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4. Solution in I-DEAS

In this section you will evaluate the solution, and apply fixes to the model, in case the solution could not be generated.

Once I-DEAS has finished with the calculations, check the status frame in the lower left corner of the screen. If no errors occurred, the status should read No warnings of errors encountered in last run, as shown in Figure 1.67. If this is the case, you can proceed to viewing the solution. If error have occured, you may be able to fix the model as explained below in sub section "Fixing the mesh".

4.1 If I-DEAS has not encountered errors ...

Check the status in the left lower frame of the I-DEAS window. If the message reads No warnings or errors encountered in last run, I-DEAS will have solved the model. If there are warnings, but no errors, you will similarly be able to view the solution. See section Fixing a degenerate mesh below, if I-DEAS has encountered errors, otherwise continue right here.

Switch to the task Post Processing. In this task, you will be able to view the different solutions.

Figure 1.67
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Click on the first icon, named Results. You will start with this step every time you would like to view a different solution.

Figure 1.68
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In the upcoming dialog, you will specify what solutions you would like to view. The main list box contains all available soltutions. In the case of this tutorial, we have solved for 4 different types: Displacement, Reaction Force, Stress, and Strain Energy. In the dialog, you can now designate which of these solutions you would like to view. For now, accept the default settings and hit OK.

Figure 1.69
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To view the solution, click on the icon featuring an arrow pointing to the right, as shown in Figure 1.70.

Figure 1.70
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Next you will be selecting all components for which you would like to view the solution. Move your mouse cursor into the visualization frame and click on the right mouse button. Select All done from the available options.

Figure 1.71
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The results are now presented to you in the visualization frame. The differently colored regions denote different stress/strain/etc. values, where the green and blue regions experience less than yellow and red regions. Ideally, you would like to minimize red regions, as they are most destructive to the structure.

The results in figure 6 show not only the Stress values, but also enforce the Displacement in a highly exaggerated way, so as to enhance the visual observations.

Figure 1.72
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A solution can be viewed either in its pure form ( Display Results), or can be applied to the model as a displacement (Displacement Results). To view a particular solution, select the solution in the listbox, and click on the large arrow button next to Display Results or Displacement Results to "activate" the solution. You can "deactivate" the solution by clicking on Clear next to the respective Results field.

Figure 1.73
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Figure 1.74 shows the same stress values as Figure 1.72, with the exception of the Displacement.

Figure 1.74
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4.2 Interpretation of Stress values

The purpose of performing stress analysis on the wheel is to predict failure of its material. In order to get a good sense of how the wheel's material performs under roughly 300 kg of pressure, we will need to compare the maximum effective stress values (also called Von Mises criterion) observed in the results to a known value that represents the limits of performance for that material.

In the case of the wheel used in this tutorial, the maximum predicted stress value is 4.18 * 106 Pascals. Depending on the units set in the beginning of the analysis, this value may appear in psi (pounds per square inch), or kpsi (1000 psi). The numeric value can be read from the vertical color bar, where dark blue is the minimum stress and red is the maximum stress.

Comparisons of the predicted maximum stress can now be made to commonly known and experimentally derived values of yield strength for the appropriate material. The yield strength tends to refer to a value at which the material exhibits substantial deformation or breaks. Steel of different quality has different yield strengths:

Type of Steel Yield Strength (PSI) Yield Strength (Pa)
Iron and Carbon Steel of different types 18,000 - 35,000 1.241 * 108 - 2.413 * 108
Iron-Copper and Copper Steel of different types 38,300 - 55,000 2.641 * 108 - 3.793 * 108
Iron-Nickel and Nickel Steel of different types 17,000 - 65,000 1.172 * 108 - 4.482 * 108
Low Alloy Steel of different types 46,500 - 55,000 3.206 * 108 - 3.793 * 108
Stainless Steel of different types 30,000 - 170,000 2.068 * 108 - 1.172 * 109
Table 1.2
Comparing the maximum predicted stress value of 4.18 * 106 Pa to the yield strength of the lowest quality steel with 1.172 * 108, we notice that the material would reach its limit of performance at 28 times the predicted value. It is thus well in the material's operating range. For a high quality steel, the factor is as high as 280. Remember that this is true for a maximum pressure of 3000N (roughly 300kg weight) on the wheel. The maximum stress value will obviously increase, if the pressure on the wheel increases.

While the analysis of this particular wheel is correct, we cannot generally assume that the following two properties will hold for a motorcycle wheel:

  1. Firstly, little material has been removed from the wheel, thus leaving behind a very solid structure of spokes, which highly decreases the maximum predicted stress. It should be trivial to understand that a wheel with N number of thin spokes is structurally less sound than a wheel with N number of much thicker spokes.
  2. Secondly, and more importantly, the width of the wheel is much too large for a typical motorcycle. If we were to build a thinner wheel, then the pressure would distribute over a much smaller surface area, thus increasing the maximum predicted stress value.

While the numeric values give us the minimum and maximum predicted stress values, we have yet to identify the specific areas, in which these values are observed. To this end we will take a closer look at the graphical, rainbow-colored representation of stress on the wheel. Most of the wheel, in particular the top and side region experiences little stress (blue regions), whereas the higher values of stress concentrate near the bottom region, between street level and hub. This corresponds to the region in which all of the pressure has been applied.

While the spokes are still in a blue/cyan/green range of stress, we clearly note the extreme stress (orange/red) in the corners, where spokes and rim meet. It is generally the goal of such analysis to identify regions of high stress, which can then be re-modeled to minimize and spread out the stress. In the case of this wheel, the corners between spokes and rim have been rounded off, but obviously not enough to spread out the stress. In most structural designs, you will find many rounded corners, as this tends to minimize the stress.

4.3 Interpretation of Displacement values

Displacement (deformation) values are interpreted in a fashion similar to that of stress values. The reported values of displacement are in Meters, if the units were set to Newton/Meter in the beginning of the analysis. Depending on the units, the minimum and maximum reported values must be interpreted accordingly. A vertical color bar graphically corelates the minimum, intermediate, and maximum displacement values to specific regions of the wheel.

In the case of our wheel, the maximum displacement takes place in the bottom regions, that is again the region in which the pressure was applied. According to the numeric values, the maximum displacement is roughly 3.44 * 10-6 Meters, i.e. 3.44 micro Meters. We must again objectively consider the very solid structure of the wheel and the relatively small pressure applied.

In a later section, we will look at a comparison of different types of wheels and their respective stress and displacement values.

4.4 Fixing a degenerate mesh

If you encounter errors during the computation, the error may possibly lie in a few degenerate mesh elements. While this is not always the case, you may wish to attempt fixing the mesh by applying the following procedure. If this does not solve the problem, you will need to consider using a simpler model for analysis. In this case, you should consult with the instructor.

If the status frames displays a message regarding errors found during the solution step, you will need to fix the mesh.

I-DEAS offers a function to fix degenerate mesh elements. In the task Meshing, find the icon labeled Move Mid Nodes, as shown in Figure 1.75.

Figure 1.75
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Click on the arrow next to the icon in row 3, column 3, as shown in Figure 1.76.

Figure 1.76
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In the expanded list of icons, select Tetra Fix.

Figure 1.77
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During the process of fixing the mesh, I-DEAS displays the mesh elements that are distorted or damaged otherwise.

Figure 1.78
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Once Tetra Fix has completed, the status window will report how many, if any, mesh elements have been repaired. You can now proceed to creating a solution, solving, and viewing the results.

Figure 1.79
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4.5 Example Analysis for several wheels

If you encounter errors during the computation, the error may possibly lie in a few degenerate mesh elements. While this is not always the case, you may wish to attempt fixing the mesh by applying the following procedure. If this does not solve the problem, you will need to consider using a simpler model for analysis. In this case, you should consult with the instructor.

Table 1.3 exhibits the wheel used in this tutorial, and 2 analyses (left to right, top to bottom): Shaded wheel, Stress, Displacement, and Stress combined with Displacement.

Table 1.3
Table 1.4 exhibits a solid wheel, much like the one used on the V-Rod, and 2 analyses (left to right, top to bottom): Shaded wheel, Stress, Displacement, and Stress combined with Displacement from 3 views.

Table 1.4
Table 1.5 exhibits a wheel with spokes, and 2 analyses (left to right, top to bottom): Shaded wheel, Stress, Displacement, and Stress combined with Displacement from 3 views.

Note the much smaller mesh size in this model. The mesh size needs to be small in order to adjust to the relatively fine structure of the spokes. If you intend to perform an analysis on a model that requires a fine mesh, you may find that I-DEAS runs out of memory. In this case you should consult with Alex to increase the available memory for I-DEAS, a relatively quick procedure.

Table 1.5
Table 1.6 exhibits a structurally unsound wheel, and 2 analyses (left to right, top to bottom): Shaded wheel, Stress, Displacement, and Stress combined with Displacement.

Table 1.6

4.6 Comparison of above Examples

A 3000N pressure has been applied to the same surface area on all wheels.

Wheel Maximum Stress (Pa) YS Factor* Maximum Displacement (m)
solid spokes (Figure 18) 4.18 * 106 28 3.44 * 10-6
solid wheel (Figure 19) 1.70 * 106 69 8.27 * 10-7
thin spokes (Figure 20) 5.66 * 107 2 4.11 * 10-5
unsound (Figure 21) 7.39 * 106 16 2.29 * 10-5
Table 1.7
* YS Factor is the factor of how many times the maximum stress lies within operating range of the cheapest steel.

Without doubt, the solid wheel experiences the least amount of stress and the least amount of displacement, i.e. it is structurally most sound. However, no material was saved in the model, which causes higher production costs, and they may not warrant the marginal improvement in strength.

The next best design is the wheel with 6 thick and rather solid spokes. This wheel experiences more stress and more displacement than the solid wheel, but the difference is negligible, even though the wheel remains structurally sound in half the range of the solid wheel, yet a factor of 28 is still extremely large.

The wheel with 2 solid spokes would theoretically work, but a design of this kind is unusual and would impact the structural quality over time, as most displacement occurs in the area without spokes. We could expect the wheel to become more eliptical over time.