Question 8.CS.4D: FEA Analysis of a Bicycle Brake Arm Problem A bicycle brake ...

See Figures 8-36 to 8-37.

1    Figure 3-9 shows the geometry of the brake arm assembly. Symmetry allowed it to be analyzed for one side only in Case Study 4B and we will do so here as well. It was broken into two cantilever beams for the classical solution, That is not necessary here and it will be analyzed as an assembly consisting of the arm, pivot pin, and constraints to represent the wheel rim. The cross section shape had to be crudely modeled as a rectangular tee shape in the classical solution and curved beam theory was used to analyze bending stress. In the FEA model, the actual geometry is used and a general stress analysis done. We should expect some differences in the results between the two models.

2    Figure 8-36 shows the solid-model assembly. The arm is supported on a pin, one end face of which is fixed to ground in x, y, and z The arm is kinematically constrained to the pin allowing the hole surface to turn on the outside diameter of the pin, but is unable to move in x or y. The z-direction of the arm is constrained by creating a “washer” detail on its hub face and this “washer” area is constrained against motion in z. Rotation of the arm about the z-axis of the pin is prevented by constraining an area “A” on the face of the slotted portion against motion in x. This represents the brake pad attached there, which is pressed against the wheel rim. The torque from the wheel and friction with the brake pad are modeled as traction forces in the y and z directions on the same area A and on area B on the back side. These traction forces appear as arrows laying on the surface both on the pad side of the arm and on the recessed surface of the slot on the back side of the arm where the bolt that holds the pad is seated. Finally, the cable force is applied at hole C as x and y components.

3    The classical stress analysis of this part done in Case Study 4B chose several locations of presumed high stress to analyze. These comprised a plane labeled X-X in Figure 3-9 through the curved beam section near its root, a plane B-B through the pivot hole, and a plane A-A cutting close to the root of the rectangular cantilever that contains the slot for mounting the brake pad. In all three planes the highest tensile stresses were at the inner surface at points shown with colored dots in Figure 3-9 (repeated) opposite.

4    Figure 8-37a shows the arm meshed with 54 432, 16th-order tetrahedral elements and Figure 8-37b shows a stress contour plot of the inside surface of the arm. This plots tensile normal stress \sigma _{y}, which is the component calculated for these points in Case Study 4B. Traces of the cut planes A-A, B-B, and X-X are shown at the inside surface. Hot spots of high stress are clearly visible at A-A and X-X, but not at B-B. This is because the stress at B-B is less than at the other locations. The von Mises stress is also shown and is close to the \sigma _{y} value because it is dominant at those points.

5    Table 8-5 compares the results from the classical stress analysis with those of this FEA for tensile stress in the y-direction at the inner fiber for the three locations. Table 8-6 compares the results from the classical stress analysis with those of this FEA for compressive stress at the outer fiber of section X-X. At the inside surface of the sections A-A and X-X the FEA results show lower stress than the classical analysis. This is most likely due to the fact that the classical analysis ignored the increase in section thickness due to the fillet radii on the outside contours of the arm and assumed that the beam depth (thickness) was constant all the way to the root on both sides of the hub. The good news is that the classical analysis gave a conservative estimate at these two locations. However, the FEA predicts nearly twice the stress at section B-B than did the classical analysis. In this case the FEA gives a better estimate of the stress.

6    The FEA gives a superior result in this case due to the complex geometry that had to be overly simplified for the classical analysis. The Solidworks model is on the CDROM in a folder labeled CASE 4-D.