Lidia Schelhorn did her honours project at the Associate Professorship of Computational Mechanics (TUM)
in cooperation with ArianeGroup. She was supervised by
Prof. Dr.-Ing. habil. Fabian Duddeck and Pablo Martinez Rodriguez M.Sc.
Fatigue failure due to damage accumulation is one of the most common failure modes of metallic structures and needs to be addressed at the early stage of the design process. Spacecraft components are subjected to random vibrations during the vehicle’s launch and must be designed to withstand a specific vibration loading environment in terms of power spectral density (PSD) specifications. In this context, the assessment of random vibration fatigue plays a significant role in the design process.
The main objective of this project is to implement a suitable approach for random vibration fatigue life estimation in the commercial FEA software ANSYS. For this purpose, the ANSYS Application Customization Toolkit (ACT) is employed. ACT provides a development environment for users in order to customize specialized processes and extend the functionality of already existing ANSYS products.
Different techniques have been developed over the years in order to calculate damage induced by random vibration loading. Time-domain methods employ cycle-counting techniques (e.g. rainflow counting) in order to identify the number of cycles in an irregular loading history. Although being the most accurate techniques, they are computationally expensive due to the required transient dynamic analysis. For application at the early stage of the design process, a rather fast fatigue damage assessment is necessary. Thus, the numerically efficient frequency-domain methods are more suitable for a first damage estimation. Here, the available methods can be roughly classified in simplified empirical approaches like Steinberg’s three-band technique, and more advanced methods such as Dirlik’s approach. For the simplified methods, only the root mean square (RMS) result values of the random vibration analysis are used, while assuming either a Rayleigh or Gaussian distribution of the peak values. The advanced techniques, on the other hand, aim at an approximation of the probability density of the stress amplitudes based on the calculated response spectrum. Since they require a computationally more expensive analysis, these techniques are rather suitable for detailed analyses. Therefore, Steinberg’s empirical technique is selected for the implementation of the fatigue life assessment tool in ANSYS. Figure 1 shows the implementation flowchart of the developed ANSYS extension.
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Steinberg’s empirical method estimates the actual number of cycles during exposure to random vibration based on the statistical frequency of positive zero crossings. The allowable number of cycles is usually extracted from fatigue test data (S-N curves). However, this data is often not available and the allowable cycles to failure need to be estimated with general approaches. In the scope of this project, the modified method of universal slopes is employed. Finally, the vibration induced damage can be calculated using Palmgren-Miner’s hypothesis of linear damage accumulation.
In a final step, the developed ANSYS extension is tested on a simple application case illustrated in Figure 2. The plate is made of an aluminum alloy and is supported at the three bolt interfaces, accommodating a point mass of 1 kg on its top surface.
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After identification of the eigen frequencies in a modal analysis, a power spectral density (PSD) base excitation is applied in X direction of the supported plate. Assuming a Rayleigh distribution of the equivalent total strain peaks, the cumulative damage after 10 minutes of vibration exposure is presented in Figure 3. With the results obtained, it can be concluded that depending on the critical value of cumulative damage (< 1.0), the structural integrity might not be fully ensured at the plate’s top region.
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Further tests were successfully performed on more complex spacecraft component structures. However, it is noted that the accuracy of the implemented method is ensured for narrow-band random processes only. Since real-world applications often involve wide-band random processes, an integration of more advanced methods in the developed ANSYS extension is highly recommended.