Introduction

Abstract

Piezoelectric devices play a major role in our everyday lives. Currently, the global demand for piezoelectric devices is valued at approximately 20 billion euros per year. Piezoelectric sensors and actuators make a substantial contribution in this respect. At the beginning of the opening chapter, we will discuss the fundamentals of sensors and actuators. Section 1.2 addresses the history of piezoelectricity and piezoelectric materials. In Sect. 1.3, application areas as well as application examples of piezoelectricity are listed. The chapter ends with a brief chapter overview of the book.

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Piezoelectric devices play a major role in our everyday lives. Currently, the global demand for piezoelectric devices is valued at approximately 20 billion euros per year. Piezoelectric sensors and actuators make a substantial contribution in this respect. At the beginning of the opening chapter, we will discuss the fundamentals of sensors and actuators. Section 1.2 addresses the history of piezoelectricity and piezoelectric materials. In Sect. 1.3, application areas as well as application examples of piezoelectricity are listed. The chapter ends with a brief chapter overview of the book.

1.1 Fundamentals of Sensors and Actuators

Sensors and actuators play an important role in various practical applications. Let us start with the fundamentals of sensors. In general, sensors convert measurands into appropriate measurement values. From the system point of view, measurands serve as inputs and measurement values as outputs of sensors. In this book, sensors will be limited to devices that convert mechanical quantities into electrical quantities. The mechanical quantities denote, thus, measurands, while the electrical quantities represent measurement values. Figure 1.1 depicts possible measurands (e.g., mechanical force) and measurement values (e.g., electric voltage).

Fig. 1.1

Typical conversion principles as well as input and output quantities of sensors and actuators

In contrast to sensors, (electromechanical) actuators convert electrical quantities (e.g., electric voltage) into mechanical quantities (e.g., mechanical force). Hence, actuators operate in opposite direction as sensors (see Fig. 1.1). From the system point of view, electrical quantities serve as inputs, whereas mechanical quantities represent outputs of actuators.

There exist several principles to convert mechanical into electrical quantities and electrical into mechanical quantities. Some conversion principles work in both directions, i.e., it is possible to convert mechanical into electrical quantities and vice versa. Due to this fact, such conversion principles can be exploited for sensors and actuators. The most common bidirectional conversion principles are listed in Fig. 1.1. If a conversion principle allows both working directions, sensors and actuators will often be called transducers . As the book title implies, we will focus on the piezoelectric conversion principle. Therefore, the book deals with piezoelectric sensors and piezoelectric actuators, i.e., with piezoelectric transducers.

Apart from the conversion principle, sensors and actuators can be classified according to other aspects. Especially for sensors, one can find several classifications like active/passive sensors. Because piezoelectric sensors do not necessarily need an auxiliary energy, they belong to the group of active sensors.

1.2 History of Piezoelectricity and Piezoelectric Materials

The word piezoelectricity originates from the Greek language and means electricity due to pressure. Piezoelectricity was firstly discovered by the Curie brothers in 1880. They recognized that electric charges will arise when mechanical forces are applied to materials like tourmaline, quartz, topaz, and Rochelle salt. This effect is referred to as direct piezoelectric effect. In 1881, Lippmann deduced the inverse piezoelectric effect from the mathematical point of view. The Curie brothers immediately confirmed the existence of the inverse piezoelectric effect.

The first practical application of piezoelectricity was the sonar, which has been developed during the First World War by Langevin. The main component of the sonar consisted of a thin quartz crystal that was glued between two steel plates. In 1921, Cady invented an electrical oscillator, which was stabilized by a quartz crystal. A few years later, such oscillators were used in all high-frequency radio transmitters. Quartz crystal controlled oscillators are nowadays still the secondary standard for timing and frequency control. The success of sonar and quartz crystal controlled oscillators was responsible that new piezoelectric materials and new applications were explored over the next decades after the First World War. For example, the development of piezoelectric ultrasonic transducers enabled viscosity measurements in fluids and the detection of flaws inside of solids.

During the Second World War, several independent research groups discovered a new class of synthetic materials, which offers piezoelectric constants many times higher than natural materials such as quartz. The synthetically produced polycrystalline ceramic materials were named ferroelectrics and piezoceramic materials. Barium titanate and lead zirconate titanate (PZT) represent two well-known solid solutions that belong to the class of these materials. In 1946, it was demonstrated that barium titanate features pronounced piezoelectric properties after an appropriate poling process. The first commercial use of barium titanate was in phonograph pickups. The strong piezoelectric coupling in PZT was discovered in 1954. The intense research in the following decades revealed that the piezoelectric properties of PZT could be controlled by means of doping. In doing so, it is possible to produce ferroelectrically soft and ferroelectrically hard materials. While ferroelectrically soft materials are well suited for piezoelectric actuators and ultrasonic transducers, ferroelectrically hard materials provide an outstanding stability for high power and filter applications. On these grounds, PZT is most commonly used in conventional piezoelectric devices, nowadays.

Even though piezoceramic materials such as PZT feature comparatively high electromechanical coupling factors and can be manufactured in arbitrary shape, quartz crystals still play an important role in practical applications, e.g., for piezoelectric force sensors. There are several reasons for this. For instance, special cuts of quartz crystals lead to material properties that are stable over a wide temperature range as well as almost free of hysteresis. Moreover, quartz crystals can also be synthetically manufactured by the so-called hydrothermal method, which was firstly applied to artificially grow quartz in the 1940s. Aside from quartz, lithium niobate and lithium tantalate are well-known representatives of piezoelectric single crystals. Both materials play a key role in modern telecommunication systems because they often serve as piezoelectric material for surface acoustic wave (SAW) devices.

Over the past decades, the research in the field of piezoelectric materials has concentrated on various topics. Many research groups work on lead-free piezoceramic materials (e.g., sodium potassium niobate) that provide a similar performance as PZT. A further research topic concerns relaxor-based single crystals since the piezoelectric constants of such piezoelectric materials can take values, which greatly exceed those of PZT. Because microelectromechanical systems (MEMS) gain in importance, much research and development are also conducted in the fabrication of thick and thin piezoelectric films. As a last example of research topics, let us mention piezoelectric polymers like polyvinylidene fluoride (PVDF) and cellular polypropylene. If the piezoelectric polymers are produced as thin films, they can be exploited for mechanically flexible sensors and actuators.

1.3 Practical Applications of Piezoelectricity

The application areas of piezoelectricity range from process measurement technology, nondestructive testing and medicine to consumer electronics and sports. Depending on the particular application, one exploits the direct piezoelectric effect, the inverse piezoelectric effect or a combination of both. The following list contains selected applications (e.g., parking sensors) in different application areas.

• process measurement technology and condition monitoring

  • sensors for, e.g., force, torque, acceleration, viscosity

  • measurement of temperature and geometric distance

• automotive industry

  • parking sensors

  • injection systems in diesel engines

• production technology

  • ultrasonic welding

  • ultrasonic cleaning

• nondestructive testing

  • flaw detection

  • material and device characterization

• medicine

  • diagnostics, e.g., pregnancy examinations

  • therapy, e.g., kidney stone fragmentation (lithotripsy)

• consumer electronics

  • loudspeakers

  • inkjet printers

  • lens settings in cameras

• smart materials and structures

  • active noise control

  • structural health monitoring

• sports, e.g., reduction of mechanical vibrations in tennis rackets

• musics, e.g., pickup for guitars

• energy harvesting for local energy supply

• transformers

Even though this list of applications seems to be very long, it could be extended almost indefinitely.

1.4 Chapter Overview

As the title suggests, the book deals with fundamentals and applications of piezoelectric sensors and actuators. According to the list in the previous section, there exists a wide variety of applications of piezoelectricity. In this book, we will concentrate on some selected examples. Many topics refer to research activities, which have been conducted at the Chair of Sensor Technology (Friedrich-Alexander-University Erlangen-Nuremberg) during the last ten years. Apart from the opening chapter, the book is divided into nine chapters.

Chapter 2 addresses the physical basics that are important for piezoelectric sensors and actuators. This includes fundamentals, characteristic quantities as well as basic equations of electromagnetics, continuum mechanics, and acoustics. In Chap. 3, we will study the fundamentals of piezoelectricity. The chapter starts with the principle of the direct and inverse piezoelectric effect. After thermodynamical considerations, the material law of linear piezoelectricity will be derived. Furthermore, the electromechanical coupling inside piezoelectric materials will be classified and quantitatively rated. The chapter ends with a comprehensive overview of piezoelectric materials (e.g., polycrystalline ceramic materials), which are used in practical applications.

Chapter 4 deals with the fundamentals of finite element (FE) simulations since such numerical simulations are nowadays the standard tool for the design and optimization of piezoelectric sensors and actuators. We will start with the basic steps of the FE method. Afterward, the FE method will be applied to the electrostatic field, the mechanical field, and the acoustic field. Due to the fact that piezoelectricity refers to coupling of mechanical and electric quantities, we study the simulation-based coupling of the underlying fields. This also includes the coupling of mechanical and acoustic fields, which is important for piezoelectric ultrasonic transducers.

In Chap. 5, we will discuss the characterization of sensor and actuator materials. The material characterization represents an essential step in the design and optimization because reliable numerical simulations demand precise material parameters. The chapter starts with standard approaches for material characterization. In doing so, a clear distinction between active and passive materials is carried out. Piezoelectric materials are active materials, whereas other materials (e.g., plastics) within piezoelectric sensors and actuators belong to the group of passive materials. The main focus of the chapter lies on the so-called inverse method, which has been developed at the Chair of Sensor Technology. Basically, the inverse method combines FE simulations with measurements. By reducing the deviations between simulation and measurement results, the material parameters get iteratively adjusted in a convenient way. The inverse method is exploited to identify material parameters and properties of selected active and passive materials.

Piezoceramic materials will show a pronounced hysteretic behavior if large electrical excitation signals are used during operation. Chapter 6 details a phenomenological modeling approach, which allows the reliable description of this large-signal behavior. Before the so-called Preisach hysteresis operator is introduced, we will briefly study various modeling approaches on different length scales. Since the Preisach hysteresis operator consists of weighted elementary switching operators, two different weighting procedures are given. The chapter also addressed generalized Preisach hysteresis models, which have been developed at the Chair of Sensor Technology. For instance, the generalization enables the consideration of mechanical stresses that are applied to a piezoceramic material. Finally, we discuss the inversion of the Preisach hysteresis model. The inversion will be of utmost importance when the Preisach hysteresis operator is used for hysteresis compensation.

Chapter 7 treats ultrasonic transducers that exploit piezoelectric materials. The chapter starts with a semi-analytical approach for calculating sound fields and transducer outputs. The approach is based on the so-called spatial impulse response (SIR) of the considered ultrasonic transducer, e.g., a piston-type transducer. Among other things, the SIR is utilized to determine the spatial resolution of spherically focused transducers. Afterward, we will study the general structure and fundamental operation modes of single-element transducers, transducer arrays, and composite transducers. A further section concerns a simple one-dimensional modeling approach that allows analytical description of basic physical relations under consideration of the internal transducer structure. At the end of the chapter, several examples for piezoelectric ultrasonic transducers will be presented.

Practical applications of ultrasonic transducers often demand the characterization of the resulting sound fields. That is the reason why Chap. 8 deals with appropriate measurement principles. The chapter starts with conventional measurement principles such as hydrophones and Schlieren optical methods. The subsequent sections exclusively concentrate on the so-called light refractive tomography (abbr. LRT), which has been realized at the Chair of Sensor Technology. This optical measurement principle enables nonreactive and spatially as well as temporally resolved investigations of sound fields that are generated by piezoelectric ultrasonic transducers, e.g., a cylindrically focused transducer. Exemplary results for sound pressure fields in water and air will be shown. Moreover, LRT is applied to study the wave propagation of mechanical waves in an optically transparent solid.

Piezoelectric sensors are frequently employed for the measurement of physical quantities. In Chap. 9, we will study typical setups of such sensors and their application in the process measurement technology. At the beginning, piezoelectric sensors for the quantities force, torque, pressure, and acceleration are detailed. This includes commonly used readout electronics such as charge amplifiers. Subsequently, a method will be presented which enables the simultaneous determination of thickness and speed of sound for solid plates. The underlying measurement principle is based on ultrasonic waves and has been developed at the Chair of Sensor Technology. The chapter also addresses fluid flow measurements that exploit ultrasonic transducers. We will discuss typical measurement principles as well as a recently suggested modeling approach, which allows efficient estimation of transducer outputs for clamp-on ultrasonic flow meters. At the end, a mechanically flexible cavitation sensor is presented that has been developed at the Chair of Sensor Technology.

The last chapter addresses piezoelectric positioning systems and piezoelectric motors. We will start with piezoelectric stack actuators, which provide much larger strokes than piezoelectric single elements. Because the large strokes call for large electrical excitation signals, Preisach hysteresis modeling from Chap. 6 is applied for a mechanically prestressed stack actuator. The subsequent section details an amplified piezoelectric actuator that was built up at the Chair of Sensor Technology. We will also study model-based hysteresis compensation for a piezoelectric trimorph actuator, which can be used for positioning tasks. The end of the chapter concerns linear and rotary piezoelectric motors.