Summary The U-bracket is a key component in the Sun Tracker team s design, and is one of the most highly loaded. The U-Bracket, shown below in Figure 1, will be replacing an existing bracket on the dish. The current bracket does not provide sufficient space to include the necessary mounting holes, and it also has a tube welded to the bottom that is not needed in our design. This report will detail the worst case loading scenario for the U- bracket, which is a situation where the linear actuator (LA) has been either installed incorrectly or incorrectly limited in its range of motion and has extended too far. The over extension of the LA causes the bottom of the declination bracket to collide with the slewing drive housing which stalls the LA and causes high loads. Under normal conditions, loading will be substantially lower than what is modeled here. Boundary Conditions The stalled LA will exert its full 400 lbf. In such a case, we expect the loading shown in Figure 2 (sectioned for clarity). The bolt holes on the right (2 total) are loaded with a bearing stress of 1000 lbf at 45, and the holes on the left (4 total) are loaded at Figure 1: CAD Model of U-Bracket an angle of 22 with a load of 400 lbf. The 400 lbf load was increased to 500 lbf in the event that the LA can exert more than 400 lbf when it first stalls. Other boundary conditions are tabulated in Tables 1 and 2. Figure 2: Loading case and boundary conditions
Supports Boundary Bolt Heads Bolt Shafts Slewing Face Type Frictionless Support Cylindrical Support Compression Only Support Description The bolt head circles were constrained as frictionless supports to alleviate unrealistic stress concentrations caused by fixed supports. This support allows the hole to deform under it, while keeping the bolt area under compression. The cylindrical support inside the bolt holes was used to prevent the holes from collapsing inwards, since this would be prevented by the bolt shaft. Transverse movement is also prevented by this condition. Table 1: Simulation supports Loads Boundary LA Mounting Pins Declination pin Type Bearing Load (500 lbf at 22 ) Bearing Load (1000 lbf at 45 ) Description Mesh LA mounting pins were given a loading of 500 lbf, higher than the expected 400 lbf. Bearing loads were applied only to the half of the hole under compression by the pin. Table 2: Simulation Loads The slewing face was modeled as a compression only support to allow for separation between the U- bracket and Slewing drive. If deformation was severe, the bracket could separate from the slewing face between the bolt holes. The declination pin hole was loaded with 1000 lbf. The load was applied to half of the hole, corresponding to an angle of 45. The U-bracket was meshed with 127,000 elements. A refinement level of 2 was used around the loading holes and the holes mounting the bracket to the slewing drive. The mesh is shown in Figure 3 below. Figure 3: Mesh use for simulations
Stresses and deformations Analyses Stress analysis was first completed for the U-bracket with all 8 slewing drive bolts constrained, and then repeated for the case where only 4 holes were constrained. This was done because there are two different slewing drives that we could use, and the bolt pattern for one of them is much larger than the other. Although the 4 bolts would not be in the same locations as this current bracket, loading 4 of the holes would still give a rough idea of how the stresses increase. It will be discussed later in this report, but with the larger bolt pattern the stresses should decrease in the part. Stress concentrations and unrealistic stresses In the images that will follow the stress scales have been modified to better reflect the stresses in the part. As shown in Figure 4 (left), the scale is somewhat deceptive in that the maximum stress is sometimes an anomalous value. In the case of Figure 4, the max stress is ~40Ksi, which would yield the metal by our criteria. However, this is a single node internal to the part and the stress is likely caused by an intersection of boundary conditions. The actual stress surrounding the bolt holes is colored green, which indicative of around 15Ksi of stress (safe). The adjusted scale to better Figure 4: Unadjusted stress scale (left), and adjusted stress scale (right) show the stress distribution is shown on the right side of Figure 4. The true high stress is beginning to occur at 15 Ksi around the end of the bolt head. Results for Case 1 [Since the model and solution are symmetric, the model has been sectioned for clarity in the following images.] With all 8 bolts holes constrained, the maximum stress in the part was found to be roughly 15 Ksi, excluding the outlier mentioned in Figure 4. Figure 5 shows the stress distribution as seen from above. Figure 6 shows the same stresses from below.
Figure 5: 8 bolts constrained, stress distribution top view Figure 6: 8 Bolts constrained, stress distribution bottom view
Contrary to what was expected, the bolts mounting the bracket to the slewing drive are causing the most stress. It was expected that the holes under a bearing load would see the most stress, since a relatively high bearing load is applied to a thin wall. Even with low grade steel with a yield strength around 29 Ksi, the part is safe under the loading conditions tested. Deformations are shown below in Figure 7. Deformations are less than.004, which will not cause any noticeable deformation in the bracket. Results for Case 1 Figure 7: 8 Total part deformation Loading for only 4 bolts holes caused more stress, but the part is still safe. The stress in the bolts is primarily being caused by the 1000 lb reaction force at the declination pin. When the bolt holes are spread farther apart for the new bolt pattern, the distance between the declination pin and bolts should decrease, reducing the bending moment the force is applying. If it is decided that the slewing drive with the larger bolt pattern is going to be used, another stress analysis will completed and appended to this report. An image of the bolt holes constrained for this analysis is shown in the appendix. Figures 8 and 9 show the stress distribution for the part as seen from above and below, respectively. For this simulation, the highest stress occurred on the bottom of the bracket near the back mounting holes (the side with the declination pin). The maximum stress is roughly 24 Ksi, which is still below the
yield stress of the steel. This stress may also be caused by the intersection of the frictionless boundary condition and the free-to-deform part. It is common for abnormally high stresses to occur at the edges of boundary conditions. Figure 8: 4 bolts constrained, stress distribution top view Figure 9: 4 bolts constrained, stress distribution bottom view
The total deformation, shown in Figure 10 below, is minor. The deformation is less than 0.006 which should cause no problems. Figure 10: Total deformation with 4 bolts constrained. Conclusions Under both bolting situations the stresses in the bracket should not exceed the yield strength of low carbon steel. The deformations will also be minimal, and not cause and issues. Further analysis will be done on the U-bracket with a larger bolting pattern, and appended to this report when finished. For now, the bracket appears to be safe with a bolt pattern of 4.
Appendix An additional picture of the mesh used in the analysis 4 bolts constrained for the second analysis