Troels Dyhr Pedersen.indd - Solid Mechanics

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The SPL of the cylinder pressure, the acceleration level and the acoustic SPL can be
calculated in short intervals and presented as in figure 15:
Figure 15: Time domain representation of the SPL of the cylinder pressure, the engine acceleration
level and the acoustic sound pressure level
Here the SPL is expressed in dB. The red line represents the cylinder SPL which is seen
to increase by more than 50 dB after combustion. The acceleration level (white line)
increase by a similar dB value and is generally coherent with the cylinder pressure SPL.
The acoustic signal (green line) also increases but remains at a higher level. As
mentioned, the acoustic signal originates from the cylinder block resonance which is not
properly measured by the accelerometer, and these vibrations are present much longer
than the higher frequencies which tend do be attenuated fast.
The time domain representation is useful to show the signal amplitude in time and how it
is attenuated. It is however not possible to determine which frequencies are present in the
signal. This may instead be visualized in with the frequency domain representation.
11.6.4 Frequency domain representation
To evaluate the frequency content in a discretely sampled signal, a DFT algorithm is
used. The specific algorithm commonly applied is called Fast Fourier Transform (FFT).
In the analysis, the frequency range from 0 Hz to the Nyquist frequency is split up into a
number of equally spaced intervals. The number of intervals is equal to the sampling
frequency divided by the number of samples, so that the frequency resolution becomes:
f s Δ f =
N s
Usually the number of samples Ns is required to be a power of two (2, 4, 8, 16 etc). It is
desired to have a short sample length in which the signal can be considered stationary.
The sampling frequency is however very high, which implies that a large number of
samples is also required to obtain an acceptable frequency resolution. To limit the sample