### Parameter Selections in Vibration Measurement

In mechanical systems, various parts of the same equipment can have different vibrations because of differences in their shapes, materials, and other factors. For example, in a conveyor system with an electric motor and a reducer, the vibrations in the reducer’s output shaft may be quite different from those of the electric motor when it runs at high frequencies. Using the same parameter selections in vibration measurement on both parts can lead to incorrect results.

**The Role of Sample Size and Sampling Rate**

In the process of turning an analog signal into a digital one (ADC), the size of the digital waveform’s samples is vital for accurately replicating the analog signal. Vibration measurements usually cover a period of time and are taken at regular intervals. The analog signal is transformed into digital format through samples taken at specific time intervals known as the sampling time (1/fs). The number of samples taken each second is called the sampling rate or sampling frequency. It’s important to remember that the interval between periodic measurements is determined by dividing the sample size by the sampling frequency. Half of the sampling frequency (fs/2) is referred to as the **Nyquist Frequency.**

Fig. 1 Time and Frequency Domain Parameters

**The Nyquist-Shannon Sampling Theorem**

Analog signals consist of components at different frequencies. The highest-frequency component, denoted as fmax, defines the signal’s bandwidth. As per the Nyquist-Shannon Sampling Theorem, the sampling rate should be at least twice the highest frequency component in the analog signal, or 2×fmax. This theorem emphasizes the importance of understanding the implications of the sampling rate. When you follow this theorem before sampling an analog signal, the sampled signal accurately represents the analog signal, preserving all its information. However, if the sampling frequency falls below 2 times the highest frequency in the analog signal (fs<2×fmax), aliasing occurs. Aliasing hides high frequencies in the analog signal spectrum and can lead to misinterpretations of the signals produced by the vibration source.

**Effect of Sampling Rate on Spectrum Bandwidth**

Fig. 2 The Effect of Sampling Rate on Spectrum Bandwidth

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**

Many measurement systems designed for vibration signals use limited high-speed sampling rates, which can affect the accuracy of time signals generated. When the sampling frequency is much lower (e.g., 2.56 times lower) than the analog signal’s frequency, oversampling (e.g., 20 times) is often applied to compensate. Despite the lower sampling frequency, it’s crucial to understand that the signal still contains all the information found in the analog signal. While the signal may seem to jump between sampling points at a lower frequency, its integrity remains intact in the frequency domain. This means that a spectrum calculated from the signal remains accurate. The limitation imposed by the low sampling frequency primarily affects the time-based representation of the signal, not the frequency-based one.

**Impact of Sampling Rate on Signal Representation**

When the sampling rate falls below the required threshold (fs<2×fmax), aliasing occurs, distorting the signal’s integrity. This means that high-frequency components in the analog signal may not appear correctly in the digital representation. Aliasing is a phenomenon we want to avoid to obtain accurate vibration measurements.

**Selecting the Right Dynamic Range**

Aside from sampling rate, another crucial aspect to consider is the dynamic range when measuring vibration. Dynamic range refers to the ability of the measurement system to capture a wide range of vibration amplitudes accurately. Different machinery and applications exhibit varying levels of vibration intensity.

To illustrate the importance of dynamic range, consider a scenario where you’re measuring vibrations from a machine. In some cases, these vibrations may be relatively small, akin to a gentle hum, and fall within a low range (e.g., 2G). However, in other instances, the vibrations might be much more intense, resembling powerful jolts, necessitating a higher dynamic range (e.g., 8G or 16G).

**The Consequences of Choosing the Wrong Dynamic Range**

If you opt for a dynamic range that’s too limited for the actual vibration amplitudes, you risk “clipping” the data. In simpler terms, you’ll lose information about the vibration’s actual intensity, like trying to capture the roar of a lion with a microphone that can only pick up whispers.

On the other hand, selecting an overly wide dynamic range for relatively low-intensity vibrations can lead to a decrease in sensitivity. It’s akin to using a microscope to read large print; you may miss finer details.

**Automatic Adjustment of Anti-Aliasing Filters**

To mitigate the challenges posed by aliasing due to insufficient sampling rates, most data collectors and analyzers incorporate anti-aliasing filters. These filters automatically adapt to changes in the sampling frequency, preventing aliasing and ensuring data integrity.

Fig. 4 Anti-aliasing filter operation

**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?

To understand vibration analysis, it’s important to first grasp the concept of vibration itself. Vibration is essentially the back-and-forth movement of a machine part from its normal position. Initially, vibrations might not seem harmful, causing only energy waste and noise. However, if not addressed, they can escalate to the point of making machines unusable. This can lead to financial problems like high maintenance costs, extended downtime, increased spending on spare parts, and even the tough decision to scrap expensive equipment.

Vibrations occur in various machine components, like gearboxes and electric motors, during their operation. These vibrations can result from different issues such as imbalanced rotating parts, lubrication problems, gear damage, or the inherent characteristics of the equipment itself. Vibration is a two-sided phenomenon – it indicates problems and can cause problems. Failing to detect these issues in time can lead to severe damage, which every industry wants to avoid.

**Understanding Vibration Data**

In vibration analysis, sensors are placed on machine parts to collect data, which is then processed to predict potential failures. These vibration signals, arising from various forces and factors, appear as complex waveforms. Interpreting this fault data by studying time-domain graphs can be challenging. (See our article: Understanding Machine Data)

This is where spectrum analysis comes in – it’s the key to understanding vibration signals. The most commonly used tool in this field is the Frequency-Amplitude graph. Frequency tells us how often vibrations repeat in a second, measured in Hertz (Hz) or revolutions per minute (RPM), especially for vibrations in rotating equipment. Amplitude, on the other hand, indicates the strength of vibrations and can be measured in different units. It’s important to note that variations in units across different software or products can sometimes lead to misinterpretations. Common amplitude units include Peak-to-Peak, Peak, and RMS.

**Vibration Spectrum and Trends**

In vibration analysis, it’s important to realize that vibration measurement is not a standalone concept; it’s more like a mathematical expression. Mechanical vibrations can be measured in terms of position, velocity, or acceleration. Acceleration, measured in millimeters per second squared (mm/s²), is typically used for frequencies above 1000 Hz, while velocity, expressed in meters per second (m/s), is suitable for frequencies in the range of 10 Hz ≤ f ≤ 1000 Hz. For lower-frequency vibrations (below 10 Hz), position is the preferred unit, measured in microns.

As spectrum analysis is a specialized field, the common practice is to monitor vibration power using the root mean square (RMS) value. While it doesn’t provide all the details, it’s an effective way to track changes in vibration intensity. You can think of the RMS value as a representation of the vibration’s power distribution on the Frequency-Amplitude (RMS) graph.

Fig. 1 Vibration Spectrum and Trend Graphs

**The Significance of Spectrum Analysis in Vibration Analysis**

For vibration analysis, spectrum analysis plays a central role in unlocking the secrets of machine health and performance. To fully understand its importance, we need to navigate the intricacies of vibration signals, which are shaped by various forces and factors.

**The Fourier Transform**

Spectrum analysis relies on the transformative capability of the Fourier Transform. This mathematical tool is key to converting complex, time-based vibration signals into a harmonious world known as the frequency domain. Here, vibrations become distinct musical notes, forming frequency spectra that reveal a machine’s condition. Frequencies, much like the tempo in a musical composition, guide us through the machine’s vibrations. Amplitude, the partner of frequency, represents the intensity of vibration. While it can be measured in different units, it’s important to be aware of potential misinterpretations when using different software or products. Common amplitude units include Peak-to-Peak, Peak, and RMS (Root Mean Square). Amplitude tells us how loud or soft a frequency is within the vibration spectrum, much like the volume of a musical note. A high-amplitude frequency indicates strong vibration, while a low-amplitude frequency suggests weaker vibration. Experts assess the severity of machine damage or defects by examining these amplitudes across frequencies.

**Faults and Frequencies**

Spectrum analysis reveals an interesting phenomenon – specific machine faults or defects manifest at particular frequencies, similar to signature melodies within the vibration spectrum. If left unaddressed, these “signature frequencies” increase in amplitude, resembling a musical note growing louder and more prominent.

**Monitoring, Interpretation, and RMS**

In practice, spectrum analysis involves careful monitoring of frequencies and amplitudes within the spectrum. This process is visualized through a Frequency-Amplitude graph, providing expert analysts with a canvas to spot irregularities and trends. It offers valuable insights into the overall health of the machine. At the core of this analysis is the root mean square (RMS) value. While it may not provide detailed information, it serves as a reliable way to track changes in vibration intensity. It quantifies the area beneath the Frequency-Amplitude (RMS) graph, a valuable tool for assessing the overall power of vibration.

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.