Time signatures

In polarography, not enough time is available for the diffusion layer to reach its stationary thickness. Instead, the current per unit electrode area decreases with the square root of time, the signature time-dependence for diffusion. On the other hand, the area of the growing drop expands, proportional to the two-thirds power of drop age r (i.e., time elapsed since the previous mercury drop fell off). These two counteracting effects, diffusion currents per area proportional to r 1/2, and area growth as t2/3, combine to yield polarographic current-time curves with a time dependence of t-1/2 X t2/3 = t1/6, as expressed in the Ilkovid equation. 

If time and circumstances permit, data should be recorded when the compressor is run on process gas to establish a new base reference point. During operation, all monitoring equipment should be observed to establish a signature of vibration and temperature, and to be sure these data are all within permissible limits. 

Other signatures may also be required. Eor example, if there are sub-eontraetors who will be performing site work, a representative from the subeontraeting firm should review and approve the plan. If the site has oversight eontraetors present, is eomplieated, large in size, or ineludes work that is projeeted to take plaee over a long period of time, there will likely be additional approvals required. 

When the signature of a machine is compared over time, it will repeat until some event changes the vibration pattern (i.e., the amplitude of each distinct vibration component will remain constant until there is a change in the operating dynamics of the machine-train). 

As shown previously, vibrations can be displayed graphically as plots which are referred to as vibration profiles or signatures. These plots are based on measurable parameters (i.e., frequency and amplitude). Note that the terms profile and signature are sometimes used interchangeably by industry. In this chapter, however, profile is used to refer either to time-domain (also may be called time trace or waveform) or frequency-domain plots. The term signature refers to a frequency-domain plot. 

Actual time-domain vibration signatures are commonly referred to as time traces or time plots (see Figure 43.17). Theoretical vibration data are generally referred to as waveforms (see Figure 43.18). 

In order to analyze this type of plot, the analyst must manually change the time scale to obtain discrete frequency curve data. The time interval between the recurrences of each frequency can then be measured. In this way, it is possible to isolate each of the frequencies that make up the time-domain vibration signature. 

With frequency-domain analysis, the average spectmm for a machine-train signature can be obtained. Recurring peaks can be normalized to present an accurate representation of the machine-train condition. Figure 43.20 illustrates a simplified relationship between the two methods (i.e., time-domain and frequency-domain). 

Comparative analysis directly compares two or more data sets in order to detect changes in the operating condition of mechanical or process systems. This type of analysis is limited to the direct comparison of the time-domain or frequency-domain signature generated by a machine. The method does not determine the actual dynamics of the system. Typically, the following data are used for this purpose (1) baseline data, (2) known machine condition, or (3) industrial reference data. 

The phrase full Fast Fourier Transform (FFT) signature is usually applied to the vibration spectrum that uniquely identifies a machine, component, system, or subsystem at a specific operating condition and time. It provides specific data on every frequency component within the overall frequency range of a machine-train. The typical frequency range can be from 0.1 to 20,000 Hz. 

Most predictive-maintenance programs rely almost exclusively on frequency-domain vibration data. The microprocessor-based analyzers gather time-domain data and automatically convert it using Fast Fourier Transform (FFT) to frequency-domain data. A frequency-domain signature shows the machine s individual frequency components, or peaks. 

The frequency-domain, or TFT, signature acquired at each measurement point is an actual representation of the individual machine-train component s motion at that point on the machine. Without knowing the specific location and orientation, it is difficult - if not impossible - to correctly identify incipient problems. In simple terms, the TFT signature is a photograph of the mechanical motion of a machine-train in a specific direction and at a specific point and time. 

A series of baseline or reference data sets should be taken for each machine-train included in a predictive-maintenance program. These data sets are necessary for future use as a reference point for trends, time traces, and FFT signatures that are collected over time. Such baseline data sets must be representative of the normal... 

Two point correlations We liave already mentioned several times that evolutions generally induce correlations between cell values at different sites indeed, the presence of correlations is a telltale signature of self-organization. The average density discussed above, however, is too crude a measure to capture these finer details. 

For regular motion, T> t) grows only linearly with time, so that the exponents are all zero. On the other hand, because chaotic flows are characterized by exponential divergences of initial nearby trajectories, a characteristic signature of such flows is the existence of at least one positive Lyapunov exponent. 

---