Frequency Resolution in Random Vibration Control

Data Physics was the first to market very high resolution random control – 6400 lines of resolution. The use of narrowly spaced spectral lines in random control has both positive and negative effects.

The first advantage of higher frequency resolution is seen when testing devices with very sharp resonances. Increasing the number of frequency lines enables finer frequency resolution to more accurately measure the sharp resonances. More importantly, it allows the random controller to generate a drive signal with higher resolution to compensate for these resonances.

High frequency resolution can also be important at low frequencies in a random test. Random tests with high amplitudes at the lowest frequencies can require significant displacement from the shaker. It is important that the controller provide a sharp roll off at frequencies below the minimum test frequency to reduce this displacement. The roll off is a function of dB per spectral line so more frequency lines below the minimum frequency will enable a sharper roll off and result in lower displacement.

While the benefits of higher resolution are obvious, there is a cost. The frequency resolution is inversely proportional to the length of the time record required for the fast Fourier transform. Doubling the number of frequency lines in a random test will double the time duration of each FFT. This increase in FFT time reduces the responsiveness of the control in two ways. The time between drive updates (loop time), is at least one FFT frame duration, and can be more. The result of increased frequency resolution is therefore increased loop time. In addition, the control power spectral density (PSD) is an average of a large number of FFT frames. The measurement accuracy is expressed in degrees of freedom (DOF), with each FFT frame representing 2 DOF. A typical random test uses 120 DOF for control averaging. This means that it will take 60 FFT frames to completely refresh the control PSD.

As an example, look at a typical test of 120 DOF with 6400 spectral lines to 2000 Hz, which means that the there is a frequency line every 0.3125 Hz and a time span of 3.2 seconds per FFT. The best possible loop time is 3.2 seconds. It will take 60 averages x 3.2 seconds = 192 seconds before the correction is fully measured. In other words, if something should change in the test, it will not be fully visible in the PSD until 192 seconds have elapsed! Depending on the control implementation, the corrective action may begin many loop times from the instant of change and every new update at least 3.2 seconds from the previous. The effect of this is easily observable at the start of a test when the system is making corrections to compensate for a resonance. A test running with 800 frequency lines will typically make the necessary corrections in 1/4 the time required for the same test running with 6400 frequency lines.

It is important when setting up a test to select the appropriate number of frequency lines for the test. More frequency lines than necessary can reduce the control performance. SignalStar controllers currently offer up to 6400 lines of resolution, which is more than most users want and considerably more than most users need. Increasing resolution to extremely high levels has very serious consequences to the speed of the control loop, and therefore to the overall safety of the test. In a sense, a controller with extremely high resolution is making its primary function of control irrelevant. This type of testing may be acceptable in low-level, low-end applications, but operators of high end tests with expensive test components need to use caution and understand the ramifications of high resolution.

Frequency Line Selection - Vibration Controllers - Data Physics CorporationFrequency Line Selection in Random Control on Vector




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