Bracket — Random Vibration Fatigue

In many engineering situations, structural components are subjected to loading that can be considered random. One example is found in consumer electronics, where vibrations exerted onto the circuit boards and similar components are more or less random. Another example is chassis-mounted auxiliary components on a commercial vehicle, where, contrary to engine vibrations, road induced vibrations are more or less random. In order to make a traditional fatigue assessment of components like these, one would need to take a very large time domain sample of the vibration, and perform a time domain fatigue analysis. In most situations, this is impractical. Instead, the statistical information about the vibration is used (typically a PSD spectrum), and fatigue assessments can instead be made using this information. In this example, it is shown how to perform a fatigue analysis of a bracket subjected to random vibration loading.

Model Definition

The bracket geometry can be seen in Figure 1. The random vibration analysis for the bracket uses loading based on a power spectral density (PSD). The computations are based on the modal reduced-order model (ROM). Additional information regarding the model set up, including loading and boundary conditions, can be found in the documentation of the application Bracket — Random Vibration Analysis, found in the Structural Mechanics Module.

Figure 1: The bracket geometry.

Fatigue Analysis

Two cycle counting models are available when performing a random vibration fatigue analysis: the empirical model by Dirlik, and the Bendat (narrow-band) model. In this example, you will use the Dirlik and Bendat models, and pair them with the Basquin fatigue criterion to compute the fatigue life of the bracket. The Basquin fatigue criterion is given by:

(1)

where, in this example, the amplitude stress σa is related to the number of cycles Nf through the parameters σf' = 2.2 GPa and b = −0.25.

Results and Discussion

Figure 2 shows the computed fatigue life according to Dirlik’s model, and Figure 3 shows the computed fatigue life according to Bendat’s model. Both models predict a critical point near a stress concentration, at a fillet. Bendat’s model predicts a shorter life (21.4 h) than Dirlik’s model (25.0 h). Bendat’s model tends to be conservative when the stress response is not narrow-band