Manufacturing Trend 2009/01-02, Technical diagnostics section

"Instead of firefighting and major repairs"

Condition-based maintenance with vibration diagnostics (VIII.)

Vibration spectrum analysis is currently the most effective machine condition assessment tool. To understand the frequency spectra, we must assume that each frequency peak, as well as the combination of frequency peaks, corresponds to a mechanically explainable alternating force found in the machine.

Common frequency units in machine diagnostics

The most common frequency unit for scaling the spectrum frequency axis is hertz (Hz, in memory of the French scientist, Hertz). This expresses the occurrence of a periodic event in one second, i.e., 1 Hz = 1 event/s. Since in machine diagnostics, it must be assumed that the strongest vibration excitation occurs at the rotational speed - thus the rotational frequency - due to the rotating part at this frequency, and most typical machine (mechanical) faults are related to the rotational frequency (or its integer multiples), scaling the spectrum frequency axis in revolutions per minute (RPM) is also common. However, the disadvantage of RPM scaling is that very large values are often displayed - disturbingly. To eliminate this, RPM multiples scaling is usually applied. In English literature, this is referred to as "order." Example for a rotational speed of 3000 RPM: rotational frequency 50 Hz = 3000 RPM = 1 order (first order) twice the rotational frequency 100 Hz = 6000 RPM = 2 order (second order) ten times the rotational frequency 500 Hz = 30000 RPM = 10 order (tenth order) The periodic vibrations of alternating forces generated during the operation of rotating machines. Each structural element has different mechanical (physical) properties - different stiffness, damping, natural frequency - and the machine structure as a whole can be modeled as a damped, multi-degree-of-freedom system in terms of the dynamic forces acting.

Since it is difficult to obtain information about the internal forces of the machine, the machine must be examined based on externally measurable vibrations that appear as a response to the force. In this, the greatest help is provided by the spectrum analysis of time signals, as the vibration components made "visible" in this way only need to be checked to see if their frequencies match those characteristic of the machine components and certain machine setting errors. These are the so-called fault frequencies, which can be clearly defined for most setting errors and damage to many machine elements.

Machine diagnostics based on fault frequencies

To understand the frequency spectra, we must assume that each frequency peak, as well as the combinations of frequency peaks, correspond to an explainable - mechanically explainable - alternating force found in the machine. To explain the mechanical aspect, one must know the structure of the machine and the resulting relationships. Despite the significant differences in machine construction, operation, and behavior, general definitions can be given for most fault phenomena, as the frequencies of expected vibrations can be calculated based on geometric or physical relationships. It is very important to consider that the frequency of most faults is speed-dependent. Therefore, knowledge of the machine's speed (numbers) is essential for the clear analysis of frequency spectra. Our table contains the expected (typical) vibration frequencies in the case of frequently occurring fault phenomena, shown in multiples of rotational speed, highlighting the dominant characteristic. Typical vibration frequencies of common fault phenomena Unbalance: 1 times rotational frequency Shaft misalignment. 1, 2, 3 (4) times rotational frequency Looseness, mechanical play: 1, 2, 3, 4, 5 (6, 7, 8, 9) times rotational frequency Gear faults. 1, 2, 3 times number of teeth × rotational frequency Blade faults (fan, pump): 1, 2, 3 times number of blades × rotational frequency Belt frequency (belt drive). calculated based on the geometrical dimensions of the pulleys, belt length, and rotational frequency Rolling bearing faults: calculated based on the bearing's geometrical dimensions and rotational frequency Electric motor electrical faults: 2 times mains frequency

As the table allows us to determine very well based on the machine's structure what frequency vibrations can be expected in the event of a specific fault, most diagnostic software assists in diagnostic work by graphically displaying fault frequencies: it only needs to be checked whether the drawn fault lines coincide with the spectrum peaks of the measured vibration signal.

Of course, based on the same principles, software can also generate list-like - textually annotated - fault reports and, through expert program modules, can detect machine faults with up to 80-95 percent certainty and provide textual evaluations. But let's stay a little longer in the realm of the "pedestrian method"...

Significance of parameters

Displacement, vibration velocity, or acceleration

While in the case of broad-spectrum vibration level measurements, we knew from standards that the vibration level characteristic of the machine state should be determined in vibration velocity, the high-frequency noise of rolling bearings is usually measured in vibration acceleration - during spectrum analysis, we must decide in which physical unit to represent the vibrations. Our decision depends on whether we want to examine the low or high-frequency components of the same vibration. Due to the frequency relationship, it is not possible to display the entire frequency range in such a way that all frequency components are scaled in the same unit and clearly visible.

However, the relationship is quite simple: low-frequency vibration components are effectively represented in displacement, the medium frequency range in vibration velocity, and high-frequency vibrations in vibration acceleration. (A display capable of showing everything at once but harder to read is logarithmic scaling, which graphically magnifies small amplitudes.) The typical display frequency ranges are shown in the diagram.

Resolution, number of spectrum lines, frequency range, averaging, measurement time

It is not a coincidence that we mention these parameters together, as they are closely related. Spectral resolution indicates the frequency distance between spectrum lines, in other words, the width of the lines. The smaller it is, the better the chance of separating closely spaced error phenomena frequency peaks. The number of spectrum lines is one characteristic of the instrument's spectral resolution capability. Knowing the adjustable frequency range, the smallest line width can be calculated.

In order for an instrument to record the desired spectrum, the laws of signal digitization and spectrum analysis must be met: the Fourier transformation requires twice as many time samples as the number of spectrum lines we want to display. However, to avoid signal distortion due to undersampling, the Shannon law must also be followed, which states that the highest frequency to be displayed must be recorded at least twice its frequency. Most handheld instrument manufacturers use 2.5 times the sampling rate to satisfy the Shannon theorem.

From the above, it follows that the time required for a spectrum measurement is as follows: t_measurement = number of spectrum lines × 2 / f_max x 2.5 To avoid wasting time unnecessarily, think about what you want to measure: increasing the resolution (width of spectrum lines) excessively, or selecting too low an upper frequency limit will also extend the measurement duration. To select the resolution, consider what the frequency difference might be between the two closest error phenomena frequencies at the given measurement point. The line width should be set to half of this - ideally a fifth. The upper frequency limit should be set depending on the nature and speed of the machine being measured. The detailed rules for this will be discussed in the next parts of our series. For noise reduction purposes (to improve the signal-to-noise ratio), multiple spectra are usually averaged. (Methods of averaging will be covered in a later article.) It has been mathematically proven that these spectra do not necessarily need to be recorded consecutively, but up to a 67% temporal overlap can be performed without information loss in data recording. Numeric example Determination of measurement time under the following conditions: averaging 8 spectra (67% overlap), 6400 lines, fmax=3200 Hz (thus, the spectrum resolution is 0.5 Hz).t_measurement = 8 × 67% × 6400 Hz × 2 / (3200 Hz × 2.5) = 8.576 s It should be noted that this time is not device-dependent and cannot be shortened, as it is mathematically necessary. The difference in instrument speed lies in how the automatic measurement range setting, offset compensation, and signal processing-display are implemented algorithmically and quickly. These time requirements are in addition to the calculated time.

Vibration Diagnostics Based on Spectrum Analysis

As mentioned earlier, to understand vibration spectra, we must assume that each frequency peak, as well as combinations of frequency peaks, corresponds to mechanically explainable alternating forces in the machine. Once we find the mechanical explanation, we are already very close to the necessary corrections. A frequency spectrum can appear as shown in the diagram.

Each spectrum contains a large number of frequency peaks, which initially make the diagram look complex. However, with systematic evaluation, the picture quickly becomes clear. To determine the nature and cause of the vibration, start with analyzing the frequency peak with the highest amplitude in the spectrum, as well as the dominant peak group (harmonic frequency peaks). It is very helpful to know the typical vibration spectra of common machine faults, as these need to be compared with the actual spectrum. In the next installment, we will examine the appearance of the most common machine faults in the spectrum.

Rahne Eric (PIM Ltd.) pim-ltd.com, machineryexpert.com

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