振动疲劳理论：软件仿真分析全攻略(Ⅰ)

In the mission profiling stage, the measured customer usage (CU) events and data are required to be identified first. For each CU event, two damage criteria such as the shock response spectrum (SRS) and the fatigue damage spectrum (FDS) are used to represent the customer usage profile in terms of damage severity. The shock response is referred to the largest displacement or acceleration response of a system subjected to a time-based excitation. For a linear SDOF system with a given natural frequency and damping ratio, the shock response (SR) and fatigue damage (FD) can be easily calculated.

Both SRS and FDS in each CU event can be generated by varying the natural frequency one at a time in a frequency range of interest. The SRS is sometimes termed the extreme response spectrum (ERS) if the system is subjected to a frequency-based excitation. To represent the worst local response likely to be seen by the linear SDOF system during the entire life of the product in all the CU events, the lifetime SRS can be obtained by using an envelope of all the measured SRSs. Moreover, the lifetime FDS is determined by the sum of all the FDSs, based on the Palmgren–Miner linear damage rule (Palmgren, 1924; Miner, 1945).

In the test synthesis stage, a close-form solution to calculate ERS and FDS due to a vibration test profile such as the power spectral density (PSD) has been successfully derived by Lalanne (2002) based on test duration. Therefore, the test PSD is obtained from the lifetime FDS. The accelerated test time can be determined based on the principle that the ERS of the test PSD should be compared with the lifetime SRS by adjusting the test duration, and be less than the lifetime SRS to minimize the risk of shock failure during testing.

the formula was derived based on the following assumptions:

• Using Miles’ equation for calculation of the root mean square acceleration in Gs

• A linear stiffness constant to relate the relative displacement to the local stress

• The narrow-band random stress process

• The Rayleigh PDF for the stress amplitude

Ncode-VibeSys Worked Examples-3. Creating Accelerated Vibration Fatigue Tests

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