Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis

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

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 1: CAD Model of U-Bracket

Figure 2: Loading case and boundary conditions

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis

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.

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.

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 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.

The declination pin hole was loaded with 1000 lbf. The load was applied to half of the hole, corresponding to an angle of 45°.

Table 2: Simulation Loads

Mesh

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

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis 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

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 4: Unadjusted stress scale (left), and adjusted stress scale (right)

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis

Figure 5: 8 bolts constrained, stress distribution top view

Figure 6: 8 Bolts constrained, stress distribution bottom view

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis 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.

Figure 7: 8 Total part deformation

Results for Case 1

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

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis 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

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis The total deformation, shown in Figure 10 below, is minor. The deformation is less than 0.006” which

should cause no problems.

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.

Figure 10: Total deformation with 4 bolts constrained.

Harrison Sprague P15571 Sun Tracker Stress Analysis U-Bracket Stress (Rev 1) Analysis

Appendix

An additional picture of the mesh used in the analysis

4 bolts constrained for the second analysis