Find the Problem Fast

TE C HNI C AL Check Plots: Find the Problem Fast Overview SolidWorks® software helps you move through the design cycle faster. With quick and easy c...
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TE C HNI C AL

Check Plots: Find the Problem Fast

Overview SolidWorks® software helps you move through the design cycle faster. With quick and easy check plots, your team will be able to effectively target problem areas for further analysis—and streamline the comprehensive design validation process.

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P A P ER

The pressure is on in one of the greatest arenas in sports. Deep into the fifth set at the Wimbledon Championships, it’s championship point. If the server can win this exchange, the trophy is his. A feeble return heads straight for his racquet— he knows he is just one shot away. He strokes a screaming forehand down the sideline, knowing his opponent has no chance of reaching it. As the ball flies along, one question holds everything in the balance: will it be good, or will it be out? The tennis player doesn’t care exactly where the ball lands. Right on the line or half a meter inside the court makes no difference to him—what matters to him is that the ball is in. Likewise, if it’s out, it’s out, no matter the distance. You could say the server faces a binary outcome: either he is or isn’t the Wimbledon champion, regardless of how far in or out his shot is. Check plots in SolidWorks Simulation work in much the same way. A check plot is a quick calculation tool that tells you if your design faces certain risks and whether further analysis needs to be done. SolidWorks Simulation has three types of check plots: pin/bolt, fatigue, and edge weld. Each of these provides a balance between “back of the envelope” calculations and full-fledged finite element analysis (FEA). This paper aims to describe each of these check plots in detail and present examples that demonstrate how to use them in real studies. Pin/Bolt Check Plot In assembly simulation, pins and bolts are commonly replaced with an idealized connector. The connector has mechanical properties similar to the pin or bolt, but without the computational overhead of the actual geometry. This results in faster solve times. The pin/bolt check plot is a fast way to visualize if the “real” bolt or pin can support the loads it is expected to withstand in an assembly. As mentioned above, this is a pass/fail system: the software does not display detailed results as it would in a complete static analysis. Rather, it tells you whether further studies and modifications are needed. When defining either a pin or bolt connector, you define the tensile stress area, connector strength, and the desired connector factor of safety. When the static analysis is complete, you can define a pin/bolt check result plot, and SolidWorks will classify each pin as either “OK” or “Needs attention.” SolidWorks Simulation accomplishes this task by computing the axial, bending, and shear forces acting on each pin or bolt. Each of these loads is then compared with other important parameters, such as strength and area terms, to make axial, bending, and shear load ratios. Then, each ratio is placed into a combined ratio, which is defined as follows:

Finally, the inverse of the combined load ratio (i.e., 1/), is compared with the factor of safety. If the factor of safety is the larger of the two values, the pin or bolt fails the test; conversely, if the factor of safety is smaller, the connector passes. The software then uses these results to place each bolt or pin into the “OK” or “Needs attention” folder.

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You could say the server faces a binary outcome: either he is or isn’t the Wimbledon champion, regardless of how far in or out his shot is.

Consider the basketball hoop shown in Figure 1.

Figure 1. A basketball hoop hit with a force on the outer edge

The scenario shown above is not uncommon: imagine that a player aims for a slam dunk but misses and hits the rim with all his strength. This could be modeled with a localized force, as shown. The hoop is fixed on the left, and four bolts connect the fixed surface to the back of the hoop. It is crucial for the designer to know if the bolts in this design can withstand these loads. Fortunately, the SolidWorks Simulation interface allows you to define and redefine forces, and the pin/bolt check plot will provide fast pass/fail results. Figure 2 shows the results in more detail.

Figure 2. Results of a pin/bolt check plot on a basketball hoop. The bolts in green are labeled “OK,” while those in red are labeled “Needs attention.”

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Note that the top two bolts are colored red while the bottom two are green. This means the top two failed, but the bottom two passed. By clicking any of the connectors listed, you can see the precise forces acting on each bolt as well as the overall magnitude of these forces. But the primary output is pass/fail— either the bolt is OK or it needs refinement. The pin/bolt connector interfaces allow for fast, effective diagnoses of potential problems without requiring all the time and resources of a comprehensive FEA study. They help prioritize simulation to answer the most basic, yet the most important, question for designers and engineers: “Will these connectors work?” Fatigue Check Plot Fatigue is defined as “failure under a repeated or otherwise varying load, which never reaches a level sufficient to cause failure in a single application.” 1 It is the most common cause of failure among metals, and often occurs in other materials as well. 2 Unfortunately, complete fatigue studies in FEA require intensive time and resources. Engineers must carefully consider the sizes of the meshes in their model when investigating fatigue. A mesh too large may miss important details, but a slightly finer mesh could mean significantly more computation time. Furthermore, analysts often have to re-mesh localized regions to fully explore the likelihood of fatigue in a design. The role of the check plot is to quickly show you where you might need to conduct a more in-depth fatigue study following a static analysis. The plot uses only two colors—red regions are those prone to fatigue failure, while blue regions are not at risk. Before further describing the outputs of the check plot, however, more background information on fatigue is warranted. Fatigue happens in three stages: crack initiation, crack propagation, and final fracture. Crack initiation is a complicated concept; but by calculating stress values, FEA provides important information about predicting crack initiation. Subsequent propagation and fracture are the subjects of nonlinear FEA studies. In order to simplify the simulation of fatigue failures, FEA systems compare the results to experimental tests. The two dominant approaches are the stress life (SN) approach and the strain life (EN) approach. In both, the computed stress or strain (S or E) are compared to the life (N) of the standard experimental test. For high cycle fatigue at low stresses, this can be done through an S-N curve, or a Wöhler curve, as shown below in Figure 3. The fatigue check plot aims to identify regions of material prone to fatigue failure by using the SN approach. As such, it is only applicable to high cycle fatigue. If the stresses are above yield, then this approach is not valid.

1. Halfpenny, Andrew (2000). A Conceptual Introduction to Fatigue. nCode International, Ltd. Retrieved August 2. Callister, W. D. (2007). Materials Science and Engineering: An Introduction. John Wiley & Sons. 3. 2009, from http://www.altairhyperworks.co.uk/technology/papers/2000/paper15.pdf.

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Engineers must carefully consider the sizes of the meshes in their model when investigating fatigue.

MOCK CARBON STEEL FATIGUE DATA

LOW CYCLE FATIGUE

HIGH CYCLE FATIGUE

Figure 3. A sample S-N curve, also known as a Wöhler curve

This graph provides valuable information about a material’s ability to endure various stresses. However, it fails to account for different load scenarios, as shown in Figure 4.

ALTERNATING vs POSITIVE MEAN STRESS

Figure 4. Alternating, positive mean, and nonuniform stress distributions

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The blue curve in Figure 4 is classified as an alternating load scenario. The stresses cycle evenly between positive and negative values centered around zero stress. The S-N curve is used on this type of loading sequence. However, the other cases are also fairly common. Many devices operate entirely in tension like the yellow curve. Others are nonuniform like the red curve—far from the alternating case. In these complicated loading scenarios, the mean stress is a crucial parameter. Studies have shown that a nonzero mean stress significantly affects fatigue life. Generally, the higher the mean stress is in tension, the lower the fatigue life is.

Figure 5. A Goodman diagram of mean correction methods based on different mean stresses

The Goodman diagram shown in Figure 5 has been developed for various materials in order to account for alterations in mean stress. The Goodman diagram compares several mean correction methods according to the mean stress and alternating stress in design experiences. Here, Syt, Se, Sa, Sm, and Sut refer to the tensile yield strength, endurance limit, alternating stress, mean stress, and ultimate tensile strength, respectively. For reference, the yield line connects the yield strengths—the stresses at which plastic deformation begins —on each axis. The Gerber line is a quadratic, nonconservative equation that is useful for modeling ductile materials. The Goodman line is a more conservative estimate that applies well to brittle materials. The Soderberg line is even more conservative than the Goodman line, since its upper bound for mean stress is the yield strength instead of the ultimate strength.

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Testing has shown that fatigue failure generally occurs somewhere in the region between the Goodman line and the Gerber line. Thus, to give some leeway in a design, it is most practical to use the conservative Goodman line as the upper bound for the “fatigue-safe” region on the Goodman diagram. In fact, SolidWorks software even goes one step further in making a more conservative estimate, as shown in Figure 6 below.

Figure 6. The green region (“OK”) and the white region (“Needs attention”) are used to give a go/ no-go analysis in the Fatigue check plot

Note the blue region at the bottom left of this graph. That is the “safe” region – if the stresses on a node fall within those boundaries, the check plot says the node will not fail due to fatigue. This region comprises only the most conservative combination of the Goodman line and the yield line. Rather than simply taking the Goodman line, SolidWorks treats the region between Sy and St as unsafe to give designs extra security. When creating a fatigue check plot following a static study, you must define a few key parameters. The first choice is fully reversed or zero-based loading. These define the lines along which stresses can be calculated, as shown in the green/red lines in Figure 6 above. Then, you alter the factor of safety by defining a surface finish factor, loading factor, and size factor (or by simply specifying a “lump sum” of these factors). Each of these parameters (which range from 0 to 1) is multiplied with the material fatigue strength to acquire an adjusted, component-specific fatigue strength. Finally, you can scale the fatigue strength and the factor of safety.

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Rather than simply taking the Goodman line, SolidWorks treats the regions between Sy and St as unsafe to give designs extra security.

Figure 7 shows the results of a fatigue check plot of a scuba tank.

Figure 7. Scuba tank fatigue check plot results, showing fatigue-prone areas in red

To determine the safety of the tank, a static study calculates the stress field due to an internal pressure. The first check a designer will make is to ensure that the stress factor of safety ( y/ max) is greater than the required minimum. If the design passes the strength test, then the fatigue check plot will indicate the regions of the material in danger of fatigue failure. A factor of safety of 10—not an uncommon value, as fatigue data often include significant scatter—was prescribed for the fatigue check plot. The red regions in Figure 7 above indicate the areas for which the stresses fall outside of the safety zone in Figure 5. The value of this plot is that it gives the analyst a place to start with more in-depth fatigue analysis. Rather than conducting an exhaustive study of the entire tank, the analyst should focus on these potential hot spots to make more productive use of time and resources.

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Edge Weld Check Plot Edge welds are common features in engineering designs, but they can be difficult to analyze. Stresses near welds in any FEA program are unreliable because the values depend on both geometry and mesh size. Fortunately, the edge weld check plot utilizes simple calculations to provide the designer with a quick pass/fail answer to determine if further weld analysis and refinement are required. This point is key: edge weld check plots rely on forces, not stresses. As stated earlier, stress values reported at welds are error-prone. This is why welds are often “hot spots” in FEA models that focus on stresses alone, even though they may or may not be the weakest points of the structure to consider. It is much easier to acquire accurate force readings than stress readings on a weld. To perform this analysis effectively, the weld is treated as a line. Using lines in place of planes eliminates mesh complications—it is far simpler (and still true) to say that the forces along a given line “weld,” instead of a face, will be equal. For this reason, shell models are preferred in weld studies because the loads are much easier to obtain. When first creating the weld, you can choose to estimate its size—this is called the “estimated weld size.” This saves time by forcing the software to compare values against a set thickness, but it is not mandatory. The check plot relies on a procedure called the “throat shear” method. In this process, normal, shear, and bending forces are ascertained at each node. The load at each node is then calculated via this formula:

Finally, the “calculated weld thickness” required can be found by comparing with the maximum allowable electrode shear:

This calculation results in a unit of length, which correctly corresponds with the units of t w. If the actual thickness at each node exceeds this minimum value, the software considers it “OK.” If not, SolidWorks Simulation places the weld in a “Needs attention” folder. This means the weld requires further investigation. Then, you can perform multiple iterations by changing that initial estimated weld size to a value near the calculated weld size when defining the edge weld connector. When all the welds are labeled “OK” and colored green in subsequent check plots, the analyst can rest assured that the welds will safely carry the loads without failing. The calculation methodology aside, it is important to note that the edge weld check plot is based on actual tests, not just theory. The standards used in the software follow the Structural Welding Code D1.1 of the American Welding Society (AWS).4 Future versions of SolidWorks Simulation may allow for different welding standards, but this methodology is generally acceptable as a basis for engineers to consider.

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Shell models are preferred in weld studies because the loads are much easier to obtain.

As an example of the edge weld check plot in action, consider a loaded, fixed brace structure with multiple welds, as detailed in Figure 8 below.

You can review multiple welds with distinct visual differences for quick reference.

Figure 8. A fixed brace with four EDGE welds (dark blue) and an applied force (maroon)

There are four edge welds (circled in dark blue) that connect cylindrical rods to the two frames. All the components are modeled here as surfaces, since the underlying theory requires the connected parts to be defined by shell elements. The frame on the right is fixed, while a downward force is applied to the one on the left. Each weld was initially estimated as 10 mm thick. After a static study was conducted, an edge weld check plot revealed the following results.

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Figure 9. Results of an edge weld check plot. Two edge welds in green are appropriately sized and are labeled “OK.” The other two in red are not large enough and require modifications

Two of the four edge welds passed the test. Both connectors in green were large enough to endure the loads induced by the downward force. The others in red were not big enough. You can then select “Details…” to see the minimum, maximum, and mean required weld sizes for any weld, as well as the forces and moments it experiences in this scenario. In addition, the required weld sizes at each node can be plotted, as shown in Figure 10 below.

Figure 10. Required weld sizes for Nodes 28 and 30 compared with the estimated weld size

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Easy comparison of weld sizes can be found in “Details.”

SolidWorks Simulation can produce a graph that immediately shows weld size and weld throat size. This graph can also be exported for use in Microsoft® Excel or another spreadsheet application, which allows you to create more detailed graphs like the one in Figure 10 above. This graph compares the required weld sizes for an “OK” node (Node 28) and a “Needs attention” node (Node 30) with the original estimated weld size. The estimated value for Node 28 is always lower than the original estimation, but that estimation does not meet the requirements at various points on Node 30. Fortunately, this calculation gives you some basis for the required weld size, so the next welds could be chosen as 13 or 14 mm thick instead of blindly guessing. Of course, follow-up studies should be conducted to make sure that changes based on the graphs produced still satisfy the necessary conditions. After adjusting the sizes of Nodes 30 and 31 to 13 mm, the edge weld check plot in Figure 11 below shows that the design will hold the required loads.

Figure 11. Results of an edge weld check plot. By increasing the two welds at the right to 13 mm in thickness, each weld passes the test

Through this procedure, the edge weld check plot in SolidWorks effectively addresses one of the most complicated parts of FEA studies in a fast, efficient manner. Relying on forces instead of stresses makes the required calculations independent of geometry so they are more reliable and applicable. Furthermore, by producing and exporting data in multiple ways, iterations of studies with different weld sizes can be conducted without difficulty.

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SolidWorks Simulation can produce a graph that immediately shows weld size and weld throat size.

CONCLUSION SolidWorks Simulation check plots are helpful, efficient tools that quickly give you important pass/fail insights. While comprehensive FEA studies go much further toward detailing a design’s ability to withstand loads, check plots can determine whether a design passes the most basic of tests—And if it doesn’t, check plots will show where the problem areas are. The pin/bolt check plot takes axial, bending, and shear load ratios into account and compares them with a desired factor of safety. The fatigue check plot utilizes states of stress, surface factors, fatigue strength, and a few other select parameters to state whether some region of a part is susceptible to fatigue. Finally, the new edge weld check plot uses simple, mesh-independent force calculations to show whether a weld of a given size can effectively hold the loads it is assigned. Generally, FEA calculations are much more powerful and consistent than hand calculations. They can take particular geometric features into account that may be very difficult to consider by hand. At the same time, traditional, complete FEA can take significant time and resources. SolidWorks Simulation check plots give you the information you need to design products faster.

To learn how SolidWorks solutions can help you successfully employ these strategies for effective CAD leadership, visit www.solidworks.com, or call 1 800 693 9000 or 1 978 371 5011.

Dassault Systèmes SolidWorks Corp. 300 Baker Avenue Concord, MA 01742 USA Phone: 1 800 693 9000 Outside the US: +1 978 371 5011 Email: [email protected] www.solidworks.com

SolidWorks is a registered trademark of Dassault Systèmes SolidWorks Corp. All other company and product names are trademarks or registered trademarks of their respective owners. ©2011 Dassault Systèmes. All rights reserved. MKCHKPLOTTpENG0311

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