Piezoelectric ActuatorsMarek Novotny, Pekka Ronkanen Email: novotny@ac.tut.fi, pekka.ronkanen@tut.fi Abstract This paper discusses piezoelectricity and piezoelectric actuators. History of the piezoelectricity is briefly reviewed and the piezoelectric effect described. General properties of the piezoelectric actuators are summarized and different types of actuators discussed. A high voltage amplifier is typically is typically needed to control the piezoelectric actuators. An overview of the important properties of piezo amplifiers is given in the end of the document. Keywords: piezoelectricity, piezoelectric actuators, piezoelectric bender, piezoelectric stack.

1. Introduction to PiezoelectricityPierre and Jacques Curie discovered the piezoelectric effect in 1880. The previous studies by Pierre Curie on the relations of pyroelectricity and crystal symmetry must have led the brothers not only to look for electrification from pressure, but to also foresee into what direction pressure should be applied and in which crystal classes the effect was to be expected. Thus, they proved that certain types of crystals develop an electrical charge when exposed to mechanical stress. Hankel proposed the name piezoelectricity where the prefix piezo is derived from the Greek word for press. In the following year, Lippmann predicted the existence of the inverse piezoelectric effect from thermodynamic considerations and the Curies verified this before the end of 1881. In the inverse piezoelectric effect, the application of an electric field to a piezoelectric crystal leads to a physical deformation of the crystal. [1], [2] The piezoelectric effect requires that the crystal structure must be asymmetric: there is at least one axis in the crystal that does not have a centre of symmetry. Piezoelectric effect occurs in some natural crystal materials, such as quartz, but only in a very small scale. Piezoelectric ceramics, discovered in the 1950s, experience much stronger piezoelectric effect. The piezoelectric ceramics must undergo a polarizing process for the piezoelectric phenomenon to occur, while crystal materials are naturally piezoelectric. The most commonly used piezoelectric ceramic is lead zirconate titanate (PbZrO3-PbTiO3 or PZT) but also other ceramic materials, such as such as barium titanate, exhibit the effect. 1.1 Piezoelectric elementary cells To understand the piezoelectric effect in ceramics, the behaviour of the material must first be considered in microscopic scale - the behaviour of the elementary cell of the material. Piezoelectric ceramics are ferroelectric materials. Above a certain temperature, called the Curie temperature, the crystal structure have a centre of symmetry and therefore no electric dipole moment, as depicted in Figure 1a, where the elementary cell of PZT is shown [3]. Above the Curie temperature, the elementary cell is cubic (three crystal axes have same lengths) and a positively charged Ti/Zr ion is centered on the lattice. This is called a paraelectric state. Below the Curie temperature, the crystal structure undergoes a phase

change into the ferroelectric state where the structure is not symmetric. The positively charged Ti/Zr ion travels from its central location forming a tetragonal structure (one axis is longer than the other two), as illustrated in Figure 1b. The electric imbalance causes a built-in electric dipole. If a large external field is applied to the cell, the Ti/Zr ion shifts in the direction of the field as shown in Figure 1c. The ion does not return to its original position when the field is removed resulting in elongation to the direction of the field. When an external field is again applied to the elementary cell, the electric imbalance becomes larger and the cell elongates further, see Figure 1d. A poled PZT elementary cell is depicted in more details in Figure 2.

Figure 1: Behaviour of the PZT elementary cell. a) The elementary cell above the Curie temperature, i.e. no electric dipole, b) the elementary cell below the Curie temperature, i.e. generation of the electric dipole, c) turning of the electric dipole using an external electric field, d) elongation of the elementary cell by an external electric field. [3]

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Figure 2: Poled PZT resulting in an asymmetrical crystal lattice [4]. 1.2 Piezoelectric ceramics As a macroscopic point of view, molecular dipoles align within small areas, domains, forming large dipole moments. The piezoelectric ceramics consist of many such domains. The domains are randomly oriented and therefore, the net external electric dipole is zero, as shown in Figure 3a. If the piezoelectric ceramics is subjected even once to a large electric field (poling), the domain dipoles align in the direction closest to the field. Because of the random original orientation of domains, it is not possible to get perfect dipole alignment with the field. However, each domain can have several allowed directions and therefore, a reasonable degree of alignment can be achieved. Due to the alignment of the domains, the material elongates in the same direction, as shown in Figure 3b. When the voltage is removed, the domains do not entirely return to their original positions, and the material remains partially polarized. The strain resulted from the partial polarization is called a remanent strain. Due to the poling, the material has become permanently piezoelectric and can convert mechanical energy into electrical and vice versa. After poling, if electric field is applied, the material elongates in the direction of the field as illustrated in Figure 3c.

Figure 3: Behaviour of piezoceramic material. a) Non-polarized state, b) polarized state, c) electric applied after poling. [3].

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Piezoelectricity involves the interaction between the electrical and mechanical behaviour of the material. This interaction has been approximated by static linear relations between two electrical and mechanical variables [1]:

S = s E T + dE D = dT + T E

,

(1)

where S is a strain tensor, T is a stress tensor, E is an electric field vector, D is an electric displacement vector, sE is an elastic compliance matrix when subjected to a constant electric field (the superscript E denotes that the electric field is constant), d is a matrix of piezoelectric constants and T is a permittivity measured at a constant stress. The piezoelectric effect is, however, very non-linear in nature. Piezoelectric materials exhibit for example a strong hysteresis and drift that is not included in the above model. It should be noted, too that the dynamics of the material is not described by Equation .

2. Actuator TypesThe simple way of producing displacement a piece of ceramics has inspired researchers to develop various actuator and motor concepts. In addition to the simple mechanical structure, other beneficial general properties of piezoelectric actuators are: a short response time, an ability to create high forces, a high efficiency and a high mechanical durability. On the disadvantage side, piezoelectric actuators have small strains: only 0.1- 0.2% [5]. Other disadvantages are a high supply voltage needed typically between 60 and 1000 Volts [5], a large hysteresis and creep (drift). Figure 4 presents a typical hysteresis and Figure 5 introduces a typical drift of a piezoelectric actuator.

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Figure 4: An illustration of the hysteresis of a piezoelectric actuator [11].

Figure 5: The drift of a piezoelectric actuator [12]. The three basic types of piezoelectric actuators are stacks, benders and linear motors. This section introduces stacks and linear motors and the following section concentrates on piezoelectric benders. 2.1 Piezoelectric Stack Actuators Perhaps the easiest way to produce a linear motion by the piezoelectric effect is to use a stack actuator, which is a multilayer construction: each stack is composed of several piezoelectric layers, as depicted in Figure 6. The required dimensions of the stack can be easily determined from the requirements of the application in question. The height is

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determined in respect to the desired movement and the crosssectional area in respect to the desired force. Figure 7 shows stack actuators from Piezo Systems Inc. (USA). The stack on the left having dimensions of 5x5x18 mm3 provides a movement of 14,5 m and a blocked force of 840 N [6].

Figure 6: Structure of a piezoelectric stack [4].

Figure 7: Piezoelectric stacks from Piezo Systems Inc. [6]. The main problem of the stack actuators is the relatively small strain (0,1 0,2 %) obtained. The movement can be increased by using for example levers or hydraulic amplifiers. It is noticeable, that in addition to the desired longitudinal movement some lateral movement typically also occurs. Therefore, a guiding has to be used if only longitudinal motion is desired. Figure 8 illustrates the deviations from the straight-line accuracy.

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Straightness

Flatness

Figure 8: Straight-line accuracy [7]. 2.2 Linear Motors Since the strain of the piezoelectric ceramics is relatively small, displacement amplifiers or hybrid structures are needed. There are many amplification techniques such as levers and hydraulic systems, and piezoelectric motors. In the lever systems, the amplification is achieved with lever arms which magnify the displacement. The output force of the lever system is significantly smaller than the actuator force. Hydraulic systems use generally a piston for the amplification. The Micro- and Nanosystems Research Group has developed a hydraulic amplifier based on the use of bellows. The principle of the piezohydraulic actuator and a 3D CAD model of a developed actuator are illustrated in Figure 9 and Figure 10, respectively.Fluid

Bellows

Piezoelectric Disk Strain Gauge

Piezoelectric actuator

Bellows

Fluid chamber

Figure 9: A schematic piezohydraulic actuator.

of

the Figure 10: A 3D-CAD piezohydraulic actuator.

model

of

the

Piezoelectric motors increase the displacement by providing many small steps. There are many different types of linear piezoelectric motors and the main categories are linear stepper motors and ultrasonic motors. The linear steppers include an inchworm motor, a stick and slip actuator, and an impact drive motor. The ultrasonic motors can be divided into standing wave and traveling wave ultrasonic motors. In this paper, the operating principles of the inchworm motor, the stick & slip actuator and the traveling wave ultrasonic motor are described. In inchworm motors, the linear movement is achieved by using three piezo elements. The operation principle is illustrated in Figure 11. The outer piezo elements work as clamps. The middle element contracts and expands which generates the movement of the rod [7].

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Figure 11: Operation of inchworm motor [7]. The stick and slip actuator is a type of an inertia device, which uses inertia of the moving mass. The actuator consists of particular legs and a slider. Each step consists of a slow deformation of the legs and fast jump backwards. In slow deformation of the legs, the moving mass follows the legs due to the friction (the frictional force is higher than the force caused by the slider inertia). In the sudden jump backwards, the slider can not follow the legs due to its inertia [10]. Figure 12 shows the operating principle of stick and slip actuator.

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Figure 12: Operating principle of the stick and slip actuator [10].

The traveling wave ultrasonic motor is driven by a voltage having two phases. The voltage is applied to the piezoelectric element at the resonance frequency. The resonance frequency produces a traveling wave. The particles on the surface move along the elliptical trajectories. The motion of the particles is on the opposite direction of the wave. When a moving body (rotor) is placed in contact with the surface, it moves in the same direction as the particles due to the frictional force produced between the moving body and the elastic body [9]. 2.3 Piezoelectric Benders Piezoelectric bending actuators (or piezoelectric cantilevers, or piezoelectric bimorphs) bear a close resemblance to bimetallic benders. The application of an electric field across the two layers of the bender result in one layer to expand, while the other contracts. The net result is a curvature much greater than the length or thickness deformation of the individual layers. With a piezoelectric bender, relatively high displacements can be achieved, but at the cost of force and speed. There are some benders that have only one piezoelectric layer on top of a metal layer (unimorph), but generally there are two piezoelectric layers and no metal (bimorph). This way, the displacement is doubled in comparison to a single layer version. If the number of piezoelectric layers exceeds two, the bender is referred as a multilayer. With thinner piezo layers, a smaller voltage is required to produce the same electric field strength, and therefore, the benefit of the multilayer benders is their lower operating voltage. Bimorph and multilayer benders can be built into one of the two types: a serial or parallel bender. In a serial bender, there are two piezoelectric layers with an anti-parallel polarization connected to each other, and two surface electrodes, as shown in Figure 13. In this arrangement, one of the electrodes is connected to the ground and the other to the output of a bipolar amplifier.

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Figure 13: A serial bender arrangement with an anti-parallel polarization in piezoelectric layers, bilateral motion for bipolar driving voltage [11]. Parallel benders can be distinguished from serial benders by their three electrodes. In between the two parallel-polarized piezoelectric layers is a middle electrode, to which the actual control signal is supplied. The two surface electrodes are connected to the ground and to a fixed voltage. The control voltage is applied to the middle electrode, and it varies between zero and a fixed voltage, Figure 14. The parallel bender can also be connected in such a way that the two surface electrodes are connected to the ground and a bipolar signal is applied to the middle electrode [11].

Figure 14: Schematic of a parallel bender in operation [11].

3. Piezo AmplifiersA voltage amplifier is typically needed to control the piezoelectric actuators due to the high operating voltage needed for the piezo actuators. In other words, before we can use the control signal provided by the computer through a DA-converter, we have to amplify it. This section describes the most important piezo amplifier characteristics such as a voltage range, peak and average currents, a slew rate, a power efficiency and a noise. 3.1 Voltage Range The output voltage range is perhaps the most important property of the amplifier, because it either limits the range of displacement when being too small or decreases the displacement resolution when being too large. 3.2 Current and Slew Rate In addition to the supply voltage range, an important property is the current driving capability of the amplifier. This together with the capacitance of the piezoelectric actuator determines the maximum operating frequency. Equation 2 presents the current as a function of the actuator capacitance C and the speed of voltage change.

I (t ) = C

dU dt

(2)

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The slew rate of the amplifier can also act as a limiting factor, because it determines the maximum dU/dt relation. For most amplifiers, both the peak and the average current limits are given. With capacitive loads, such as piezo actuators, the peak current is more important but average current cannot still be forgotten. The required peak and average currents ratio show a fixed ratio of approximately 3:1 for a sine oscillation, for example [13].3.3 Power Efficiency

One aspect to consider, is the power efficiency of the supplied power. This is important especially in portable devices, in devices that have wireless power supply and in devices operating on high frequencies. More information about the power efficiency can be found in [13].3.4 Noise

Piezoelectric actuators have theoretically an unlimited resolution. Therefore, every infinitely small voltage step caused by the noise of the amplifier, for example, is transformed into an infinitely small mechanical shift [13]. Therefore, an important property of the amplifier when designing a precision positioning system is the noise characteristics of the amplifier.

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