Page 52 - Prosig Catalogue 2005

SOFTWARE PRODUCTS
A SIMPLE FREQUENCY RESPONSE FUNCTION

of rotation or the second harmonic. In the case of rotating machinery we
call this second order.
Orders
Training & Support Figure 5: Tacho signal (slow speed)

Figure 9: Orders and overall level
Condition Monitoring Figure 6: Tacho signal (high speed) Figure 9 shows the 2nd, 4th and 6th orders overlaid with the overall level.
Details of the orders can be extracted from the waterfall plot and an
example from our data can be seen in Figure 9.

The overall level represents the total energy at each speed.
Synchronously Sampled Data (The Order or Angle
Domain)
Once data has been captured along with a tacho signal, software such
as Prosig’s DATS package, can resample the data and convert it to the
processing software analyses the entire tacho signal and produces
angle domain. This means that each data point represents equally spaced
another signal with represents speed over the time of the test. This can
positions around a rotation cycle rather than equally spaced points in
be seen in Figure 7.
time. This enables easy analysis with a DFT to extract the orders directly,
even if the speed varies dramatically during a cycle. Data which is
synchronously sampled in this way can be averaged across cycles in the
angle domain, thus eliminating the noise of signals from other sources
which are not related to the rotation. Further details of these techniques
Software Measurement Blog - http://blog.prosig.com.
can be found elsewhere in this handbook and on the Noise & Vibration
A Simple Frequency

Response Function
Figure 7: Speed v Time
The following article will attempt to explain the basic theory of the
Here we can see that, during our test the engine accelerated from just frequency response function. This basic theory will then be used to
over 1000rpm to over 6000rpm in around 5.5 seconds. calculate the frequency response function between two points on a
Waterfall Plots structure using an accelerometer to measure the response and a force
gauge hammer to measure the excitation.
The next step in our processing is to perform our “Hopping FFT”
Hardware processing again, but this time instead of calculating the FFTs at equally representation of the relationship between the input and the output of
Fundamentally, a frequency response function is a mathematical
spaced time steps we calculate them at equally spaced speed steps using
a system.
the information from our speed v time data. This is what is known as
“Waterfall” processing. The waterfall plot of our noise signal can be seen
So, for example, we can measure the frequency response function between
two points on a structure. It would be possible to attach an accelerometer
at a particular point and excite the structure at another point with a force
gauge instrumented hammer. Then by measuring the excitation force
and the response acceleration the resulting frequency response function
would describe as a function of frequency the relationship between those
two points on the structure.
The basic formula for a frequency response function is
System Packages in Figure 8. Figure 8: A Waterfall Plot (Frequency v Speed) Where H(f) is the frequency response function,

Y(f) is the output of the system in the frequency domain
and X(f) is the input to the system in the frequency domain.
Frequency response functions are most commonly used for single input
Now we can clearly see the linear nature of the speed related noise.
and single output analysis, normally for the calculation of the H1(f) or
This shows up as sloped lines in the waterfall plot. Because this is a four
H2(f) frequency response functions. These are used extensively for

52 cylinder, four stroke engine, the dominant frequency is twice the speed hammer impact analysis or resonance analysis.
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