Vibration Test Simulation
Vibration Test: Theoretical Foundations
What is Vibration Test Simulation?
Professor, what is the purpose of conducting FEM simulation for vibration tests?
Two purposes:
1. Pre-test Risk Assessment โ Identify the risk of failure due to resonance beforehand
2. Optimization of Test Conditions โ Review excessive test conditions (prevention of over-testing)
Types of Vibration Tests
| Test Type | Input | Purpose | Standards |
|---|---|---|---|
| Sinusoidal Sweep | Sine wave (frequency sweep) | Understanding resonance characteristics | MIL-STD-810 |
| Random Vibration | PSD Input | Replication of actual usage environment | MIL-STD-810, IEC 60068 |
| Shock Test | SRS or Half-sine wave | Verification of shock resistance | MIL-STD-810 |
| Sine Burst | Burst of sine waves | Verification of response at resonance | Internal company standards |
Replication in FEM
Replicate the state mounted on a vibration test shaker in FEM:
1. Modeling of the Fixture โ Fixture connecting the test specimen and the shaker
2. Base Excitation Input โ Acceleration input from the shaker
3. Frequency Response or Time History Analysis โ Depending on test conditions
4. Response Evaluation โ Maximum values of acceleration, stress, displacement
Do we also model the fixture?
If the natural frequency of the fixture falls within the test frequency band, the fixture's resonance affects the test results. Model the fixture to check for fixture resonance beforehand.
Summary
Key Points:
- Pre-test risk assessment and condition optimization โ The two purposes of FEM
- Sinusoidal sweep / Random / Shock โ The three main test types
- Fixture modeling is important โ Be cautious of fixture resonance
- MIL-STD-810, IEC 60068 โ Major vibration test standards
Theoretical Background of Vibration Test Standards
Many vibration test standards are established by statistically processing measured PSD data from actual usage environments. MIL-STD-810G (2008) is a US Department of Defense environmental test standard for military equipment, categorizing transport/usage environments into 10 PSD profile categories. The "Taylor Category C (Ground Vehicles)" shown in Annex C specifies a test level of 0.04 Gยฒ/Hz from 20 to 500Hz. However, the concept of safety factors differs between IEC 60068 and MIL-STD, and some harmonization is progressing through international harmonization (2016 revision of IEC 60721-3).
Computational Methods for Vibration Test
FEM for Sinusoidal Sweep
Sinusoidal Sweep = Frequency Response Analysis:
Nastran
```
SOL 111
CEND
METHOD = 10
FREQUENCY = 20
DLOAD = 100
```
Input acceleration as base excitation with frequency sweep.
FEM for Random Vibration
```
SOL 111
CEND
RANDOM = 20
```
Random response with PSD input.
Acceleration Response Evaluation
Main evaluation items for test results:
| Item | Sinusoidal Sweep | Random |
|---|---|---|
| Peak Acceleration | FRF peak value ร input | 3ฯ (3รRMS) |
| Resonance Frequency | FRF peak location | โ |
| Stress | Stress conversion from FRF | 3ฯ stress |
Summary
Mechanism of Shaker Control Loop
Control of random vibration tests using electrodynamic shakers is a closed-loop process: โ Set reference PSD (Target PSD), โก Controller corrects shaker dynamics via inverse system identification (FRF measurement), โข Drive signal is iteratively updated so that the PSD at the control point (usually an accelerometer on the mounting table) converges to the target value. Convergence criteria are generally ยฑ3dB RMS error, and the time to achieve 1Hz resolution control averages 20โ60 seconds. The Vibration Research VR9500 controller's convergence algorithm is considered among the fastest in the industry.
Vibration Test in Practice
Prevention of Over-testing (Force Limiting)
In vibration tests, differences in impedance between the test article and the shaker can cause inputs greater than the actual environment (over-testing). Calculate the actual environmental input with FEM and optimize test conditions (Force Limiting). The method is specified in NASA-HDBK-7004.
So test conditions can sometimes be more severe than the actual environment?
The test shaker is an "ideal rigid wall", but the actual mounting state (e.g., upper stage of a rocket) is a "flexible structure". Applying the rigid shaker's input to equipment mounted on a flexible structure can cause resonance response to be many times greater than in the actual environment. Calculate the mounted impedance with FEM and notch (cut out) the test conditions.
Practical Checklist
So "prevention of over-testing" is one of the important purposes of FEM simulation.
Failure of test articles is costly. Optimizing test conditions beforehand with FEM can prevent unnecessary failures due to over-testing.
Vibration Test Certification Process for Automotive ECUs
Vibration test certification for automotive ECUs (Engine Control Units) is conducted in accordance with ISO 16750-3. Products mounted in the engine compartment require combined sine + random tests of Category M (10โ2000Hz, including engine components), with a test duration of 96 hours per axis. Bosch's DE10-type ECU completed the Category M2 equivalent test (RMS 22G) at BMW's certification test facility in 2022 and was adopted for the BMW 5 Series (G60 model). Test costs typically range from 2 to 5 million yen per lot (3 samples).