Scuola di Ingegneria
Department of Civil and Industrial Engineering
Master of Science in Aerospace Engineering
STUDY OF PIEZOELECTRIC ACTUATORS AND PRELIMINARY
DESIGN OF AN ION ENGINE PIEZOELECTRIC THRUST
VECTORING SYSTEM
Supervisor:
Candidate:
Prof. Mario Rosario Chiarelli
Arjun Jayaprakash Chaliyath
29 September 2020 Academic Year 2019/2020
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D
edicated to my Family and Friends
S
pecial thanks to our guide and mentor Prof. Mario Rosario Chiarelli
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ABSTRACT
Ion propulsion systems are reliable enough to promise future space systems with high operational efficiencies. Conventionally, to control the thrust vector, ion engines are mounted on gimbals and oriented as a whole. To date, several studies and experiments have been conducted mounting compact thrust-vectoring systems within the thruster itself to reduce overall system mass. The gridded ion thruster is one of the most reliable propulsion systems with comparably higher operational efficiency, which allows for such vectoring techniques. The use of a microelectromechanical system combined with piezoelectric actuators for this process is promising. The thesis presents a study for a possible implementation of these actuators in a grid suspension mechanism in an Ion-engine, to obtain ion beam deflection and thereby thrust vectoring. A preliminary application is studied, and a proof of concept model is developed.
This thesis presents the study of piezoelectric actuators and the implementation of piezo actuators in the ion engine thrust vectoring system. The work is carried out in three phases. The study of ion engine thrust vectoring systems was carried out in the first phase and the study of piezoelectric actuators was carried out in the second phase and final phase was carried out to design the thrust vectoring system, by using piezo actuator as the main driver and designing promising suspension by considering mass, accuracy, compactness, and robustness of the system.
The proposed design in theory can eliminate the use of existing complex gimbal systems and thereby reduce the overall thruster vectoring system mass considerably. The preliminary application of the mechanism is studied, and a proof of concept model is developed. The findings and possible future works for the implementation of this idea in real life are discussed in the coming chapters.
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Table of Contents
LIST OF FIGURES ... VI LIST OF TABLES ... VIII
1 ION THRUSTERS ... 1
1.1INTRODUCTION ... 1
1.2THETHRUSTERSYSTEM ... 2
1.2.1 Past... 2
1.2.2 Present ... 3
1.3THRUSTVECTORINGSYSTEM ... 4
1.3.1 Introduction ... 4
1.3.2 Vectoring Mechanisms ... 5
1.3.3 Acceleration Grid Thrust Vectoring ... 8
1.4CONCLUSIONS ... 8
2 ION OPTICS STUDY... 9
2.1INTRODUCTION ... 9
2.2GRIDCONFIGURATIONS ... 9
2.3IONOPTICSSTUDY ... 12
2.3.1 Elementary Modes of Electrode Misalignment ... 12
2.3.2 Transverse Displacement of the Acceleration Grid ... 13
2.3.3 Design and geometry of the grids ... 14
2.4CONCLUSION ... 14 3 PIEZO-ELECTRICITY ... 15 3.1INTRODUCTION ... 15 3.1.1 Piezo-Electricity ... 15 3.1.2 History ... 15 3.2PIEZOELECTRICITYTODAY ... 16 3.2.1 Actuators ... 16
3.2.2 Speakers and Buzzers ... 16
3.2.3 Sensors ... 17
3.3GOVERNING EQUATIONS ... 17
3.3.1 Governing equation for the Piezoelectric materials ... 18
3.3.2 Coupling Equations ... 19
3.3.3 Lagrangian Formulation ... 19
3.4PRINCIPLESOFPIEZOACTUATION ... 20
3.4.1 Types Of Piezo-Actuators ... 21
3.5CONCLUSION ... 21
4 STACK TYPE ACTUATORS ... 22
4.1INTRODUCTION ... 22
4.1.1 Stack Design (Translators) ... 22
4.2THEORYOFSTACKTYPEACTUATORS ... 23
4.2.1 Voltage and Electric Field ... 23
4.2.2 Force and Stiffness ... 23
4.2.3 Tensile Strength and Preload ... 23
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4.3.1 Maximum Applicable Forces (Compressive Load Limit, Tensile Load Limit) ... 24
4.3.2 Stiffness ... 24
4.3.3 Force Generation ... 24
4.3.4 Displacement and External Forces ... 25
4.4MATERIALPROPERTIES ... 26
4.5DESIGNOFTHESTACKMODEL ... 27
4.5.1 FEM Model... 27
4.6FREESTROKEANALYSIS ... 29
4.7BLOCKINGFORCE ... 33
4.7.1 Boundary Conditions ... 34
4.7.2 Results ... 36
4.8STUDYONSTACKSTIFFNESSANDPRE-LOADING ... 38
4.8.1 Boundary Conditions ... 39
4.8.2 Results ... 40
4.9CONCLUSION ... 41
5 BENDER TYPE ACTUATORS ... 42
5.1INTRODUCTION ... 42
5.1.1 Bimorph and Multi-morph Design ... 42
5.2MACRO-FIBERCOMPOSITES(MFC) ... 43
5.3DESCRIPTIONOFTHEMFCSPECIMEN ... 44
5.4CONCLUSION ... 51
6 PIEZOELECTRIC LINEAR ACTUATORS... 52
6.1INTRODUCTION ... 52
6.2PIEZOACTUATORMECHANICALAMPLIFIERS ... 52
6.2.1 Mechanical lever ... 52
6.2.2 Diamond flexure amplifier structure ... 52
6.2.3 Inertial drive actuator ... 53
6.2.4 Inchworm actuator ... 53 6.2.5 Ultrasonic motor ... 54 6.3STICK/SLIPMECHANISM ... 54 6.4ACTUATORREQUIREMENTS ... 55 6.5CONCLUSION ... 56 7 PIAK10 ACTUATOR ... 57 7.1INTRODUCTION ... 57 7.2PIAK10 ... 57 7.3CADMODEL ... 60 7.4MOTIONSTUDY ... 61 7.5CONCLUSION ... 62
8 ONE DIMENSIONAL MOTION ANALYSIS ON THE GRID ... 63
8.1INTRODUCTION ... 63
8.2COMPONENTS ... 63
8.2.1 Grid ... 63
8.2.2 Holder ... 64
8.3ONE DIMENSIONAL MOTION STUDY... 67
8.4CONCLUSION ... 68
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9.1TWO-DIMENSIONALMOTIONSTUDY ... 69
9.2SUSPENSIONSYSTEMDESIGN ... 74
9.2.1 Introduction ... 74
9.2.2 NASA NSTAR Engine ... 74
9.2.3 Temperature Profile ... 76
9.3MOTIONSTUDY ... 82
9.3.1 Introduction ... 82
CONCLUSIONS AND FUTURE DEVELOPMENTS... 86
APPENDIX ... 87
ANSYS PIEZO-MEMS ACT ... 87
ENGINEERING DRAWINGS ... 88
Original Inspiration... 96
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List of Figures
Figure 1-1Gridded Ion Thruster ... 2
Figure 1-2 NASA NSTAR Ion Thruster ... 3
Figure 1-3 Example of a gimbal assembly for electric propulsion engines ... 5
Figure 1-4 NASA NEXT Ion Engine mounted on gimbal assembly... 5
Figure 1-5 Scheme for achieving electrostatic beam deflection ... 6
Figure 1-6 External magnetic deflection configuration for one axis ... 7
Figure 1-7 Ion beam deflection using accelerator grid translation. A single aperture is shown ... 8
Figure 2-1 Child–Langmuir sheath length versus ion mass for two ion current densities at 1500-V acceleration voltage ... 10
Figure 2-2 Simplified 1-D view of an accelerator aperture in contact with a plasma ... 10
Figure 2-3 Electrical schematic of a DC discharge ion thruster without the cathode ... 11
Figure 2-4 Example of grid translation and corresponding beam deflection ... 13
Figure 2-5 Transverse displacement of the accelerator grid ... 13
Figure 3-1 Piezoelectric effect in Quartz ... 15
Figure 3-2 actuation using piezoelectric materials ... 16
Figure 3-3 piezoelectric buzzer ... 16
Figure 3-4 piezoelectric sensor ... 17
Figure 3-5 a. stack actuator. b Bender actuator ... 20
Figure 4-1 Piezoelectric stack ... 22
Figure 4-2 Preload, either external or internal to the actuator, ensures suitable tensile strength ... 23
Figure 4-3 Piezo Material Properties ... 27
Figure 4-4 FEM model of the piezoelectric stack ... 28
Figure 4-5 Free-stroke analysis settings, highlighting polarization axis and the extension ... 29
Figure 4-6 Voltages applied on the piezoelectric body ... 30
Figure 4-7 Input voltage (500 V) vs time ... 30
Figure 4-8 Directional deformation (z axis) ... 31
Figure 4-9 Deflection vs time ... 31
Figure 4-10 Displacement vs Voltage ... 32
Figure 4-11 Equivalent stress for an input of 100 Volts ... 33
Figure 4-12 Blocking force ... 34
Figure 4-13 Applied Force vs time ... 35
Figure 4-14 Applied Voltage vs time ... 35
Figure 4-15 Force applied on the stack model (z axis) ... 36
Figure 4-16 Deflection vs Time (for 500 V applied voltage) ... 36
Figure 4-17 Displacement vs Time for different applied voltages ... 37
Figure 4-18 Deformation vs Force for different voltages ... 38
Figure 4-19 Results obtained ... 39
Figure 4-20 Input voltage (500 V) vs time ... 39
Figure 4-21 The stack model applied with the spring load ... 40
Figure 4-22 Directional deformation (z axis) at time step 5 with applied voltage 500V ... 40
Figure 4-23 Directional deformation (z axis) at time step 6 with applied voltage 0V ... 40
Figure 4-24 Deflection vs Time ... 41
Figure 5-1 Bender type piezo actuator ... 42
Figure 5-2 MFC Patch ... 43
Figure 5-3 Fiber orientation and operational voltages ... 44
Figure 5-4 Dimensions of the MFC patch, Bending specimen ... 45
Figure 5-5 Fiber orientation ... 45
Figure 5-6 Cross sectional view of the bending specimen ... 45
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Figure 5-8 MFC Patch dimensions ... 46
Figure 5-9 Deflection on the bending specimen 1 ... 47
Figure 5-10 Directional deformation 1 ... 47
Figure 5-11 Deflection on the bending specimen 2 ... 48
Figure 5-12 Directional deformation 2 ... 48
Figure 5-13 Deformation on the bending specimen 3 ... 49
Figure 5-14 Directional deformation 3 ... 49
Figure 5-15 Deformation on the bending specimen 4 ... 50
Figure 5-16 Directional deformation 4 ... 50
Figure 6-1 Piezo actuator with lever amplifier ... 52
Figure 6-2 Flexure amplifier structure ... 53
Figure 6-3 Stick/Slip Mechanism ... 53
Figure 6-4 Components and working principle of piezo-actuated stick–slip micro-drives ... 54
Figure 6-5 Thor labs Piezoelectric Inertia Actuators ... 55
Figure 7-1 PIA Series Piezo Inertia Actuator – Features ... 57
Figure 7-2 PIAK10 Piezo Inertia Actuator – Features... 58
Figure 7-3 CAD model of PIAK10 ... 60
Figure 7-4 Rotating Manual adjustment knob with 6.299 RPM ... 61
Figure 7-5 Threading Connection ... 62
Figure 7-6 Linear displacement (z axis) vs time ... 62
Figure 8-1 Acceleration Grid properties ... 64
Figure 8-2 Acceleration grid showing apertures ... 64
Figure 8-3 Material properties, Holder ... 65
Figure 8-4 Acceleration Grid Holder ... 65
Figure 8-5 Grid assembly with holder and actuators attached ... 66
Figure 74 Holder and actuator connection ... 66
Figure 8-7 Assembly showing axial force (2N) ... 67
Figure 8-8 Plot, Linear displacement of the Grid vs Time under axial load condition ... 67
Figure 9-1 Actuator Module ... 69
Figure 9-2 Exploded view of the module ... 70
Figure 9-3 Two directional translation achievable by the module ... 71
Figure 9-4 Exploded view showing different parts of the module ... 72
Figure 9-5 Modules attached to the acceleration grid ... 73
Figure 9-6 NASA NSTAR Engine ... 74
Figure 9-7 Schematic of the NASA NSTAR engine ... 75
Figure 9-8 Temperature profile of the engine (No Sun) ... 75
Figure 9-9 Temperature profile of the engine (Sun 30° off-Axis) ... 76
Figure 9-10 Modules attached to the acceleration grid with the support structure ... 76
Figure 9-11 Section view of the assembly showing the modules with the actuators inside ... 77
Figure 88 Final Assembly Exploded view ... 78
Figure 9-13 Front view, Assembly attached to the thruster ... 79
Figure 9-14 Exploded view of the assembly ... 79
Figure 9-15 Cross section view of the mount and grid ... 80
Figure 9-16 Cross section view of the thruster showing mounting, assembly and actuator modules . 80 Figure 9-17 Grid spacing ... 81
Figure 9-18 Section view showing the axial force and the movement of the actuators (Y Axis) ... 82
Figure 9-19 Section view showing the axial force and the movement of the actuators (Z Axis) ... 83
Figure 9-20 Displacement vs Time of the Acceleration Grid Y AXIS ... 83
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List of Tables
Table 2-1 Assumed Grid Geometry ... 14 Table 7-1 Technical Specifications ... 59 Table 8-1 Grid geometry ... 63
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1 ION THRUSTERS
1.1 INTRODUCTION
Ion thrusters have been shown to be an appropriate and effective solution to standard propulsion systems. Due to very high specific impulse generation, with very low fuel demand, ion thrusters can compete readily with chemical propulsion technologies even if the thrust generated is much smaller. The system can be used for different mission requirements such as maintaining orbit stations for geostationary satellites, controlling orbit and attitude, and multi-goal tasks. While chemical propulsion is extremely inappropriate for deep space missions, ion thrusters also make it possible to reach deeper space further.
Modern ion thrusters use inert gasses as propellant. Most thrusters use the chemically inert, colorless, odorless, and tasteless Xenon. The propellant is injected from the thruster's downstream end and flows upstream. This technique of injection is preferred because it improves the time remaining in the chamber for the propellant. Electrons are produced in a standard ion thruster by a hollow cathode, called the discharge cathode, situated on the north end at the middle of the engine. The electrons flow out of the cathode of release and are drawn to the walls of the disposal chamber, loaded by the power supply of the thruster to a large positive potential.
Through electron bombardment, the electrons from the discharge cathode ionize the propellant. High-strength magnets are positioned along the walls of the discharge room to redirect the magnetic fields to the discharge room as electrons approach the walls. The chance of ionization is maximized by maximizing the length of time that electrons and propellant atoms remain in the discharge chamber, making the ionization process as efficient as possible. Electrostatic forces accelerate electrons in an ion thruster. The electrical fields used for acceleration are produced by electrodes placed at the thruster's downstream end. There are thousands of coaxial apertures in each set of electrodes, called ion optics or grids. Each set of openings functions as a lens through the optics that electrically focuses ions.
NASA ion thrusters use a two-electrode system with extremely favorable charging of the upstream electrode (called the display grid) and extremely adverse charging of the downstream electrode (called the accelerator grid). Because the ions are produced in a highly favorable region and the potential of the accelerator grid is negative, the ions are drawn to the accelerator grid and concentrated through the apertures out of the discharge chamber, producing thousands of ion jets. The ion beam is called the stream of all the ion jets together. The thrust force is the force that exists between the upstream ions and the accelerator grid. The ion exhaust speed in the beam is based on the voltage applied to the optics. While the top speed of a chemical rocket is restricted by the rocket nozzle's heat capacity, the top speed of the ion thruster is restricted by the voltage applied to the ion optics (which is theoretically unlimited). Because the ion thruster expels a large number of positive ions, it is necessary to expel an equal amount of negative charge to keep the total exhaust beam charge neutral. A second hollow cathode, the neutralizer, is located on the thruster's downstream perimeter and expels the electrons needed.
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Figure 1-1Gridded Ion Thruster
1.2 THE THRUSTER SYSTEM
The ion propulsion system (IPS) consists of five main components: the power source, the power processing unit (PPU), the propellant control system (PMS), the control computer, and the ion thruster. Any source of electrical power can be the IPS energy source, but the main choices are solar and nuclear. Sunlight and solar cells are used by a solar electric propulsion scheme (SEP) to generate electricity. A nuclear electric propulsion system (NEP) utilizes an electric generator combined with a nuclear heat source. The PPU transforms the energy produced by the energy source into the energy needed for each ion thruster element. It produces the voltages needed by the chamber of ion and discharge and the elevated currents needed for the hollow cathodes. The PMS regulates the propellant flow to the thruster and hollow cathodes from the propellant tank. Modern PMS units have evolved to a level of sophisticated design that no longer requires moving parts. The control computer controls and monitors system performance. The ion thruster then processes the propellant and power to perform work. Modern ion thrusters can propel up to 90,000 meters per second (more than 200,000 miles per hour (mph)) of a spacecraft. The space shuttle is capable of a top velocity of around 18,000 mph to put that into view. The tradeoff is low thrust (or low acceleration) for this high velocity. Thrust is the force applied to the spacecraft by the thruster. Modern ion thrusters can provide a thrust of up to 0.5 Newtons (0.1 pounds).Ion thrusters use inert gas for propellant, eliminating the risk of explosions associated with chemical propulsion. The usual propellant is xenon, but other gases such as krypton and argon may be used.
1.2.1 Past
Since the research on ion propulsion started there in the 1950s, NASA Glenn Research Center has been the lead for electrical propulsion. The first operational test of an ion propulsion system in space was the Space Electric Rocket Test 1 (SERT 1), which flew on July 20, 1964 and completed its goal of 31 minutes of operation successfully before returning to Earth. There followed many effective ion propulsion experiments. From 1974 to 1983, the Ion Auxiliary Propulsion System (IAPS) project created an 8-centimeter satellite station holding mercury IPS. The NASA Solar Technology Application Readiness (NSTAR) project developed a 30-centimeter IPS that was used as the main propulsion on the Deep Space 1 (DS1) spacecraft from 1998 to 2001. DS1 was the first use of electric
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propulsion for spacecraft main propulsion. The NSTAR thruster on DS1 propelled the spacecraft 263,179,600 kilometers (163,532,236 miles) at speeds up to 4,500 meters per second (10,066 mph). Over the entire mission, the NSTAR thruster demonstrated 200 starts and 16,246 hours of operation. NASA's Glenn Energy Program developed the key technologies that allowed ion propulsion systems to be significantly improved. The study includes powerful development and testing attempts, computer modeling, advances in hollow cathode technology, and, to name a few, improved ion optics systems. Models can be produced by studying the fundamental concepts engaged in plasmas that decrease the cost of designing future ion thrusters. Enhancements in component technologies produce components that can last longer or operate in extreme conditions.The NASA Evolutionary Xenon Thruster (NEXT) project developed a high-power SEP IPS that reduce mission cost and trip time. NEXT is capable of performing a wide variety of missions to targets of interest such as Mars and Saturn. In 2003, a single NEXT thruster demonstrated over 2000 hours of operation at 7 kilowatts.
The NEXT single string integration test, also completed in 2003, demonstrated operation of the NEXT PPU, PMS, and thruster as a complete IPS. Early tests in 2004 demonstrated power levels of 40 kilowatts and exhaust velocities in excess of 90,000 meters per second (over 200,000 mph).Dawn, launched on September 27, 2007, to explore the asteroid Vesta and the dwarf planet Ceres. It used three Deep Space 1 heritage xenon ion thrusters (firing one at a time). Dawn's ion drive is capable of accelerating from 0 to 60 mph (97 km/h) in 4 days of continuous firing. The mission ended on November 1, 2018, when the spacecraft ran out of hydrazine chemical propellant for its attitude thrusters.
Figure 1-2 NASA NSTAR Ion Thruster
1.2.2 Present
More and more companies are beginning to use satellites with electric propulsion to extend the operational life of satellites and reduce launch and operation costs. This produces savings that can be passed along to consumers.
NASA’s primary application of ion propulsion will be for main propulsion on long missions that are difficult or impossible to perform using other types of propulsion.
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Dual-Stage 4-Grid (DS4G)
The Dual-Stage 4-Grid (DS4G) is an electrostatic ion thruster design developed by the European Space Agency, in collaboration with the Australian National University. The design was derived by D. Fern from Controlled Thermonuclear Reactor experiments that use a 4-grid mechanism to accelerate ion beams.
A 4-grid ion thruster with only 0.2 m diameter is projected to absorb 250 kW power. With that energy input rate, the thruster could produce a thrust of 2.5 N. The specific impulse (a measure of fuel efficiency), could reach 19,300 s at an exhaust velocity of 210 km/s if xenon propellant were used. The potentially attainable power and thrust densities would substantially extend the power absorption of current ion thrusters to far more than 100 kW. These characteristics facilitate the development of ion thrusters that can result in extraordinary high-end velocities.
Like with thruster concepts such as VASIMR, the dual-stage-4-grid ion thrusters are mainly limited by the necessary power supply for their operation. For example, if solar panels were to supply more than 250 kW, the size of the solar array would surpass the size of the solar panels of the International Space Station. To provide 250 kW with Stirling radioisotope generators would require roughly 1 ton of plutonium-238 (for which the US stockpile as of 2013 was no more than 20 kg), and so a nuclear thermal reactor would be needed.
HiPEP
The High-Power Electric Propulsion (HiPEP) project is developing a high-power NEP IPS for the Jupiter Icy Moons Orbiter (JIMO) spacecraft. The HiPEP thruster, which is under development at Glenn, is unique in that it has the ability to operate at high power levels in both a conventional hollow cathode configuration and a microwave ECR configuration. The HiPEP ion thruster is currently the most powerful inert gas ion thruster ever built.
1.3 THRUST VECTORING SYSTEM
1.3.1 Introduction
Thrust vectoring is required in an Ion Engine for various applications like attitude keeping, trajectory changes etc. Various methods have been employed to achieve thrust vectoring which includes the use of externally mounted gimbals, electrostatic and electromagnetic beam deflection, mechanical actuators. A concept of thrust vectoring utilizing grid translation and employing this translation to produce a beam deflection is studied in this chapter. The assembly constitutes of planarly mounted screen grid and an accelerator grid. The relative translation of the grids produces an ion beam deflection, which in turn creates the required thrust vectoring. A concept to attain the grid translations employing piezo-electric actuators fitted to the accelerator grid is studied.Various Electric propulsion systems have been developed and are under development like Hall Effect Thrusters, Ion Thrusters, Magneto-plasma-dynamic Thrusters. For the effective utilization of these thrusters in space applications, precise and easy thrust vectoring is required. The ability to control the thrust vector of any spacecraft propulsion system is extremely advantageous. It can be used both to improve or optimize mission performance and also to compensate for the shift in position of the center of mass in order to minimize attitude control requirements. Thrust vectoring is required for attitude control, orbit control and various other maneuvers. Main techniques under use presently include the use of gimbals, mechanical systems etc. The main disadvantage of the gimbal system is its weight. In a weight sensitive system like an ion thruster, this plays a significant disadvantage. On the other hand, the mechanical systems are complex in design and are difficult to manufacture. The state of the art of current thrust vectoring techniques are studied in the following sections and the disadvantages of each mechanism is discussed. A possible mechanism by which the thrust vectoring can be achieved mitigating the disadvantages of current mechanical systems is discussed in this chapter.
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1.3.2 Vectoring Mechanisms
The straightest forward solution to the problem of thrust vectoring is mounting the thruster on a gimbal mount. It has an important advantage of not changing the thruster design and therefore not affecting its performance. In a Hughes Research Laboratories (HRL) study, however, it was rated last because of the need to use mechanical actuators and its high system mass. Since the time of study (1971) signi2cant progress in mechanical actuation methods has taken place and building a reliable gimbal system is nolonger a problem. Such system was successfully usedon Artemis and NASA Deep Space spacecraft. Nevertheless,a large mass penalty, as well as the spaceoccupied by the actuators remains a significant disadvantageof this system.
Gimbal Systems
In a gimbaled thrust system, the exhaust nozzle of the rocket can be swiveled from side to side. As the nozzle is moved, the direction of the thrust is changed relative to the center of gravity of the rocket. The straight-line flight configuration in which the direction of thrust is along the center line of the rocket and through the center of gravity of the rocket. When the nozzle has been deflected and the thrust line is now inclined to the rocket center line at an angle called the gimbal angle. Since the thrust no longer passes through the center of gravity, a torque is generated about the center of gravity and the nose of the rocket turns to the other direction.
The main disadvantage of a gimbal system is its weight and complex mechanical construction. It is also very difficult to control the gimbal system very precisely due to the mechanical nature of the assembly. This matters a lot when we are dealing with small ion engines which produce very less thrust. Therefore, precise control of the thrust vectoring is required and thereby arises a need for alternate methods of thrust vectoring.
Figure 1-3 Example of a gimbal assembly for electric propulsion engines
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External Electrostatic Deflection
This very simple concept involves the passage of the beam through two pairs of orthogonal deflector plates to which high potentials are applied. These plates are shaped to maintain a constant distance from the beam as shown in Fig 4. This shaping includes a flare along the z-axis to match the divergence of the beam, with an additional allowance to accommodate the vectoring angle required. If the beam divergence is β, which is usually of the order of 10 to 20 deg depending on operating conditions, the plates diverge at a total angle to the axis of (α + β). The deflector plates are connected to a pair of power supplies which can reverse the polarity of their outputs if necessary; this is required to change the direction of the deflection. The simplest non-mechanical method is electrostatic deflection of the beam after it leaves the engine. This can be achieved by placing electrically charged plates around the beam. The potential needed to deflect the thrust vector by a desired 8◦ is about 400 V for a 5-cm diameter thruster, however much higher voltages would be needed for larger engines. Furthermore, the danger of creating of plasma sheaths around the plates appears, leading to the need of using much higher voltages in order to achieve the desired deflection. Because of these difficulties, the electrostatic system is not considered feasible and no laboratory tests have been conducted so far.
Figure 1-5 Scheme for achieving electrostatic beam deflection
This mechanical arrangement should be simple to implement, provided that the external deflecting plates are not too long; it is suggested that they cannot be significantly longer than the thruster. Another requirement is to ensure that the sputtering damage caused to the internal surfaces of the plates by ions at the periphery of the beam is acceptably small.The remaining unknown concerns the output voltages and currents required of the power supplies. The latter should not be a problem, since current continuity demands that the electron current collected by one electrode be balanced exactly by the ion current to the other, assuming that neither are emitters. Although the electron current could be large, the ion current is restricted to that generated by charge-exchange reactions in the ion beam. As can be judged from the acceleration and deceleration grid currents of the T5 thruster, these are likely to be of the order of a few mA.
Magnetic deflection
The magnetic deflection system has a similar layout, with charged plates replaced with magnet pole pieces. It has been calculated that the power consumed by electromagnets needed to deflect the exhaust beam of a 5 cm thruster only in one plane can reach
271 W. Also, the mass of such a system will be prohibitively large (44:5 kg). This makes this system infeasible.
While it is certain that the ion beam can be deflected by using a transverse magnetic field, calculations are necessary to establish how large this field would have to be to provide deflections of interest and to indicate the likely mass and power consumption of the necessary equipment. The configuration under consideration is shown in Fig 6. In this, the ion beam passes between the poles of an
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electromagnet designed to provide an approximately uniform field over a substantial length of the beam, just outside the grid system of the thruster. The polepieces must be separated sufficiently to avoid any direct impingement on them by high energy ions. This separation can of course vary with distance from the thruster, but this would provide a significantly non-uniform magnetic field. An electromagnet configured to provide a deflection in the perpendicular direction is also indicated in Fig 6.
Figure 1-6 External magnetic deflection configuration for one axis
Electrostatic Deflection within the Grid System
Many attempts were reported in the 1970s to achieve a thrust vectoring capability using systems having low mass and power consumption, and a minimum impact on the size and shape of the thruster. As electrostatic acceleration and focusing of the ion beam are essential to these thrusters, a clear way forward was to influence these processes to provide the desired vectoring. The approach adopted by Hughes in a NASA-funded program was to build a complex accel grid in which minute secondary electrodes were inserted into the individual apertures. These were interconnected so that bias potentials could be applied to set up a transverse electric field, thereby deflecting the ion beam to the required extent. After considerable effort, success was achieved, but the sputtering processes within the grids, and the associated deposition of conducting layers, caused serious problems with leakage currents and electrical breakdowns. A more practical solution was to use thin ceramic strips slotted together to form an interlocking structure when assembled. The electrodes were formed from a continuous molybdenum strip brazed to each side of the ceramic, resulting in a symmetrical unit from which the final assembly was constructed. This scheme gave high structural integrity and required only a few electrical connections at the periphery of the grid. A later design modification aimed to shield the downstream surfaces of the insulator strips from material back sputtered from the ion beam target. This was accomplished by bending the downstream edges of the molybdenum strips to provide shadow shields.
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1.3.3 Acceleration Grid Thrust Vectoring
Another technique that aims to deflect the beam inside of the grid system is that of using an accel grid that can be translated within its plane. The resulting change in electrostatic field between the grids causes ions to change direction. Various theoretical and experimental analyses have shown that deflection angle is directly proportional to grid movement with coefficient of 0.03–0:04 mm=deg. Several tests of thrusters utilizing this technique were conducted by HRL and NASA. Each of the models employed different mechanical designs to perform the accel grid translation. The tests revealed its high potential in application to various sizes and models of thrusters. Therefore, this technique was chosen for the thrust vectoring mechanism that developed within this project.
Figure 1-7 Ion beam deflection using accelerator grid translation. A single aperture is shown
The main limitation to increasing the vectoring angle is grid sputtering caused by ions. However, if deflection of as low as 8◦ is needed, sputtering poses no major threat.
1.4 CONCLUSIONS
The attitude and orbit control of geostationary communications satellites is a complex task often employing numerous chemical thrusters, as well as devices such as momentum wheels. The associated propellant consumption is of serious concern, since it adds considerably to launch costs, so anything which affects this significantly is of importance. One such factor is the utilization of ion engines for station keeping, since any misalignment of their thrust vectors with respect to the center of mass of the spacecraft can add to the attitude and orbit control requirements.
In this Introductory chapter, It is discussed the necessity for thrust vectoring systems and the state of the art of thrust vectoring for Ion Engines.
After our preliminary study, it was concluded that beam deflection within the Grid system using two adjacently placed grids (screen grid and acceleration grid) to produce a thrust vectoring is the most promising method of thrust vectoring. The coming chapters discuss in detail about this technique and how this can be implemented in Ion Engines.
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2 ION OPTICS STUDY
2.1 INTRODUCTION
Several reasons justify the development of an ion propulsion system thrust vectoring system. Spacecraft launched to date have used ion thrusters mounted on gimbals to control the thrust vector within a range of about ±5◦. Such devices have large mass and dimensions; hence the need exists for a more compact system, preferably mounted within the thruster itself. Since the 1970s several thrust vectoring systems have been developed, with the translatable accelerator grid electrode being considered the most promising.
The ion accelerator consists of electrically biased multi-aperture grids, and this assembly is often called the ion optics. The design of the grids is critical to the ion thruster operation and is a trade between performance, life, and size. Since ion thrusters need to operate for years in most applications, life is often a major design driver. However, performance and size are always important in order to satisfy the mission requirements for thrust and specific impulse (Isp) and to provide a thruster size and shape that fits onto the spacecraft. There are many factors that determine the grid design in ion thrusters. The grids must extract the ions from the discharge plasma and focus them through the downstream accelerator grid (accel grid) and decelerator grid (decel grid) (if used). This focusing has to be accomplished over the range of ion densities produced by the discharge chamber plasma profile that is in contact with the screen grid, and also over the throttle range of different power levels that the thruster must provide for the mission. Since the screen grid transparency directly impact the discharge loss, the grids must minimize ion impingement on the screen grid and extract the maximum number of the ions that are delivered by the plasma discharge to the screen grid surface. In addition, the grids must minimize neutral atom loss out of the discharge chamber to maximize the mass utilization efficiency of the thruster. High ion transparency and low neutral transparency drives the grid design toward larger screen grid holes and smaller accel grid holes, which impacts the optical focusing of the ions and the beam divergence. The beam divergence also should be minimized to reduce thrust loss and plume impact on the spacecraft or solar arrays, although some amount of beam divergence can usually be accommodated. Finally, grid life is of critical importance and often drives thruster designers to compromises in performance or alternative grid materials. In this chapter, the factors that determine grid design and the principles of the ion accelerators used in ion thrusters will be described.
2.2 GRID CONFIGURATIONS
To accelerate ions, a potential difference must be established between the plasma produced inside the thruster plasma generator and the ambient space plasma. Simply biasing the anode of a DC plasma generator or the electrodes of a radio frequency (rf) plasma generator relative to a spacecraft or plasma in contact with the space potential does not result in ion beam generation because the voltage will just appear in the sheath at the plasma boundary with the walls. If the potential is small compared to the electron temperature, then a Debye sheath is established, and if the potential is very large compared to the electron temperature, then a Child–Langmuir sheath exists. Therefore, to accelerate ions to high energy, it is necessary to reduce the dimension of an aperture at the plasma boundary to the order of the Child–Langmuir distance to establish a sheath that will accelerate the ions with reasonable directionality(good focusing) and reflect the electrons from the plasma. Figure 2.1 shows the Child– Langmuir length calculated for two singly charged ion current densities at an acceleration voltage of 1500 V. For xenon, the characteristic aperture dimension at this voltage is on the order of 2 to 5 mm and will decrease if the applied voltage is reduced or the current in the aperture is increased.
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Figure 2-1 Child–Langmuir sheath length versus ion mass for two ion current densities at 1500-V acceleration voltage
The ion current obtainable from each grid aperture is then limited by space charge. For a 0.25-cm-diameter aperture extracting the space-charge-limited xenon current density of about 5 mA/cm2 at 1500 V, the total ion current per aperture is only 0.25 mA. Assuming this produces a well-focused beamlet, the thrust produced by this current and voltage according to Eq. is only about 16 mnewtons. Therefore, multiple apertures must be used to obtain higher beam currents from the ion engine to increase the thrust. For example, to extract a total of 1 A of xenon ion current for this case would require over 4000 apertures, which would produce over 60 mN of thrust. In reality, for reliable high-voltage operation, and due to non-uniformities in the plasma generator producing varying ion current densities to the boundary, the current density is usually chosen to be less than the Child–Langmuir space charge maximum, and an even larger number of apertures are required. This ultimately determines the size of the ion thruster.
Figure 2-2 Simplified 1-D view of an accelerator aperture in contact with a plasma
Figure 2.2 shows a simplified one-dimensional (1-D) view of one of these biased apertures facing the thruster plasma. The Child–Langmuir sheath is established by the bias potential between the thruster plasma and the accelerator grid and is affected by the current density of the xenon ions arriving at the sheath edge from the Bohm current. Ions that arrive on axis with the aperture are accelerated through to form the beam. However, ions that miss the aperture are accelerated into the accel grid and can erode it rapidly. For this reason, a “screen” grid with apertures aligned with the accel grid is placed upstream of the accel grid to block these ions. This is the classic two-grid accelerator system. The screen grid is normally either allowed to float electrically or is biased to the cathode potential of the
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plasma generator to provide some confinement of the electrons in the plasma and so that ions that strike it have a relatively low energy and cause little sputtering. In practice, the grids are made of refractory metals or carbon-based materials, and the apertures are close packed in a hexagonal structure to produce a high transparency to the ions from the plasma
generator. These grids are also normally dished to provide structural rigidity to survive launch loads and to ensure that they expand uniformly together during thermal loading.
The electrical configuration of an ion thruster accelerator is shown schematically in Fig. 2.3. The high-voltage bias supply (called the screen supply) is normally connected between the anode and the common of the system, which is usually connected to the neutralizer cathode (called “neutralizer common”) that provides electrons to neutralize the beam. Positive ions born in the discharge chamber at high positive voltage are then accelerated out of the thruster. The accel grid is biased negative relative to the neutralizer common to prevent the very mobile electrons in the beam plasma from back-streaming into the thruster, which produces localized heating in the discharge chamber by energetic electron bombardment, and ultimately overloads the screen supply if the back-streaming current becomes large. The ion beam is current neutralized and quasi-neutral (nearly equal ion and electron densities) by the electrons extracted from the neutralizer cathode. Fortunately, the thruster self-biases the neutralizer common potential sufficiently negative relative to the beam potential to produce the required number of electrons to current neutralize the beam.
Figure 2-3 Electrical schematic of a DC discharge ion thruster without the cathode
In actual design, the diameter of each accel grid aperture is minimized to retain unionized neutral gas in the plasma generator, and the screen grid transparency is maximized so that that the grids extract the maximum possible number of ions from the plasma. The electrode diameters and spacing are then optimized to eliminate direct interception of the beam ions on the accel grid, which would cause rapid erosion due to the high ion energy. A schematic example of a three grid system showing the ion trajectories calculated by a two-dimensional (2-D)ion optics code is shown in Fig.2.4. The ions are focused sufficiently by this electrode design to pass through the accel grid without direct interception. On the downstream side of the accel grid, the negative accel-grid bias applied to avoid electron back-streaming results in a relatively small deceleration of the ions before they enter the quasi-neutral beam potential region. This high transparency, strong “accel–decel” geometry typical of ion thrusters results in some beamlet divergence, as suggested by the figure. However, this small beamlet angular divergence of typically a few degrees causes negligible thrust lost because the loss scales as cosθ, and
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because most of the beam divergence related to the thrust correction factor is due to the dishing of the grids.
2.3 ION OPTICS STUDY
The total thrust of an ion thruster consisting of a range of circular apertures is given by the rate of momentum change of the exhausted ion particles. Each ion's velocity and therefore momentum is determined by the electrical fields that it experiences during its movement. A disturbance of these fields caused by an electrode misalignment will therefore interfere with the overall thrust (both magnitude and direction).
Consideration is given to the effect of some basic electrode misalignments. These are selected to include the expected types of disturbances that an acceleration electrode may experience during assembly or thruster operation. In this section the perturbations in the thrust vector of a single engine which result from a number of modes of electrode misalignment are given. The perturbations may be changes in the thrust magnitude and direction, or in the location of the center of thrust. Each mode of misalignment is analyzed independently. The effects of multiple modes can then be obtained by superposition.
2.3.1 Elementary Modes of Electrode Misalignment
The beam intensity profile from an aligned Kaufman thruster is axisymmetric but varies radially from a maximum current at the center to a minimum current at the edge. The thrust (rector from a thruster with misaligned electrodes will be found by summing the perturbed thrusts contributed from each hole pair. First, we consider the results of the ion optical study which gives the current density for a single hole pair under three modes of misalignment: change in hole spacing, relative displacement of the holes transverse to the beam, and tilt of one hole out of its original plane. It turned out that only the first two modes produce significant thrust changes. Expressions for total engine thrust vector misalignment will then be derived for various electrode motions. Changing the distance d between holes causes the plasma sheath position to move and results in a change in the total current from the hole pair.
In Fig:2.5 a, the spacing of the electrode is reduced while preserving the rotational symmetry. This results in an increase in the thrust magnitude from this aperture, which may cause the thrust vector direction to rotate from the thruster. In Fig:2.5 b the electrodes are displaced normally to the beam axis, thus destroying their symmetry and causing a change in thrust vector magnitude and direction. The case illustrated in Fig:2.5 c can be considered as a combination of the two effects mentioned, which alters the thrust vector's magnitude and direction.
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For the purpose of this thesis, the effect of the previously mentioned misalignments are studied and it was decided to focus our attention on case 2, ie the transverse displacement of the electrode by a value of s. The technique employed and the effects on the thrust vector are discussed.
2.3.2 Transverse Displacement of the Acceleration Grid
When the electrode is displaced transversely, the axis of symmetry of the aperture is destroyed. A transverse misalignment is illustrated in fig:2, where the axes of the screen grid and the acceleration grid are displaced by a distance of s . The polar equation of the displaced surface can be found by;
R = x + iy where, x = s cosθ y = s + s sinθ hence, R = (x2 + y2)1/2 which gives, R = (a2 + 2s2 sinθ)1/2 = a (1 + s sinθ)
It can thus be seen that a transverse displacement introduces a perturbation in the radial direction R which varies by sinθ.
Figure 2-5 Transverse displacement of the accelerator grid Figure 2-4 Example of grid translation and corresponding
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From the case study based on the reports ‘ION ENGINE THRUST VECTOR STUDY’ published by NASA JPL, THRUST STEERING OF A GRIDDED ION ENGINE and ION THRUST VECTORING TECHNIQUES AND REQUIREMENTS, it is concluded that an ion beam deflection of 80 is attainable for a displacement of the acceleration grid by about .32 mm. The geometry of the grids is assumed from the mentioned studies.
2.3.3 Design and geometry of the grids
PARAMETER Screen Accelerator
Diameter 30 cm 30 cm
Thickness .75 mm 1.5 cm
Hole Diameter 4.75 mm 3.6 mm
Hole Spacing 5.4 mm 5.4 mm
Table 2-1 Assumed Grid Geometry
The grids are formed from continuous titanium-molybdenum-zirconium (TZM) alloy. The choice of the material was finalized by going through the afore mentioned reports considering the thermal and structural properties of various materials.
2.4 CONCLUSION
Various configurations of screen-accelerator grid pairs are studied and focus of the thesis is fixed on the transverse displacement of the grids. An average ion beam deflection of 80 can be obtained by
translating the grids by about .2 - .4 mm, which is found to be suitable for many practical purposes. The design geometry is assumed from the afore mentioned studies and material selection is done. Fixing our focus on these design aspects, a piezo-electric actuator assembly which can create the require grid translation is designed and studied in this thesis, which will be discussed in the coming sections of the report.
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3 PIEZO-ELECTRICITY
3.1 INTRODUCTION
3.1.1 Piezo-Electricity
Piezoelectricity (also called the piezoelectric effect) is the appearance of an electrical potential across the sides of a piezo-electric material when you subject it to mechanical stress. The reverse is also true, when you apply a potential to the material, a mechanical stress is induced in the material thereby producing a deformation on the material. When piezoelectric material is placed under mechanical stress, there is a shift of the material's positive and negative charge centers, resulting in an external electrical field. The piezoelectric material is either stretched or compressed by an external electrical field when reversed.
Most day to day materials are characterized by their organized and repeating structure of atoms, held together by bonds. These structures are characterized into units, one such unit is called a unit cell. Most crystals, like iron, have a cell with a symmetric unit, making them useless for piezoelectric purposes. Other crystals such as piezoelectric materials are lumped together and the structure in these crystals is not symmetrical, but they still exist in an electrically neutral way. If mechanical pressure is applied to a piezoelectric crystal, however, the structure deforms, atoms are pushed around, and the crystal conducts an electrical current. If you take the same piezoelectric crystal and apply an electrical current to it, the crystal expands and contracts and converts electrical energy into mechanical energy.
Fig:3.1 example,
3.1.2 History
Piezoelectricity was first discovered in 1880 by two brothers and French scientists, Jacques and Pierre Curie. While experimenting with a variety of crystals, they discovered that applying mechanical pressure to specific crystals like quartz released an electrical charge. They called this the piezoelectric effect. The next 30 years saw Piezoelectricity reserved largely for laboratory experiments and further refinement. It wasn’t until World War I when piezoelectricity was used for practical applications in sonar. Sonar works by connecting a voltage to a piezoelectric transmitter. This is the inverse piezoelectric effect in action, which converts electrical energy into mechanical sound waves. The sound waves travel through the water until they hit an object. They then return to a source receiver. This receiver uses the direct piezoelectric effect to convert sound waves into an electrical voltage, which can then be processed by a signal processing device. Using the time between when the signal left and when it returned, an object’s distance can easily be calculated underwater. With sonar a success,
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piezoelectricity gained the eager eyes of the military. World War II advanced the technology even further as researchers from the United States, Russia, and Japan worked to craft new man-made piezoelectric materials called ferroelectrics.
3.2 PIEZOELECTRICITY TODAY
In today’s world of electronics piezoelectricity is used everywhere. Asking Google for directions to a new restaurant uses piezoelectricity in the microphone. There’s even a subway in Tokyo that uses the power of human footsteps to power piezoelectric structures in the ground. You’ll find piezoelectricity being used in these electronic applications
3.2.1 Actuators
Actuators use piezoelectricity to power devices like knitting and braille machinery, video cameras, and smartphones. In this system, a metal plate and an actuator device sandwiches together a piezoelectric material. Voltage is then applied to the piezoelectric material, which expands and contracts it. This movement causes the actuator to move as well.
3.2.2 Speakers and Buzzers
Speakers use piezoelectricity to power devices like alarm clocks and other small mechanical devices that require high quality audio capabilities. These systems take advantage of the inverse piezoelectric effect by converting an audio voltage signal into mechanical energy as sound waves.
Figure 3-2 actuation using piezoelectric materials
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3.2.3 Sensors
Sensors are used in a variety of applications such as microphones, amplified guitars, and medical imaging equipment. A piezoelectric microphone is used in these devices to detect pressure variations in sound waves, which can then be converted to an electrical signal for processing.
3.3 Governing Equations
The strain vector ε in material Cartesian coordinates is defined in terms of infinitesimal and large displacement components as,
where u, v. w are the displacement and the apostrophe denote the partial differentiation. Similarly, the electric field vector E is related to the electric potential V by
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3.3.1 Governing equation for the Piezoelectric materials
The Equations governing the linear piezoelectric material are described asWhere,
where, superscript T denotes the transpose of a matrix, ε is the mechanical strain vector, σ is the mechanical stress vector, D is the electric displacement vector and E is the electric field vector. In principal material direction, the matrix for material stiffness C, the piezoelectric stress matrix e and the dielectric constant matrix ζ for piezoelectric material with orthotropic behavior can be written as:
For composite material with orthotropic properties the stiffness matrix is reduced to 9 independent constants.
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3.3.2 Coupling Equations
The electro-mechanical coupling equations can be given by
Where,
3.3.3 Lagrangian Formulation
In the Lagrangian formulation all static and kinematic variables are referred at time t. The principle of virtual work for piezoelectric material is given by:
Where,
δ denotes small arbitrary virtual variation tv - volume of body at time t, t+t R is the external virtual
work and t+tt , t+tt ε denote the generalized stress and strain vector at times t and t+Δt respectively.
Assuming the loading is deformation independent and can be specified prior to the incremental analysis. The only body force is the inertial D’Alembert force defined by 0ρt+Δt𝒖̈ having a mass density 0ρ at t=0. The external virtual work is given by,
Where u is the displacement vector, is the boundary traction vector at time t= 0 and t=t+Δt, t+ΔtQ is the surface charge, 0v is the original body volume and 0T is the original area on which boundary traction and electrical charges are prescribed. The generalized Cauchy stresses and , giving us,
By substituting the equation for stress, strain and external virtual work in to the main equation of principle of virtual work for piezoelectric materials and using approximation t = t C t ε and δt ε gives
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3.4 PRINCIPLES OF PIEZO ACTUATION
There are two basic types of piezo actuator; the stack and the bender. Based on these two types of actuator, amplifier structures have been designed to increase the available displacement. Both the stack and the bender work on the same underlying principles. If we ignore the hysteresis effect, the relationship between strain and electric field strength for a single piece of piezo element can be expressed as Δl/l =dE. The proportional constant d is called the piezoelectric strain constant (mV-1). Where E is the electric field strength and Δl/l is the strain. Because of E = U/l , then we get Δl = dU . So, we can deduce that the deformation Δl is independent of the dimensions, where U is the applied voltage (v).As piezoelectric strains are generally extremely small, with the strain constant d typically around 10-10 to 10-9mV-1, a practical piezo actuator can be manufactured by putting many thin slices of piezo ceramics together to produce large deformation. This type of arrangement results in the stack actuator. Fig:3.5 a shows the structure of a stack actuator.
Figure 3-5 a. stack actuator. b Bender actuator
Fig: 3.5 b illustrates the typical structure of the bender actuator. Usually, the bender consists of two piezo plates which are joined together. During actuation, one piezo plate is extended and the other one is simultaneously contracted. This produces abending action which results in the desired output orce and displacement. Table 1 shows the equations describing the bender’s force and displacement. Compared with the stack piezo actuator, the bender piezo actuator can give only very small output forces(typically about 1 N) and about +/-1mm maximum displacement. It is the cheapest practical piezo actuator and has been successfully used in inkjet printers, hard-disk drives, micro pumps and small valves.
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3.4.1 Types Of Piezo-Actuators
This section reviews typical arrangements used for applying the piezoelectric effect to actuation. The different approaches to developing piezo actuators may be classified as follows.
Piezo actuator with mechanical amplifier.
Because the displacement of the stack piezo actuator is too small in many applications, it is increased using a mechanical amplifier such as a lever. This type of actuator can produce more than 10 times the displacement typically obtained directly from a stack type actuator but its force and frequency are decreased accordingly.
Inertial drive actuator.
These actuators use friction and inertial forces to produce large displacements.
Inchworm actuator
In theory, the inchworm piezo motor can produce unlimited linear displacement, but with limited force and response frequency
Ultrasonic motor
The ultrasonic motor is similar to the inchworm actuator, but works at its resonant frequency and so can produce a larger output force. The performance of an ultrasonic motor depends heavily on its design and its structure.
3.5 CONCLUSION
In this section, the theory of piezo-electricity and its applications were studied. Also we extended the study to the different types of actuation mechanisms employable to design the final actuator. In the coming chapters we detail the study on bending type and stack type piezo-actuation mechanisms, to reach a conclusion to choose the type of final actuator design to go for.
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4 STACK TYPE ACTUATORS
4.1 INTRODUCTION
4.1.1 Stack Design (Translators)
A piezo element is a ceramic that expands or contracts when an electrical charge is applied, generating linear movement and force. Multiple piezo elements can be layered on top of each other, creating what is known as a stacked piezo actuator. These devices take advantage of the combined effect of each element’s expansion to produce a useful movement and force.
Individual piezo elements in a stacked actuator have alternating polarity, and the electrical field is applied parallel to the direction of polarization. When a voltage is applied, a strain, or displacement, is induced in the direction of polarization. The movement of a piezo element equals the amount of voltage applied multiplied by the piezo electric coefficient. (The piezo electric coefficient, d33, relates to the material’s efficiency in transferring electrical energy to mechanical energy.) Because they are connected mechanically in series, the total movement of a stacked piezo actuator is the product of a single element’s movement, times the number of elements in the stack.
The active part of the positioning element consists of a stack of ceramic disks separated by thin metallic electrodes. The maximum operating voltage is proportional to the thickness of the disks. Most high-voltage actuators consist of ceramic layers measuring 0.4 to 1 mm in thickness. In low-high-voltage stack actuators, the layers are from 25 to 100 µm in thickness and are cofired with the electrodes to form a monolithic unit.
Stack elements can withstand high pressures and exhibit the highest stiffness of all piezo actuator designs. Standard designs which can withstand pressures of up to 100 kN are available, and preloaded actuators can also be operated in push-pull mode. For further information see “Maximum Applicable Forces”.
Displacement of a piezo stack actuator can be estimated by the following equation:
where:
L = displacement [m]
d33 = strain coefficient (field and displacement in polarization direction) [m/V] n = number of ceramic layers
U = operating voltage [V]
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4.2 THEORY OF STACK TYPE ACTUATORS
4.2.1 Voltage and Electric Field
Stacked piezo actuators are generally classified as either low voltage (below 200 V) or high voltage (up to 1000 V), referring to the maximum input voltage for maximum stroke. The amount of voltage that can be applied is determined by the material and the thickness of each element. The relationship between the electrical field and the driving voltage is given by the equation:
E = V/th
E = electric field (V/m) V = applied voltage (V)
th = thickness of one piezo layer (m)
Thus, the electric field increases as the layer thickness decreases. Similarly, for a given electrical field, the driving voltage must decrease as the layer thickness decreases.
4.2.2 Force and Stiffness
Actuator stiffness has a significant influence on force generation and is determined by the modulus of elasticity of the piezo ceramic material, the actuator’s cross-sectional area, and its length. kA = (E*A) / l
kA = actuator stiffness (N/m) E = modulus of elasticity (N/m2) A = actuator cross-sectional area (m2) l = actuator length (m)
Despite their small size, stacked piezo actuators have a force density in the range of 30 N/mm2, which allows them to produce useful forces in the tens of thousands of Newtons. It’s important to note that in steady state operation (no movement, constant force), no current is flowing, and no power is required. Stacked actuators are also able to hold their position when power is off and can do so without generating heat.
4.2.3 Tensile Strength and Preload
Stacked piezo actuators often see both compressive and tensile forces, especially during highly dynamic movements. The tensile strength of a stacked actuator is largely determined by the method used to laminate the individual elements together and is generally an order of magnitude lower than the compressive strength. Preloading the actuator to a value greater than the applied tensile load will ensure that the actuator always stays in compression and can operate in highly dynamic, bi-directional applications. Successful integration of a stacked piezo actuator requires that any applied forces be axial and compressive only. Manufacturers typically offer a variety of mounting options to help prevent bending, shear, or torsional forces.
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4.3 PIEZO DESIGN: Forces & Stiffness in Piezoelectric Actuation
4.3.1 Maximum Applicable Forces (Compressive Load Limit, Tensile Load
Limit)
The mechanical strength values of PZT ceramic material (given in the literature) are often confused with the practical long-term load capacity of a piezo actuator. PZT ceramic material can withstand pressures up to 250 MPa (250 x 106 N/m2) without breaking. This value must never be approached in practical applications, however, because depolarization occurs at pressures on the order of 20 % to 30 % of the mechanical limit. For stacked actuators and stages (which are a combination of several materials) additional limitations apply. Parameters such aspect ratio, buckling, interaction at the interfaces, etc. must be considered.
Tensile loads of non-preloaded piezo actuators are limited to 5% to 10% of the compressive load limit. PI offers a variety of piezo actuators with internal spring preload for increased tensile load capacity. Preloaded elements are highly recommended for dynamic applications.
The PZT ceramic is especially sensitive to shear forces; they must be intercepted by external measures (flexure guides, etc.).
4.3.2 Stiffness
Actuator stiffness is an important parameter for calculating force generation, resonant frequency, full-system behavior, etc. The stiffness of a solid body depends on Young’s modulus of the material. Stiffness is normally expressed in terms of the spring constant kT, which describes the deformation of the body in response to an external force.
This narrow definition is of limited application for piezoceramics because the cases of static, dynamic, large-signal and small-signal operation with open and shorted electrodes must all be distinguished. The poling process of piezoceramics leaves a remnant strain in the material which depends on the magnitude of polarization. The polarization is affected by both the applied voltage and external forces. When an external force is applied to poled piezoceramics, the dimensional change depends on the stiffness of the ceramic material and the change of the remnant strain (caused by the polarization change). The equation DLN = F/kT is only valid for small forces and small-signal conditions. For larger forces, an additional term, describing the influence of the polarization changes, must be superimposed on the stiffness (kT).
Since piezo ceramics are active materials, they produce an electrical response (charge) when mechanically stressed (e.g. in dynamic operation). If the electric charge cannot be drained from the PZT ceramics, it generates a counterforce opposing the mechanical stress. This is why a piezo element with open electrodes appears stiffer than one with shorted electrodes. Common voltage amplifiers with their low output impedances look like a short circuit to a piezo actuator.
Mechanical stressing of piezo actuators with open electrodes, e.g. open wire leads, should be avoided, because the resulting induced voltage might damage the stack electrically.
4.3.3 Force Generation
In most applications, piezo actuators are used to produce displacement. If used in a restraint, they can be used to generate forces, e.g. for stamping. Force generation is always coupled with a reduction in displacement. The maximum force (blocked force) a piezo actuator can generate depends on its stiffness and maximum displacement. At maximum force generation, displacement drops to zero.
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Where:
L0 = max. nominal displacement without external force or restraint [m] kT = piezo actuator stiffness [N/m]
In actual applications the spring constant of the load can be larger or smaller than the piezo spring constant. The force generated by the piezo actuator is:
Effective force a piezo actuator can generate in a yielding restraint
Where:
L0 = max. nominal displacement without external force or restraint [m] kT = piezo actuator stiffness [N/m]
kS = stiffness of external spring [N/m]
4.3.4 Displacement and External Forces
Like any other actuator, a piezo actuator is compressed when a force is applied. Two cases must be considered when operating a piezo actuator with a load:
a) The load remains constant during the motion process. b) The load changes during the motion process.
a) Constant Force
Zero-point is offsetA mass is installed on the piezo actuator which applies a force F = M · g (M is the mass, g the acceleration due to gravity).
The zero-point will be shifted by DLN » F/kT, where kT is the stiffness of the actuator.
If this force is below the specified load limit (see product technical data), full displacement can be obtained at full operating voltage.
Zero-point offset with constant force
Where:
LN = zero-point offset [m]
F = force (mass x acceleration due to gravity) [N] kT = piezo actuator stiffness [N/m]
b) Changing Force
Displacement is reducedFor piezo actuator operation against an elastic load different rules apply. Part of the displacement generated by the piezo effect is lost due to the elasticity of the piezo element (Fig. 21). The total available displacement can be related to the spring stiffness by the following equations:
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Maximum displacement of a piezo actuator acting against a spring load.
Maximum loss of displacement due to external spring force. In the case where the restraint is infinitely rigid (ks = ∞), the piezo actuator can produce no displacement but acts only as a force generator.
Where:
L = displacement with external spring load [m]
L0 = nominal displacement without external force or restraint [m] LR = lost displacement caused by the external spring [m]
ks = spring stiffness [N/m]
kT = piezo actuator stiffness [N/m]
4.4 MATERIAL PROPERTIES
Apart from the standard types described in detail below, we can perform a multitude of application-specific and custom-engineered modifications. PIC materials compare favorably with the best materials internationally available today. The properties are specified according to the EN 50324 European Standard.
“Soft” piezo ceramics are characterized by a comparatively high domain mobility and a resulting “ferroelectrically soft” behavior, i.e. relatively easy polarization.
In contrast, ferroelectrically “hard” PZT materials can be subjected to high electrical and mechanical stresses. The stability of their properties destines them for high-power applications.
