CubeSat Modal Analysis

Project Overview:

This project consist of a Modal Analysis performed for a CubeSat, designed by a group of me and my peers for a class project. The Analysis will actually consist of 2 separate analysis; a free-free analysis to evaluate the CubeSat's performance in orbit, and a constrained analysis to evaluate the performance of the CubeSat during launch. The free free analysis was then compared to possible excitations generated by onboard systems to ensure that resonance wasn't excited. The constrained analysis combined Random Vibration Loading calculations along with the Quasi-Static loading environment inside of launch vehicles to give a worst case scenario loading environment, this environment was then applied to the CubeSat in a static analysis to evaluate the structural integrity during Launch.

Free-Free Analysis

To analyze the behavior of the CubeSat in orbit a free free, or unconstrained modal analysis was done. This analysis will be used to calculate the resonant frequencies and determine if resonance will be excited by any onboard system. As you can see in the table below, the first 6 modes are near-zero which verifies that the results for the analysis are valid for the free free condition

Constrained Analysis

After we performed the free free analysis we performed a launch environment analysis. This analysis consisted of calculating the modes of the constrained model with the highest mass participation in the principle directions. This would then be used to calculate the random vibration loading. the results from this calculation would then be used with manufacturer provided launch environment data to calculate worst case scenario loading. The Launch vehicle with the highest acceleration forces will then be used to evaluate the CubeSat’s structural integrity during launch.

The following 2 images show the results of the constrained modal analysis; the first figure shows the tabulated data and the next figure show the modes with the highest mass participation in the principle directions.

Random Vibration Loading (RVL)

To Calculate RVL the n-degree of freedom Miles formula is used.

Quasi-Static Loading

The Quasi Static loading environment comes from data acquired from the Launch vehicle. Each launch vehicle has a different axial and lateral loading environment, and the CubeSat must be able to survive each.

Root Sum Square (RSS) Loading

The root sum square method accounts for the random vibration and the quasi static loading to determine a worst case scenario loading environment. This load factor will then be used in a static SolidWorks analysis to determine whether the CubeSat will survive the Launch.

These are the results from our code that calculates worst case scenario loading for each launch vehicle. As you can see the scenario with the highest acceleration forces is the Nano-Racks. This scenario was used in the following static analysis

Structural Analysis

The factor of safety according to the Von Mises failure criteria is 1.2. This factor of safety is likely a conservative estimate because the model is only constrained on the corners, massive stress concentrations build up there because of this. The real CubeSat would likely be constrained to the Nano-Racks system by non-zero thickness mounting brackets; thus, drastically increasing the factor of safety.