Engineering Analysis with Ansys Software Episode 2 Part 1 potx

2 The calculated result for the first mode of vibration appears on ANSYS Graphics window as shown in Figure 4.71.. Then the window Library of Element Types as shown in Figure 4.79 opens.

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F

G

Figure 4.69 Window of Subspace Modal Analysis.

(2) The calculated result for the first mode of vibration appears on ANSYS Graphics

window as shown in Figure 4.71 The resonant frequency is shown as FRQE at the upper left side on the window

4.3.4.3 READ THE CALCULATED RESULTS OF HIGHER MODES OF

VIBRATION

C o m m a n d ANSYS Main Menu → General Postproc → Read Results → Next Set

Perform the same steps described in Section 4.2.4.2 and the calculated results from the second mode to the sixth mode of vibration are displayed on the windows as shown in Figures 4.72–4.76 From these vibration modes, it is found that a large radial displacement appears at the fifth mode of vibration

B

Figure 4.70 Window of Plot Deformed Shape.

Figure 4.71 The first mode of vibration

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Figure 4.72 The second mode of vibration

Figure 4.73 The third mode of vibration

Figure 4.74 The fourth mode of vibration.

Figure 4.75 The fifth mode of vibration

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Figure 4.76 The sixth mode of vibration

moving table using elastic hinges

A one-axis table using elastic hinges has been often used in various precision equip-ment, and the position of a table is usually controlled at nanometer-order accuracy using a piezoelectric actuator or a voice coil motor Therefore, it is necessary to confirm the resonant frequency in order to determine the controllable frequency region

Obtain the resonant frequency of a one-axis moving table using elastic hinges when the bottom of the table is fixed and a piezoelectric actuator is selected as an actuator:

• Material: Steel, thickness of the table: 5 mm

• Young’s modulus, E = 206 GPa, Poisson’s ratio ν = 0.3

• Density ρ = 7.8 × 103kg/m3

• Boundary condition: All freedoms are constrained at the bottom of the table and the region A indicated in Figure 4.77, where a piezoelectric actuator is glued

30 40

35 50

23 32

7.2

13

Piezoelectric Actuator

Figure 4.77 A one-axis moving table using elastic hinges

4.4.2.1 SELECT ELEMENT TYPE

In this example, the solid element is selected to analyze the resonant frequency of the moving table

C o m m a n d ANSYS Main Menu → Preprocessor → Element Type → Add/Edit/Delete

Then the window Element Types as shown in Figure 4.78 opens.

(1) Click [A] add button Then the window Library of Element Types as shown in

Figure 4.79 opens

(2) Select [B] Solid in the table of Library of Element Types and, then, select [C]

Quad 4node 42 and Element type reference number is set to 1 and click [D] Apply Select [E] Brick 8node 45, as shown in Figure 4.80.

(3) Element type reference number is set to 2 and click [F] OK button Then the window Library of Element Types is closed.

(4) Click [G] Close button in the window of Figure 4.81 where the names of selected

elements are indicated

4.4.2.2 MATERIAL PROPERTIES

This section describes the procedure of defining the material properties of solid element

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A

Figure 4.78 Window of Element Types.

1

D

Figure 4.79 Window of Library of Element Types.

C o m m a n d ANSYS Main Menu → Preprocessor → Material Props → Material Models

(1) Click the above buttons in order and the window Define Material Model

Behavior opens as shown in Figure 4.82.

(2) Double click the following terms in the window

Structural → Linear → Elastic → Isotropic

2

F

E

Figure 4.80 Window of Library of Element Types.

A

G

Figure 4.81 Window of Element Types.

Then the window Linear Isotropic Properties for Material Number 1 opens (3) Input Young’s modulus of 206e9 to EX box and Poisson’s ratio of 0.3 to PRXY box.

Next, define the value of density of material

(1) Double click the term of Density, and the window Density for Material

Number 1 opens.

(2) Input the value of Density, 7800 to DENS box and click OK button Finally, close the window Define Material Model Behavior by clicking X mark at the upper

right end

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Figure 4.82 Window of Define Material Model Behavior.

A

B

Figure 4.83 Window of Create Keypoints in Active Coordinate System.

4.4.2.3 CREATE KEYPOINTS

To draw the moving table for analysis, the method using keypoints is described in this section

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Create → Keypoints → In

Active CS

The window Create Keypoints in Active Coordinate System opens (Figure 4.83) (1) Input A 0,0 to X,Y,Z Location in active CS box, and then click [B] Apply button.

Do not click OK button at this stage.

Table 4.3 Coordinates of KPs

(2) In the same window, input the values as shown in Table 4.3 in order When all

values are inputted, click OK button.

(3) Then all input keypoints appear in ANSYS Graphics window as shown in

Figure 4.84

4.4.2.4 CREATE AREAS FOR THE TABLE

Areas are created from keypoints by proceeding the following steps

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Create → Arbitrary →

Through KPs

The window Create Area thru KPs opens (Figure 4.85).

(1) Pick the keypoints, 1, 2, 3, and 4 in order and click [A] Apply button in Figure 4.85 Then pick keypoints 5, 6, 7, and 8 and click [B] OK button Figure 4.86

appears

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Operate → Booleans →

Subtract → Areas

(2) Click the area of KP No 1–4 and OK button Then click the area of KP No 5–8 and OK button The drawing of the table appears as shown in Figure 4.87.

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Figure 4.84 ANSYS Graphics window.

A B

Figure 4.85 Window of Create Area thru KPs.

Figure 4.86 ANSYS Graphics window.

Figure 4.87 ANSYS Graphics window.

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Figure 4.88 ANSYS Graphics window.

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Create → Arbitrary →

Through KPs

(3) Pick keypoints 9, 10, 11, and 12 in order and click [A] Apply button in Figure 4.85 Then pick keypoints 13, 14, 15, and 16 and click [B] OK button Figure 4.88

appears

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Operate → Booleans →

Add → Areas

The window Add Areas opens (Figure 4.89).

(4) Pick three areas on ANSYS Graphics window and click [A] OK button Then

three areas are added as shown in Figure 4.90

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Create → Areas → Circle →

Solid Circle

The window Solid Circle Area opens (Figure 4.91).

(5) Input the values of 0, 12.2e −3, 2.2e−3 to [X], [Y] and Radius boxes as shown in

Figure 4.91 and click [A] Apply button Then continue to input the coordinates

Figure 4.89 Window of Add Areas Figure 4.90 ANSYS Graphics window.

of the solid circle as shown in Table 4.4 The radius of all solid circles is 0.0022 When all values are inputted, the drawing of the table appears as shown in Figure

4.92 Click [B] OK button.

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Operate → Booleans →

Subtract → Areas

(1) Subtract all circular areas from the rectangular area by executing the above steps Then Figure 4.93 is displayed

4.4.2.5 CREATE MESH IN AREAS

C o m m a n d ANSYS Main Menu → Preprocessor → Meshing → Mesh Tool

The window Mesh Tool opens (Figure 4.94).

(1) Click [A] Lines Set and the window Element Size on Picked Lines opens

(Figure 4.95)

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A B

Figure 4.91 Window of Solid Circular Area.

Table 4.4 Coordinates of solid circles

0.0022

(2) Click [B] Pick All button and the window Element Sizes on Picked Lines opens

(Figure 4.96)

(3) Input [C] 0.001 to SIZE box and click [D] OK button.

(4) Click [E] Mesh of the window Mesh Tool (Figure 4.97) and, then, the window

Mesh Areas opens (Figure 4.98).

Figure 4.92 ANSYS Graphics window.

Figure 4.93 ANSYS Graphics window.

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A

Figure 4.94 Window of Mesh Tool.

B

Figure 4.95 Window of Element Size on Picked Lines.

D

Figure 4.96 Window of Element Sizes on Picked Lines.

(5) Pick the area of the table on ANSYS Graphics window and click [F] OK button Then the meshed drawing of the table appears on ANSYS Graphics window as

shown in Figure 4.99

Next, by performing the following steps, the thickness of 5 mm and the mesh size are determined for the drawing of the table

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Operate → Extrude →

Elem Ext Opts

The window Element Extrusion Options opens (Figure 4.100).

(1) Input [A] 5 to VAL1 box This means that the number of element divisions is 5 in the thickness direction Then, click [B] OK button.

C o m m a n d ANSYS Main Menu → Preprocessor → Modeling → Areas → By XYZ Offset

The window Extrude Area by Offset opens (Figure 4.101).

(1) Pick the area of the table on ANSYS Graphics window and click [A] OK button Then, the window Extrude Areas by XYZ Offset opens (Figure 4.102).

(2) Input [B] 0,0,0.005 to DX,DY,DZ box and click [C] OK button Then, the drawing

of the table meshed in the thickness direction appears as shown in Figure 4.103

4.4.2.6 BOUNDARY CONDITIONS

The table is fixed at both the bottom and the region A of the table

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E

Figure 4.97 Window of Mesh Tool.

F

Figure 4.98 Window of Mesh Areas.

Figure 4.99 ANSYS Graphics window.

A

B

Figure 4.100 Window of Element Extrusion Options.