Condition monitoring and diagnostics of machines — Vibration condition monitoring — Reference numberISO 13373-2:2016E... ISO 13373 consists of the following parts, under the general titl
General
Vibration measurements are typically captured using transducers that generate an analog electrical signal proportional to vibratory acceleration, velocity, or displacement This signal can be recorded on dynamic system analyzers, displayed on oscilloscopes, or analyzed later for diagnostic insights To determine accurate vibration magnitudes, the output voltage is multiplied by a calibration factor that considers transducer sensitivity, amplifier, and recorder gains While most vibration analysis is conducted in the frequency domain, analyzing the time history of vibrations also provides valuable information for condition monitoring and troubleshooting.
Figure 1 illustrates the relationship between vibration signals in the time and frequency domains, highlighting four overlapping signals that form the composite trace observed on the analyzer screen The gray trace in the XY plane represents this combined vibration data By applying Fourier analysis, the analyzer separates the composite signal into four distinct frequency components, providing a clear understanding of the underlying vibrations This process enhances diagnostic accuracy and is essential for effective vibration analysis in machinery health monitoring.
Y amplitude/magnitude 2 frequency domain spectrum
Figure 1 — Time and frequency domains
Figure 2 demonstrates a straightforward example of a composite trace from a single transducer displayed on the analyzer screen This example features three overlapping signals, clearly illustrated in Figure 3 The different frequencies of these signals are detailed in Figure 4, providing valuable insights into the signal analysis process and the importance of accurate frequency identification for reliable diagnostics.
Figure 2 — Basic spectra composite signal
Understanding the relationship between vibrations at different structural points or in various directions is crucial in many investigations, along with analyzing individual vibration data Multi-channel signal analyzers with built-in dual-channel analysis features facilitate this process by allowing simultaneous examination of multiple signals This technique emphasizes the importance of both amplitude and phase relationships between vibration signals, providing a comprehensive understanding of the structural dynamics Utilizing multi-channel analysis enhances diagnostic accuracy and helps identify complex vibration behaviors more effectively.
Analogue and digital systems
General
Analog signals from transducers can be processed using either traditional analog systems or modern digital methods While analog systems utilize components like filters, amplifiers, and recorders to modify signals without changing their inherent nature, digital processing involves converting these signals into numerical data through an analog-to-digital converter (ADC), which samples the signal repeatedly at an appropriate frequency Once digitized, signals can be processed using computer algorithms for filtering, integration, spectral analysis, and histogram development, greatly enhancing analysis capabilities Both analog and digital signals carry the same essential information, provided the sampling frequency is correctly chosen, allowing for accurate representation and analysis of the original signal.
Understanding the sensitivity of the signal is crucial when using either analogue or digital measurement methods, as it determines the ratio of the output voltage to the measured parameter Ensuring the signal is sufficiently above ambient noise levels guarantees adequate signal definition, while avoiding excessive signal strength prevents distortion or clipping of peaks Proper sensitivity management enhances measurement accuracy and ensures reliable data acquisition across different methods.
Digitizing techniques
Key parameters in digitizing include the sampling rate and resolution, with the sampling rate determined by the analysis type and the signal’s frequency content To avoid distortions and aliasing effects, it is essential that no frequencies exceed half the sampling rate, and anti-aliasing filters are employed to remove high-frequency noise above this threshold For time-based vibration plots, a sampling rate about 10 times the highest relevant frequency is recommended, while Fourier Transform analyses require a rate exceeding twice the highest frequency to be measured Additionally, the bit depth used to represent each sample must be sufficient to ensure the desired accuracy in the digitized data.
Signal conditioners
General
Vibration signals from transducers typically require signal conditioning to ensure proper voltage levels for recording and to eliminate noise or unwanted components Key signal conditioning equipment includes transducer power supplies, pre-amplifiers, amplifiers, integrators, and various types of filters Filtering techniques play a crucial role in enhancing signal quality and are discussed in detail in section 3.4.
Integration and differentiation
Vibration records can be expressed in terms of displacement, velocity, or acceleration, with the choice depending on the frequency range of interest, such as low-frequency signals being more visible with displacement and high-frequency signals with acceleration To analyze different parameters, vibration signals can be converted through integration or differentiation—for instance, integrating acceleration over time yields velocity, while integrating velocity provides displacement Double integration of acceleration directly produces displacement, whereas differentiation reverses the process to extract the original signal.
Mathematically, for harmonic motion, the following relationships apply: displacement: x = v td = a t td d = i v a
−ω2 ω (3) where ω is the angular frequency of the harmonic vibration with ω = 2πf.
Accelerometers are the most common type of vibration transducers, making signal integration more prevalent than differentiation This approach is advantageous because integrating signals is generally easier than differentiating them However, when working with low-frequency signals, it's essential to exercise caution during integration To improve measurement accuracy, a high-pass filter should be applied beforehand to remove frequencies below the range of interest.
Root-mean-square vibration value
The root-mean-square (r.m.s.) value of the vibration signal is a key parameter used in vibration evaluation standards, representing the most commonly used measure of vibration over a specified time period It is most effective within a designated frequency range, providing a consistent metric despite complex signal components or modulation Unlike other measures, the r.m.s value is a universal mathematical quantity that can be calculated for any vibration signal, with most instruments specifically designed for this purpose Additionally, the r.m.s value can be accurately determined using a spectrum analyzer by integrating the spectrum over the relevant frequency range.
A vibration signal can be filtered and displayed on an RMS meter when the readings remain stable over a short period If the readings fluctuate significantly, an average should be calculated over a specific time interval to ensure accurate measurement Utilizing an instrument with a longer time constant helps obtain reliable average readings when signal variability is high.
1 2 a) Sinusoidal signal where the r.m.s value equals 0,707 times the peak value
Dynamic range
The dynamic range refers to the ratio between the largest and smallest signal magnitudes that an analyzer can handle simultaneously These signal magnitudes are proportional to the output voltages generated by transducers, typically measured in millivolts Understanding the dynamic range is essential for selecting the right analyzer to accurately measure a wide spectrum of signal strengths in various applications.
In analogue systems, the dynamic range is primarily constrained by electrical noise, which often originates from filters, amplifiers, and recorders rather than the transducer itself These components contribute additional noise levels, leading to a surprisingly high overall noise floor that limits the system's ability to accurately capture signals Efficient management of noise sources is crucial for optimizing the dynamic range in analogue signal processing.
In digital systems, the dynamic range is primarily determined by the sampling accuracy, which depends on the number of bits used for analog-to-digital conversion Ensuring an adequate sampling rate is essential to accurately capture the frequencies of interest without aliasing The relationship between the number of bits, N, used to sample an analog signal and the resulting dynamic range, D (measured in decibels), is foundational for optimizing digital system performance, with the dynamic range increasing proportionally with the number of bits (considering one bit for the sign).
Therefore, a dynamic signal analyzer (DSA) with 16 bits of resolution will have a dynamic range of
90 dB, but any inaccuracies will reduce the dynamic range.
Calibration
Transducer calibration is thoroughly documented in standards like ISO 16063-21 and is typically performed in the laboratory before field deployment However, it is advisable to conduct a calibration check in the field to ensure system accuracy Field calibration primarily verifies the performance of the entire measurement system—including amplifiers, filters, integrators, and recorders—by introducing a known signal such as a DC step, sinusoid, or random noise This check helps confirm that the system's output accurately reflects the input signal without recalibrating the transducer itself.
Some transducers, like displacement transducers and proximity probes, come pre-calibrated, but their calibration must be verified in the field to ensure accuracy with the specific surface being measured Proximity probes are particularly sensitive to shaft metallurgy and surface finish, making in-situ calibration essential Calibration is performed on-site using micrometer spindles, and the output readings for each probe are carefully recorded for precise measurement.
When checking the calibration of seismic transducers in the field, a shake table is required.
Strain gauges are commonly calibrated in the field after installation to ensure accurate measurements The most effective calibration method involves applying a known load to the component being measured, providing precise verification of the gauge's performance When applying a known load is impractical, a shunt calibration offers an alternative; this involves connecting a calibration resistor in parallel with the strain gauge to alter its apparent resistance by a known amount This change in resistance simulates a specific strain based on the gauge factor, allowing for reliable calibration in various field conditions Proper calibration methods enhance the accuracy and reliability of measurements using strain gauges.
Filtering
There are three basic types of filters available for signal conditioning and analysis:
Low-pass filters allow only low-frequency components of a signal to pass through while blocking high-frequency components above the cutoff frequency They are commonly used as anti-aliasing filters to prevent high-frequency signals from causing errors during digital sampling Additionally, low-pass filters are employed in specialized applications to exclude unwanted high-frequency components, such as in gear meshing analysis for balancing and vibration studies.
High-pass filters are essential for removing low-frequency transducer noise, such as thermal noise, and other unwanted signal components before analysis This process enhances measurement accuracy by preventing these irrelevant signals from interfering with the data By filtering out low-frequency noise, high-pass filters help to maximize the useful dynamic range of measurement equipment, ensuring more precise and reliable results Proper application of high-pass filters is crucial for obtaining clean, high-quality signals in various analytical and measurement scenarios.
Bandpass filters are essential tools in signal analysis, as they isolate specific frequency bands for precise examination Among the most common types are octave filters and 1/n octave filters, which effectively segment the spectrum into defined frequency ranges These filters are particularly valuable for correlating vibration measurements with noise measurements, enabling more accurate diagnostics and analysis in various industrial and engineering applications.
Filtering is essential for analyzing signals with wide dynamic ranges, ensuring accurate results When spectra contain frequencies with both high and low amplitudes, the analyzer's limited dynamic range can hinder precise analysis of all components Proper filtering helps isolate these different amplitude signals, improving measurement accuracy across diverse signal components.
In such cases, it can be necessary to filter out the high‑amplitude components to examine more closely those of low amplitude.
Filtering is also important for separation of informative signals and disturbances (as electronic noise is in the high‑frequency range or seismic waves are in a very low‑frequency range).
When using filters to isolate specific frequency components of a waveform, it is crucial to ensure that the filter effectively excludes all unwanted frequencies outside the target range Simple analogue and digital filters often lack sharp cut-off characteristics, as their filter slopes outside the transmission band are relatively poor, potentially allowing undesired frequency components to pass through.
A 24 dB per octave filter passes approximately 15% of a component at twice the cutoff frequency and about 45% at 1.5 times the cutoff frequency To enhance the filter’s suppression capabilities, cascading multiple simple filters or adopting a higher-order filter design can be effective.
General
Data processing is essential for accurate diagnosis, involving raw data acquisition, noise filtering, and formatting signals for analysis Adequate resolution in the vibration signal acquisition device—both in amplitude and time—is crucial for reliable results When using digital data acquisition, high amplitude resolution enhances accuracy and sensitivity; however, this often necessitates more advanced and costly hardware with greater processing capabilities.
Once signals are acquired, they are processed and displayed in various useful formats such as Nyquist plots, polar plots, Campbell diagrams, cascade and waterfall plots, and amplitude decay plots to facilitate easier diagnosis These visualization methods help users better understand machine conditions by providing comprehensive insights The goal is to present these different presentation techniques to enable more accurate assessment of machine health and performance.
Time domain analysis
Time wave forms
Historically, waveform analysis was the primary method for vibration analysis, involving graphical analysis of instantaneous vibration versus time strips or oscillographs to identify broadband peaks Although broadband techniques remain in use, incorporating basic waveform analysis techniques enhances diagnostic capabilities For instance, examining waveform data from displacement transducers can help detect issues such as scratched journals, while waveform clipping at the top or bottom may indicate mechanical problems like rubs or looseness.
Time-domain signatures offer basic insights into the waveforms and the nature of phenomena within machinery; however, for more detailed analysis, advanced frequency analysis techniques outlined in section 4.3 are often necessary to fully understand the underlying conditions.
Waveform analysis relies on the principle that any periodic signal can be decomposed into a sum of sinusoids with frequencies that are integer multiples of the fundamental frequency This concept, known as Fourier analysis, underpins various signal processing techniques Figures 6 through 9 illustrate several examples of waveforms, demonstrating how complex periodic signals can be broken down into simpler sinusoidal components for detailed examination Understanding these principles is essential for applications in audio processing, communications, and engineering, aiding in accurate signal analysis and synthesis.
Figure 6 displays a one-cycle sinusoidal waveform with a consistent amplitude, representing vibration data The peak-to-peak amplitude is determined by measuring the trace and multiplying by the system's calibrated sensitivity to ensure accurate readings Frequency is calculated by counting the number of complete cycles within a specific time frame, with the oscillograph's timing lines and paper speed aiding this measurement In this case, 60 timing lines per second indicate a fundamental period (T) of 0.2 seconds, resulting in a vibration frequency (f) of 5 Hz To improve measurement accuracy, it is advisable to analyze longer segments of the recorded trace, capturing more cycles for a more reliable frequency assessment.
Figure 7 illustrates the superposition of two sinusoids displaying three cycles of the lowest frequency, with sinusoidal envelopes outlining peaks and troughs The amplitude and frequency of the low-frequency component are represented by these envelopes, while the vertical distance between them indicates the peak-to-peak amplitude of the high-frequency component In this example, the frequencies of the two signals differ by a factor of three, allowing for straightforward separation when the frequency ratio is high When the frequency difference is significant, envelope-based separation is effective; otherwise, Fourier analysis provides a more accurate method for distinguishing overlapping sinusoids.
Beating
Beat signals often resemble a Figure 8 pattern, characterized by out-of-phase envelopes that create bulges and waists, caused by two components close in frequency and amplitude This phenomenon, known as beating, is a special case of superposition, exemplified by the varying interference of twin propeller blade frequencies on ships, where peaks alternately add and subtract Beating features include beats of approximately equal length and differing spacing between bulges and waists, with the distances between envelopes representing the sum and difference of the component peak-to-peak values Another common example is vibration forced by two coupled machines, such as compressors driven by asynchronous electrical motors, which produce similar beating patterns.
Y amplitude (arbitrary unit) a Peak-to-peak value at waist: 0,2. b Peak-to-peak value at bulge: 0,7. c Waist. d Bulge. e Vibration cycle: 0,33 s corresponds to 3 Hz. f Beat cycle: 2 s corresponds to 0,5 Hz.
In this example, the component amplitudes are Xₘ for the major and Xₙ for the minor, with measurements showing that Xₘ + Xₙ = 0.7 and Xₘ − Xₙ = 0.2, leading to Xₘ = 0.45 and Xₙ = 0.25 To obtain the actual amplitudes, these recorded values must be multiplied by the system sensitivity The major frequency is determined by counting the number of peaks; in Figure 8, this is 3 Hz This frequency is an integer multiple of the beat frequency, in this case six times The minor component's frequency is either one more (7 Hz) or one less (5 Hz) than the beat frequency, with peak spacing at the waist indicating the correct value In Figure 8, the narrower spacing suggests the major component has the higher frequency Specifically, the beat frequency is 0.5 Hz, and the minor frequency is five times that, totaling 2.5 Hz.
The beat frequency is defined as the difference between the frequencies of the two components, calculated using the formula: f_b = f_m - f_n, where f_b represents the beat frequency, f_m is the frequency of the major component, and f_n is the frequency of the minor component Additionally, the average peak frequency is equal to half the sum of both component frequencies, providing a straightforward method for analyzing combined signals This understanding of beat and average frequencies is essential for accurate signal processing and audio analysis.
In the example illustrated in Figure 8, six peaks are observed within 2 seconds, indicating a main frequency (fₘ) of 3 Hz The beat cycle corresponds to one complete cycle in the same time frame, resulting in a beat frequency (f_b) of 0.5 Hz Using the inverted form of Formula (5), fₙ = fₘ − f_b, the minor component frequency is calculated as fₙ = 3 Hz − 0.5 Hz = 2.5 Hz.
Modulation
Figure 9 illustrates a modulated vibration signal, which appears similar to beating but is characterized by a single component with amplitude variation over time Unlike beating, the spacing between peaks remains consistent at both the bulges and waists, although the length of the bulges may vary Gear issues often lead to modulation of the gear mesh frequency at the gear's rotational frequency, which can be identified through this vibration pattern.
Many vibration records often contain more than two components and may include modulation and beating, making analysis challenging However, by identifying sections where a single component is temporarily dominant, analysts can determine its frequency and amplitude, simplifying the interpretation of complex vibration signals.
Envelope analysis
Envelope analysis is a vital technique for demodulating low-level signals within narrow frequency bands that are often masked by high-level broadband vibrations, such as impulse-excited free vibrations and gear meshing vibrations This method enhances early defect detection and improves reliability in fault diagnosis It is most commonly applied in analyzing gears and rolling element bearings, where low-frequency, low-amplitude repetitive events—like a defective gear tooth engaging or a spalled ball striking a race—excite high-frequency resonances These high-frequency signals are modulated by the defect frequency, enabling precise identification of faults An example of an envelope trace illustrating this process is shown in Figure 10, highlighting the effectiveness of envelope detection in condition monitoring.
It should be noted that the modulated component needs to be separated previously by narrow band filtering.
Monitoring of narrow‑band frequency spectrum envelope
Monitoring narrow-band frequency spectrum envelopes involves detecting any penetration beyond a predefined alarm limit around a reference spectrum, ensuring early fault detection The use of constant-bandwidth envelopes, which maintain an equal number of frequency lines at both low and high frequencies, is particularly effective for machinery operating at a constant rotational speed, facilitating accurate condition monitoring.
A constant-percentage bandwidth envelope adjusts the frequency offset proportionally to the increase in frequency, ensuring that the harmonic components remain within the same frequency band during small speed variations This approach offers the advantage of maintaining consistent signal monitoring, as all harmonic components stay within a stable frequency range despite changes in speed.
Amplitude limits for individual frequency components come in two types, with the most common being a constant-percentage offset This approach is favored due to its simplicity, as it is easy to calculate and only requires a single reference spectrum.
Calculating the statistical mean for each segment within the envelope provides a more representative method for monitoring machine conditions Setting alarm limits between 2.5 to 2.8 standard deviations above this mean ensures effective anomaly detection This statistical approach requires either four or five high-resolution spectra, allowing for accurate analysis It automatically accounts for normal amplitude variations typically observed in machinery spectra, enhancing reliability in condition monitoring.
Shaft orbit
Orbit analysis is a versatile technique that can be performed on any machine using displacement transducers mounted at 90° intervals, providing valuable insights into machine health On large rotating machinery with sleeve bearings, shaft orbit analysis is typically employed to monitor the shaft's movement within the bearing clearance, helping identify potential issues It is essential to account for shaft mechanical and electrical run-out to avoid distortion of the orbit display, ensuring accurate interpretation Proper analysis of the orbit can reveal the nature of the forcing function and indicate whether rotor whirl is forward (in the direction of rotation) or backward (against the rotation) Orbit signals are presented as either unfiltered broadband data or filtered single-frequency signals, aiding in comprehensive condition monitoring and fault diagnosis.
The common synchronous (1×) filtered display provides a clear view of fundamental rotational vibrations, but additional harmonics and sub-synchronous frequencies are often shown in an orbit presentation to enhance diagnostic capabilities Using specific markers, such as points or highlights that serve as shaft references—like once-per-revolution signals—offers valuable insights into the relationship between vibrational and rotational frequencies, aiding in accurate problem identification and resolution.
The orbit plot presents the dynamic motion of the centre of the rotating shaft at the measurement plane
An orbit, also known as a Lissajous presentation, is best represented when using identical transducers mounted orthogonally at a 90° angle to ensure accurate measurement If the transducers are not properly aligned, the resulting orbit will be skewed, compromising data accuracy In cases involving notched shafts, the standard convention is to use a blank segment to indicate the beginning of the notch and a bright segment for its end, aiding in clear interpretation Specifically, as shown in Figure 11, the whirl direction is clockwise, reflecting the directional analysis of the shaft's vibration Proper transducer setup and clear conventions are essential for precise orbit analysis and fault diagnosis.
The direction of shaft rotation—clockwise or counter-clockwise—is determined independently based on the viewing perspective Forward whirl occurs when the whirl direction aligns with the rotation direction, while backward whirl happens when the whirl opposes the rotation For example, as shown in Figure 11, both the rotation and whirl directions are clockwise, indicating a forward whirl Understanding shaft whirl directions is essential for diagnosing and managing vibration issues in rotating machinery.
d.c shaft position
Displacement transducers are commonly used to determine the d.c shaft position by indicating the relative loading of sleeve bearings through eccentricity ratios Monitoring the attitude of journals within bearings via the d.c signal (such as the shaft gap) is essential for effective large machine maintenance Accurate d.c position measurements help verify proper bearing lift and ensure correct shaft alignment However, it is important to prevent misinterpreting data caused by d.c signal drift over extended periods.
Transient vibration
Transient speed vibration refers to the vibration data collected during a machine's start-up and coast-down phases, providing crucial insights into its operational behavior This type of vibration analysis is essential for diagnosing potential issues and ensuring machinery reliability The collected vibration information is typically visualized using various presentation formats, including cascade (waterfall) diagrams, Bode plots, polar diagrams (Nyquist diagrams), and Campbell diagrams, which aid in interpreting the dynamic response of the equipment Incorporating transient speed vibration analysis into maintenance strategies can enhance predictive maintenance and prevent unexpected failures.
Transient vibration occurs when a structure is excited by an instantaneous force, such as a single pulse or a short-duration oscillating excitation After the excitation stops, the structure tends to vibrate at its natural frequencies, with damping causing the vibrations to decay exponentially over time.
The structural response time history after the force ceases is characterized by a combination of decreasing sinusoidal waves A typical example of a damped sinusoid is illustrated in Figure 12 The composite waveform results from the superposition of the system's natural modes, all excited simultaneously by the instantaneous force Generally, higher frequency components decay more rapidly, causing the overall response to gradually simplify into a damped sinusoid dominated by the lowest frequency mode, as the higher modes become damped out over time.
Faults in rolling element bearings are often detected from repeated high‑frequency transient responses to ball or race defects.
Y amplitude a Exponential decay of peak amplitude envelope. b Composite waveform. c Waveform of lowest frequency mode. d Degenerated waveform.
Impulse
Impulse response represents the vibratory behavior of a mechanical system when subjected to an impulse force, which is applied over a very short duration It can be described as the system's time history in reaction to a force, F, applied over an infinitesimally small time interval, Δt The impulse itself is calculated as the integral of force F over time, from t to t + Δt, illustrating how the system responds dynamically to sudden excitations.
In many cases, impulse response is used to identify resonance frequencies in stationary structures.
Damping
Damping is the process where vibratory motion is converted into other energy forms, typically heat, leading to the reduction of vibration amplitudes The damping coefficient, c, is often proportional to the vibratory velocity and is commonly assumed for analysis purposes, even if not strictly accurate Critical damping occurs when a system has the minimum damping level, c_c, necessary to return to equilibrium without oscillation Systems with damping less than this threshold will exhibit oscillations with decreasing amplitudes, while those with more damping will recover smoothly (see Figure 14 and ISO 2041) In multi-degree-of-freedom systems, some modes may be less than critically damped, resulting in varied vibratory behaviors across different modes.
Figure 14 — Decaying amplitudes due to damping
The logarithmic decrement, denoted as d, quantifies the rate of vibration decay for a specific mode, X, over time It is calculated using the formula d = (1/n) ln(X₁ / Xₙ₊₁), where n represents the number of cycles required for the amplitude to decrease from X₁ to Xₙ₊₁ This measurement provides valuable insights into the damping characteristics of the vibrating system.
The loss factor is a common measure of the relative damping in a system The logarithmic decrement, d, is related to the loss factor, h, by h = d/π.
NOTE 1 Typically, the symbols used to denote the loss factor include h, z and η Those for the logarithmic decrement include α and Λ
The loss factor can also be found in terms of the decay rate, X’, in decibels per second, as follows: h X= / 27, 3 f
′ ( n ) (7) where f n is the natural frequency, in hertz.
The damping amount, represented by c, is indicated by the quality factor Q, which measures the system's response at its undamped natural frequency Q is a frequency-dependent magnification factor, reflecting the ratio of the system’s dynamic displacement amplitude to its static displacement under an equivalent constant force When there is minimal interaction between modes, Q for a specific mode can be determined directly, providing insight into the system’s resonance behavior and damping characteristics.
The quality factor, Q, can be estimated from measured response curves by analyzing the resonance frequency, f_r It is calculated as the ratio of the resonance frequency to the bandwidth between the half-power points, which are located at 0.707 times the maximum amplitude on either side of the peak This method provides an accurate approximation of Q for a specific mode, essential for understanding the resonance behavior of the system.
∆ (9) where f r is the resonance frequency; Δf = f 2 − f 1 with f 1 and f 2 being the half-power points.
The magnification factor is related to the logarithmic decrement by the following approximation:
NOTE 2 If the damping is small, Q = 1/h.
As an example, Figure 15 shows a typical representation of the Q factor derived from a Bode plot A similar result can be obtained from a polar diagram.
Damping is a useful quantity when investigating the cause and effect of vibration in rotating machinery
A mode near the operating speed can be acceptable if it is well damped, ensuring it does not significantly contribute to the system's response Conversely, a mode with minimal damping may become highly sensitive, causing the machine to respond violently or potentially preventing it from passing through resonance speeds safely Proper damping is essential to maintain stable and safe operation near resonance conditions.
Time domain averaging
Signals from monitored machines consist of both synchronous components, aligned with the machine’s processes or motions, and non-synchronous components, which originate independently of the system Frequency analysis is an essential technique used to separate these components, enhancing fault detection and condition monitoring Additionally, time domain averaging is a widely used method to identify these occurrences, improving measurement accuracy and revealing underlying machine behavior.
In time domain averaging, each data sample is synchronized to rotating elements using a reference pulse or trigger, ensuring accurate alignment This averaging process, which can include from a few to over 200 samples, is performed in the time domain to produce an averaged waveform By filtering out non-synchronous signal components that cancel each other, this method enhances signal clarity Increasing the number of averages improves the signal-to-noise ratio, with the optimal count depending on specific application requirements.
Time domain averaging involves algebraically adding corresponding samples across multiple records and dividing by the total number of records This process preserves the desired repeating waveform while suppressing random noise and other non-repeating signals, causing them to tend toward zero The effectiveness of noise reduction improves with more averages, as the decay rate of unwanted signals is proportional to the square root of the number of averages, enhancing signal clarity and accuracy.
NOTE 100 averages (records) will reduce the unwanted signals by a factor of ten; 10 000 averages will reduce them by a factor of 100.
This technique is highly effective for identifying the specific rotor responsible for vibration issues in multi-rotor machines It enables precise detection of various faults, including damaged gears, blades, and rolls in paper manufacturing equipment Utilizing this method enhances diagnostic accuracy and helps maintain optimal machine performance.
An effective example is a turbine-driven pump with gear drive operating at different shaft speeds, featuring a synchronizing trigger on each shaft Mounting an accelerometer on the gearbox allows for analysis through time domain averaging, where signals are synchronized with each trigger When synchronized with the turbine shaft trigger, the resulting sinusoidal waveform indicates the level of imbalance in the turbine shaft Conversely, using the pump shaft trigger reveals a periodic pattern at the vane passing frequency, highlighting a fixed radial offset of the pump shaft within its housing.
Strain gauge bridges mounted on large hydroturbine blades, with signals transmitted via telemetry, enable precise monitoring of blade performance Using a once-per-revolution trigger for synchronization, time domain averaging reduces flow noise, revealing consistent uneven patterns across blades These patterns indicate uneven flow through wicket gates, leading to dynamic stresses on the blades By analyzing this data, operators can re-adjust the wicket gates to achieve balanced flow and mitigate stress, enhancing turbine efficiency and longevity.
Although very effective, time domain averaging, by its very nature, cannot show asynchronous events such as antifriction bearing faults.
Averaging complex frequency spectra of successive realizations generally requires a steady-state vibration condition When there is unsteady excitation or changing rotational speed, simple time-domain averaging is not suitable Instead, signals should be sampled at constant intervals of the excitation process, such as equidistant rotor angle positions using an encoder The resulting frequency transformation produces an ordering spectrum rather than a traditional frequency spectrum For impulse response signals, averaging can be performed in the time domain through event triggering, such as a trigger aligned with the excitation impulse.
Trigger sources extend beyond rotating equipment, including applications like paper machine belts and conveyor belts The signal source is not limited to vibrations; it can also be a process signal linked to the machine that detects malfunctions or monitors critical process parameters for fault development Additionally, a frequency multiplier can be employed instead of traditional shaft-based triggers, especially in systems with multiple shafts, such as gearboxes.
Frequency domain analysis
General
Vibration analysis is predominantly performed in the frequency domain because it allows for the isolation of different vibration sources based on their specific frequencies Analyzing a single channel in the frequency domain provides valuable insights, but for comprehensive understanding, it is often essential to relate vibration data from a second channel as either a phase or amplitude reference—or both—to identify correlations and diagnose issues accurately.
Fourier transform
The Fourier transform (FT) is a fundamental technique for converting broadband time traces into discrete frequency bands, allowing identification of the sinusoidal components within a vibration signal, including noise This analysis can be performed using computers with signal processing software, specialized devices known as Fourier analyzers, or hardware microchips like digital signal processors (DSPs) Today, the most commonly used method in analyzers is the fast Fourier transform (FFT), which offers a more efficient and rapid way to analyze frequency data.
The frequency spectrum of a vibration signal can be effectively analyzed by converting its time waveform into sinusoidal components using the Fast Fourier Transform (FFT), as illustrated in Figure 16 When setting up an FFT analyzer, it is crucial to consider factors such as the bandwidth of frequency bins, overall frequency span, and the length of the time trace to obtain accurate results Additionally, there is a direct relationship between the bandwidth of the frequency lines, the span of the frequency range, and the duration of the recorded signal; for example, Figure 16 shows a bandwidth of 2 Hz. -**Sponsor**Struggling to rewrite your article for better SEO and coherence? It can be tough! With [Article Generation](https://pollinations.ai/redirect-nexad/xHCuFdI1), you can instantly create 2,000-word, SEO-optimized articles Imagine saving over $2,500 a month compared to hiring a writer Get your own content team—minus the hassle!
100 frequency lines between 0 Hz and 200 Hz These parameters should be chosen to optimize the frequency range of interest.
Due to the effects of aliasing (see 4.3.7), higher frequency components can be falsely identified as lower frequency Anti‑aliasing filters should be used in order to avoid this possibility.
The result of a Fourier transform is a complex spectrum, which can be displayed as
— real and imaginary part of each frequency component.
From a practical viewpoint, the amplitude spectrum (magnitude spectrum) has more information; therefore, the phase spectrum is mostly ignored.
Leakage and windowing
Sampling a waveform can cause leakage if the sample includes a non-integral number of cycles, leading to smeared frequency domain peaks due to inaccurate waveform representation Applying a window function, such as the Hanning window, effectively reduces these errors by mitigating spectral leakage The Hanning window performs well for both periodic sine waves and non-periodic time records, making it a popular choice However, other window types are also available that can further enhance signal analysis and improve accuracy.
For transient events, a Uniform (rectangular) window provides better results, while the Hamming window offers a narrower spectral peak at higher levels, trading off with more prominent flaring skirts The Blackman window and its variants, Blackman Exact and Blackman Harris, feature wider peaks than the Hanning window but with lower sidelobes, enhancing spectral clarity The Flat Top window improves amplitude accuracy over the Hanning window by providing the flattest peak, making it ideal for precise level measurements, although it may reduce the resolution of closely spaced signals Additionally, the Flat Top window is useful for calibration purposes and helps correct sampling bias, thereby enhancing asynchronous waveform plots such as spectrum, cascade, and waterfall displays Incorporating appropriate window functions is essential for accurate spectral analysis in various signal processing applications.
NOTE Time domain windows for Fourier Transform analysis are described in ISO 18431‑2.
Frequency resolution
The mathematics of an FFT requires that the frequency span of interest be divided into a finite number of sections, and the amplitude of vibration within each section is displayed as a vertical line, sometimes referred to as a “baseband” spectrum The number of sections is referred to as the number of lines of resolution (LOR), N LOR There can be more than one frequency component at frequencies within a single LOR bin, and the analyzer includes this total energy and displays it as a single line at the centre frequency of the bin.
To effectively distinguish between closely spaced frequency components, it is essential to have a sufficient number of Lines of Resolution (LOR) and to utilize a frequency span that encompasses all relevant frequencies Typically, a larger number of LOR enhances the ability to resolve subtle differences, ensuring accurate analysis of the signal's frequency spectrum Selecting an appropriate frequency span is crucial for capturing all frequencies of interest and obtaining reliable results.
400 LOR are used, but many machines require finer resolution than that The following relationship applies:
N LOR is the number of lines of resolution; f max is the maximum frequency of interest;
B is the bandwidth (line spacing).
As the relationship shows, for the same frequency range of interest, the finer the resolution, the smaller the bandwidth.
Record length
A single realization of the Fourier transform requires only a short record length, T, and the length of record required for an FFT is dependent on the bandwidth, B, as follows:
The length of record available can restrict the resolution As an example, if a spectrum has a span of
With a 100 Hz system frequency and a resolution of 400 lines, the required bandwidth is 0.25 Hz, and the minimum record length should be at least 4 seconds To maintain the same resolution while increasing the measurement span, the record length decreases proportionally, resulting in a wider bandwidth by the same factor This relationship highlights how changes in span impact bandwidth and recording duration, crucial for optimizing signal analysis in measurement systems.
When a machine's rotational speed varies slightly during testing, it is essential to use bins wide enough to capture all relevant frequency components within a single bin In cases of significant speed changes, the signal should be sampled at consistent angular intervals, and the resulting spectral data must be processed accordingly to ensure accurate analysis.
Amplitude modulation (sidebands)
Amplitude modulation (AM) in the time domain is illustrated in section 4.2.3, where an FFT analysis of a modulating sine wave reveals the original frequency along with sidebands located equally on either side at a distance corresponding to the modulating frequency When the modulation is a sine wave, the sidebands are clearly distinguishable, with only one appearing on each side of the main frequency, which is typical in scenarios like gear mesh frequencies with eccentric or worn gears Periodic, non-sinusoidal modulations produce multiple distinct sidebands, whereas a non-periodic modulation causes the sidebands to become smeared and indistinct, indicating a lack of regularity in the modulation pattern.
Detecting broken rotor bars in large induction motors can be effectively achieved by analyzing sidebands through decibel down measurements The decibel down (L_D) quantifies the fault severity by calculating 20 times the logarithm of the ratio between the rotor bar fault peak value and the line frequency value This measurement provides a clear and measurable indicator of rotor faults, aiding in predictive maintenance and ensuring motor efficiency.
L D = 20 lg(l 1 /l ref ) dB (13) where l 1 is the amplitude of the sideband; l ref is the amplitude at line frequency (50 Hz or 60 Hz).
A healthy motor's spectrum, as depicted in Figure 17, features a distinct peak at the line frequency accompanied by sidebands equally spaced on both sides, indicating normal operation The magnitude of these sidebands can be significant, providing essential insights into the motor's condition Monitoring these spectral features is crucial for diagnosing motor health and detecting early signs of potential issues.
60 dB down from the magnitude of the line frequency (60 Hz in this case).
Figure 17 — Motor with no problems
Figure 18 is the spectrum for a motor with a fault In this case, there is a distinct peak at line frequency and elevated sidebands at the rotor bar fault frequencies.
It can be noted that the structure of the sidebands in the frequency domain has the same information as the envelope spectrum in the time domain.
Aliasing
Aliasing occurs when a digital analyzer's sampling rate is too low to accurately capture a frequency, causing the signal to appear at a lower frequency This phenomenon is similar to a strobe light synchronizing with a rotating disc, where the disc appears stationary or slow-moving if not precisely synchronized To prevent aliasing, low-pass filtering should be applied before sampling to remove frequency components above half the sampling rate When the sampling frequency is lower than half the signal's frequency, the signal can be misinterpreted as a lower-frequency alias, leading to inaccurate measurements of the original high-frequency signal.
The Nyquist frequency is reached when the sampling rate is exactly twice the maximum expected signal frequency To ensure accurate signal reconstruction and accommodate practical filtering, most sampling rates are set slightly above this threshold—approximately 2.56 times the maximum frequency—allowing for effective low-pass filtering without the need for a sharp cutoff.
Modern digital analyzers utilize anti-aliasing filters that eliminate frequencies above 40% of the sampling rate, ensuring accurate digital conversion This effectively minimizes aliasing concerns in most cases However, analysts should verify the filtering effectiveness prior to data analysis to ensure reliable results.
Y excitation a 3/rev excitation b 13/rev excitation c 3 and 13 excitation
Synchronous sampling
Using an external signal to control the sampling rate in analyzers, rather than sampling at a fixed rate, offers significant advantages, especially in rotating machinery analysis When the sampling rate is set as a multiple of the external signal frequency, it ensures that frequency components associated with rotational speed—such as blades, vanes, or gear mesh vibrations—remain in the same frequency bin, improving measurement accuracy This method maintains all vibration orders centered within their respective frequency bins, allowing for more precise amplitude measurement Additionally, it allows for the averaging of digitized data without being affected by changes in rotational speed and ensures that vibrational signals maintain the same phase angle relative to the external signal Consequently, spectra can be averaged vectorially, enhancing relevant vibration orders while minimizing noise and unrelated signals, leading to clearer and more reliable analysis results.
The result of the Fourier transform of a synchronously sampled signal is the ordering spectrum X(n)
It is noted that digital order tracking is an approach used in practice (see 4.6).
When performing synchronous averaging, care should also be taken to avoid averaging out any non‑harmonic signals of significance (e.g bearing instability).
Spectrum averaging
The duration required for an FFT analysis depends on the component frequencies of the signal, with shorter records typically lasting only a fraction of a second or a few seconds However, when analyzing modulating signals, longer time periods are necessary to achieve a stable average amplitude Therefore, averaging successive FFTs is a crucial function of spectrum analyzers to ensure accurate results When using a single channel, the analyzer averages the absolute amplitudes in each bin regardless of phase, while full-spectrum averaging (including real and imaginary parts) requires synchronization of successive spectra through a process-dependent trigger signal for accurate phase alignment.
There are other averaging techniques that can be applied, such as frequency domain averaging, but this technique quickly becomes very complicated and is therefore used only for special applications.
Many analyzers utilize exponential averaging, which weights FFTs with an exponentially increasing function to emphasize the most recent data This technique is particularly effective for studying transient vibrations, especially when amplitude decreases exponentially over time By applying exponential averaging, analysts can enhance the detection of quickly changing signals and improve accuracy in dynamic vibration analysis.
Peak averaging on analyzers identifies the maximum amplitude within a specified time period across all FFTs in each frequency bin, effectively highlighting peak signal levels This method calculates the average amplitude for each peak, providing a clear representation of the highest signal strengths within the analyzed timeframe By capturing these peak values, peak averaging offers valuable insights into transient and maximum signal behaviors, making it a critical feature for detailed spectral analysis.
Logarithmic plots (with dB references)
Vibration records often contain numerous frequency components with widely varying amplitudes While smaller amplitude components are crucial for accurate analysis, they can be difficult to detect on a linear scale Using a logarithmic plot effectively compresses larger signals and amplifies smaller ones, revealing all significant components and the noise level The amplitude is expressed as a level in decibels (dB), with the decibel scale providing a clearer representation of the vibration spectrum.
Frequency axes are often displayed on a logarithmic scale to enhance detection and distinguish low-frequency components effectively Unlike the vertical axis, the decibel unit is not applied on the horizontal axis (see section 4.7) Understanding differences in decibels is crucial, as they represent ratios, with several examples provided in Table 1 to illustrate these relationships.
Table 1 — Differences in decibels and equivalent ratios
Ratios smaller than one are reflected by negative decibel values, e.g a ratio of 1/2 is −6 dB.
Reference values for logarithmic levels are specified in ISO 1683 For vibration analyses, the values given in Table 2 should be used.
Table 2 — Reference values for logarithmic levels
Zoom analysis
Frequency components that are close together can be difficult to distinguish with standard FFTs, which typically have around 400 lines in their baseband spectrum To achieve higher resolution, many analyzers utilize zoom spectra, which focus on a specific frequency range by creating a spectrum that begins at a user-selected frequency rather than zero This method narrows the bandwidth and expands the frequency range of interest, but it requires more stable frequencies due to the narrower bandwidth Despite the smaller bandwidth, the record length remains related to the bandwidth, which can impact the analysis accuracy.
Zoom spectra are effectively used in gear fault analysis, revealing sidebands of the gear mesh frequency that indicate potential issues The spacing between these sidebands helps identify the specific faulted gear wheel This technique enhances diagnostic accuracy in condition monitoring of gear systems.
Zoom analysis is a valuable technique for detecting faults in rolling element bearings, enhancing fault visibility beyond the standard spectrum As demonstrated in Figure 20, performing a zoomed-in frequency analysis reveals components that are not apparent in the original spectrum, allowing for more accurate fault diagnosis and early maintenance interventions This approach underscores the importance of detailed spectral examination to identify subtle bearing defects effectively.
Key a section of original spectrum b higher resolution translated spectrum
Differentiation and integration
Differentiation and integration are essential in vibration analysis for converting signals between displacement, velocity, and acceleration In rotating machinery, vibration signals are often dominated by the synchronous component, allowing modeling as harmonic motion The corresponding formulas in the time domain include displacement \(x = \hat{x} \sin \omega t\), velocity \(v = \omega \hat{x} \cos \omega t\), and acceleration \(a = - \omega^2 \hat{x} \sin \omega t\) These relationships facilitate the transformation between different vibration parameters, highlighting the harmonic nature of the motion and enabling accurate signal analysis in machinery diagnostics.
Displacement lags velocity by 90°, while velocity lags acceleration by 90°, highlighting their phase relationships In the frequency domain, converting between these quantities involves dividing or multiplying by the angular frequency, enabling differentiation and integration Most analyzers are equipped with these functions, facilitating effective analysis in the frequency domain.
To effectively utilize integration and differentiation formulas in vibration analysis, it is essential that the vibration signal is predominantly synchronous Ensuring that the 1× component constitutes more than 90% of the unfiltered or raw signal is crucial for accurate results If this condition is not met, each spectral frequency must be individually processed to maintain analysis precision.
Display of results during operational changes
Amplitude and phase (Bode plot)
When analyzing harmonic vibration signals, a reference signal is essential for accurately determining phase, which can be derived from sources like a shaft revolution marker, a measurement at a different location or direction, or a known force The chosen reference signal's frequency should correspond to the frequencies of interest, such as using a shaft revolution marker to serve as a phase reference for rotational frequency or its higher harmonics This approach ensures precise phase comparison and effective vibration analysis.
The phase may be expressed as between 0° and 360°, or ± 180°.
When analyzing signals representing different physical quantities such as force, velocity, or acceleration, it is essential to interpret their physical significance accurately Sine waves exhibit phase relationships where displacement lags velocity by 90°, and velocity lags acceleration by 90°, highlighting the importance of understanding these phase differences Signal-conditioning equipment can alter the phases of signals, so it is crucial to compensate for these phase shifts between channels to ensure accurate data interpretation.
A Bode plot visualizes the relationship between the amplitude and phase of machine vibrations and the rotational speed of the machine Unlike plotting sine wave amplitude and phase over time, this approach allows for analyzing how vibration characteristics change with varying rotational speeds As illustrated in Figure 21, plotting amplitude and phase against rotational speed provides valuable insights into machine behavior and helps detect potential issues related to vibrations Utilizing Bode plots is essential for condition monitoring and vibration analysis in mechanical systems for optimized performance and predictive maintenance.
Figure 21 — Amplitude and phase (Bode plot)
Polar diagram (Nyquist diagram)
A polar diagram displays amplitude and phase vectors for discrete frequencies, as illustrated in Figure 22 When multiple vectors corresponding to different rotational speeds or parameters are included, and only the connecting lines between their tips are shown, this representation is called a Nyquist diagram.
A polar diagram requires a phase reference, like a shaft revolution marker, to indicate each 360° rotation of the shaft These diagrams, along with Bode plots, are essential tools for accurately identifying the rotational speed at which resonances occur in rotor, bearing, and support systems Incorporating a phase reference ensures precise analysis of system vibrations and resonance locations Using polar diagrams and Bode plots enhances condition monitoring and helps in diagnosing potential mechanical issues.
NOTE The parameter is the rotor rotational speed (r/min).
Figure 22 — Polar diagram (Nyquist diagram)
Cascade (waterfall) diagram
The cascade or waterfall diagram offers a straightforward comparison of multiple frequency analyses, presenting a three-dimensional spectrum display that highlights vibration signal changes This visualization effectively illustrates how signals vary in relation to parameters like rotational speed, load, temperature, or time, providing clear insights into dynamic system behavior under different conditions.
The sample cascade spectrum shown in Figure 23 offers a comprehensive view of multiple vibration spectra during a machine's start-up or coast-down phases Typically, the cascade spectrum display presents frequency (Hz or orders) versus the machine's rotational speed, along with the vibration amplitudes of individual discrete frequency components This visualization is essential for diagnosing machine conditions and identifying potential issues related to vibrations during critical operational transitions Optimizing the interpretation of cascade spectra enhances predictive maintenance and ensures reliable machine performance.
In certain situations, machine speed can be replaced by alternative variables such as time or load, resulting in a waterfall diagram for better visualization When utilizing machine speed for this display, it is essential to accurately record a rotor speed or phase reference signal to ensure precise analysis This approach enhances the understanding of dynamic machine behavior and is important for effective troubleshooting and performance monitoring.
The cascade spectrum illustrated in Figure 24 highlights the fundamental rotor speed (1×) along with other significant harmonic frequencies It also reveals the presence of rotor resonance speeds, particularly when operating within the transient speed range These insights are crucial for understanding rotor dynamics and ensuring operational stability.
The shape of the plot varies depending on the machine type and operational phase For instance, Figure 24 illustrates a cascade plot of a steam turbine operating at 3,000 rpm (50 Hz) during start-up and coast-down, highlighting the typical performance patterns observed during these processes.
A spectrogram offers an effective alternative for representing time-dependent spectra It provides a two-dimensional visualization of a cascade plot, illustrating how frequency or speed varies over time Additionally, the vibration amplitude is depicted through different colors or shades of gray, enhancing the clarity of the data Refer to Figure 25 for an example of this visual representation.
NOTE The example in Figure 25 shows another machine than those in Figure 23 and Figure 24.
Y time, s v vibration amplitude, mm/s (indicated by different colours)
Campbell diagram
The Campbell diagram (see Figure 26) is a specialized cascade diagram that visualizes the relationship between the actual frequencies of various components—such as blades, vanes, and gear meshes—and the rotational speed By incorporating vibration amplitude as the third dimension, represented by the height of the bars, the diagram provides a comprehensive view of vibrational behavior Campbell diagrams are particularly valuable for identifying self-excited natural vibrations in rotating machinery, aiding in fault detection and system optimization.
Y frequency, Hz a 1 st speed harmonic e Resonance speed. b 2 nd speed harmonic f Resonance speed. c Amplitude g Limit speed of instability. d Natural frequency h Sub‑synchronous vibration arising from rotor instability.
Real‑time analysis and real‑time bandwidth
Real-time analysis involves displaying measurement results instantly as data is collected, allowing test engineers to observe data as it is recorded It primarily depends on the speed of data acquisition versus processing; if processing takes longer than data collection, true real-time analysis is not achieved Sometimes, signals need to be recorded and replayed multiple times for thorough analysis Additionally, when data exceeds processing capacity, excess data may be skipped to maintain real-time performance, ensuring continuous monitoring without delays.
Analog systems often utilize real-time analyzers equipped with a bank of filters that display multiple outputs simultaneously Early octave and one-third-octave analyzers exemplify this type, providing comprehensive frequency analysis in real-time for various applications.
In digital systems, vibration signals are sampled to generate successive time records, which are then processed to extract spectra and other characteristics Complete sampling of each time record must occur before processing begins, although sampling of a new record can occur simultaneously with the processing of the previous one When sampling takes longer than processing, the analysis is considered real-time, ensuring continuous monitoring The maximum frequency span at which data can be processed without delay defines the system’s real-time bandwidth, varying across different analyzers based on processing speeds.
For most machinery measurements conducted at steady rotational speeds, real-time analysis is generally unnecessary However, during transient events such as start-ups and coast-downs, using a narrow real-time bandwidth can lead to missing critical data To ensure comprehensive analysis of these events, it is best to record the entire occurrence and review it later at a reduced speed, enabling detailed examination of all relevant details.
Order tracking (analogue and digital)
Order tracking is a crucial technique in vibration analysis that addresses challenges caused by variable machine speeds When rotational speed fluctuates, energy from specific vibration orders can spread across multiple frequency bins and appear at lower levels, making meaningful averaging difficult To overcome this, controlling the sampling rate in relation to the machine’s speed—using external sampling methods—ensures that all energy from a particular vibration order is captured within a single frequency bin This is typically achieved by providing a once-per-revolution signal to a dynamic signal analyzer, known as order tracking, which enhances the accuracy and clarity of frequency spectra for rotating machinery analysis.
Order tracking initially utilized a tracking filter for alias protection and a ratio synthesizer to convert the r/min signal into a sampling frequency of 2.56 times the highest order of interest Due to noise, accuracy concerns, and limitations on the rate of change in r/min, computed order tracking was developed to digitize the process for more precise analysis.
In computed order tracking, both vibration and r/min signals are digitized at fixed sampling rates to ensure precise analysis The r/min signal determines the sampling rate for each revolution, allowing for accurate cycle synchronization The vibration signal is then interpolated and resampled at appropriate intervals using either stepwise changing sampling frequencies or polynomial interpolation, enabling continuous and effective order analysis This approach ensures high-resolution tracking of rotating machinery vibrations across varying rotational speeds.
According to section 4.3.8, this method offers two key advantages over time-based sampling Firstly, all the energy for each order is captured at the center of the window for each bin, minimizing errors associated with off-center sampling This approach reduces potential inaccuracies that can reach up to 15%, ensuring more precise and reliable measurement results.
The other advantage is that it is possible to obtain averaged records with the rotational angle a
Ordering spectra enable accurate analysis of vibrations at specific rotational frequencies, regardless of fluctuating rotational speeds Unlike vector averaging, which causes vibrations at non-constant frequencies to cancel out, ordering spectra preserve the phase information and allow for meaningful averaging This approach prevents smearing of vibration components and ensures precise identification of vibration characteristics at specific shaft rotation orders.
Octave and fractional‑octave analysis
An octave is a musical and acoustical term that signifies doubling or halving a frequency, such as 100 Hz increasing to 200 Hz or decreasing to 50 Hz Unlike decibels, which express amplitude ratios, octaves provide a simple way to represent frequency ratios in sound analysis For more detailed frequency resolution, octaves can be subdivided logarithmically into fractional parts, like one-third octaves, allowing for more precise audio measurements.
Cepstrum analysis
Cepstrum analysis is a technique that transforms the logarithmic power spectrum of vibration data from the time domain into a spectral format, highlighting detailed features It displays amplitude on the vertical axis and "quefrency"—a pseudo time—on the horizontal axis, effectively representing a spectrum of a spectrum By applying cepstrum analysis, fundamental frequencies and their harmonic series are condensed into a single component, making it a powerful tool for vibration signal processing and fault detection.
A cepstrum is ideally suited for analyzing complex signals with multiple harmonic series, such as those generated by gearboxes or rolling element bearings Its main advantage lies in its ability to isolate and enhance periodic functions, making it easier to identify relationships within the signal For a detailed overview of the development of cepstrum analysis, refer to Table 3, which outlines the step-by-step progression of this technique.
Measurement of the time history digitized signal x(t)
FFT of the digitized signal amplitude spectrum X ( f )
Square the magnitudes of the components of the amplitude spectrum power spectrum
Calculate 10 times the logarithm of the power spectrum 10 lg S XX ( f ) dB
10 lg S XX ( f ) dB power cepstrum C XX ( t )
This section of ISO 13373 outlines the most widely used techniques for narrowband vibration condition monitoring and diagnostics, ensuring effective fault detection and machinery health assessment While these standard methods are essential, there are additional advanced procedures that can be highly beneficial for addressing specific, complex issues in specialized cases These supplementary techniques, listed below, provide further options for tailored vibration analysis and problem-solving in challenging scenarios, enhancing the overall reliability of machinery maintenance programs.
— multi‑trend analysis (r.m.s values, frequency components, hours, calendar time, high speed);
[1] ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
[2] ISO 2954, Mechanical vibration of rotating and reciprocating machinery — Requirements for instruments for measuring vibration severity
[3] ISO 5348, Mechanical vibration and shock — Mechanical mounting of accelerometers
[4] ISO 7919 (all parts), Mechanical vibration — Evaluation of machine vibration by measurements on rotating shafts
[5] ISO 10816 (all parts), Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts
[6] ISO 10817-1, Rotating shaft vibration measuring systems — Part 1: Relative and absolute sensing of radial vibration
[7] ISO 13372, Condition monitoring and diagnostics of machines — Vocabulary
[8] ISO 16063-21, Methods for the calibration of vibration and shock transducers — Part 21: Vibration calibration by comparison to a reference transducer
[9] ISO 18431 (all parts), Mechanical vibration and shock — Signal processing
[10] ISO 20816 (all parts), Mechanical vibration — Measurement and evaluation of machine vibration
[11] VDI 3839 Part 1, Instructions on measuring and interpreting the vibrations of machine —
[12] MITCHELL J.S An introduction to machinery analysis and monitoring Pennwell Publishing, 1993