Engineering Analysis with Ansys Software Episode 2 Part 1 potx

Ch04-H6875.tex 24/11/2006 17: 47 page 184 184 Chapter 4 Mode analysis 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 Command 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. Ch04-H6875.tex 24/11/2006 17: 47 page 185 4.3 Mode analysis of a suspension for Hard-disc drive 185 A B Figure 4.70 Window of Plot Deformed Shape. Figure 4.71 Thefirstmodeofvibration. Ch04-H6875.tex 24/11/2006 17: 47 page 186 186 Chapter 4 Mode analysis Figure 4.72 Thesecondmodeofvibration. Figure 4.73 The third mode of vibration. Ch04-H6875.tex 24/11/2006 17: 47 page 187 4.3 Mode analysis of a suspension for Hard-disc drive 187 Figure 4.74 The fourth mode of vibration. Figure 4.75 The fifth mode of vibration. Ch04-H6875.tex 24/11/2006 17: 47 page 188 188 Chapter 4 Mode analysis Figure 4.76 The sixth mode of vibration. 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 4.4.1 Problem description 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 ×10 3 kg/m 3 • 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. Ch04-H6875.tex 24/11/2006 17: 47 page 189 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 189 A 30 40 35 50 23 32 12.2 15 20 7.2 7.2 13 Piezoelectric Actuator Figure 4.77 A one-axis moving table using elastic hinges. 4.4.2 Create a model for analysis 4.4.2.1 SELECT ELEMENT TYPE In this example, the solid element is selected to analyze the resonant frequency of the moving table. Command 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. Ch04-H6875.tex 24/11/2006 17: 47 page 190 190 Chapter 4 Mode analysis A Figure 4.78 Window of Element Types. 1 D B C Figure 4.79 Window of Library of Element Types. Command 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 Ch04-H6875.tex 24/11/2006 17: 47 page 191 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 191 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) InputYoung’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. Ch04-H6875.tex 24/11/2006 17: 47 page 192 192 Chapter 4 Mode analysis 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. Command 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. Ch04-H6875.tex 24/11/2006 17: 47 page 193 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 193 Table 4.3 Coordinates of KPs KP No. X Y 100 2 0.04 0 3 0.04 0.05 4 0 0.05 5 0.005 0.01 6 0.035 0.01 7 0.035 0.045 8 0.005 0.045 9 0.005 0.015 10 0.013 0.015 11 0.013 0.02 12 0.005 0.02 13 0.023 0.01 14 0.032 0.01 15 0.032 0.02 16 0.023 0.02 (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. Command 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. Command 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. [...]... 4.95) 19 8 Chapter 4 Mode analysis B Figure 4. 91 Table 4.4 A Window of Solid Circular Area Coordinates of solid circles No X Y Radius 1 2 3 4 5 6 7 8 9 10 0 0.005 0.035 0.04 0 0.005 0.035 0.04 0.00 72 0.00 72 0.0 12 2 0.0 12 2 0.0 12 2 0.0 12 2 0.0 428 0.0 428 0.0 428 0.0 428 0. 015 0. 02 0.0 022 (2) Click [B] Pick All button and the window Element Sizes on Picked Lines opens (Figure 4.96) (3) Input [C] 0.0 01 to SIZE... 4.84 ANSYS Graphics window B Figure 4.85 Window of Create Area thru KPs A 4.4 Mode analysis of a one-axis precision moving table using elastic hinges Figure 4.86 ANSYS Graphics window Figure 4.87 ANSYS Graphics window 19 5 19 6 Chapter 4 Mode analysis Figure 4.88 Command ANSYS Graphics window ANSYS Main Menu → Preprocessor → Modeling → Create → Arbitrary → Through KPs (3) Pick keypoints 9, 10 , 11 , and 12 . .. 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 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 19 7 A 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 0.0 022 When... Areas opens (Figure 4.98) 4.4 Mode analysis of a one-axis precision moving table using elastic hinges Figure 4. 92 ANSYS Graphics window Figure 4.93 ANSYS Graphics window 19 9 20 0 Chapter 4 Mode analysis A B Figure 4.94 Window of Mesh Tool Figure 4.95 Window of Element Size on Picked Lines 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 20 1 C D Figure 4.96 Window of Element... opens (Figure 4 .1 02) (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 .10 3 4.4 .2. 6 BOUNDARY CONDITIONS The table is fixed at both the bottom and the region A of the table 20 2 Chapter 4 Mode analysis E F Figure 4.97 Window of Mesh Tool Figure 4.98 Window of Mesh Areas Figure 4.99 ANSYS Graphics... window Element Extrusion Options opens (Figure 4 .10 0) (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 Command ANSYS Main Menu → Preprocessor → Modeling → Areas → By XYZ Offset The window Extrude Area by Offset opens (Figure 4 .10 1) (1) Pick the area of the table on ANSYS Graphics window and click [A] OK button Then,... button in Figure 4.85 Then pick keypoints 13 , 14 , 15 , and 16 and click [B] OK button Figure 4.88 appears Command 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 Command ANSYS Main Menu → Preprocessor → Modeling... as shown in Figure 4. 92 Click [B] OK button Command 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 Command CREATE MESH IN AREAS ANSYS Main Menu → Preprocessor → Meshing → Mesh Tool The window Mesh Tool opens (Figure 4.94) (1) Click [A] Lines Set... 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 Command ANSYS Main Menu → Preprocessor → Modeling → Operate → Extrude →... fixed at both the bottom and the region A of the table 20 2 Chapter 4 Mode analysis E F Figure 4.97 Window of Mesh Tool Figure 4.98 Window of Mesh Areas Figure 4.99 ANSYS Graphics window A B Figure 4 .10 0 Window of Element Extrusion Options . circles No. X Y Radius 1 0 0.0 12 2 2 0.005 0.0 12 2 3 0.035 0.0 12 2 4 0.04 0.0 12 2 5 0 0.0 428 0.0 022 6 0.005 0.0 428 7 0.035 0.0 428 8 0.04 0.0 428 9 0.00 72 0. 015 10 0.00 72 0. 02 (2) Click [B] Pick All. glued. Ch04-H6875.tex 24 /11 /20 06 17 : 47 page 18 9 4.4 Mode analysis of a one-axis precision moving table using elastic hinges 18 9 A 30 40 35 50 23 32 12 . 2 15 20 7 .2 7 .2 13 Piezoelectric Actuator Figure. hinges 19 3 Table 4.3 Coordinates of KPs KP No. X Y 10 0 2 0.04 0 3 0.04 0.05 4 0 0.05 5 0.005 0. 01 6 0.035 0. 01 7 0.035 0.045 8 0.005 0.045 9 0.005 0. 015 10 0. 013 0. 015 11 0. 013 0. 02 12 0.005 0. 02 13