Introduction to Fault Diagnosis (Part 3)

Understanding vibration signals: discovering equipment abnormalities from waveform to spectrum

In the first two issues, we have learned about "what vibration is" and "how vibration signals are collected". And once the signals are collected, the real challenge is just beginning - we need to understand these signals and discover hidden fault features from complex data.

Today's issue, let's take a look at how vibration signals are "translated" into information that can reveal the health status of devices.

1、Waveform diagram: the "primitive language" of vibration

The most direct manifestation of vibration signals is the time-domain waveform diagram, which shows the variation of vibration over time - equivalent to recording the "jitter" of the device at every moment.

Figure 1 Schematic diagram of time-domain waveform

However, the vibration signal in reality is not a single waveform, but the result of the superposition of multiple vibration sources. Vibration has the property of superposition, and vibrations from different sources will mix and form complex waveforms on the time axis.

For example, at the measuring point near the motor end of the gearbox, the collected signals may simultaneously include:

Low frequency fluctuations caused by rotor imbalance

Periodic changes caused by misalignment of the coupling

High frequency pulses during gear meshing

Amplitude enhancement caused by structural resonance

These superimposed signals form the complex time-domain waveform we see.

Figure 2 Schematic diagram of superposition of multiple vibration sources

1.Parameters and Applications of Waveform Analysis

Time domain waveform analysis is an important tool for fault diagnosis. By observing the amplitude, period, phase and other parameters of the waveform, we can determine:

Whether the vibration is stable: judging the smoothness of operation

Whether there is impact: Suspect bearing or gear problems

Is there periodic unevenness: there may be imbalance or misalignment

If we compare the operation of a device to a human heartbeat, the waveform is like an electrocardiogram:

Regular and stable waveform → normal heartbeat, equipment running smoothly

Significant mutations, periodic shocks, or uneven amplitudes → arrhythmia, equipment may have malfunctions

2.The role of waveform analysis

In fault diagnosis, time-domain waveforms are usually the "first impression":

It allows us to quickly determine whether the vibration is stable, periodic, or if there is a sudden change or impact.

Waveform analysis provides a fundamental basis for further spectrum, envelope, or time-frequency analysis.

2、Spectrum diagram: Change "time" to "frequency"

If the time-domain waveform is a "curve of vibration over time", then the spectrogram "unfolds" time into frequency, allowing us to see what different frequency components coexist in this vibration signal.

Just by looking at the waveform, we may know that the device is shaking, but we don't know why it's shaking. And spectrum analysis can help us find the cause, it is the most commonly used and important tool in mechanical fault diagnosis.

1. Fourier Transform: Translating Time into Frequency

In reality, any complex vibration signal can be seen as a superposition of many sine waves of different frequencies, amplitudes, and phases.

The core idea of Fourier transform is:

Decompose a complex signal that varies over time into a combination of several sinusoidal signals with fixed frequencies.

In other words, Fourier transform is like a "frequency scanner": it tells us which frequency is strongest and which frequency is almost non-existent in the signal.

Figure 3: Schematic diagram of Fourier transform

This precisely demonstrates the power of Fourier analysis - breaking down complex waveforms into simple frequency components.

2. The appearance and significance of spectrum

After Fourier transform, the result we obtain is a spectrogram. On the spectrogram:

The horizontal axis represents frequency (unit: Hz, Hertz)

The vertical axis represents the amplitude of each frequency component

Each spectral line represents a sine component:

High spectral line → Strong component at this frequency

Low spectral line → corresponding frequency energy is weak

In this way, we can "see at a glance" the main frequency components of the equipment vibration, and also determine which frequencies correspond to specific mechanical movements or faults.

Simple understanding:

The waveform tells us when to shake

Spectrum tells us at what frequency it shakes

3. Frequency doubling and spectrum analysis ideas

In rotating machinery, most fault signals are closely related to speed and frequency. We usually refer to the frequency corresponding to the rotational speed as 1X (power frequency), while its integer multiples (2X, 3X, 4X...) are called harmonics.

Figure 4: Schematic diagram of frequency doubling and spectrum analysis

Different types of mechanical faults will exhibit characteristic energy at different harmonics:

1X → mostly related to rotor imbalance

2X → Commonly seen in misaligned couplings or bent shafts

Higher harmonics may be related to looseness, gear meshing, blade failure, etc

The core idea of spectrum analysis is to determine the source and development trend of faults by observing frequency distribution and changes.

4. A practical example: frequency characteristics of multi-level devices

Let's take a typical multi-stage transmission system as an example: the motor drives the compressor through the gearbox. The equipment parameters are as follows:

The rated speed of the motor is X Hz;

The non drive end of the motor has 6 blades;

The gearbox has 16 input teeth and 64 output teeth;

The compressor has 8 impellers.

At different measurement points, we can usually observe the following characteristic frequencies:

Non driving end of motor: blade passing frequency of 6X appears;

Motor drive end: manifested as motor rotation frequency X;

Compressor drive end: Due to a reduction ratio of 16/64=0.25, it is manifested as 0.25X;

Non driving end of compressor: The visible impeller passes through a frequency of 8 × 0.25X=2X.

Figure 5: Distribution of characteristic frequencies of multi-level devices

These frequency components and their harmonics often reflect the operating status of various components: abnormal enhancement of characteristic frequencies or the emergence of new modulation components usually indicate problems such as imbalance, misalignment, or abnormal gear meshing.

Identifying and understanding the frequency distribution patterns of these features is an important basis for determining the location and nature of faults.

3、Envelope analysis: hearing a 'masked signal'

In many cases, the impact signals generated by bearing or gear failures are masked by other strong vibrations. These weak impulses are often difficult to detect on waveforms or ordinary spectra.

At this point, envelope analysis is needed to capture the signals that are "obscured".

1. Modulation concept

Before introducing envelope analysis, let's first understand a concept - modulation.

When the amplitude or frequency of one signal changes with another signal, modulation occurs.

Taking damage to the inner ring of a bearing as an example:

Rolling elements passing through damage points during rotation will generate periodic impacts

The inner ring of the bearing rotates with the shaft, and the amplitude of these impacts is modulated by the rotational frequency of the shaft

The result is that the signal contains both high-frequency shock waves and low-frequency modulation changes.

Figure 6: Modulation schematic diagram

2. The role of envelope demodulation

Envelope demodulation is the process of extracting low-frequency modulation information encapsulated by high-frequency carriers, in order to identify fault frequencies.

Figuratively speaking, it's like separating a faint beat sound from a noisy background music.

3. Application examples

When there is slight peeling off of the bearing raceway or rolling elements, a small impact will be generated every revolution. These impulse frequencies are fixed, and these characteristic frequencies can be captured through the envelope spectrum.

Envelope analysis is particularly suitable for identifying:

Rolling element damage

Defects in the inner or outer ring

Abnormal holder

Through envelope spectrum, we can clearly present fault signals that are difficult to detect in the time domain or ordinary spectrum, providing reliable basis for early diagnosis.

Figure 7: Envelope analysis and characteristic frequency identification of bearing inner ring faults

4、Characteristic Parameters and Trends: The Health Curve Behind Numbers

In daily vibration monitoring, in addition to observing waveforms and spectrograms, we can also quantify the vibration state of equipment by extracting a series of characteristic parameters.

1. Common feature parameters

Root mean square value (RMS) → reflects the overall vibration energy

Peak value → reflects impact strength

Peak to peak value → reflects the maximum vibration amplitude range

Kurtosis → Determine impact or abrupt vibration

Frequency center → observe the energy changes of characteristic spectral lines

Energy distribution → Which frequency bands are the vibration energy concentrated in

Spectral line energy and → reflect the total energy change of characteristic frequencies

2. The role of trend analysis

Plotting feature parameters as trend curves over time can detect abnormal development trends in advance and achieve predictive maintenance. For example:

RMS continues to rise → bearing wear intensifies

Sudden increase in kurtosis → Defects in gear meshing

RMS decreases but peak increases → local looseness or impact fault

Frequency center moves up or down → gear meshing frequency offset, rotor imbalance or misalignment

Abnormal energy distribution → Abnormal increase in vibration energy in a certain frequency band, such as local loosening or blade damage

Spectral line energy and variation → overall amplitude increase or decrease of characteristic frequencies, such as gear wear, bearing raceway damage, or coupling looseness

Through these trend analyses, not only can the current vibration status be determined, but the development of potential faults can also be predicted, providing scientific basis for equipment maintenance and management.

5、 Time Frequency Analysis: Understanding "Vibration in Change"

When the operating conditions of the equipment change rapidly (such as speed changes, start stop, load fluctuations), a single time-domain analysis or frequency-domain analysis often cannot fully reflect the vibration characteristics. At this point, it is necessary to use time-frequency analysis methods to simultaneously observe the changes in vibration signals over time and frequency.

1.Why is it necessary

Time domain analysis: tells us when vibration occurs, but it is difficult to distinguish between different frequency components

Frequency domain analysis: displays the frequency components of vibration, but cannot determine when these frequencies appear

Time frequency analysis: simultaneously solving time and frequency problems, observing when and at which frequency the vibration in the signal increases or decreases

This method is particularly important in transient impact, variable operating conditions, or early fault diagnosis.

2. Common methods

3. Application and Value

Through these methods, we can clearly see the frequency components of the vibration signal that vary over time,

For example:

During the start stop process, some frequencies suddenly appear, which may be due to loose couplings or gear collisions

High frequency impact enhancement during load changes → may be due to local bearing wear or gear cracks

When the speed changes, the frequency changes synchronously → it can distinguish between rotor imbalance and bearing impact

Time frequency analysis enables us to understand the dynamic characteristics of vibration signals under complex operating conditions, providing reliable basis for early fault identification and predictive maintenance.

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