical Discharge Machining (EDM). The diameter of the cylindrical path is selected as 1mm. A 1mm diameter wire can EDM the path for the required distance of about 9cm with reasonable accuracy. In order to calculate the thickness of the housing wall, around the fuel path, a thick-walled cylinder problem is considered where pressure is applied inside the fuel path [34]. Using a factor of safety of 2 and the equations for radial and tangential stresses, a wall thickness of 8mm has been selected. The wall thickness is slightly higher than required based on the calculations. This is done to allow machining threads and other features required on the outside of the injector’s housing.
3.5.2
End Cap
The end cap seals the injector from the top after all components have been put in place. By tightening the end cap, the desired preload is applied. Furthermore, it is assumed that once the end cap is tightened, it stays fixed, thus, provides a rigid support for the actuator. The most practical way to keep track of the applied preload is to keep track of the deflection of the disc springs. A torque wrench that measures both applied torque and angle of rotation is used to apply
34
the preload. Since the amount of torque applied varies based on the friction of the threads, the measured torque alone is not very reliable for checking the preload. Using the known pitch of the threads and the measured angle of rotation, however, the vertical travel distance of the end cap can be calculated. An assumption is made at this point, that all intermediate components are rigid in comparison to the disc springs and the piezoelectric stack actuator. Thus, the distance traveled by the end cap is equal to the sum of the compression of both the disc springs and the piezoelectric stack. This assumption is validated using FEA in Chapter 4. This is analogous to two springs placed in series and fixed on one side while a force is applied to them from the opposite side, as shown in Figure 3.13. Applied preload force
Piezoelectric stack actuator
Disc springs
Figure 3.13: Preloading problem A pitch of 1mm was chosen for the threads in order to provide the necessary resolution for the poreloading. A tolerance class of 2A/2B is used for fabrication of the threads. This is a typical tolerance class and allows for multiple assembly and dis-assembly of the threaded components. The equivalent stiffness for the preloading problem is calculated using the equation below.
1 1 1 kM k piezo kspring where KM is the equivalent stiffness of the piezoelectric actuator, Kpiezo, and that of the disc springs, Kspring.
(3.18)
35
In order to ensure that the threads of the end cap and the housing can endure the tension force of the energized piezoelectric actuator, the end cap and housing assembly is considered to be similar to a bolt and nut problem. The piezoelectric actuator and the disc springs are the members that are being compressed. The end cap performs the role of the nut and the housing acts similarly to a bolt. In order to calculate the stiffness of the bolt, KB, the following equation is used, which is based on the stiffness of the threaded and unthreaded portions of the housing.
1 1 1 kB kThreaded _ portion kUnthreaded _ portion
(3.19)
The above equation was adapted from the Mechanical Engineering Design textbook (Shigley, 2008). Next, a preload of 1000N was assumed to be present and the fraction of external load carried by the bolt (housing in this case) was calculated once a separation force of 2000N is applied by the actuator. Using the ultimate tensile strength of the Steel alloy, AISI1045, the maximum tensile load for failure of the housing was calculated to be 4.49x105N. As a result, the separation force of 2000N will not cause failure or affect the position of the end cap significantly. Furthermore, minimum length of thread engagement to prevent thread stripping was calculated as 21.56mm. The actual length of thread engagement in the fabricated components is 28mm.
3.5.3
Motion Inverter Housing
The housing for the motion inverter, as shown in Figure 3.14, is designed for experiments conducted in the laboratory. A vision system is used in these experiments to monitor the deflections of the motion inverter disc. The housing for the motion inverter must have holes or openings that allow the camera to take pictures of the edge of the disc inverter. It is important to ensure that the openings created in the body of the housing do not cause a significant vertical deflection once the actuator is energized. As a result, Finite Element Analysis is performed to ensure that any deflections in the housing are minimal.
36
Figure 3.14: Motion inverter housing
3.6 Alignment of Axial Forces Ensuring that the piezoelectric stack actuator is properly aligned in the fuel injector housing is essential for proper operation of the actuator and to protect it against shear and torsion. The upper and lower interfaces for the actuator have been designed to align the preload and the output force along the axis of the actuator. The upper interface, as shown in Figure 3.15, consists of a thrust bearing that prevents the torsion from being transferred to the actuator when the end cap is being torqued. The outside surface of the upper interface and the inside surface of the piezoelectric housing are both fabricated under a sliding tolerance to ensure that the two surfaces run smoothly against each other. The seat for the thrust bearing is machined according to the manufacturer’s specifications to ensure that the bearing is firmly held in place. Additionally, the upper interface has openings for electrical wires that are connected to the actuator as well as a finely finished contact surface that comes into contact with the actuator. This ensures that local stress concentration is reduced by removing defects and burrs from the contact surface. The dimensions for the upper interface are selected so that under maximum loading condition of 2000N, the maximum vertical deflection of this component is no more than 1µm. To ease the assembly process, the upper interface was fabricated as two components and then joined using two screws after passing the electrical wires through the openings.
37
Shaft key location
Outside surface with sliding tolerances
Thrust bearing
Contact surface for stack actuator Opening for electrical wires
Figure 3.15: Isometric and cross-sectional views of the upper interface assembly Additionally, a shaft key was placed in a slot fabricated on the upper interface and the housing of the injector to ensure that the upper interface cannot rotate about its axis and can only translate vertically. The lower interface includes two components as shown in Figure 3.16. The top part provides a seat for the piezoelectric stack actuator. This part has a thickness of 5mm, half the width of the stack actuator. This allows for efficient distribution of the force generated by the actuator, as recommended by the actuator’s manufacturer, Noliac. The lower part is in tangential contact with the upper part. The arc allows the stack actuator to align itself with the axis of the force applied on it. The lower part also aligns and compresses the disc springs. The ideal lower interface would be in contact with the actuator at only one point rather than an arc. This would provide two rotational degrees of freedom for the actuator to align itself with the axis of the compression force. However, Hertzian calculations show that in order to prevent local failure for a single point of contact, a spherical radius of at least 35cm is required [34]. Whereas, an arc, which creates a contact line, requires a minimum radius of 3.5cm. Both calculations were performed in the case of application of a 2000N force and with a safety factor of 2 for Steel alloy, AISI1045. Since the latter case is more practical due to size constraints, an arc with a 3.5cm radius was fabricated.
38
Seat for piezoelectric actuator
Tangential contact
Flat surface for compressing disc springs
Flats for set screws Figure 3.16: Lower interface
39
Chapter 4
4
Finite Element Analysis of Prototype Components
Finite Element Analysis helped verify the design and finalize the dimensions of the essential components of the prototype. These components include the motion inverter, the actuator housing, the motion inverter housing and the upper interface. Chapter 3 includes a description of each of these components and their role in the fuel injector prototype. In this chapter, the material model, meshing technique, failure criteria, and the FEA results for the motion inverter disc, actuator housing and upper interface are described.
4.1 Material Model The disc motion inverter is made of Grade 5 Titanium alloy, Ti-6Al-4V, and all other fabricated components are made of High-Carbon Steel alloy, AISI1045. Table 4.1 shows the material properties of the Titanium alloy. Both materials are elastic and isotropic for the purposes of the FEA. Table 4.1: Material properties of Grade 5 Titanium alloy [1] Young’s modulus , E (GPa)
110
Yield strength , S y (MPa)
900
Ultimate strength , u (MPa)
950
Poisson’s ratio ,
0.34
Density , (kg/m3)
4430
Table 4.2 shows the material properties of the Steel alloy, AISI11045.
40
Table 4.2: Material properties of High-Carbon Steel alloy [1] Young’s modulus , E (GPa)
200
Yield strength , S y (MPa)
505
Ultimate strength , u (MPa)
625
Poisson’s ratio ,
0.29
Density , (kg/m3)
7850
Solid92 was selected as the element type for the FEA analysis of three dimensional components. This element has 10 nodes and is well adapted for modeling irregular meshes. The nodes have three translational degrees of freedom in x, y, and z directions [3]. This element type has been recommended in a study evaluating the strength of fuel injector housing by Liu et al. in 2011 [27]. Figure 4.1 shows a schematic of the element with the faces and nodes labeled.
Figure 4.1: Solid92 element [3]
4.2 Meshing Both mapped and free meshing operations were performed to mesh the analyzed components. A free mesh has no restrictions in terms of element shapes, and has no specified pattern applied to it. However, a mapped mesh is restricted in terms of the element shape it contains and the pattern of the mesh. A mapped mesh typically has a regular pattern, with obvious rows of elements. Mesh density determination was based on a series of convergence tests performed on each component. In the convergence tests, the procedure outlined by Shaorong el al. was followed [43]. The initial analysis was started using a coarse mesh. Next, the mesh density was doubled
41
and the problem was solved again. Results were compared to the first analysis, and mesh density was doubled again in areas where the stress change exceeded 0.1%. The last step was repeated until all stress changes remained less than 0.1%. Furthermore, areas of interest in each component were given a finer mesh compared to other areas. It was ensured that the FEA was performed with reasonable mesh density as well as computation time.
4.3 Failure Criteria The Distortion Energy Theory for Ductile Materials was used as the basis of the failure criteria. This is the most widely used theory for failure of ductile materials [34]. Yielding occurs when the distortion strain energy per unit volume reaches or exceeds the distortion strain energy per unit volume for yield in simple tension or compression of the same material. The safety factor is applied as shown below:
S y'
(4.1)
Sy n
where S y is the yield strength and n is the safety factor. For the general state of stress, yield is predicted when:
von S y' where and
von
(4.2)
is the von Mises Stress for three-dimensional stress.
Von Mises Stress is a single quantity which can be compared against the yield strength of the material for any stress situation and is formulated as: 1
von
2 2 1 2 2 2 z x 6 xy2 xz2 yz x y y z 2
(4.3)
where i is the normal stress in the i direction and ij is the shear stress in the i, j plane and i and j could take on x, y or z values [34].
42
4.4 Motion Inverter The motion inverter disc was modeled as a quarter disc in order to use symmetry boundary conditions. The dimensions for the model are the same as those of the optimized design. Based on the theoretical calculations, a total force of 425N is applied on the edge of the disc. A quarter of this load was applied to the disc model in the FEA. The force is applied on the outermost edge of the disc. Simple supports are placed at a distance of 4mm from the edge of the disc, similar to the theoretical calculations. Symmetry boundary conditions are applied at the cross-sections of the disc. Figure 4.2 shows the modeled disc and the applied boundary conditions.
Applied force Symmetry boundary condition
Simple support
Figure 4.2: Disc motion inverter model in ANSYS Figure 4.3 shows the nodal deflection of the disc in the z-direction. The maximum upward displacement is 88µm at the center of the disc and the maximum downward displacement is 65µm at the edge of the disc. The input and output displacement agree with the theoretical results calculated using the optimization code.
43
Center deflection, 88µm
Edge deflection, 65µm
Zero deflection at the location of the fulcrum
Figure 4.3: Disc deflection in the y-direction Additionally, the Von Mises stress reaches a maximum at the location of the fulcrum as shown in Figure 4.4. The maximum stress is well below the yield strength of Titanium using a safety factor of 2. This figure also confirms the correlation between the FEA of the disc and the plate theory. The Von Mises stress demonstrates a neutral plane in the middle of the disc where stress and deflection are both zero.
Figure 4.4: Von Mises stresses of disc
44
4.5 Actuator Housing The goal of the FEA for the housing was to ensure that the flange has the necessary strength to counteract the force of the high pressure fuel. Several simulations were performed to find the optimal flange thickness, flange radius and thickness of the bottom section of the housing. It was also necessary to ensure that the bottom of the housing, where the disc springs are located, does not deflect significantly after the actuator applies a force of over 2000N. The housing for the piezoelectric stack actuator is modeled using symmetry about the XZ plane. Figure 4.5 shows the model of the housing as well as the boundary conditions. The stress criteria for the fuel path were verified using the theoretical calculations in Chapter 3, so the fuel path is excluded from this analysis. Symmetry boundary conditions as well as the flange and clamp constraints are labelled on the figure. The clamp constraints are applied to the slot created for the clamp and prevent rigid body translation and rotation. The flange boundary conditions include those applied to the flange holes to represent the bolts and nuts as well as those applied to the external surface of the flange. The input force applied by the piezoelectric stack and the fuel pressure act in opposite directions. The two forces have been calculated for conditions of maximum output by the piezoelectric stack (2000N) and maximum fuel pressure (200MPa). Forces are applied as pressures over their respective areas as shown in Figure 4.5.
Clamp constraints Symmetry boundary condition
Flange constraints
Location of applied force due to actuator constraints
Location of applied pressure due to fuel
Figure 4.5: Model of the injector housing
45
Figure 4.6 shows the Von Mises stress of the housing for the finalized case. The maximum Von Mises stress is 275Mpa, which satisfies the failure criteria. The stress distribution shows good uniformity in the model. Since the bolt and nut boundary conditions are represented as fixed constraints without including the bolt and nut as contact elements, there is some stress concentration visible at the bolt holes. However, the overall stress distribution of the housing shows no signs of possible failure. Figure 4.7 shows the deflection of the housing. A maximum deflection of 22µm is detected immediately at the location of the application of the fuel pressure. The deflection, at the location of the disc springs decreases to about 12 to 14µm. This means that under the condition of maximum fuel pressure, the maximum deflection that affects the performance of the stack actuator is 12 to 14µm. Although this deflection seems significant, it will only act to preload the piezoelectric actuator further and remains as a constant force. Thus, for tests that use pressurized fuel, the initial preload has to be adjusted to compensate for the additional force applied by the fuel. Additionally, the inner workings of the injector should be designed in such a way that the fuel pressure effects are minimized. Doing so will further reduce the deflection of the housing.
Figure 4.6: Von Mises stress for the injector housing
46
Figure 4.7: Deflection of the injector housing
4.6 Motion Inverter Housing The housing for the motion inverter is modeled using symmetry boundary conditions. As a result, only a quarter of the housing is modeled in ANSYS. The openings for the camera as well as the opening for the capacitive sensor are included in the model. Boundary conditions are applied such that the housing stays fixed at the flange location, while the reaction force of the motion inverter, 425N, is applied to the bottom of the housing. Symmetry boundary conditions are also applied at the two cross-sections of the housing. Figure 4.8 shows the y-component of the deflection in the housing. The maximum deflection is about 1µm, which is within the acceptable limits.
47
Flange
Capacitive sensor opening
Openings for camera
Figure 4.8: Y-component of deflection Figure 4.9 shows the Von Mises stress of the housing. The maximum Von Mises stress is 50MPa, which is well below the yield strength of the Steel alloy. This maximum stress is due a sharp corner in one of the openings in the body of the housing. All corners are to be filleted during the fabrication of the components to relieve locations of stress concentration.
Figure 4.9: Von Mises Stress
48
4.7 Upper Interface The goal of performing FEA on this component was to ensure that its deflection under due to forces generated by the piezoelectric actuator is minimal. The upper interface consists of a thrust bearing and a fabricated part. According to the manufacturer, the bearing is highly stiff and can sustain high compressive loads on the order of 4000N. Therefore, the bearing is excluded from this analysis. The features of the fabricated component include seats with finished surfaces for the bearing and the piezoelectric stack actuator. Additionally, to gain access to the electrical wires, this component contains two sets of slots that run from the center outwards, one for the positive and the other for the negative wires. The sizes of the openings are based on the diameters of the wires, which are about 4mm for each set of wires. To model the upper interface, symmetry boundary conditions are applied on the cross-section of the model. The constraints are due to the cylinder housing that constrains the piece along its outer cylindrical circumference and allows only for axial movement. The end cap is designed in a way that it will hold down the thrust baring and the seat. Thus, the area where the thrust bearing sits can be assumed to be fixed in the Z-direction. A force of 2000N was applied based on the working conditions of the piezoelectric stack actuator. Figure 4.10 shows the deflection of the component and Figure 4.11 shows the Von Mises stress. The maximum deflection is 2µm and the maximum stress value is 136Mpa. Both the deflection and stresses are within reasonable limits.
Figure 4.10: Deflection of the upper interface component
49
Figure 4.11: Von Mises stress of the upper interface component
4.8 Summary Finite Element Analysis of the components of the prototype helped provide a validation that failure would not occur in any of the components and that the compression of each of the intermediate components is less than 1µm. This ensures that there is no loss of displacement in the intermediate components. To verify the results of the Finite Element Analysis for the motion inverter a set of experiments were designed and carried out. The details of the experimental setup and discussion on the results are presented in Chapter 5. Furthermore, to verify the results of the Finite Element Analysis for the other prototype components, the prototype was assembled and tested without the motion inverter section. Therefore, the output displacement of the piezoelectric stack actuator under various preloads was measured. Comparison of the theoretical and experimental displacement values helps in verifying the results of the Finite Element Analysis.
50
Chapter 5
5
Experiment Results and Discussion for Prototype
The experiments conducted were designed to verify the functionality of each of the prototype components. Additionally, understanding the behaviour of the system as a whole and characterizing it under static and dynamic conditions were two other essential aims of the experiments. The sections that follow elaborate on the setup and purpose of the experimental procedures as well as a summary of the obtained results.
5.1 Experimental Equipment The equipment can be categorized in two categories: input and output. Please see the flowchart below, Figure 5.1, with regards to the arrangement of the equipment.
Input Voltage
Real-time
Captured
Signal
Controller
Frames and Output of Capacitive sensor
Voltage
Fuel Injector
Amplifier
Prototype
Figure 5.1: Flowchart of equipment Figure 5.2 shows the setup that I put together to conduct the experiments.
51
Real-time controller
Sensor amplifier
Prototype
Data acquisition
Voltage amplifier
Light source
Capacitive sensor
Figure 5.2: Setup The Real-time controller, NI PXIe8133, manages the signal generator, NI PXI5412, the camera interface, NI PXI 8252, and the Data Acquisition (DAQ) module, NI 6070E. Using this setup, data collection and signal generation are performed without any interference from other background processes. The input signal is generated using LabVIEW and is sent to the power amplifier from the function generator. At the same time, the camera starts recording images, at a rate of 30 frames per second. The time instant for recording each image is also saved. Simultaneously, the DAQ module starts recording measurements of the output of the capacitive sensor. Table 5.1 shows a summary of the modules mentioned above. Table 5.1: Modules used to perform experiments [38] Equipment
Purpose
Specifications
NI PXIe8133
- Real-time controller - Runs VIs - Manages inputs and outputs - Multifunction data acquisition (DAQ)
- Quad core processor - 2 GB dual-channel RAM - 8 GB Memory - 2 analog outputs - Resolution: 12 bits - Sampling rate: 1.25 MS/s - Input voltage range: -10V to 10V - Resolution: 14 bits - Output voltage range: -10V to 10V - Connection ports for camera (IEEE1394a)
NI 6070E
NI PXI 5412
- Signal generator
NI PXI 8252
- Camera interface
52
To provide the necessary commands, three LabVIEW programs, VIs, were developed using LabVIEW, each for controlling one of the modules installed on the PXI unit. Each VI is briefly explained and a screenshot is provided. The DAQ VI controls the DAQ module and saves the output of the capacitive sensor. Voltage range, sampling rate, total number of samples and lowpass filter value are specified in this VI. The CAMERA VI saves the frames captured by the camera as well as the time of the capture. The FGEN VI provides various options for creating the input voltage signal. It controls the function generator module on the PXI unit and provides the waveform of the input signal, its frequency, and number of cycles.
5.1.1 Capacitive Sensor The capacitive sensor, ASP-20-CTA, has a maximum range of 500 µm and a sensing diameter of 5mm. An amplifier system, Accumeasure 9000, is used to amplify the output of the sensor. Using this amplifier, the resolution is 0.005% of the full-scale range and the accuracy is 0.02% of the full scale range. The manufacturer has calibrated the capacitive sensor and its signal amplifier.
5.1.2 High-Speed Camera In order to visually monitor the performance of the motion inverter, a high-speed camera, Sony DFW-V500, was used. The camera is capable of capturing 30 frames per second (fps) and has a 640pixel by 480pixel field of view. Although the camera is not fast enough to capture the dynamic performance of the fuel injector, it is very useful in assessing the static performance. The camera was coupled with an auxiliary lens with variable zoom options and a 5x objective lens from Mitutoyo. The lens configuration results in a focal length of 3.5 cm. The camera was mounted on a linear stage to accurately align and focus it during experiments. The camera and lens assembly were calibrated at different zoom options and the pixel size was calculated for each zoom setting. In order to perform the calibration, a precision scale was used. The cameralens configuration was used to take pictures of the scale as shown in Figure 5.3.
53
0.1mm
0.5mm
1mm
Figure 5.3: CAT 1400 Precision scale at 5x magnification The number of pixels in each image was acquired using Photoshop CS5.1, and the pixel size was then calculated. For the sake of consistency, the number of pixels was always counted from the center of one line to the center of the next. Furthermore, to remove human errors and increase repeatability of measurements, ten measurements were done at different locations on each image and the results were averaged. A summary of the results is displayed in Table 5.2 and the calibration curve is shown in Figure 5.4. The results were verified using another calibration performed with MATLAB. Table 5.2: Calibration of camera Auxiliary Lens Zoom Setting
Overall Zoom
Pixel Size (µm)
1.0 1.5 2.0 2.5 3.0
5.0 7.5 10.0 12.5 15.0
1.80 1.23 0.92 0.74 0.62
Size of the Field of View (mm) Horizontal Vertical 1.15 0.86 0.78 0.59 0.59 0.44 0.47 0.35 0.40 0.30
54
2
Pixel Size (µm)
Calibration curve
1.5 1 0.5 0 0
1
2 3 4 Auxiliary Zoom Option
5
Figure 5.4: Calibration Curve of the Camera, Auxiliary Lens and 5x Objective Lens In order to ensure that the camera and capacitive sensor provide consistent measurements, another test was performed as shown in Figure 5.5. A precision stage was used to move a target in the vertical direction while the camera and the sensor were used to measure the traveled distance. The results showed a reasonable correlation between the measurements of the capacitive sensor and those of the camera. Tests were repeated three times at zoom settings of 1x, 1.5x, 2x and 2.5x.Table 5.3 shows the percent difference between the measurements of the capacitive sensor and those of the camera. An overall zoom setting of 5x, was used in the majority of the experiments performed. Table 5.3: Percent difference of the measurements Auxiliary Lens
Overall
Percent Difference
Zoom Setting
Zoom
1
5
1.13
-0.82
-1.65
1.5
7.5
1.85
-0.80
0.93
2
10
-0.89
0.80
2.04
2.5
12.5
0.80
-2.58
-0.68
Test1 Test2 Test3
55
Capacitive sensor
Precision stage
5x objective lens Target for capacitive sensor
Ground wire
Auxiliary lens
Figure 5.5: Camera and sensor correlation test
5.1.3 Power Amplifier The VF-500 voltage amplifier is used to amplify the output voltage for static tests, which are performed at a frequency of 0.1 Hz. This amplifier provides a maximum current of 1Amp and has a gain of 20. Due to the relatively high capacitance of the piezoelectric actuator, the VF-500 can only amplify input signals with frequencies of up to 40Hz when connected to this actuator. Dynamic tests, however, require an amplifier capable of tracking square input signals of frequencies of up to 200Hz. Thus, the Noliac NDR6880 Single Channel Dynamic Driver is used to carry out dynamic tests. This power amplifier has a fixed gain of 30 and can generate a peak current of 20Amps. The device operates by charging an internal capacitor and then pumps the electrical charge to the actuator. During discharging of actuator, the electric charge is pumped back from the actuator to storing capacitors [5]. The operation of this device is comparable to that of the EFS IPoD piezo Driver used for testing of commercially available piezoelectric fuel injectors [4].
5.2 Experimental Procedure The prototype is assembled by following the steps that follow. First, the disc springs are placed inside the actuator housing. Next, the lower interface pin is lowered into the housing such that the pin guides the spring stack. The piezoelectric actuator and the plastic tube are then brought in
56
place followed by the upper interface. The upper interface is placed such that the shaft key can be assembled. Next, the end cap is loosely placed and the electrical wires are moved out of the end cap’s opening. Finally, the end cap is tightened using a torque wrench to apply the preload. A preload of 1000N was applied in order to satisfy the minimum required preload for dynamic tests. To apply this preload, a torque of 9.2Nm was required over an angle of 41.7o and a total travel distance of 116µm for the end cap. Figure 5.6 shows a schematic of the assembled prototype up to the application of the preload.
End cap opening
Thrust bearing
End cap Upper interface Actuator
Clamp
Plastic tube Housing
Disc spring
Lower interface cap
Lower interface pin Figure 5.6a) Isometric view of the prototype b) cross-section view of prototype The preload is applied using a torque wrench that measures both angle and torque. Using the calculations presented in Chapter 3, the preload was verified. The next set of steps is for assembling the lower section of the prototype. The motion inverter assembly is first placed inside its housing. Next the two flanges are brought together and held tightly using bolts and nuts. Any spacing in between the two flanges is filled with shims. The bolts were tightened and torqued to ensure that any potential gaps are closed. Prior to assembling the motion inverter section of the prototype, the actuator was tested to ensure that its performance matched what was expected of it. Furthermore, it was deduced from these initial tests that there is minute displacement loss in
57
the prototype components. The data for these tests are used only as a tool for verifying the performance of the actuator and do not provide much insight regarding the performance of the prototype as a whole. As a result, it should suffice to mention that the difference between the performance of the piezoelectric stack actuator as assembled in Figure 5.6 was different from its theoretical performance by only 2%. Figure 5.7 shows the cross-sectional view of the assembled prototype.
Motion inverter housing Fork Disc Opening for camera Fulcrum Opening for capacitive sensor Figure 5.7: Cross-section of assembled prototype After completion of the assembly, the capacitive sensor and camera are installed. Figure 5.8 shows the location of the camera and capacitive sensor. Static tests were then performed to verify that the motion inverter exhibits the expected behaviour. After the completion of the static tests,
58
the dynamic tests followed to verify the performance of the prototype with signals similar to those of commercial fuel injectors.
Motion inverter assembly
Stage for mounting the capacitive sensor
Figure 5.8: Lower section of prototype
5.3 Experiment Results and Analysis In this section, the results of the experiments performed using the disc motion inverter are presented and analyzed. The camera is aligned with the edge of the disc and tracks the displacement of this edge. By comparing two snapshots of the camera, as shown in Figure 5.12, the deflection of the edge of the disc is found. This deflection is verified with the characteristic curve of the actuator and is also compared to the output deflection at the center of the plate. This allows us to see if there is an amplification of the output deflection. The capacitive sensor is used to measure the output deflection at the center of the disc. Figure 5.9 shows a sample input voltage signal. The rise time, holding time and rest time are labeled on the figure.
Voltage (V)
59
12 10 8 6 4 2 0
Holding time
Input voltage signal
Rise time
Rest time
0
250
500
750
Points
1000
Figure 5.9: Sample input voltage signal In commercial fuel injectors, different types of injections, such as pilot injection and main injections are generated by varying the holding time and rest time of the signal. For example, if three injections are to be generated during a single combustion cycle, the pilot injection would have a holding time of 250µs, the main injection 600µs and the post injection 400µs. The holding time of a signal can also be specified in terms of its duty cycle, which is the percentage of time that the actuator is energized.
5.3.1 Static Performance The static test was performed at a frequency of 0.1Hz. The signal for the static tests is shown in Figure 5.10. The input voltage provided to the actuator reaches 200Vand is maintained at this level for 2.5seconds. A sampling frequency of 10.0Hz and a cut-off frequency of 1.0Hz were selected in the DAQ VI, which is used to record the output deflection. The rise time and holding time are also both 2.5 seconds. To ensure the repeatability of the tests, each test was repeated three times. 12 Voltage (V)
10
Static test input signal
8 6 4 2 0 0
250
500
750 Points
Figure 5.10: Input voltage signal for static tests
1000
60
The deflection of the edge of the plate as measured by the camera and verified by the characteristic curve of the stack is 65µm downward. The output deflection as measured by the capacitive sensor is 76µm upward. Although the housing of the injector was clamped and the flanges were tightly held together, the housing was displaced during the test by about 5µm. This loss of displacement could not be prevented in the lab experiments due to the nature of the setup. The static tests show that the motion inversion satisfactorily performs and also amplifies the output motion by a factor of 1.17. The results also correlate reasonably with the optimization results. There is a 10 to 15% difference, partly due to the loss displacement in the housing and partly due to other losses in the system, such as compression of the intermediate components. The actuator has provided an output force of 2250N and an output displacement of 65µm. The working point, thus, is close to the midpoint of the actuator’s characteristic curve, Figure 3.2, as previously planned. Figure 5.11 shows the output deflection of the plate as a result of the applied input voltage for the static test for one of the oscillations. The red curve is the reading of the capacitive sensor, which shows the output displacement at the center of the disc and the green curve is the input voltage.
Delay in fall Holding time
Rise time
Figure 5.11: Output deflection vs. input voltage for static performance Figure 5.12 shows the images captured by the vision system of the initial and final positions of the edge of the disc motion inverter. The vertical positions of several points on the two images were compared and the total number of pixels of difference in the vertical positions have been
61
calculated and averaged. Then, using the calibration of the camera for a 5x magnification, the total deflection of the edge of the disc was calculated. The image on the right shows the final position of the edge of the disc, which has been deflected downwards as expected. The field of view is 1.15mm in width and 0.86mm in height. The maximum output displacement in Figure 5.11 is 76µm and the measured input displacement is 65µm as measured from Figure 5.12. Interface between the upper edge of the disc and lower edge of the fork 100µm
Plate edge deflection
Figure 5.12: a) Initial and b) final positions of the edge of the disc motion inverter at 5x magnification
5.3.2 Dynamic Performance The dynamic tests were performed at four different frequencies: 10, 50, 100 and 150Hz. At each frequency, a number of different input signals were tested. The rise time and holding time of the signals were varied to simulate different types of injections. Table 5.4 shows a summary of dynamic tests with the shortest possible rise time and lowest holding time. To ensure the repeatability of the tests, each test was repeated three times. Table 5.4: Summary of results of dynamic tests Signal frequency, f (Hz) 10 50 100 150
Measured actuator rise time (µsec) 300 280 300 300
Holding time (µsec) 47000 8400 900 800
Measured output Delay in deflection (µm) rise (µsec) 76 74 73 70
0 300 200 300
Delay in fall (µsec) 0 200 200 300
The signals in the dynamic tests are square waves of varying duration and rise time. Thus, the sampling rate was selected to be 5 to 10 times higher than (1/rise time) of the signal in order to
62
capture the results of the output deflection. For the purposes of commercial fuel injectors, frequencies of 150Hz to 170Hz are of interest. However, lower frequencies were tested in order to provide information on a range of signal frequencies. The Noliac voltage amplifier used for dynamic tests limits the rise time of the actuator to about 0.3ms due to a safety trigger that cuts off higher currents required for faster rise times. As a result, the best rise time achieved in the dynamic tests has been 0.3ms. However, using a more powerful amplifier, such as the IPoD PiezoDriver, faster rise times could be achieved. Figure 5.13 to Figure 5.20 provide the characteristic curves of the dynamic tests. The different parameters indicated in Table 5.4 are labeled on each curve as well. To clearly differentiate between the different input signals, first an overview of the entire signal is shown and then the first oscillation is scaled up and displayed in detail.
63
Figure 5.13: Input voltage and recorded deflection at 10Hz
Delay in fall, 0.0µs
Holding time, 47ms
Delay in rise, 0.0µs
Rise time, 300µs
Figure 5.14: Zoomed input voltage and recorded deflection at 10Hz
64
Figure 5.15: Input voltage and recorded deflection at 50Hz
Delay in fall, 200µs Holding time, 8.4ms
Delay in rise, 300µs
Rise time, 280µs
Figure 5.16: Zoomed input voltage and recorded deflection at 50Hz
65
Figure 5.17: Input voltage and recorded deflection at 100Hz
Voltage overshoot Displacement overshoot
Delay in rise, 200µs
Delay in fall, 200µs Holding time, 900µs
Rise time, 300µs
Figure 5.18: Zoomed input voltage and recorded deflection at 100Hz
66
Figure 5.19: Input voltage and recorded deflection at 150Hz
Voltage overshoot Displacement overshoot
Delay in fall, 300µs Holding time, 800µs
Delay in rise, 300µs
Rise time, 300µs
Figure 5.20: Zoomed input voltage and recorded deflection at 150Hz
67
5.4 Discussion of Static and Dynamic Tests 5.4.1
Analysis of Results
The actuator is preloaded to 1000N and the input voltage signal is applied. As a result, the ceramic layers of the actuator expand and transfer the output force to the disc springs and the disc. Since both components have stiffness values on the same order of magnitude as the piezoelectric actuator, they reduce the working displacement of the actuator. The system reaches equilibrium and stays that way until the actuator is de-energized. The recorded data shows that in both energizing and de-energizing of the actuator, a delay exists in the response of the system. In the static tests, it has been confirmed that 76µm of output deflection can be expected from the prototype. In each dynamic test, a delay of about 200µs to 300µs is observed between the start of increase of the voltage and the generation of output deflection. Since the piezoelectric actuator is under a constant preload of 1000N, it will not generate any output deflection until the output force of the stack increases beyond 1000N. Another reason for the initial delay is the presence of potential gaps between the intermediate components or the motion inverter components that have to be closed before any output deflection is achieved. In 1994 Wolff mentioned the existence of a similar lag in a study to characterize piezoelectric stack actuators. The reported delay was between start of the voltage pulse and start of the stack movement and was independent of driving current [46]. A second delay of about 200µs to 300µs exists at the end of the cycle, between the onset of decrease in voltage and reduction of the output deflection. This delay could be a result of the hysteresis of the piezoelectric actuator. Due to hysteresis, the stack may be generating slightly higher displacements once it is being de-energized, which may be causing the lag. The delays mentioned do not pose a significant issue since fuel injectors in diesel engines are controlled using feedback loops through the Electronic Control Unit. As a result, lags can be compensated for by modifying the start point and duration of injections. As the frequency is increased, the output displacement of the prototype is reduced slightly from 76µm to 70µm. High-frequency operations allow less settling time and can have some adverse effects on the performance of the motion inverter. However, the required frequency range for fuel injection operations is between 100Hz to 200Hz.
68
The holding time for 10Hz and 50Hz input signals were, respectively, 47msec and 8.4msec. These values comply with the input signal generated by the function generator. At higher frequencies of 100Hz and 150Hz, a holding time of 6msec was the desired value. However, the results show holding times of 9msec and 8msec for these two frequencies. The discrepancy comes from the power amplifier used to amplify the input signal. The NDR6880 cannot follow the original input signal and, thus, extends the holding time of the input. The motion inverter, therefore, has to follow the amplified input signal. In other words, the hardware limitations impede the proper evaluation of the motion inverter to some extent. However, it is clear that the system follows the amplified input signal, despite the distortion of the signal. As a result the motion inverter shows good compliance with the provided input. The fuel injector prototype was built to in order to verify the concept of motion inversion in a piezoelectric actuator. The prototype was tested to check its performance in terms of proper preloading of the actuator, and inversion of input motion under static and dynamic conditions. Based on the presented data in section 5.3 and the optimization results in section 3.4, it is evident that the plate theory and Finite Element Analysis have been successful in capturing the behaviour of the disc. Thus, assumptions of the optimization method, such as static loading, axisymmetric boundary conditions, and presence of simple supports have been validated. Since the rise times of the input voltage signals have always been relatively small compared to the holding time of the signal, it has been assumed that the disc undergoes a static load. In other words, the output force provided by the actuator and transferred to the disc motion inverter has enough time to stabilize during the holding period, thus, can be treated as a static load. This simplification was used in the theoretical calculations and appears to be valid as the experimental results for dynamic tests are in agreement with the optimization results. With shorter rise times and higher frequencies, the validity of this assumption may be reduced. Furthermore, it has to be noted that for tests at frequencies of 100Hz and 150Hz, the output displacement of the motion inverter has a negative slope during the holding time and decreases slightly. This decrease is partially due to the overshoot in voltage that drives the output displacement to a higher value. After the voltage overshoot drops to 200V, the output displacement also drops sharply.
69
5.4.2
Potential Sources for Discrepancies
The 10 to 15% differences between theoretical and experimental values have several potential sources. The camera and the capacitive sensor were used to measure the displacement of the housing. It has been confirmed that about 4 to 5µm of loss in deflection (equivalent to about 5% of the discrepancy) has occurred due to the movement of the entire injector housing. The reason is the support for the housing is not rigid enough to fully constrain the prototype. This issue will be resolved once the injector is installed in an engine due to better physical constraints. Theoretical calculations have used a reported spring stiffness value that is subject to variation. Since two disc springs have been stacked to provide the necessary stiffness, the friction between the springs can cause a variation in the opposing force on the actuator. The result is further deviation from the theoretical values. Additionally, the output force generated by the piezoelectric actuator has to be transferred through several intermediate components to the disc. This could result in a reduced efficiency of force transfer. However, since the intermediate components are necessary for alignment of the actuator, further modifications could not be made. Furthermore, the theoretical calculations assume an ideal loading case for the disc, in which the input force is applied precisely on the outer perimeter of the disc. However, in the fabricated motion inverter, the contact between the disc and the fork is over a relatively small area. This causes a small variation in the output displacement from the theoretical calculations. Although the end cap and the bolts of the flange were tightened before each experiment, there could still be gaps between different components. Such gaps would have to be closed before any motion inversion is provided. Thus, some actuator output could be lost to closing the gaps rather than getting transferred to the disc.
5.4.3
Applicability of Concept
The prototype has been designed with the potential for commercialization. The components used in the prototype are mostly available on the market and the fabricated components are not complex. The preload required can be set with the help of a torque wrench without the need for other measurement devices. Although the first prototype is somewhat larger than current fuel
70
injectors, it can be made more compact by reducing the wall thickness of the housing and the diameter of the flange. The signal and voltage required to energize the piezoelectric actuator are compatible with those used in engine test rigs and Electronic Control Units. The limitations of the Noliac power amplifier did not allow for testing rise times faster than 0.3ms. However, faster rise times can be achieved with more powerful electronics. The needle stroke of 75 to 80µm, which is currently achieved, can be improved further by using disc springs of lower stiffness that can still provide the 1000N preload. Additionally, fuel injector manufacturers do not specifically measure the stroke of the needle and instead focus on injection performance in terms of spray formation and response time. The experiments conducted by Ficarella and Coppo in separate studies, however, measure needle stroke of some commercially available fuel injectors. For example, a maximum needle stroke of 300µm is measured by Ficarella and Laforgia in 1993 [18]. Furthermore, the Bosch injector for heavy-duty applications has a maximum stroke of 500µm as measured using an optical sensor [15]. Although the injector needle displacement is essential in the injection process, there is no standard requirement on the required value of needle stroke. This is due to the fact that, ECUs control the injection process and can vary the injection timing to complement the different needle stroke values [7]. In short, needle displacements of 75 to 80µm can be very well sufficient for injection purposes. This claim, however, will have to be confirmed using actual fuel injection tests.
5.5 Recommendations for Future Work The next phase of the project is to test the current prototype in an engine test rig in order to evaluate its performance under more realistic conditions. Spray formation, response time, performance under different fuel pressures, and various injection types are some of the parameters that have to be considered. In order to accomplish this task, the prototype has to be completed by adding the nozzle assembly as well as high pressure seals. Standard nozzles have already been found and studied and they can be readily added to the prototype. Additionally, the interface between the motion inverter and the needle of the nozzle assembly has to be designed. This interface should provide a low friction contact that allows the needle to move up once the center of the disc is deflected upwards. Further steps should also be taken to ease the assembly process of the motion inverter. One such step would be to connect the fork and disc via local welding or to combine them into
71
one part. This reduces the human error in assembly of the motion inverter and prevents misalignments of the disc and fork after several rounds of testing. Future tests can be performed at the engine testing facilities at University of Windsor. Before performing such tests, however, it may be useful to develop a simpler but similar test rig that uses pressurized fuel to perform the initial set of injection tests. This in-lab test rig could use a high pressure gas cylinder in order to pressurize the fuel and feed it into the prototype. Furthermore, the injected fuel quantity can be measured using flow rate sensors in order to estimate the performance of the unit. The initial tests can provide a baseline for the behaviour of the prototype and allow for detection of potential flaws. Consideration of fatigue failure for the disc motion inverter and disc springs is also an important future step since the motion inverter will be performing under a relatively high frequency.
72
Bibliography [1] Metals Handbook, Vol.1 - Properties and Selection: Irons, Steels, and High-Performance Alloys (10th ed., Vol. 1). (1990). ASM International. [2] Handbook for Disc Springs. (2003). Schnorr Corporation. [3] (2010). ANSYS Mechanical APDL Programmer's Manual. Southpointe: ANSYS Inc. [4] (2010). Ipod Piezo Driver. Montagny: EFS. [5] (2010). Single Channel Dynamic Driver for Piezoelectric Actuators. Noliac Systems s.r.o. [6] Bauer, H. (1996). Automotive Handbook (4th ed.). Stuttgart, Germany: Bosch. [7] Bosch, R. (2004). Diesel Engine Management. West Sussex: John Wiley & Sons Ltd. [8] Bouchiloux, P., Letty, R. L., Lhermet, N., Patient, G., Claeyssen, F., & Lang, M. (2003). Application of Amplified Piezoelectric Actuators to the Construction of Gas Valves. Proceedings of SPIE- The International Society for Optical Engineering, 5054, pp. 309-319. [9] Bucker, P., Gotz, B., & Martin, T. (1988). Piezoelectrical Actuators for Dynamical Applications. Proc. Smart Structures and Materials: Smart Structures and Integrated Systems, 3329, pp. 550-561. [10]
Randall, C. A. (2005). High Strain Piezoelectric Multilayer Actuators - A Material
Science and Engineering Challenge. Journal of Electroceramics, 14, 177-191. [11]
Catania, A. E., Ferrari, A., & Manno, M. (2008). Development and Application of a
Complete Mulitjet Common-Rail Injection-System Mathematical Model for Hydrodynamic Analysis and Diagnostics. Journal of Engineering for Gas Turbines and Power, 130. [12]
Chiu, A. S. (2010). The development of a piezoelectric fuel injector for diesel engines.
Toronto: Ryerson University. [13]
Cooke, M. P. (2009). Patent No. 116. United States.
[14]
Cooke, M. P. (2009). Patent No. Delphi Technologies. United States of America.
73
[15]
Coppo, M., Claudio, D., & Negri, C. (2007). A linear optical sensor for measuring needle
displacement in common-rail diesel injectors. Sensors and Actuators, 134, 366-373. [16]
Craig, R. R. (2000). Mechanics of Materials. John Wiley & Sons, Inc.
[17]
Dober, G., Tullis, S., Greeves, G., Milovanovic, N., Hardy, M., & Zuelch, S. (2008). The
impact of injection strategies on emissions reudction and power output of future diesel engines. SAE International. [18]
Ficarella, A., & Laforgia, D. (1993). Injection Characteristics Simulation and Analysis in
Diesel Engines. Meccanica, 28, 239-248. [19]
Gee, M. G., Cain, M. G., & Stewart, M. (1997). Materials and test conditions for project
cam 7. Teddington: National Physical Laboratory. [20]
Shigley, J. E. (2003). Mechanical Engineering Design. McGraw-Hill college.
[21]
Lee, J. W. (2006). Effect of piezo-driven and solenoid-driven needle opening of
common-rail diesel injectors on internal nozzle flow and spray development. International Journal of Engine Research, 7, 489-502. [22]
Kim, J. S., Kotkoff, D., & Cernosek, J. (1990). Structural Analysis of Fatige Cracking in
an Injector Body. SAE International, 81-87. [23]
Laforgia, A. F. (1993). Injection Characteristics Simulation and Analysis in Diesel
Engines. Meccanica, 28, 239-248. [24]
Lee, K. H., Senthilnathan, N. R., & Lim, S. P. (1989). Axisymmetric Bending of Thick
Circular Plates. Mechanics Research Communications, 17(2), 111-116. [25]
Leo, D. J., Weddle, C., Naganathan, N., & Buckley, S. J. (1998). Vehicular Applications
of Smart Material Systems. Proc. Smart Structures and Materials 1998: Industrial and Commercial Applications of Smart Structures and Technologies, (pp. 106-116). [26]
Lim, S. P., Lee, K. H., & Chow, S. T. (1988). Linear and Nonlinear Bending of Shear-
Deformation Plates. Computers & Structures, 30(4), 945-952.
74
[27]
Liu, J. Y., He, Z. X., Wang, Q., & Huang, Y. L. (2011). Finite Element Analysis of High-
Pressure Common-Rail Injector Body. Advanced Materials Research, 199-200, 579-582. [28]
Senousy, M. S. (2007). Dynamic thermo-electro-mechanical performance of piezoelectric
stack actuators. Proceedings of SPIE - The International Society for Optical Engineering, 6526. [29]
MacLachlan, B. J., Elvin, N., Blaurock, C., & Keegan, N. J. (2004). Piezoelectric valve
actuator for flexible diesel operation. Smart Structures and Maerials, 5388, 167-178. [30]
Manz, H., & Breitbach, E. (2001). Application of Smart Materials in Automotive
Structures. Proc. Smart Structures and Materials 2001: Industrial and Commerical Applications of Smart Structures Technologies, (pp. 197-204). [31]
Mock, R., & Lubitz, k. (2008). Piezoelectric Injection Systems. Springer Series in
Materials Science, 114, 299-310. [32]
Chung, N. H. (2008). Modelling and injection rate estimation of common-rail injectors
for direct-injection diesel engines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 2, 1089-1101. [33]
Near, C. D. (1996). Piezoelectric Actuator Technology. Proc. SPIE Vol. 2717, 2717, pp.
246-258. [34]
Norton, R. (2006). Machine Design: An Integrated Approach. Pearson Prentice Hall.
[35]
Oki, M., Matsumoto, S., Toyoshima, Y., Ishisaka, K., & Tsuzuki, N. (2006). 180MPa
piezoelectric common rail system. SAE International. [36]
Ouyang, P. R. (2008). A New Compliant Mechanical Amplifier Based on a Symmetric
Five-Bar Topology. Journal of Mechanical Design, 104501-5. [37]
Piezo Nano positioning. (n.d.). Retrieved August 20, 2012, from Physik Instrumente:
http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=400800.00
75
[38]
Products and Services. (n.d.). Retrieved August 29, 2012, from National Instruments:
www.ni.com [39]
Puccio, F. D., Ciulli, E., & Squarcini, R. (2006). Comparison of two sealing coupling
geometries. Tribology International, 39, 781-788. [40]
Randall, C. A., Klenberger, A., Yang, G. Y., Eitel, R. E., & Shrout, T. R. (2005). High
Strain Multilayer Piezoelectric Actuators – A Material Science and Engineering. Journal of Electroceramics, 14, 177-191. [41]
Park, S. W. (2006). Effect of injector type on fuel-air mixture formation of high-speed
diesel sprays. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering,, 220, 647-659. [42]
Schoor, M. V., Prechtl, E., Masters, B., MacLachlan, B., & Makar, P. (2002). Innovative
Technology for Clean, Lean, and Mean Diesel Fuel Injection. SAE International. [43]
Shaorong, Y., Yihui, Y., Bing, X., & Yun, T. (2010). Finite Element Analysis for a Two-
layered Spherical High-pressure Vessel. Second International Conference on Computer Modeling and Simulation. Sichuan: Institute of Structural Mechanics. [44]
Specification of Piezo Ceramics. (n.d.). Retrieved June 2011, from Noliac:
www.noliac.com [45]
Suh, H. K., Park, S. W., & Lee, C. S. (2007). Effect of piezo-driven injection system on
the macroscopic and microscopic atomization characteristics of diesel fuel spray. Fuel, 86, 2833–2845. [46]
Wolff, C. A., Hellebrand, D., Probst, I., & Lubitz, K. (1994). Optical Two Channel
Elongation Measurement of PZT Piezoelectric Multilayer Stack Actuators. Proc. Ninth IEEE International Symposium on Applications of Ferroelectrics, (pp. 755- 757). [47]
Xu, W., & King, T. (1996). Flexure hinges for piezoactuator displacement amplifiers:
flexibility, accuracy, and stress considerations. Precision Engineering, 19:4-10.
76
Appendices Appendix A: Engineering Drawings and Pictures of Components The engineering drawings as well as pictures of the main fabricated components are presented in this section.
Figure A.1: Prototype assembly and bill of material
77
Figure A.2: Actuator Housing
Figure A.3: Actuator Housing
78
Figure A.4: Adapter for connecting high-pressure fuel line
Figure A.5: Upper Interface a) bottom View b) top View
79
Figure A.6: Upper interface assembly
80
Figure A.7: Upper interface part1
81
Figure A.8: Upper interface part2
82
Figure A.9: Lower Interface pin
Figure A.10: Lower interface pin
83
Figure A.11: Lower Interface cap
Figure A.12: Lower interface cap
84
Figure A.13: Clamp
Figure A.14: Clamp
85
Figure A.15: End Cap
Figure A.16: End cap
86
Figure A.17: Motion inverter housing
87
Figure A.18: Motion inverter assembly
88
Figure A.19: Titanium disc motion inverter
89
Figure A.20: Disc fulcrum
Figure A.21: Disc fulcrum
90
Figure A.22: Disc fork
Figure A.23: Disc fork
