During a modal impact test, a Frequency Response Function (FRF) is calculated to determine the natural frequencies of the structure under test. A FRF is a measure of the systems output in response (usually acceleration, velocity or displacement) to a known input (usually force).
To calculate an experimental FRF function, both the input and output response signals are measured using sensors, like load cells and accelerometers.
For a good measurement the input force must:
excite a broad range of frequencies at high amplitude (eg, above the noise floor of the instrumentation)
have amplitude evenly distributed versus frequency
An ideal input force should be uniformly distributed vs. frequency
The general idea is that resonant frequencies can be easily identified by applying the same force level across the entire frequency range. Frequency peaks in response to the force correspond to resonant frequencies.
Time vs Frequency domain
The width of the input force is controlled by the length of time of the impact pulse. The shorter the impulse duration, the broader the frequency domain response becomes.
In general, there is an inverse relationship between the time and frequency domain of a signal. Signals with short durations is time, have a broad response in frequency and vice versa.
For example, a sine wave, which is continuous in the time domain has a narrow frequency spectrum.
Short, transient pulses in the time domain, on the other hand, have a wide frequency spectrum.
So a short pulse is desired for a wide excitation frequency range, but how is this achieved in practice?
Modal impact hammers come with a variety of tips with different stiffness values as well as mass extensions.
The input force frequency range can be controlled by changing the hammer tip in two ways:
Hammer Mass – Decreasing the mass of the hammer tip causes the hammer to contact the structure for a shorter amount of time. The reduced mass allows the hammer to reverse directions more easily after hitting the structure, reducing the time it is in contact.
Hammer Stiffness – Increasing the stiffness of the tip allows shortens the duration that the hammer is in contact with the structure. For example, one could replace a rubber tip with a metal tip.
The desired result is a clean FRF over the full frequency range of interest and a relatively even input spectrum throughout that same frequency range.
If the FRF becomes noisy at higher frequencies and the input spectrum drops off significantly, this is an indication that our hammer tip may be too soft.
Tip "too" soft - Green: coherence, Red: FRF, Blue: input force spectrum
If all the modes of the structure are excited, far beyond the frequency range of interest, there may be noise on the FRF at lower frequencies which indicates that the hammer tip may be too hard. This would be caused by creating “out-of-band” overloads.
Tip "too" hard - Green: coherence, Red: FRF, Blue: input force spectrum
The mass of the hammer is also important for assuring that enough force is being input into the structure to excite it. So a heavier hammer tip may be needed to ensure that the force levels are high. For example, hitting a 50 ton boat with a one pound hammer will not excite the modes of the boat.
Like Goldie Locks looking for a bowl of porridge or a place to sleep, we are looking for hammer tip that is ‘just right’.
The correct tip will cause enough energy to excite the full frequency range of interest, but not significantly beyond.
The correct tip will also ensure that enough force is being input into the structure to excite the modes of the structures.
Tip "just right" - Green: coherence, Red: FRF, Blue: input force spectrum