⚡Piezoelectric Energy Harvesting Unit 8 – Piezoelectric Stack Actuators

Fundamentals of Piezoelectricity

• Piezoelectricity is the ability of certain materials to generate an electric charge in response to applied mechanical stress or strain
• Conversely, piezoelectric materials also exhibit the reverse effect, where an applied electric field induces mechanical deformation or strain
• The piezoelectric effect arises from the asymmetric crystalline structure of piezoelectric materials, such as quartz, lead zirconate titanate (PZT), and polyvinylidene fluoride (PVDF)
  • The asymmetry in the crystal lattice allows for the separation of positive and negative charges when the material is subjected to stress or strain
• Piezoelectric materials exhibit anisotropic properties, meaning their piezoelectric response varies depending on the direction of the applied stress or electric field relative to the crystal axes
• The piezoelectric effect is characterized by the piezoelectric coefficients, denoted as $d_{ij}$ or $e_{ij}$, which relate the mechanical and electrical properties of the material
  • The subscripts $i$ and $j$ represent the directions of the applied stress or electric field and the resulting strain or electric displacement, respectively
• Piezoelectric materials have a Curie temperature, above which they lose their piezoelectric properties due to a phase transition in the crystal structure
• The piezoelectric effect is reversible, allowing piezoelectric materials to be used as both sensors (converting mechanical energy to electrical energy) and actuators (converting electrical energy to mechanical energy)

Structure and Components of Piezoelectric Stack Actuators

• Piezoelectric stack actuators are composed of multiple thin layers of piezoelectric material, typically lead zirconate titanate (PZT), stacked together to amplify the displacement and force output
• The individual piezoelectric layers are electrically connected in parallel, allowing for a higher capacitance and lower operating voltage compared to a single piezoelectric element of the same thickness
• Electrodes, usually made of silver or nickel, are placed between each piezoelectric layer to apply the electric field and collect the generated charge
• The piezoelectric layers and electrodes are bonded together using a conductive adhesive, such as epoxy or solder, to ensure proper electrical contact and mechanical integrity
• Insulating materials, such as ceramic or polymer, are used to encapsulate the stack and provide electrical insulation between the electrodes and the external environment
• End caps or mounting plates are attached to the top and bottom of the stack to facilitate mechanical connection to the load or support structure
• Electrical leads or terminals are connected to the electrodes to allow for the application of the driving voltage and the measurement of the generated charge or current
• The overall dimensions of the stack actuator, including the number of layers, layer thickness, and cross-sectional area, determine its displacement, force, and capacitance characteristics

Operating Principles and Mechanics

• Piezoelectric stack actuators operate based on the inverse piezoelectric effect, where an applied electric field induces mechanical strain in the piezoelectric layers
• When a voltage is applied across the electrodes of the stack actuator, an electric field is generated in the thickness direction of each piezoelectric layer
• The electric field causes the piezoelectric layers to expand or contract, depending on the polarity of the applied voltage and the orientation of the piezoelectric material
• The mechanical strain generated in each layer is proportional to the applied electric field and the piezoelectric coefficient of the material, typically ranging from 0.1% to 0.2% for PZT
• The individual layer displacements are summed up through the stack, resulting in an overall displacement that is much larger than that of a single layer
  • For example, a stack actuator with 100 layers, each having a thickness of 100 μm and a strain of 0.1%, can achieve a total displacement of 10 μm
• The force generated by the stack actuator depends on the stiffness of the piezoelectric material, the cross-sectional area of the stack, and the applied electric field
• The stack actuator exhibits hysteresis in its displacement-voltage relationship due to the nonlinear and history-dependent behavior of the piezoelectric material
• The dynamic response of the stack actuator is influenced by its resonant frequency, which depends on the mass and stiffness of the stack and the load conditions
• Piezoelectric stack actuators can operate in both static and dynamic modes, with typical operating frequencies ranging from DC to several tens of kilohertz

Performance Characteristics and Parameters

• Displacement: The maximum displacement achieved by the stack actuator under a given applied voltage, typically expressed in micrometers (μm) or nanometers (nm)
  • The displacement is linearly proportional to the applied voltage and the number of layers in the stack
• Blocking force: The maximum force generated by the stack actuator when its displacement is fully constrained, typically expressed in newtons (N) or kilonewtons (kN)
  • The blocking force is proportional to the cross-sectional area of the stack and the applied electric field
• Stiffness: The ratio of the applied force to the resulting displacement, typically expressed in newtons per micrometer (N/μm) or newtons per meter (N/m)
  • The stiffness of the stack actuator depends on the elastic properties of the piezoelectric material and the geometry of the stack
• Capacitance: The electrical capacitance of the stack actuator, determined by the permittivity of the piezoelectric material, the electrode area, and the number of layers
  • The capacitance affects the electrical impedance and the power consumption of the stack actuator
• Resonant frequency: The natural frequency at which the stack actuator exhibits maximum displacement amplitude for a given input voltage
  • The resonant frequency depends on the mass and stiffness of the stack and the load conditions, and it sets the upper limit for the operating frequency range
• Hysteresis: The nonlinear and history-dependent relationship between the applied voltage and the resulting displacement, typically expressed as a percentage of the maximum displacement
  • Hysteresis can lead to positioning errors and reduced efficiency in precise control applications
• Response time: The time required for the stack actuator to reach a specified percentage (e.g., 90%) of its final displacement value when a step voltage is applied
  • The response time is limited by the mechanical and electrical time constants of the stack actuator and the driving electronics
• Durability: The ability of the stack actuator to maintain its performance characteristics over a specified number of operating cycles or a given time period
  • Piezoelectric stack actuators can undergo millions of cycles without significant degradation, depending on the operating conditions and the material properties

Applications in Energy Harvesting

• Piezoelectric stack actuators can be used as energy harvesters to convert mechanical energy from vibrations, impacts, or deformations into electrical energy
• In energy harvesting applications, the stack actuator is typically operated in the direct piezoelectric effect mode, where mechanical stress or strain induces an electric charge in the piezoelectric layers
• The generated electrical energy can be used to power small electronic devices, such as wireless sensors, or to charge batteries for later use
• Piezoelectric stack actuators are well-suited for energy harvesting from low-frequency, high-force sources, such as human motion, machinery vibrations, or structural deformations
  • For example, a stack actuator embedded in the sole of a shoe can generate electrical energy from the compressive force during walking or running
• The energy harvesting performance of a stack actuator depends on factors such as the piezoelectric material properties, the stack geometry, the input mechanical excitation, and the electrical load conditions
• To optimize the energy harvesting efficiency, the stack actuator should be designed to match the frequency and amplitude of the input mechanical excitation and to operate near its resonant frequency
• Energy harvesting circuits, such as rectifiers, voltage regulators, and storage elements, are used to condition and manage the generated electrical energy for practical use
• Piezoelectric stack actuators can be integrated with other energy harvesting technologies, such as electromagnetic or electrostatic generators, to create hybrid energy harvesting systems with improved performance and versatility

Design Considerations and Optimization

• Material selection: Choosing the appropriate piezoelectric material based on its piezoelectric coefficients, dielectric properties, mechanical strength, and temperature stability
  • Lead zirconate titanate (PZT) is the most commonly used material for stack actuators due to its high piezoelectric coefficients and good temperature stability
• Layer thickness: Determining the optimal thickness of the individual piezoelectric layers to balance the displacement, force, and capacitance of the stack actuator
  • Thinner layers result in higher displacement and capacitance but lower force output and higher operating voltage
• Number of layers: Selecting the number of layers in the stack to achieve the desired displacement and force characteristics while considering the available space and the manufacturing constraints
  • Increasing the number of layers improves the displacement and force output but also increases the stack height and the manufacturing complexity
• Electrode design: Optimizing the electrode geometry and material to ensure uniform electric field distribution, minimize electrical losses, and improve the mechanical bonding between the layers
  • Interdigitated electrodes or segmented electrodes can be used to create localized actuation patterns or to reduce the driving voltage requirements
• Insulation and encapsulation: Designing the insulation and encapsulation layers to provide adequate electrical insulation, mechanical protection, and environmental stability for the stack actuator
  • Polymer or ceramic materials with high dielectric strength and low moisture absorption are commonly used for insulation and encapsulation
• Mechanical interface: Designing the end caps, mounting plates, and mechanical connectors to efficiently transfer the generated force and displacement to the load or support structure
  • The mechanical interface should be rigid, stable, and compatible with the operating environment and the application requirements
• Electrical interface: Selecting the appropriate electrical connectors, cables, and driving electronics to supply the required voltage and current to the stack actuator and to measure the generated charge or displacement
  • The electrical interface should have low resistance, high insulation, and good shielding to minimize losses and interference
• Finite element analysis (FEA): Using FEA tools to simulate the mechanical and electrical behavior of the stack actuator under various operating conditions and to optimize the design parameters for specific applications
  • FEA can help predict the displacement, force, stress, and electric field distributions in the stack actuator and identify potential failure modes or performance limitations

Fabrication Techniques and Materials

• Tape casting: A process for producing thin, flat sheets of piezoelectric material by dispersing the ceramic powder in a solvent with binders and additives, casting the slurry onto a moving carrier tape, and drying the resulting film
  • Tape casting allows for precise control of the layer thickness and composition and enables the production of large-area, multilayer structures
• Screen printing: A process for depositing the electrode patterns onto the piezoelectric layers by forcing a conductive paste through a patterned screen or stencil using a squeegee
  • Screen printing provides high resolution and repeatability for the electrode geometry and allows for the integration of multiple electrode materials or functions
• Lamination: The process of stacking and bonding the individual piezoelectric and electrode layers together using heat and pressure to form a compact, mechanically stable structure
  • Lamination requires careful control of the temperature, pressure, and duration to ensure proper bonding and to avoid damage or delamination of the layers
• Dicing: The process of cutting the laminated stack into the desired shape and size using precision sawing or laser cutting techniques
  • Dicing allows for the fabrication of stack actuators with various cross-sectional geometries and dimensions and enables the integration of multiple stack actuators on a single substrate
• Sintering: A high-temperature treatment process that densifies the piezoelectric layers and promotes the formation of a stable, crystalline structure with the desired piezoelectric properties
  • Sintering is typically performed at temperatures between 1000°C and 1300°C for several hours, depending on the piezoelectric material composition and the desired density
• Poling: The process of applying a strong electric field to the stack actuator to align the electric dipoles in the piezoelectric material and to induce the macroscopic piezoelectric effect
  • Poling is typically performed at elevated temperatures (50°C to 150°C) and electric fields (1 to 5 kV/mm) for several minutes to several hours, depending on the material properties and the desired performance
• Piezoelectric materials: The most common materials used in piezoelectric stack actuators are lead zirconate titanate (PZT), barium titanate (BaTiO3), and bismuth ferrite (BiFeO3)
  • These materials offer high piezoelectric coefficients, good temperature stability, and compatibility with standard fabrication processes
• Electrode materials: The electrodes in stack actuators are typically made of silver (Ag), nickel (Ni), or copper (Cu) due to their high conductivity, good adhesion to the piezoelectric layers, and compatibility with the sintering and poling processes
  • Other electrode materials, such as platinum (Pt), palladium (Pd), or conductive oxides, can be used for high-temperature or corrosive environments

Challenges and Future Developments

• Hysteresis and nonlinearity: Piezoelectric stack actuators exhibit hysteresis and nonlinear behavior in their displacement-voltage relationship, which can lead to positioning errors and control challenges
  • Research is ongoing to develop advanced control algorithms, such as feedforward compensation or inverse models, to mitigate the effects of hysteresis and nonlinearity
• Temperature sensitivity: The piezoelectric properties of the stack actuator materials are temperature-dependent, which can cause variations in the displacement and force output over the operating temperature range
  • Development of temperature-stable piezoelectric materials or active temperature compensation techniques can help reduce the temperature sensitivity of stack actuators
• Fatigue and degradation: Piezoelectric stack actuators can experience mechanical fatigue, crack propagation, or depolarization under high-cycle or high-stress operating conditions, leading to performance degradation over time
  • Research is focused on understanding the fatigue mechanisms in piezoelectric materials and developing new materials or fabrication processes to improve the long-term reliability of stack actuators
• Integration and miniaturization: The integration of piezoelectric stack actuators into complex systems or miniaturized devices requires advances in packaging, interconnection, and assembly technologies
  • Development of novel packaging materials, such as flexible polymers or low-temperature co-fired ceramics (LTCC), and 3D integration techniques can enable the realization of compact, multifunctional stack actuator modules
• Energy harvesting efficiency: The energy conversion efficiency of piezoelectric stack actuators in energy harvesting applications is limited by factors such as the electromechanical coupling, the mechanical quality factor, and the electrical impedance matching
  • Research is directed towards optimizing the stack actuator design, the energy harvesting circuits, and the power management strategies to maximize the energy harvesting performance and the overall system efficiency
• Multifunctional materials: The development of multifunctional piezoelectric materials that combine high piezoelectric coefficients with other desirable properties, such as high thermal conductivity, low dielectric loss, or self-sensing capabilities, can expand the application range of stack actuators
  • Examples include piezoelectric-magnetostrictive composites, piezoelectric-pyroelectric materials, or piezoelectric-semiconductor heterostructures
• Additive manufacturing: The adoption of additive manufacturing techniques, such as 3D printing or inkjet printing, for the fabrication of piezoelectric stack actuators can enable the rapid prototyping, customization, and optimization of stack actuator designs
  • Additive manufacturing can also facilitate the integration of stack actuators with complex geometries, functional gradients, or multi-material structures for enhanced performance and functionality
• Sustainable and eco-friendly materials: The development of lead-free piezoelectric materials or the recycling and reuse of stack actuator components can contribute to the sustainability and environmental friendliness of piezoelectric energy harvesting technologies
  • Examples of lead-free piezoelectric materials include potassium sodium niobate (KNN), bismuth sodium titanate (BNT), or sodium bismuth titanate (NBT) based ceramics