Assignment 2

Assignment-2 (Solution)

Questions:

1. Check the material properties of the rail component and calculate the speed of sound in steel rail=_______

2. The length of the rail is about 1000 mm.calculate the time takes for a shock wave to travel from one end of the rail to the other.

3. Time for sound to travel length of rail=______

4. Edit the engine file so that the stress wave can be monitored, moving from one end of the rail to the other during an impact -this will require a termination time equal to the time it takes for the sound to travel the length of the rail(set on/RUN card).

5. Set the frequency of animation output to a time that will give 20 animation steps(/ANIM/DT)

6. Change /print -10.

7. 3d meshing tetra mesh and hex mesh

• Repeat class examples and, maintain quality.
• Target tet size=5mm,hex size=10mm,tet collapse=0.15.

Solution:

1. The speed of sound through the rail component can be calculated using the element time-step formula as described in Equation (1).

`Deltat_e=l/c=l/sqrt(E/rho)`

...............................................................Equation (1)

Where,

`Delta t_e` is the element time-step

`l` is the length of the element

`E` is the Young's Modulus of the material

`rho` is the density of the material

Hence, from Equation (1), it is observed that;

`c = sqrt(E/rho)`

..................................Equation (2)

Also, from the file, FIRST_RUN_0000.rad illustrated in Figure 1, a Young's Modulus of 210000.0 MPa and a density of 0.0078 K kg/l (g/(cm)^3).

Figure 1: Material card describing the Jhonson-Cook material parameters.

Substituting the values in Equation (2) we get `c` = 5188.75 m/s (or mm/ms).

2. For a 1000 mm rail, assuming a unit 1D element of 1000mm size, the time for the shockwave to travel from one end to the other can be calculated using the formula described in Equation (1). Substituting the values of `c` as 5188.75 mm/ms and `l` as 1000mm, we get `Deltat`= 0.193 ms.

3. Similarly, assuming a 500 mm rail and assuming a unit 1D element of 500mm size, the time for the shockwave to travel from one end to the other can be calculated using the formula described in Equation (1). Substituting the values of `c` as 5188.75 mm/ms and `l` as 500mm, we get `Deltat`= 0.096 ms.

4. The ENGINE file was edited to include the termination time of 0.193 ms, which is equal to the time required for the shock wave to travel the rail from one end to the other. (Refer to text highlighted in orange in figure-2)

5. To obtain 20 animation steps, the TFREQ (Frequency for writing the animation files) was set as 0.000965 ms (0.096/20 ms). (Refer to text highlighted in Cyan in Figure-2)

6. For the /PRINT ENGINE Keyword, the line was changed from /PRINT/-10 to /PRINT/-1000/55. Here, -1000 signifies that the printout is made every 1000 cycles in the standard output as well in the output file. Also, 55 denotes the column headers will be printed after 55 lines of output. (refer to text highlighted in yellow in Figure-2)

The updated Engine file with the changes is illustrated in Figure-2 and is also included with this assignment as an attachment.

Figure-2: Updated ENGINE File.

7. 3D meshing (Tet and Hex Mesh)

Hub (Tetra Meshing)

Figure-3 illustrates the Hub geometry that has been used to generate tetra mesh.

Figure-3: Hub geometry for generating tetra mesh.

Here, a 2D surface mesh was generated for a target mesh size of 5 mm using 'tri' mesh type. Figure-4a describes the meshed geometry where elements are masked to illustrate the hollow volume generated due to the surface mesh. Furthermore, the 2d mesh has been transformed into a 3d solid meshed component using tetramesh option in 3d panel and has been illustrated in Figure-4b. Here, a tet collapse and min tetra size were set to 0.150 and 5 mm, respectively. The tet collapse for the mesh was checked using the check elems option in Tools. Zero elements were found having tet collapse less than 0.50. The model (.hm) file has been included for the Hub geometry has been included for review.

Figure-4: (a) 2D shell mesh generated over the Hub geometry with a few elements masked showing the hollow interior; (b) 3D tetra mesh generated over the Hub geometry with a few elements masked to show solid volume.

Cover (Volume Tetra Mesh)

Figure-5a illustrates the Hub geometry that has been used to generate tetra mesh. Figure-5b illustrates the 3D solid meshed component.

Figure-5: (a) Cover geometry for generating volume tetra mesh; (b) 3D solid meshed cover geometry with a few elements masked.

Here, the mesh was generated using the Volume Tetra options in 3D mesh panel. A 2D and 3D element type of Tri and tetras was selected. Also, the element size was set to 5mm. Here again, a tet collapse and min tetra size were set to 0.150 and 5 mm, respectively. The tet collapse for the mesh was checked using the check elems option in Tools. Zero elements were found having tet collapse less than 0.50. The model (.hm) file has been included for the Hub geometry has been included for review.

Furthermore, the tetra mesh was also generated using the Quick Tetra Mesh option in the utility browser for an element size of 5 mm. The meshed geometry is illustrated in Figure-6. The model (.hm) files containing the meshed components have been included with this assignment for review.

Figure-6: Meshed cover geometry using quick tetra feature.

Arm Bracket Meshing

Base (HEXA Meshing: 3D Solid Map)

Figure-7a illustrates the Base geometry of the Arm Bracket that has been used to generate Hexa mesh using solid map option.

Figure-7a: (a) Base geometry of arm bracket used for generating 3D solid map; (b) Surface mesh generated on top of the base as a reference for solid map generation.

For generating a 3D solid map, a surface mesh was generated using the automesh feature in 2D meshing panel using an element size of 10 mm. Here, the geometry was split to obtain better mesh flow, as illustrated in Figure-7a. The surface mesh generated is illustrated in Figure-7b.

A 3D mesh was generated using the element offset option found in 3D meshing panel. Five elements were generated through a thickness of 25 mm. The meshed base geometry is illustrated in Figure-8.

Figure-8: Meshed base geometry of arm bracket.

Arm Curve (HEXA Mehsing: Spin Elements)

Figure-9a illustrates the arm curve geometry of the arm bracket that has been using for generating HEXA elements using spin elements feature in 3D meshing panel. For the 2D elements required for spin element feature, the 3D elements of the base of the arm bracket were masked such that only the 2D elements on the top surface are visible and is illustrated in Figure-9b. Here, only the elements common between the base and the arm curve were selected. A centre point to the arc was generated to act as a rotating axis through x-axis for a 90-degree rotation.

Figure-9a: (a) Arm curve geometry of arm bracket used for generating Hexa elements using spin element feature; (b) Arm curve geometry with reference surface mesh of arm bracket base.

Figure 14 illustrates the meshed arm curve geometry.

Figure-14: Meshed arm curve geometry.

Arm Straight (HEXA Mehsing: Linear Solid)

Figure-15a illustrates the arm bracket geometry of the arm bracket assembly used for generating Hexa mesh using the linear solid feature in the 3D meshing panel. for reference, face mesh of the arm curve geometry was extracted using the faces feature in the tools panel. Also, a face mesh was generated on the face common to the arm curve and the arm straight. The number of elements on both the faces was kept equal for better mesh flow and is illustrated in Figure-15b.

Figure-15a: (a) Arm curve geometry of arm bracket used for generating Hexa elements using spin element feature; (b) Arm curve geometry with reference surface mesh of arm bracket base.

Figure 16 illustrates the meshed arm curve geometry.

Figure-16: Meshed arm curve geometry.

Boss (HEXA Mehsing: Solid Map)

Figure-17 illustrates the boss geometry of the arm bracket assembly used for generating Hexa mesh using the solid map feature in the 3D meshing panel.

Figure-17: Boss geometry of arm bracket assembly used for generating Hexa elements using a solid map.

Figure-18a describes the number of mesh elements required on the inner and outer rings of the boss to obtain good mesh flow for a surface mesh. Under solid map option in 3d meshing panel, the general option was selected. The source geom was selected as none, the along geom was set as mixed. The node path, as illustrated in Figure-18b was selected for mesh propagation reference. The surface elements generated in the previous step was selected for elems to drag. The elements size was set to 10 mm.

Figure-18: (a) Boss geometry of arm bracket assembly used for generating Hexa elements using solid map feature; (b) node path used for solid map propagation.

Meshed boss geometry is illustrated in Figure 19a. All QUAD4 elements generated during the meshing process were deleted. The complete meshed assembly is illustrated in Figure 19b. The final model (.hm) have been included for review.

Figure-19: (a) Meshed boss geometry ; (b) meshed arm bracket assembly.