### Parameter Selections in Vibration Measurement

Vibration measurements are performed to determine the response of machine equipment to both internal and external forces. In mechanical systems, different points of the same equipment are different in geometry, material, etc. That’s why they may have distinctive vibrations due to effects. As an example, when an electric motor operates at high frequencies, frequency of reducer output shaft will be much lower in a system consisting of electric motor and reducer in a conveyor line. Using the same parameters for vibration measurement of both parts may cause misleading measurements. In such cases, vibration measurement parameters must be edited.

In the analog-to-digital conversion (ADC), so-called sample size of the digital waveform must often be taken to reproduce the signal accurately. Vibration measurements are usually taken over a duration of time and repeated periodically. The analog signal is converted into a digital signal with samples taken at specific time intervals called sampling time (1/fs). The number of samples taken per second is called sampling rate or sampling frequency. Periodic measurement times are obtained by dividing sample size by the sampling frequency. Half of the sampling frequency (fs/2) is often referred to as **Nyquist Frequency.**

Fig. 1 Time and Frequency Domain Parameters

Any analog signal consists of components of various frequencies. The highest frequency (*f*_{max}) component in an analog signal determines the bandwidth of that signal. Assuming that the highest frequency component for a given analog signal is f_{max}, according to the Nyquist-Shannon Sampling Theorem, the sampling rate should be at least 2×*f*_{max}, or twice the highest analog frequency component. It is important to understand what the sampling theorem means. If the sampling theorem is performed before sampling an analog signal, then the sampled signal exactly represents the analog signal. In this case, the sampled signal contains all the information in the analog signal. Aliasing occurs when the sampling frequency is less than 2 times the largest frequency in the analog signal (*f*_{s}<2*×f*_{max}). Aliasing prevents the high frequencies in the analog signal to be seen in the spectrum and causes the signals generated by the vibration source to be misinterpreted. Just as insufficient sampling frequency causes aliasing, insufficient sampling size also weakens the frequency resolution in the spectrum and block intermediate frequencies from appearing. Before vibration measurement, not only the bandwidth and sampling frequency must be determined, but also the dynamic range of the vibration amplitude must be determined. For instance, while the measurement accuracy in the 2G range offered by Sensemore products is sufficient for low amplitude vibrations caused by bearing wear, measurements should be made with 8G / 16G intervals in high amplitude vibrations caused by a press line. Since the vibrations in the press line are low frequency and high amplitude, if the dynamic range of 2G is selected, the amplitudes that are out of range cannot be processed. If large dynamic ranges such as 16G are selected for bearing vibration measurements, the sensitivity of the sensor and the resolution of the graphics in the time/frequency domains decreases.

Fig. 2 The Effect of Sampling Rate on Spectrum Bandwidth

**Aliasing**

If we do not follow the sampling theorem, a phenomenon called aliasing is going to occur. In case of aliasing, analog signals are transformed to digitals signals in a different way and this will prevent high frequencies to be appear in spectrum. Therefore, aliasing is an undesirable phenomenon in which digital signals are processed. All data collectors/analyzers have built-in sampling rates to avoid aliasing. Theoretically, there should be no vibrations with a frequency more than half of this sampling rate. However, this can never be achieved in practice. That is why all analyzers have anti-aliasing filters. These are low-pass electronic filters that allow lower frequencies to pass but block higher ones. Filters eliminate all vibrations in an analog signal with frequencies greater than half the sampling rate. These filters automatically adjust to the appropriate values as the sampling frequency changes. This happens when the analyzer’s frequency range is changed by the user.

Fig. 3 Aliasing

**Discrete Representation of Analog Signals**

The limited high-speed sampling rate used in most measurement systems designed for vibration signals can affect the accuracy of time signals when generated. In the figure below, a signal is marked with 2.56 times lower sampling frequency and 20 times oversampling. It is clear that the signal with low sampling frequency does not correctly identify the analog signal from a careful study of the figure. The signal seems to bounce between impossible sampling points. Hovewer, it is important to understand that with the 2.56 times lower sampling frequency, the signal still contains all the information in the analog signal. This means that a spectrum calculated from the signal will be correct. The low sampling frequency only limits the time domain representation of the signal. There is no such limitation in the frequency domain. If the equipment being measured is operating at low frequency, choosing a sampling rate at very high frequencies will slow down the data flow and require more storage space. On the other hand, if the dynamic range is not selected correctly, the problem arises that the vibration peak values cannot be captured even with high resolution. To avoid such problems, it is necessary to predict the dynamic range(amplitude) and bandwidth of the equipment to be measured before the measurement is made.

**References**

- C. Scheffer, P. GirdharMachinery Vibration Analysis & Predictive Maintenance(Oxford:Elsevier, 2004)
- A. Brandt, Noise and Vibration Analysis(New Delhi: Wiley, 2011)
- Bertoletti, 2020, Nyquist-Shannon Sampling Theorem

### What is Vibration Analysis?

Vibration can be simply stated as a mechanical oscillation around an equilibrium point. In the first stage, vibrations can cause energy wastage and noise, but in later stages; they can even cause the machines to become unusable. This can lead to high maintenance costs, downtime, spare parts costs and even scrapping the equipment you spent tens of thousands of dollars. Please consider that; we are dealing with gearboxes, electric motors or any machine element, their movements during operation generate vibration. This vibration can be caused by the unbalance of rotating parts in motors, lubrication problems, gear cracks and many other problems as well as the characteristics of the equipment itself. At this point, vibration is a parameter pointing out the problems. On the other hand, it is also a problem. Failures to detect defects can lead to catastrophic damages to the equipment. For this reason, vibration analyzes are performed in the design and quality control stages of products with moving parts. As a result, final products are produced. However, despite these design studies, many external factors such as improper assembly, insufficient lubrication, looseness in the field applications of the products cause vibration and interrupt system continuity especially in important places such as production lines, air conditioning, and energy systems. To avoid the destructive effects at this stage, vibration measurements and analyzes are made on the products within the scope of predictive/preventive maintenance activities. In this way, critical winnings are achieved in maintenance costs and there are no interruptions in production. In this way, savings are achieved by lowering the costs arising from production interruptions.

In the vibration analysis, the vibration data received from the sensors placed on the machine elements are processed and the failure occurrence is predicted. Vibration signals received from different points contain a complex waveform due to different forces and factors. Therefore, it is really difficult to determine the faults by examining the graphs in the time-wave form. The signals received in the time-wave form from the vibration sensors are created in the frequency band spectra using the Fourier Transform in the software. The frequencies in the spectrum indicate the type and source of the faults or defects, and the frequency amplitudes indicate the severity of the damage. Certain faults occur at specific frequencies and if these faults are not remedied, the amplitude of that frequency continues to increase.

Spectrum analysis is the most effective method used in the interpretation of the vibration signals. The most widely used is the Frequency-Amplitude graph. Frequency indicates how many times the vibration repeats per second. The unit of frequency is “1/second”, in other words, Hz, or “RPM”, that is, rev/minute units, especially for rotating equipment vibrations. Amplitude, on the other hand, refers to the power of vibration, which can be expressed in different units, it should be noted that these differences in different software or products will cause misinterpretation. Peak-to-Peak, Peak, RMS are commonly used amplitude display units.

Fig. 1 Vibration Spectrum and Trend Graphs

Another mistake made while interpreting vibration data is to consider that vibration measurement has a unit of its own and ignore that it is a more likely to be an mathematical expression. Units measured in mechanical vibrations is in fact position, velocity or acceleration. Acceleration (mm/s^{2}) at frequencies higher than 1000 Hz and velocity (m/s) in the range of 10 Hz ≤ *f* ≤ 1000 Hz are preferred. For vibrations smaller than 10 Hz, position(micron) is used. This situation cannot be called either true or false. The standards have been shaped in this direction due to the ease of reading/interpretation and measurement techniques. Since spectrum analysis is a field that requires expertise, in general, the monitoring of the vibration power can be done through the RMS value. Although it does not provide detailed information, the increase or decrease of the vibration density can be followed over this value. This value is the area under the Frequency-Amplitude (RMS) graph.

Fig. 2 Frequency-Amplitude (RMS) graph

### We are powerful together!

Nowadays, when any software application is developed, it is almost impossible to achieve this without using open source tools. As Sensemore, we frequently use open source tools while developing our technology. We develop our technology by taking the power of the Committee behind our back and try to give back what the Committee gave us at every opportunity.

We are eager to share not only the software but also the know-how we have created during our development. We will be publishing blog posts about signal analysis, software samples, design, and predictive maintenance on the Sensemore.io blog.

We want to create an open github repository soon. Until it is worthy of you, of course.

Because information increases as it is shared.