Piezoelectric Valve

Piezoelectric valves are frequently employed in medical and laboratory applications. They have a number of advantages over competing technologies, including minimal heat dissipation, quiet operation, energy efficiency, durability, low weight and fast response times. These valves typically consist of a seal that is pushed up against an opening to close the valve, or moved away from the opening to open the valve, by a piezoelectric actuator. The actuator itself often has a complex internal structure, with stacked layers of piezoelectric separated by thin conducting layers that are connected together in such a way that the applied field leads to a large deformation.

This model shows how to model a piezoelectric valve in COMSOL. The valve is actuated by a stacked piezoelectric bimorph disc actuator, which compresses a hyperelastic seal against the valve opening to shut off the flow. The detailed construction and operation of the stacked actuator is considered in the model.

This application requires the Nonlinear Structural Materials Module.

Model Definition

Figure 1 shows both an axisymmetric slice through the geometry and a 3D rendering of the geometry. In this simple valve design a disc actuator compresses a hyperelastic seal directly onto an annular opening in a stainless steal support structure. The construction of the actuator itself is illustrated in Figure 2. The outer edge of the disc annulus is clamped to a stainless steel base and supporting structure. When a voltage is applied to the actuator the disc bends causing a vertical motion of the central opening of the annular actuator. With an appropriate polarity the opening moves downward, toward an annular opening in the base (supported at regular intervals by struts not included in the model). As the actuator moves towards the opening a hyperelastic seal is compressed against a mating structure, sealing up the opening. Within the model, the contact between the seal and the mating structure is modeled in detail, as is the operation of the actuator.

Figure 1: Axisymmetric model geometry (top) and full 3D geometry (bottom). Key components of the geometry are labeled.

Figure 2: Detail of the actuator and seal region, showing the construction of the actuator itself. The actuator consists of layers of PZT with metal layers between the various layers. Alternate metal layers are connected to ground whilst a voltage is applied to the other layers. Alternate layers of PZT are polarized in opposite directions. Two such actuators are stacked in such a manner that the applied potential causes contraction of one half of the beam and expansion of the other half. This results in a net bending moment acting on the beam.

Results and Discussion

Figure 3 shows the strain in the hyperelastic seal when the applied voltage is 60 V. The strain is localized in the vicinity of the contact region. Figure 4 shows the von Mises strain in the piezoelectric and its supporting structures at the same applied voltage. The stress is maximal in the PZT close to the contact. The potential within the actuator is shown in Figure 5. It is clear that the applied potentials match those shown in Figure 2. Finally the contact pressure is shown in Figure 6. The maximum pressure is 6×105 Pa on the surface of the seal that separates the inlet of the valve from the outlet.

Figure 3: ZZ component of the strain in the vicinity of the contact.

Figure 4: Three-dimensional visualization of the von Mises stress in the valve at an applied voltage of 50 V.

Figure 5: Electric potential inside the actuator in the vicinity of the contact.

Figure 6: Contact pressure as a function of position along the surface of the seal.

MEMS_Module/Piezoelectric_Devices/piezoelectric_valve

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

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In the tree, select .

Click .

Click

In the tree, select .

Click

Geometry 1

For convenience, the device geometry is inserted from an existing file. You can read the instructions for creating the geometry in the Appendix — Geometry Instructions.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file piezoelectric_valve_geom_sequence.mph.

In the toolbar, click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
V0	50[V]	50 V	Applied voltage

Definitions

+ Polarized

In the toolbar, click

Select Domains 5, 7, 9, 10, 12, 14, 18, 20, 22, 23, 25, 27, 32, 34, 36, 37, 39, 41, 47, 49, 51, 52, 54, and 56 only.

In the window for , type + Polarized in the text field.

- Polarized

In the toolbar, click

In the window for , type - Polarized in the text field.

Select Domains 4, 6, 8, 11, 13, 15, 17, 19, 21, 24, 26, 28, 31, 33, 35, 38, 40, 42, 46, 48, 50, 53, 55, and 57 only.

Piezoelectric

In the toolbar, click

In the window for , type Piezoelectric in the text field.

Locate the section. Under , click

In the dialog box, in the list, choose and .

Click .

Ground

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type Ground.

Select Boundaries 10, 14, 18, 22, 26, 30, 33, 36, 40, 44, 48, 52, 56, 59, 76, 80, 84, 88, 92, 96, 99, 109, 113, 117, 121, 125, 129, and 133 only.

Voltage

In the toolbar, click

In the window for , type Voltage in the text field.

Locate the section. From the list, choose .

Select Boundaries 12, 16, 20, 24, 28, 32, 38, 42, 46, 50, 54, 58, 78, 82, 86, 90, 94, 98, 111, 115, 119, 123, 127, and 131 only.

Mapped Mesh Steel

In the toolbar, click

In the window for , type Mapped Mesh Steel in the text field.

Select Domains 1, 2, 29, 43, and 44 only.

Mapped Mesh

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In the window for , locate the section.

Under , click

In the dialog box, in the list, choose and .

Click .

In the window for , type Mapped Mesh in the text field.

Contact Pair 1 (p1)

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and choose .

Select Boundaries 8, 62, 71, 72, and 150–153 only.

In the window for , locate the section.

Click to select the

toggle button.

Select Boundaries 61 and 66 only.

+Z Polarized

In the window, under click .

In the window for , type +Z Polarized in the text field.

-Z Polarized

Right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


	r	z
x1	1	0
x3	0	-1

In the text field, type -Z Polarized.

Solid Mechanics (solid)

Piezoelectric Material 2

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Piezoelectric Material 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Hyperelastic Material 1

In the toolbar, click

and choose .

Select Domain 16 only.

In the window for , locate the section.

From the list, choose .

In the κ text field, type 1e4[MPa].

Fixed Constraint 1

In the toolbar, click

and choose .

Select Domains 1, 2, 29, 43, and 44 only.

Contact 1a

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and choose .

In the window for , locate the section.

Under , click

In the dialog box, select in the list.

Click .

In the window for , locate the section.

From the list, choose .

Electrostatics (es)

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In the window for , locate the section.

From the list, choose .

Terminal 1

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and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the V0 text field, type V0.

Ground 1

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and choose .

In the window for , locate the section.

From the list, choose .

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

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In the tree, select .

Right-click and choose .

Materials

Lead Zirconate Titanate (PZT-5H) (mat1)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Steel AISI 4340 (mat2)

In the window, click .

Select Domains 1–3, 29, 30, and 43–45 only.

Seal

In the window, right-click and choose .

In the window for , type Seal in the text field.

Select Domain 16 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Model parameters	C10	0.37[MPa]	Pa	Mooney-Rivlin
Model parameters	C01	0.11[MPa]	Pa	Mooney-Rivlin
Density	rho	1800[kg/m^3]	kg/m³	Basic

In the toolbar, click

to close the window.

Mesh 1

Edge 1

In the toolbar, click

Select Boundaries 61, 62, 66, 71, and 150–153 only.

Size 1

Right-click and choose .

In the window for , locate the section.

Click

Select Boundaries 61 and 66 only.

Locate the section. From the list, choose .

Click the button.

Locate the section. Select the check box.

In the associated text field, type w0/100.

Size 2

In the window, right-click and choose .

In the window for , locate the section.

Click

Select Boundaries 62, 71, and 150–153 only.

Locate the section. From the list, choose .

Click the button.

Locate the section. Select the check box.

In the associated text field, type w0/50.

Size

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click the button.

Locate the section. In the text field, type w0.

Mapped 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Distribution 1

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Select Boundaries 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, and 97 only.

In the window for , locate the section.

In the text field, type 2.

Distribution 2

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Select Boundaries 36 and 109 only.

In the window for , locate the section.

In the text field, type 40.

Distribution 3

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In the window for , locate the section.

In the text field, type 1.

Select Boundaries 2, 63, 67, and 101 only.

Free Triangular 1

In the toolbar, click

In the window for , click

Compare the resulting mesh with that shown below. Note that there are purposefully very few elements in the rigid domains.

Study 1

Step 1: Stationary

In the window, under click .

In the window for , click to expand the section.

Select the check box.

Click

From the list in the column, choose , then specify values and unit as follows:


Parameter name	Parameter value list	Parameter unit
V0 (Applied voltage)	range(0,5,60)	V

For assistance in entering ranges of different kinds in the column, click the button to launch the dialog.

Solution 1 (sol1)

When modeling contact, both the contact pressure and the auxiliary pressure need to be manually scaled. It is good practice to modify the manual scaling of these variables to an appropriate value.

In the toolbar, click

In the window, expand the node.

The contact pressure is expected to be of the order of MPa, so set the scales accordingly.

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type 1e6.

In the window, under click .

In the window for , locate the section.

In the text field, type 1e6.

In the window, expand the node.

Use the Automatic Newton solver for faster and more reliable convergence.

In the window, expand the node, then click .

In the window for , click to expand the section.

From the list, choose .

In the toolbar, click

Results

Strain (ZZ component)

In the toolbar, click

and choose .

In the window for , type Strain (ZZ component) in the text field.

Locate the section. From the list, choose .

Surface 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

In the toolbar, click

Zoom in on the contact region and compare the plot with Figure 3.

Electric Field (Z component)

In the window, right-click and choose .

In the window, click .

In the window for , type Electric Field (Z component) in the text field.

Surface 1

In the window, click .

In the window for , click to collapse the section.

Click in the upper-right corner of the section. From the menu, choose .

In the toolbar, click

Contact Pressure

In the toolbar, click

and choose .

In the window for , type Contact Pressure in the text field.

Locate the section. From the list, choose .

Line Graph 1

Right-click and choose .

Select Boundaries 60, 61, 65, 66, and 73 only.

In the window for , click in the upper-right corner of the section. From the menu, choose .

In the toolbar, click

Appendix — Geometry Instructions

From the menu, choose .

In the window, click

In the window, click

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
t0	0.05[mm]	5E-5 m	Piezoelectric layer thickness
ID	7[mm]	0.007 m	Disc actuator inner diameter
OD	50[mm]	0.05 m	Disc actuator outer diameter
n	12	12	Number of layers in actuator
ts	0.2[mm]	2E-4 m	Thickness of seal
w0	0.5[mm]	5E-4 m	Through hole dimension
w1	ID/2	0.0035 m	Clamp region dimension
w2	ID/4	0.00175 m	Overall clamp dimension
h0	5t0n	0.003 m	Base thickness
deltaz	16[um]	1.6E-5 m	Contact offset at 0[V]