The Calculation of gRMS, by Neil Doertenbach, from Qualmark Corporation describes the process of calculating gRMS values when using a repetitive shock table used in Qualmark’s line of HALT chambers. gRMS is typically used to specify and compare the energy in repetitive shock vibration systems.

## Introduction

The metric of gRMS is typically used to specify and compare the energy in repetitive shock vibration systems. However, the method of arriving at the gRMS measurement (input signal filtering, cutoff frequency of the measurement) can have a dramatic effect on the value. It is important to understand how the measurement is made, and to understand its limitations, in order to use it effectively. This paper will describe the metric of gRMS, how it is calculated in both the frequency and time domains and what factors can cause variations in gRMS calculations.

## What is gRMS?

Repetitive shock (RS) vibration systems produce a continuously varying pseudorandom broad spectrum vibration. A typical real time signal from an accelerometer mounted on an RS table is shown in figure 1. The root mean square (rms) value of this signal can be calculated by squaring the magnitude of the signal at every point, finding the average (mean) value of the squared magnitude, then taking the square root of the average value. The resulting number is the gRMS metric. (Note: Since this paper addresses gRMS calculations specifically, all of the discussion here assumes a signal source that is representative of g’s (acceleration). However, the discussion would apply equally well to any measured signal.)