GRMS from PSD Calculator
Calculate the Root Mean Square Acceleration (GRMS) for a flat Power Spectral Density (PSD) profile.
What is GRMS?
GRMS stands for Root Mean Square Acceleration in units of gravity (g). It is the standard metric used in random vibration testing to quantify the overall energy of a vibration profile. Unlike sine vibrations which have a specific peak, random vibrations are described statistically across a frequency spectrum.
The Math Behind the Calculation
For a flat PSD (where the energy is constant across a range of frequencies), the formula to find the GRMS value is:
GRMS = √[ PSD × (f2 – f1) ]
- PSD: Power Spectral Density in g²/Hz.
- f2: High frequency limit of the spectrum.
- f1: Low frequency limit of the spectrum.
Step-by-Step Calculation Example
- Calculate the bandwidth: 500 Hz – 20 Hz = 480 Hz.
- Multiply PSD by bandwidth: 0.05 × 480 = 24 g². (This is the Area under the curve).
- Take the square root: √24 ≈ 4.89 GRMS.
Why do we use GRMS?
Engineers use GRMS to compare the severity of different vibration environments. However, it is important to remember that GRMS is a single-number summary. It doesn't tell you if the energy is concentrated at low frequencies (which cause high displacement) or high frequencies (which cause high stress). Always review the full PSD plot for a complete structural analysis.
Common PSD Levels
| Application | Typical GRMS |
|---|---|
| Commercial Transport | 0.2 – 0.5 GRMS |
| Jet Aircraft Equipment | 5.0 – 12.0 GRMS |
| Rocket Launch | 15.0 – 40.0+ GRMS |