PSI - Issue 57

Sven Maier et al. / Procedia Structural Integrity 57 (2024) 731–742

734

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S. Maier et al. / Structural Integrity Procedia 00 (2023) 000±000

2.2. Considered uncertain input parameter

In this study a focus is set on the following epistemic input parameters: Concentrated mass of the automotive com ponent, modal damping, the thickness of the body-in-white plates and the thickness of the mounting. In a preceding concept investigation by means of sensitivity analysis these parameters have shown to be influential for the oscillation behaviour and fatigue for this type of mass force excited component Maier and Bachmann (2023). Without a previous measurement the distribution and scatter limits of the parameters have to be estimated. In Schueller (2007) a proposal for the scatter of the mentioned parameters based on experimental data and experience on similar structures can be found. According to this proposal the distributions of the considered parameters are assumed to be Gaussian, except of the modal damping which is assumed to be lognormally distributed. The parameters nominal value and coe ffi cient of variance (C.o.V.) are displayed in Table 1. For the nominal values, references of the Catia (computer-aided design (CAD) software) model were chosen. For the modal damping, according to Adams (1999), a value of 3% - 7% can be assumed for metallic structures with connections. The lower, more conservative limit of 3% was chosen for this study. Besides the nominal variant two additional variants with an increased mass and reduced sti ff ness are investigated:

• Variant 1: nominal • Variant 2: nominal with additional mass ( + 200 gram) • Variant 3: nominal with reduced plate thickness (-0.2 mm)

Table 1. Considered Parameters with assumed scatter.

Parameter

Nominal value

Unit

C.o.V. ( σ/µ )

Component’s concentrated mass m c

7.49E-01 4.0E-03 1.0E-03 8.0E-04

kg

3% 4% 4% 4%

Thickness of mounting t m

m m m %

Thickness of plate t p

Thickness of thinner plate t tp

Modal Damping ζ

3.0

20%

2.3. Simulation workflow

The simulation workflow starts with definition of the PSD loads, the model, investigated input parameters. Then a modal frequency response analysis (SOL111) by means of the software MSC Nastran is performed. The outputs of the dynamic analysis are the eigenfrequencies and eigenmodes of the system obtained with the aid of the Lanczos method. Further outputs are modal stresses, participation factors and transfer functions which are used in the followed vibration fatigue simulation with the aid of FemFat Spectral. The output of the FemFat computation is the damage or the fatigue lifetime. As mentioned above a frequency based method is used for the structural durability assessment. The linear damage accumulation depends on the probability density distribution of the stress amplitudes p a ( σ a ), which is determined by an empirical approximation formula proposed by Dirlik (1985) for broadband PSD signals. In addition to the distribution, the material constant of SN-curve ( σ k a N a = C s ) and total duration T of the load is used to estimate the damage. Thereby an expected value of the damage is calculated:

T C s

∞

σ k

a p a ( σ a ) d σ a

(1)

E ( D ) = ϑ p

0

Whereas ϑ p describes the expected rate of occurrence of peaks in a Gaussian process and depends on the spectral moments of the PSD load. For more detailed information regarding the used calculation technique the interested reader