Page 53 - Prosig Catalogue 2005

SOFTWARE PRODUCTS
A SIMPLE FREQUENCY RESPONSE FUNCTION

The H1(f) frequency response function is used in situations where the In this case the response or output would be the accelerometer, as shown
output to the system is expected to be noisy when compared to the input. in Figure 2.
The H2(f) frequency response function is used in situations where the However as discussed earlier the frequency response function is a
input to the system is expected to be noisy when compared to the output. frequency domain analysis, therefore the input and the output to the
Additionally there are other possibilities, but they are outside of the scope system must also be frequency spectra. So the force and acceleration
of this article. must be first converted into spectra.
H1(f) or H2(f) can be used for resonance analysis or hammer impact The first part of the analysis requires the Cross Spectral Density of the
analysis. H2(f) is most commonly used with random excitation. input and output, this is S (f). This is calculated using the response as Training & Support
xy
The breakdown of H1(f) is as follows, the first input and the excitation as the second input to the Cross Spectral
Density Analysis in DATS. The result is shown in Figure 3. Were S (f)
xy
being calculated for use with H2(f), for example, then the excitation
would be the first input and the response the second input to the Cross
Spectral Density Analysis in DATS.
Where H1(f) is the frequency response function,
S (f) is the Cross Spectral Density in the frequency domain of X(t) and
xy
Y(t)
and S (f) is the Auto Spectral Density in the frequency domain of X(t).
Condition Monitoring
xx
In very basic terms the frequency response function can be described as

The breakdown of H2(f) therefore is as follows,

Figure 3: Sxy(f)
Where H2(f) is the frequency response function,
S (f) is the Cross Spectral Density in the frequency domain of Y(t) and Next the Auto Spectral Density of the input, or excitation signal is required.
yx
X(t) This is calculated using the Auto Spectral Density Analysis in DATS, this
analysis is sometimes known as Auto Power, the result of which is shown
and S (f) is the Auto Spectral Density in the frequency domain of Y(t) in Figure 4, this is S (f).
yy
In very basic terms the frequency response function can be described as xx
Software

In the following example we will discuss and show the calculation of the
H1(f) frequency response function.
The excitation or input would be the force gauge instrumented hammer,
as shown in Figure 1 as a time history.

Figure 4: Sxx(f)
Hardware
The Cross Spectrum is then divided by the Auto Spectrum and the
resulting frequency response function is shown in Figure 5.

Figure 1: X(t)

System Packages

Figure 5: H1(f)
The response function would normally be shown in modulus & phase form
as shown in Figure 6.
The entire analysis as used in DATS.toolbox is shown in Figure 7, the
data flow from the original input and output, force and response, can
Figure 2: Y(t)

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