# Difference between G-force and Grms

I am currently doing a vibration analysis using a random vibration machine which gives Grms value based on Power Spectral Density (PSD) plot using Fast Fourier transform(FFT).

Before I ran the test on my specimen, I tried to characterise the vibration using a DDSR board (accelerometer). Interestingly, the G-force recorded from the accelerometer far exceeds the values i've set on the random vibration machine.

Anyone knows why?

Mech_Engineer
Gold Member
The maximum acceleration from the accelerometer is probably a larger value, but what is the root mean squared (RMS) average over a period of time? I think the Grms value is an average of the random acceleration vibrations for a "long" period of time.

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The maximum acceleration from the accelerometer is probably a larger value, but what is the root mean squared (RMS) average over a period of time? I think the Grms value is an average of the random acceleration vibrations for a "long" period of time.

Yes the accelerometer is of a larger value as i'm referring to the peak values and Grms is derived from the integral of the PSD plot.

But how do i convert the g-force values of the accelerometer such that i can compare it with the Grms value the vibration machine gives? (both the accelerometer and vibration machines are done over the same time interval)

I've attached the plotted graphs, The shape of the graphs coincides, however the magnitude differs quite significantly. How would you suggest to reconcile both graphs?

Thanks!

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Out of interest, why do you want to do that anyway? In my experience the important thing from that graph is being able to identify the natural frequencies. The graph you have is quite awesome compared to a lot that you get doing vibrational stuff. If you don't mind me asking, how are you going to do this? By looking at the graph or have you found an easier way? Again, that's a damm nice output. It's either luck that you excited it at the right range or you got some skill.

- I want to reconcile the graphs as I want to confirm the magnitude of vibration applied by the vibration machine to the test specimen. ( however by using an accelerometer, it gives g-force while machine gives Grms)
- The vibration machine is a random vibration machine, as such does not follow a defined frequency but instead a range of frequency.
- I am still thinking of how to meaningfully compare the graphs, that's why I have posted on the forum to seek advice. ( I don't think it's right to just compare the shape + inherently I think I'm comparing two different things i.e. G-force& Grms)

Grms is the root mean square of the accelerometer output. It is calculated by squaring the magnitude of the signal at every point, finding the mean value of the squared magnitude, then taking the square root of the average value. Mech is right, it's just the RMS over a range. Obviously I can't check this for you without the data, but it'd be easy in excel or matlab. I did a quick one by approximating the average and calculated the Grms for a couple points, and it comes to about right.

Also, can you alter the sampling rate for the FFT? Would be nice to get a better graph for comparison. It doesn't really matter, but would just be nice to see if it makes any difference when getting the RMS.

I still don't see why you're comparing them. I usually stop when I get a graph I can read properly, doesn't matter how you got it, the excitation peaks will be the same. Unless you're using it for other stuff. Just interested.

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Grms is the root mean square of the accelerometer output. It is calculated by squaring the magnitude of the signal at every point, finding the mean value of the squared magnitude, then taking the square root of the average value. Mech is right, it's just the RMS over a range. Obviously I can't check this for you without the data, but it'd be easy in excel or matlab. I did a quick one by approximating the average and calculated the Grms for a couple points, and it comes to about right.

You are both right. But thanks for the detail in explanation for the part on RMS @Vadar2012.

I'm comparing because I want to ensure that the level of excitation at the component on the test specimen is really experiencing the desired magnitude of vibration that I've set on the vibration machine. (unique because the specimen is placed in a non-conventional orientation)

--The excitation peaks are the same, but the magnitude is not.--
For example, look at the highest peak which is at 20Grms , but on the accelerometer graph it gives approx. 38G. That doesn't seem to agree with each other. After I've done an RMS calculation, I still got 38. ( But that is probably because the G -values on the accelerometer are the peak values??)

cheers

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Mech_Engineer
Gold Member
I notice the magnitude is close for a single axis rather than the vector sum of the 3; is it possible the Grms value is along a single axis (say the X axis)?

Also, how is the table measuring the Grms value? Where is its accelerometer? Ideally if you want the numbers to match you want the two accelerometers close together...

I notice the magnitude is close for a single axis rather than the vector sum of the 3; is it possible the Grms value is along a single axis (say the X axis)?

Also, how is the table measuring the Grms value? Where is its accelerometer? Ideally if you want the numbers to match you want the two accelerometers close together...

Your first statement gave me clues. I went to look at the drawings for the vibration machine and it has only ONE accelerometer measuring a single axis. It is placed close to the specimen.

However, upon reading some literature (attached file), the Grms and G-force values are correlated by a amplification factor blah blah... but i cannot place a accelerometer measuring g-force in to random vibration machine to expect it to coincide with each other.

Nevertheless, after applying a correlation formula, the correlation is sufficiently consistent and close! I guess this is where this thread ends! Thanks.

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• Test_my_product_using_Sine_or_Random.pdf
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Mech_Engineer