Models.mems.Microgripper

Solved with COMSOL Multiphysics 4.4

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Introduction

This is a tutorial model of a piezoelectrically actuated microgripper with mechanical contact. The microgripper contains a piezoelectric actuator that operates in the longitudinal mode. Elongation in the longitudinal direction creates a lifting movement to the structure. Simultaneous contraction in the transversal direction closes the gripper and allows it to move objects, Ref. 1.

Model Definition

The model geometry is shown in Figure 1.

Figure 1: Microgripper geometry. The part in the middle represents the piezoelectric actuator.

The actuator is made of lead zirconate titanate (PZT-5A), and the gripper itself consists of polycrystalline silicon (poly-Si). Both materials are available in COMSOL Multiphysics’ material libraries. The material properties are prescribed using the rotated coordinate system shown in Figure 2.

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Figure 2: Orientation of the coordinate system for the material.

The gripper is operated by applying an electric potential difference at the piezoelectric actuator ends. When the arms come together, a mechanical contact is modeled including the contact pressure computations.

Results and Discussion

The applied voltage gradually increases from zero to the value of 6000 V. This causes the gripper arms to close up and eventually come in contact with each other.

The final distributions of the stress and displacement magnitude in the deformed microgripper are shown in Figure 3 and Figure 4, respectively.

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Figure 3: Logarithm of the von Mises stress in the gripper for V0 = 6000 V.

Figure 4: Total displacement distribution at V0 = 6000 V.



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The resulting contact pressure at the end surfaces is shown in Figure 5.

Figure 5: Contact pressure at V0 = 6000 V.

Notes About the COMSOL Implementation

In this example you learn how to model a piezoelectric material aligned in a user-defined coordinate system and how to include contact modeling.

You create the geometry within COMSOL Multiphysics. First, draw a 2D footprint as shown in Figure 6, and then apply extrusion to create the final 3D geometry. Use a swept mesh as shown in Figure 7.

You set up a contact pair for two end surfaces of the gripper arms and obtain the solution via a parametric sweep over the applied voltage V0.

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Figure 6: Intermediate 2D geometry

Figure 7: Meshed final geometry.



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References

1. R. Keoschkerjan and H. Wurmus, “A Novel Microgripper with Parallel Movement of Gripping Arms,” Proc. Actuator 2002, 8th International Conference on New Actuators, Bremen, Germany, June 10–12, pp. 321–324, 2002.

Model Library path: MEMS_Module/Piezoelectric_Devices/microgripper

Modeling Instructions

From the File menu, choose New.

N E W

1 In the New window, click the Model Wizard button.

M O D E L W I Z A R D

1 In the Model Wizard window, click the 3D button.

2 In the Select physics tree, select Structural Mechanics>Piezoelectric Devices (pzd).

3 Click the Add button.

4 Click the Study button.

5 In the tree, select Preset Studies>Stationary.

6 Click the Done button.

G E O M E T R Y 1

1 In the Model Builder window, under Component 1 (comp1) click Geometry 1.

2 In the Geometry settings window, locate the Units section.

3 From the Length unit list, choose µm.

Work Plane 1 (wp1)1 On the Geometry toolbar, click Work Plane.

This gives a default work plane aligned with the xy-plane at z = 0.

Rectangle 1 (r1)1 In the Model Builder window, under Component 1 (comp1)>Geometry 1>Work Plane

1 (wp1) right-click Plane Geometry and choose Rectangle.

2 In the Rectangle settings window, locate the Size section.

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3 In the Width edit field, type 10.

4 Locate the Position section. In the xw edit field, type -5.

5 In the yw edit field, type -1.

6 Click the Build Selected button.

7 Click the Zoom Extents button on the Graphics toolbar.

Rectangle 2 (r2)1 Right-click Plane Geometry and choose Rectangle.


3 In the Width edit field, type 2.

4 In the Height edit field, type 10.








5 In the yw edit field, type -1.







5 In the yw edit field, type 19.5.



Fillet 1 (fil1)1 On the Work plane toolbar, click Fillet.



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2 On the object r4, select Point 3 only.

3 In the Fillet settings window, locate the Radius section.

4 In the Radius edit field, type 0.2.


Next, use the Bezier Polygon as instructed below. Alternatively, you can use the Draw line tool and click on the top-left and top-right corners of r3 and the bottom-right and bottom-left corners of fil1.

Bézier Polygon 1 (b1)1 Right-click Plane Geometry and choose Bézier Polygon.

2 In the Bézier Polygon settings window, locate the Polygon Segments section.

3 Find the Added segments subsection. Click the Add Linear button.

4 Find the Control points subsection. In row 1, set xw to -6.

5 In row 1, set yw to 15.

6 In row 2, set xw to -5.




10 In row 2, set yw to 19.5.






16 Click the Close Curve button.

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Mirror 1 (mir1)1 On the Work plane toolbar, click Mirror.

2 Select the objects fil1, r3, and b1 only.

3 In the Mirror settings window, locate the Input section.

4 Select the Keep input objects check box.



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Extrude 1 (ext1)1 On the Geometry toolbar, click Extrude.

2 In the Extrude settings window, locate the Distances from Plane section.

3 In the table, enter the following settings:


5 Click the Go to Default 3D View button on the Graphics toolbar.

Distances (µm)

2

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The model geometry is now complete.

G L O B A L D E F I N I T I O N S

Parameters1 On the Home toolbar, click Parameters.

2 In the Parameters settings window, locate the Parameters section.


This is a stacked actuator, and V0 corresponds to the number of layers multiplied by the applied potential of the layer.

D E F I N I T I O N S

Rotated System 2 (sys2)1 On the Definitions toolbar, click Coordinate Systems and choose Rotated System.

2 In the Rotated System settings window, locate the Settings section.

Name Expression Value Description

V0 6000[V] 6000 V Applied voltage



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3 Find the Euler angles (Z-X-Z) subsection. In the β edit field, type 90[deg].

This coordinate system defines the orientation of the piezoelectric material's main polarization axis.

4 On the Definitions toolbar, click Pairs and choose Contact Pair.

5 Select Boundaries 21 and 27 only.

6 In the Pair settings window, locate the Destination Boundaries section. Select Boundaries 30 and 37 only.

M A T E R I A L S

On the Home toolbar, click Add Material.

A D D M A T E R I A L

1 Go to the Add Material window.

2 In the tree, select MEMS>Semiconductors>Poly-Si.

3 In the Add material window, click Add to Component.

M A T E R I A L S

A D D M A T E R I A L

1 Go to the Add Material window.

2 In the tree, select Piezoelectric>Lead Zirconate Titanate (PZT-5A).

3 In the Add material window, click Add to Component.

M A T E R I A L S

Lead Zirconate Titanate (PZT-5A) (mat2)1 In the Model Builder window, under Component 1 (comp1)>Materials click Lead

Zirconate Titanate (PZT-5A) (mat2).

2 Select Domain 5 only.

All other domains use polysilicon as the material.

P I E Z O E L E C T R I C D E V I C E S ( P Z D )

Piezoelectric Material 11 In the Model Builder window, expand the Component 1 (comp1)>Piezoelectric Devices

(pzd) node, then click Piezoelectric Material 1.

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2 In the Piezoelectric Material settings window, locate the Coordinate System Selection section.

3 From the Coordinate system list, choose Rotated System 2 (sys2).

Linear Elastic Material 11 On the Physics toolbar, click Domains and choose Linear Elastic Material.

2 Select Domains 1–4 and 6–8 only.

Ground 11 On the Physics toolbar, click Boundaries and choose Ground.

2 Select Boundary 23 only.

Electric Potential 11 On the Physics toolbar, click Boundaries and choose Electric Potential.


3 In the Electric Potential settings window, locate the Electric Potential section.

4 In the V0 edit field, type V0.

Fixed Constraint 11 On the Physics toolbar, click Boundaries and choose Fixed Constraint.


Contact 11 On the Physics toolbar, click Pairs and choose Contact.

2 In the Contact settings window, locate the Pair Selection section.

3 In the Pairs list, select Contact Pair 1.

M E S H 1

Free Triangular 11 In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and

choose Free Triangular.

2 Select all boundaries on top of the geometry.

Size 11 Right-click Component 1 (comp1)>Mesh 1>Free Triangular 1 and choose Size.

2 In the Size settings window, locate the Element Size section.

3 From the Predefined list, choose Extra fine.




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Swept 1In the Model Builder window, right-click Mesh 1 and choose Swept.

Distribution 11 In the Model Builder window, under Component 1 (comp1)>Mesh 1 right-click Swept

1 and choose Distribution.

2 In the Distribution settings window, locate the Distribution section.

3 In the Number of elements edit field, type 2.


S T U D Y 1

Step 1: Stationary1 In the Model Builder window, expand the Study 1 node, then click Step 1: Stationary.

2 In the Stationary settings window, click to expand the Study extensions section.

3 Locate the Study Extensions section. Select the Auxiliary sweep check box.

4 Click Add.


Solver 1On the Study toolbar, click Show Default Solver.

Before setting up the solver, define a plot to display while solving.

R E S U L T S

3D Plot Group 11 On the Home toolbar, click Add Plot Group and choose 3D Plot Group.

2 In the Model Builder window, under Results right-click 3D Plot Group 1 and choose Surface.

3 Right-click Results>3D Plot Group 1>Surface 1 and choose Deformation.

4 In the Deformation settings window, locate the Scale section.

5 Select the Scale factor check box.

Auxiliary parameter Parameter value list

V0 range(0,600,6000)

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S T U D Y 1

Step 1: Stationary1 In the Model Builder window, under Study 1 click Step 1: Stationary.

2 In the Stationary settings window, click to expand the Results while solving section.

3 Locate the Results While Solving section. Select the Plot check box.

Solver 11 In the Model Builder window, expand the Study 1>Solver Configurations>Solver

1>Dependent Variables 1 node, then click Electric potential (comp1.V).

2 In the Field settings window, locate the Scaling section.

3 From the Method list, choose Manual.

4 In the Scale edit field, type 1000.

5 In the Model Builder window, under Study 1>Solver Configurations>Solver

1>Dependent Variables 1 click Contact pressure, contact pair p1 (comp1.pzd.Tn_p1).


7 In the Scale edit field, type 1e6.

8 In the Model Builder window, under Study 1>Solver Configurations>Solver

1>Dependent Variables 1 click Displacement field (Material) (comp1.u).


10 In the Scale edit field, type 1e-6.

11 On the Home toolbar, click Compute.

R E S U L T S

3D Plot Group 1Compare the finished displacement-field plot with that in Figure 4.

Follow the steps below to reproduce the plot in Figure 3.

3D Plot Group 21 In the Model Builder window, under Results right-click 3D Plot Group 1 and choose

Duplicate.

2 In the Model Builder window, expand the 3D Plot Group 2 node, then click Surface 1.

3 In the Surface settings window, locate the Expression section.

4 In the Expression edit field, type log10(pzd.mises+1).

On the 3D plot group toolbar, click Plot.



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Next, reproduce the plot in Figure 5 of the contact pressure at the end surfaces as follows.

Data Sets1 On the Results toolbar, click More Data Sets and choose Surface.



2 In the 3D Plot Group settings window, locate the Data section.

3 From the Data set list, choose Surface 1.

4 Right-click Results>3D Plot Group 3 and choose Surface.

5 In the Surface settings window, locate the Expression section.

6 Click Contact pressure, contact pair p1 (pzd.Tn_p1) in the upper-right corner of the section. On the 3D plot group toolbar, click Plot.


Finally, add a coordinate system plot to verify that the piezoelectric material has the correct orientation.


2 On the 3D plot group toolbar, click More Plots and choose Coordinate System Volume.

3 In the Coordinate System Volume settings window, locate the Coordinate System section.

4 From the Coordinate system list, choose Rotated System 2 (sys2).

5 On the 3D plot group toolbar, click Plot.


Compare the resulting plot with that in Figure 2.

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Models.mems.Microgripper

Documents

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i cfigure

i creferences1

comsol implementationin

mechanical contact

microgripper geometry

gripper arms