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How Sensitive are your “Feet” to Vibration?

October 11, 2016 By: Peter Barrett

When performing dynamic analyses of structures with support feet, the boundary conditions imposed on these feet can play a major role in their vibrational response. In this blog, I will explore, by example, different modeling assumptions of bolted support feet and compare their influence on the structural response.   

Prior to physical dwell testing, finite element modeling is often performed as a pre-test predictive tool to validate and optimize products against design safety margins and thus minimize design iterations by assuring a successful test on the first try! The accuracy of the analysis, and thus corresponding calibration between test and analysis, can be greatly improved with accurate modeling. The accuracy of the support mount connection model between the design feet and the shaker table is critical.  

The image on the left of Figure 1 (shown above) illustrates a typical vibration test illustrating an example of support “feet” subject to vibration. In most tests, the table itself can be safely represented by a fixed or “rigid” surface in the finite element simulation.  

A centrifuge frame subject to a hypothetical vibration dwell sweep analysis (Figure 2) is used to demonstrate the sensitivity of the table-to-device connection on the vibrational system response. Post-processing techniques illustrated in a previous CAE Associates blog are used to extract the peak stresses over the harmonic frequency range simulated.
 

Figure 2- Centrifuge Frame Geometry and Lateral Acceleration Loading vs. Frequency


Three different boundary conditions are analyzed, representing upper and lower bound estimates as well as the more accurate pre-stress bolt simulation.  
The simplest method of support modeling is to fix the base of the feet pads. However, fixing the entire foot base is typically non-conservative, while fixing just the bolt can be overly conservative. If the difference in critical stresses between these two bounding assumptions is significant, then a more accurate modeling approach is warranted. Modeling the actual bolted connection with a bolt pre-load and contact provides a much more realistic footprint of the load transfer between the feet and support plate, and hence more accurate natural frequency predictions and corresponding harmonically driven stresses. Figure 3 illustrates the modeling of these three boundary conditions (bolt fixed, base fixed, and bolt-pretension analysis). For the bolt pre-tension case, a static pre-load analysis is first performed to determine the foot-support interface contact status. Figure 4 illustrates the computed sticking/sliding/open interface and corresponding pressure distribution generated from the bolt preload. This response is used as input to the modal and harmonic simulations.
 

Figure 3 – Three Different Support Foot to Shaker Table Boundary Conditions



 

Figure 4 - Bolt Pre-Load Contact Status and Pressure (psi)



A mode-superposition harmonic analysis is performed to simulate the dwell test where a 2.5% uniform damping is assumed in each of the three analyses. For the bolt-pretension case, a pre-stressed modal analysis is performed where the contact status from the static analysis is imported as an initial condition using the linear perturbation methodology.

The harmonic analyses utilized a mode cluster approach to provide computationally more efficient and accurate results at the resonant frequencies. Peak displacements and stresses are graphed as a function of frequency in Figures 5 and 6.  The peak stress and displacement response at resonance changes significantly in both frequency and amplitude. For this design, the critical fillet stress varies by roughly an order of magnitude between the upper and lower bound support assumptions, thus justifying the need for a more accurate support model. Hence the value of the bolt pre-load case where the support surface is modeled explicitly.
 

Figure 5 – Lateral Displacement vs. Frequency under Lateral Acceleration Frequency Sweep Loading



Figure 6 – Maximum Stress (psi) vs. Frequency under Lateral Acceleration Frequency Sweep Loading


 


How do you handle the vibration response of your feet? I welcome your input and feedback on how you validate boundary condition assumptions in your vibration simulations.