Question 8.6: Modal Analysis of a Cam-Follower Arm Problem: Find the eigen...
Modal Analysis of a Cam-Follower Arm
Problem: Find the eigenvalues (natural frequencies) and eigenvectors (mode shapes) of the part in Example 8-5 if its pivot pins are subjected to random excitation from the machine in which it is mounted.
Given: The beam geometry is as defined in Example 8-5 and Figure 8-23.
Assumptions: Loading and support reactions are parallel but out of plane. Pin supports are significantly stiffer than the beam. The beam supports are subjected to random vibration.
1 Example 8-5 analyzed this beam statically. The mesh and kinematic coupling boundary constraints that worked for the static analysis can also be used for the modal analysis, which was analyzed here with the same model.
2 Figure 8-29 shows the first mode shapes of both the pocketed and unpocketed beam designs of Example 8-5. The first natural frequency of the pocketed beam is 49.48 Hz. Removing the pockets more than doubles this value to 104.44 Hz.
3 Figure 8-30 shows the second mode shapes of both beam designs. The second natural frequency of the pocketed beam is 219.98 Hz which increases to 455.63 Hz when the pockets are removed.
4 Figure 8-31 shows the third mode shapes of both beam designs. The third natural frequency of the pocketed beam is 298.29 Hz which increases to 620.38 Hz when the pockets are removed.
5 It is clear from this study that the pockets are hurting this design more than helping it. The pockets doubled the static deflection and reduced the natural frequencies by more than a factor of 2. Despite the mass reduction delivered by the removal of the pocket material, the cost in stiffness probably makes it not worth doing in this case. It would have been more difficult and time consuming to reach this conclusion without the use of FEA.
