Case Studies - Avionics Structural Analysis
Avionics structural evaluation
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Introduction
Electronics designed for the aerospace industry must stand up to rigorous shock, vibration and temperature environments. Before the products are deemed flight worthy, they must adhere to strict flight substantiation or air-worthiness requirements, be verified through analysis, and then qualified through testing. This study walks through a typical structural evaluation of an avionics chassis designed for an aerospace application, briefly illustrating each one of these analyses types:
- Frequency Analysis
- Random Vibration Analysis
- Acceleration Spectral Density (ASD) inputs
- Stress and Deflection
- Miner’s Cumulative Damage
- Circuit Card Assembly (CCA) Component Analysis
- Shock Analysis
- Response Spectrum
- CCA Component Analysis
Analysis Setup
The first steps in any product structural analysis are understanding the environment and then defining the analysis model to insure the proper inputs and outputs can be achieved.
Understanding the Environment
Let us consider the environment of a space flight vehicle. For this case, NASA has developed a set of test standards that can be used as an analysis baseline. These standards can be found at https://standards.nasa.gov, and more specifically, this study will reference the GSFC-STD-7000A standard for General Environmental Verification developed at the Goddard Space Flight Center. This standard provides guidelines for analysis, test, qualification, and acceptance of products and electronics used for this space flight vehicle application.
Defining the Analysis Model
The analyst should understand the objective to be accomplished, the inputs and outputs, and then modify the CAD data to ensure that the mesh is optimized relative to the fidelity needed in the solution. The CAD model can often be simplified by defeaturing, idealization, and clean-up. Components and features that are not considerably affecting the stiffness or the mass of the system should be removed for efficiency. In this case, our avionics chassis has been reduced to the following analysis model comprised of a machined AL 6061-T6 chassis, defeatured connectors, and a CCA populated with components of concern as shown in Figure 2.
Frequency Analysis
Modal Analysis
The next step is to determine how the system might be excited during a dynamic loading event by performing a modal analysis. The model is constrained in the analysis environment with supports through the bolted holes to simulate the actual use case environment while on the vehicle. A modal analysis is performed to extract the primary resonant frequencies and their corresponding mode shapes. We’ve limited the frequency range to 2000 Hz for this analysis to reduce computation time. The primary modes and frequencies of the CCA are shown in Figures 3-5.
The primary modes and frequencies of the avionics chassis are shown in Figures 6-8.
For the sake of brevity, we will assume that the shock and vibration input direction is in a single, vertical axis that is orthogonal to the top of the avionics chassis as this will be the direction that produces the most severe stresses and deflections for this application.
A graphical representation of the modes is shown in Figure 9.
The modes that will most likely be excited by the input for both the CCA and the chassis will also have the highest mass participation along that same axis. A simple definition for mass participation is percent of mass moving in each mode. Generally, a majority of the structural mass will be represented in the first 10 to 20 modes, as is the case for the CCAs. The chassis cumulative mass participation does not rise above ~40% within the first 20 modes due to the high stiffness and robust mounting. In most cases the structural dynamic behavior is adequately simulated by the lowest frequency modes. For a uniform dynamic load (equal across the frequency spectrum), stresses and deflections are inversely proportional to the squared value of the model frequency. Thus, higher frequency modes contribute little to the overall structural dynamic response, unless the dynamic environment also has much (exponentially) higher acceleration levels at higher frequencies.
For this analysis, the mass participation relative to the modes is shown Figure 10.
In looking at the data, one can see that the cumulative mass participation of the CCA in this axis exceeds >95% in the first 2000 Hz, while the bulk of the participation from the chassis doesn’t start peaking until well beyond the 2000 Hz initial sweep. What this implies is that the chassis has much greater stiffness than the CCA, which is to be expected for this analysis model.
Harmonic Analysis
Another beneficial analysis that visually shows how the system will react to a given input is a harmonic analysis. Assuming a damping (ζ) of 5%, for purposes of simplicity and a general rule of thumb for mechanical systems, if one excites the system with a base motion input of 1G, then the output of the harmonic analysis would indicate the amplification, or queuing, of the system. The output extracted from the main processor in the center of the CCA is shown in Figure 11.
Looking at the harmonic analysis output, we can see that the peaks in the acceleration plot coincide with the modal frequencies, especially with respect to the CCA. In particular, one can see that the lowest mode of the CCA is being excited at the resonant frequency of 160 Hz resulting in amplification from the base motion input to an amplitude of approximately 12 G with a 1 G sinusoidal input. In fact, each of the subsequent peaks corresponds to a CCA mode shape and does not appear to significantly couple with the chassis modes. The amplification above the 1 kHz range is not generally an immediate cause of concern since damage producing deformations of the design are inversely proportional to the square of the frequency, as illustrated in Figure 12.
Octave Rule
Random Vibration Analysis
Moving beyond the frequency analysis of the system and the Octave Rule consideration, we consider the random vibration environment. As previously mentioned, the GSFC-STD-7000A provides a minimum Qualification specification in the form of an Acceleration Spectral Density (ASD). The specification is shown below for payloads weighing less than 50 lbs.2
Applying this ASD as an input into the analysis model, the 3σ stress within the avionics chassis can be extracted and is presented in Figure 13.
In this study, the chassis happens to be very stiff and likely over designed for this application. The magnitude of the 3σ stress, predicted to be approximately 6 ksi, is much lower than the endurance limit of the material and should not be at risk of failure from the prescribed 14.1 Grms input prescribed.
Fatigue and Miner’s Cumulative Damage Calculation
While our study predicted that the chassis would easily survive the vibration environment, let us assume that the 3σ stress on the aluminum chassis is probed and found to be approximately 13.5 ksi. To determine if this value constitutes a possible fatigue failure, a Miner’s Damage calculation can be performed based on the fatigue properties of the aluminum material and the expected duration of the testing. We will assume that this chassis is manufactured from AL 6061-T6, which has been extensively documented with respect to its endurance limits and fatigue life – normally found on an S-N curve, shown in Figure 14.3
The corresponding Miner’s Damage calculation will use the chassis’ first fundamental mode for the cycle time and 3.8 hr total duration. The 1σ, 2σ, and 3σ stresses (13.5ksi assumption) for the damage calculation are used to determine the R value.3 The R value should remain below the value of 1 to indicate that a failure does not occur during the 3.8 hrs time limit. Thus, as shown below:
Using a 3σ stress limit of 13.5ksi, the Miner’s rule suggests that chassis would have survived the duration of qualification testing with a margin of 2.3 and a predicted failure time of 8.7 hrs.
CCA Component Failure Evaluation
The 3σ corresponding deflection was an output parameter from the random vibration analysis. The maximum deflection appears to occur in the same manner as the first fundamental mode shape; bending through the center of the CCA as shown in Figure 15.
The predicted 3σ deflection is 0.031 inches, occurring approximately at the center of the CCA. In this example, we will focus on the ARM i.MX6 processor on the CCA and determine if this chip is at risk of failure.4
These particular processors have a surface mounted ball grid array (BGA) type package construction, which Steinberg characterizes with a C value of 1.75.1 Inputting the rest of the values, the allowable 3σ deflection in this model is:
Based on the empirically derived formula, the maximum allowable deflection of the CCA is 0.013 inches. The predicted 3σ deflection is approximately 2.4 times the allowable deflection. This indicates that the ARM Processor is at risk of failure.
There are several methods to employ in order to address this failure risk. Depending on the state of the design, the most straight forward method would be to add additional mounting points towards the center CCA to limit the deflection induced by the random vibration input. However, this method will also increase the natural frequency of the CCA and possibly start violating the Octave Rule as previously evaluated. Iteration will be needed, but this adequately demonstrates the importance of analysis during the design process. For this white paper, we will assume that this analysis proved positive and will move to the next study.
Shock Analysis
Response Spectrum
The NASA Standard also provides a Shock Response Spectrum (SRS) to evaluate the analysis model for space flight vehicles.2 This SRS is shown below:
Rather than approximating static loads from this 1 DOF SRS input using the Dynamic Design Analysis Method (DDAM), a response spectrum analysis is performed using the SRS input and the resulting stress of the chassis is shown in Figure 17.
The maximum stress in the housing was predicted to be approximately 11.5 ksi. While this is much higher than those previously reported during the random vibration study, we can assume that the shock input for this environment is limited to less than 200 occurrences. Therefore, the maximum stress value can be evaluated against the ultimate and yield strengths of the material. The Factor of Safety is calculated below along with the minimum Safety Factor required for flight hardware design applied to limit loads, required for Margin of Safety calculations3:
The stress induced by the shock event has a very large Factor of Safety against the ultimate and yield strengths of the material. The Margin of Safety is also exceedingly high, suggesting that there is plenty of room for weight reduction. We could have addressed these items if we were to iterate to solve the random vibration CCA failure indicated above.
CCA Component Failure Evaluation
Similar to the random vibration evaluation, the best method to evaluate the CCA for failure over shock is to return to Steinberg’s empirical data. Steinberg states that the maximum desired displacement of a CCA during a shock event is approximately 6X the displacement calculated for the random vibration threshold.1 The displacement plot from the response spectrum analysis is shown in Figure 18.
The maximum displacement from the response spectrum analysis is predicted to be 0.066”. The maximum allowable displacement and corresponding Factor of Safety is as follows:
While the deformation of the CCA exceeded the random vibration threshold, the deflection limit over shock is much more forgiving. Based on the results above, both the CCA and the chassis are expected to successfully pass the shock testing.
Conclusion
As the industry focuses on getting lighter and smaller all the while obtaining better performance, following good design practices is critical. As we’ve seen from this study, even though the chassis is over designed for this application, the results from the analysis of the CCA shows concern for reliability and indicates that failures are likely to occur.
Iteration is a natural function of design, but in almost all cases, it is cheaper and more expedient to identify the problems through analysis than it is to correct the failures in the field. Performing analyses such as those described in this document to cap off the design phases of your project provide opportunities to predict risk areas allowing iterative improvement without the expense of test and discovery phases. In turn, your product development cycle is condensed and the end result is a successful design that can be qualified and deemed flight worthy.
References
The methods outlined here are universally accepted by the avionics industry and can be found in the following references:
1Steinberg, Dave. Vibration Analysis for Electronic Equipment. John Wiley & Sons, 2000
2https://standards.nasa.gov/
3Juvinall and Marshek. Fundamentals of Machine Component Design, John Wiley & Sons, 2000
The CCA model used in this study is the Novena PVT1 from the following:
FEA Tool: ANSYS
CAD Tool: SolidWorks