Piezo Stack

Electrical and force characteristics of piezoelectric stacked actuator

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Libraries:
Simscape / Electrical / Electromechanical / Mechatronic Actuators

Description

The Piezo Stack block represents the electrical and force characteristics of a piezoelectric stacked actuator using the following equations:

$$\begin{array}{l}S=s^{E}T+d^{\text{'}}E\\ D=dT+{\epsilon }^{T}E\end{array}$$

where

• S is the strain tensor.

• T is the stress tensor.

• E is the electric field vector.

• D is the electric displacement vector.

• s^E is the elastic compliance matrix when subjected to a constant electric field.

• d is the piezoelectric constant matrix.

• ε^T is the permittivity measured at a constant stress.

Note

The block models one-dimensional lumped parameter behavior, so S, T, E and D are all scalar values.

You can specify the block parameters that determine static force using either datasheet parameters or material properties, as determined by the value of the Parameterization parameter on the Static Force tab of the block dialog box.

The Dynamic Forces tab of the block dialog box lets you include optional effective mass and mechanical damping effects.

• If you specify a nonzero value for the Effective mass parameter or a finite value for the Resonant frequency at constant field parameter, the block attaches a lumped mass to the mechanical R port. When you specify a finite resonant frequency, the block calculates the effective mass to achieve the correct resonant frequency.

• If you specify a nonzero value for the Damping parameter or a finite value for the Mechanical quality factor parameter, the block adds a damping term across the R to C mechanical ports. When you specify a mechanical quality factor, Q_m, the block calculates the damping from this parameter value as$$\sqrt{Mk}/Q_m$$, where k is the short-circuit device stiffness, or equivalently the stiffness at constant field.

A positive voltage across the electrical + to - ports creates a positive displacement acting from the mechanical C to R ports.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. You can specify nominal values using different sources, including the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Hybrid Linear Actuator

A hybrid actuator consisting of a DC motor plus lead screw in series with a piezoelectric stack. The DC motor and lead screw combination supports large displacements (tens of millimeters), but is dynamically slow when tracking the reference demand x_ref. Conversely the piezoelectric stack only supports a maximum displacement of +-0.1mm, but has a very fast dynamic response. Combining the two actuator technologies creates a large stroke actuator with highly precise positioning.

• Open Model

Assumptions and Limitations

• The model does not include hysteresis effects.

Ports

Conserving

+ — Positive terminal

electrical

Electrical conserving port associated with the piezo stack positive terminal.

- — Negative terminal

electrical

Electrical conserving port associated with the piezo stack negative terminal.

C — Case

mechanical

Mechanical translational conserving port associated with the case.

R — Rotor

mechanical

Mechanical translational conserving port associated with the rotor.

Parameters

Static Force

Parameterization — Static force parameterization

Specify from a datasheet (default) | Specify material properties

Select one of the following methods for static force parameterization:

• Specify from a datasheet — Provide datasheet parameters that the block converts to static force values.

• Specify material properties — Provide material properties that the block converts to static force values.

Stack area — Cross-sectional stack area

100 mm^2 (default) | positive scalar

Cross-sectional area of the stack.

Stack length — Stack length

36 mm (default) | positive scalar

Stack length when no load and no electrical potential are applied.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

No-load displacement at V0 volts — No-load unconstrained displacement

0.038 mm (default) | positive scalar

Unconstrained displacement of the stack when a voltage of V0 volts is applied.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Blocking force at V0 volts — Blocking force

3800 N (default) | positive scalar

Force the stack produces when a voltage of V0 volts is applied and the stack is physically prevented from expanding.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Test voltage V0 — Test voltage

120 V (default) | positive scalar

Voltage used to determine the no-load displacement and blocking force.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Capacitance — Capacitance

13 uF (default) | positive scalar

Capacitance.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Piezo layer thickness — Piezo layer thickness

0.3 mm (default) | positive scalar

Thickness of each layer in the piezo stack.

Dependencies

To enable this parameter, set Parameterization to Specify material properties.

Number of layers — Number of layers

50 (default) | scalar greater than or equal to 1

Number of layers in the piezo stack.

Dependencies

To enable this parameter, set Parameterization to Specify material properties.

Piezoelectric charge constant — Piezoelectric charge constant

500e-12 m/V (default) | positive scalar

Mechanical strain per unit electric field applied.

Dependencies

To enable this parameter, set Parameterization to Specify material properties.

Dielectric constant — Dielectric constant

2.1240e-08 F/m (default) | positive scalar

Permittivity or dielectric displacement per unit electric field measured at constant stress.

Dependencies

To enable this parameter, set Parameterization to Specify material properties.

Elastic compliance — Elastic compliance

19e-12 m^2/N (default) | positive scalar

Strain produced in a piezoelectric material per unit of stress applied.

Dependencies

To enable this parameter, set Parameterization to Specify material properties.

Dynamic Forces

Parameterization — Dynamic force parameterization

Specify from a datasheet (default) | Specify material properties

Select one of the following methods for dynamic force parameterization:

• Specify from a datasheet — Provide datasheet parameters that the block converts to dynamic force values.

• Specify material properties — Provide material properties that the block converts to dynamic force values.

Resonant frequency at constant field — Resonant frequency at constant field

inf kHz (default) | positive scalar

Frequency at which the actuator naturally resonates if mechanically perturbed with the electrical ports shorted.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Mechanical quality factor — Mechanical quality factor

inf (default) | positive scalar

Factor that affects the damping across the R and C mechanical ports.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Damping — Translational damping

0 N/(m/s) (default) | nonnegative scalar

Translational damping term.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Effective mass — Effective mass

0 g (default) | nonnegative scalar

Mass that approximates the distributed dynamics of the device and causes the stack to resonate at the correct frequency when attached to the mechanical R port. This mass is usually about one third of the actual stack mass.

Dependencies

To enable this parameter, set Parameterization to Specify from a datasheet.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2008b