# Master the Skills of Rotating Machinery Diagnostics with Donald E Bently's Book

## Fundamentals of Rotating Machinery Diagnostics by Donald E Bently

Rotating machinery is a broad term that encompasses any machine that has rotating parts, such as turbines, compressors, pumps, fans, generators, etc. These machines are widely used in various industries such as power generation, oil and gas, aerospace, automotive, etc. Rotating machinery diagnostics is the science and art of detecting and identifying malfunctions in rotating machinery using vibration measurements and analysis. It is a vital skill for engineers, technicians, operators, and managers who work with rotating machinery.

## fundamentals of rotating machinery diagnostics donald e bently

One of the pioneers and leading experts in this field is Donald E Bently, who founded Bently Nevada Corporation in 1961 and developed innovative products and services for rotating machinery diagnostics. He also authored several books and papers on this topic, including his magnum opus "Fundamentals of Rotating Machinery Diagnostics", which was published in 2002 by ASME Press. This book is a comprehensive and practical guide that covers the essential concepts and methods for effective machinery malfunction diagnosis.

In this article, we will review some of the main topics covered in this book and provide some examples and illustrations to help you understand them better. We will cover the following topics:

Vibration fundamentals

Data plots

Rotor dynamics

Malfunctions

By the end of this article, you will have a basic understanding of rotating machinery diagnostics and its applications. You will also learn about some of the valuable contributions made by Donald E Bently to this field.

## Vibration fundamentals

Vibration is the oscillatory motion of a body or a system around a reference position. It can be caused by various internal or external forces acting on the body or system. Vibration can be desirable or undesirable depending on the context. For example, vibration can be used for testing, cleaning, or entertainment purposes. However, vibration can also cause noise, wear, fatigue, or failure in machines or structures.

Vibration can be measured using various sensors or transducers that convert mechanical motion into electrical signals. The most common sensors used for rotating machinery diagnostics are accelerometers, velocity sensors, displacement sensors, or proximity probes. These sensors can measure different aspects of vibration such as amplitude, frequency, phase, or direction.

Amplitude is the magnitude of vibration and it can be expressed in different units such as acceleration (g), velocity (in/s), displacement (mil), or gap voltage (mV). Frequency is the number of cycles of vibration per unit time and it is expressed in hertz (Hz) or cycles per minute (cpm). Phase is the angular position of vibration relative to a reference point and it is expressed in degrees () or radians (rad). Direction is the orientation of vibration relative to a coordinate system and it can be expressed in terms of horizontal, vertical, axial, or radial components.

Vibration vectors are graphical representations of vibration that show both amplitude and phase. They can be used to analyze the vibration behavior of rotating machinery and to diagnose malfunctions. Vibration vectors can be plotted on different types of diagrams such as polar, Bode, orbit, etc.

## Data plots

Data plots are graphical representations of vibration data that show the relationship between different variables such as time, frequency, amplitude, phase, etc. Data plots can provide useful information about the operating condition, performance, and health of rotating machinery. They can also help to identify the type, location, and severity of malfunctions.

There are different types of data plots that can be used for rotating machinery diagnostics. Some of the most common ones are:

Timebase plots: These plots show the variation of vibration amplitude versus time. They can reveal the presence of transient or periodic events such as impacts, rubs, or resonance.

Spectrum plots: These plots show the distribution of vibration amplitude versus frequency. They can reveal the dominant frequencies or harmonics of vibration and their sources such as rotational speed, imbalance, misalignment, etc.

Orbit plots: These plots show the trajectory of the shaft centerline motion in a plane perpendicular to the shaft axis. They can reveal the shape and size of the orbit and its relation to the bearing clearance or geometry.

Average shaft centerline plots: These plots show the average position of the shaft centerline relative to the bearing centerline in a plane perpendicular to the shaft axis. They can reveal the static or dynamic displacement of the shaft due to unbalance, thermal growth, load changes, etc.

Polar plots: These plots show the variation of vibration amplitude and phase versus rotational speed. They can reveal the resonance frequencies or critical speeds of the rotor system and their effects on vibration.

Bode plots: These plots show the variation of vibration amplitude and phase versus frequency. They can reveal the natural frequencies or modes of vibration of the rotor system and their effects on stability.

APHT plots: These plots show the variation of average peak-to-peak amplitude, peak phase angle, harmonic distortion, and total harmonic distortion versus rotational speed. They can reveal the nonlinear behavior of the rotor system due to rubbing, cracking, fluid forces, etc.

Half and full spectrum plots: These plots show the distribution of vibration amplitude versus frequency for half or full rotation of the shaft. They can reveal the presence of asymmetries or anisotropies in the rotor system such as bent shaft, cracked shaft, ovality, etc.

Trend and XY plots: These plots show the variation of one or more vibration parameters versus another parameter such as time, speed, load, temperature, etc. They can reveal the trends or patterns of vibration over time or under different operating conditions.

The following table shows some examples of data plots for common malfunctions in rotating machinery:

## Malfunction Data plot Description --- --- --- Unbalance Spectrum plot Shows a peak at 1X rotational frequency Misalignment Spectrum plot Shows peaks at 1X and 2X rotational frequency Looseness Spectrum plot Shows peaks at multiple harmonics of rotational frequency Rotor bow Orbit plot Shows an elliptical orbit with major axis aligned with bow direction High radial loads Average shaft centerline plot Shows a large displacement from bearing centerline Rubbing APHT plot Shows an increase in harmonic distortion and total harmonic distortion Fluid-induced instability Bode plot Shows a negative slope in phase versus frequency Shaft crack Half spectrum plot Shows a peak at 2X rotational frequency Rotor dynamics

Rotor dynamics is the study of the motion and forces of rotating shafts and their interactions with bearings and other components. Rotor dynamics can affect the performance, reliability, and safety of rotating machinery. Rotor dynamics can cause various phenomena such as resonance, instability, whirl, whip, etc.

## the mass, stiffness, and damping properties of the shaft and the bearings. A rotor system model can be classified into two types: lumped-parameter model and distributed-parameter model. A lumped-parameter model is a simplified model that assumes the shaft is a series of rigid disks connected by massless springs and dampers. The disks represent the concentrated masses of the shaft segments and the attached components. The springs and dampers represent the flexibility and damping of the shaft segments and the bearings. A lumped-parameter model can be solved using analytical or numerical methods such as transfer matrix method, finite element method, modal analysis, etc. A distributed-parameter model is a more realistic model that considers the shaft as a continuous elastic body with distributed mass, stiffness, and damping. The shaft can be modeled using beam or shell elements with various cross-sectional shapes and material properties. A distributed-parameter model can be solved using numerical methods such as finite element method, finite difference method, etc. The choice of the rotor system model depends on the accuracy and complexity required for the analysis. A lumped-parameter model is usually simpler and faster to solve, but it may not capture some important effects such as gyroscopic effect, shear deformation, rotary inertia, etc. A distributed-parameter model is usually more accurate and comprehensive, but it may require more computational resources and time. One of the key aspects of rotor dynamics is to determine the natural frequencies or modes of vibration of the rotor system. These are the frequencies at which the rotor system vibrates when it is disturbed by a small perturbation. The natural frequencies depend on the mass, stiffness, and damping properties of the rotor system and they can change with rotational speed due to various effects such as centrifugal force, gyroscopic effect, fluid forces, etc. The natural frequencies can be classified into two types: forward whirl and backward whirl. Forward whirl is when the vibration frequency is higher than the rotational speed and the vibration direction is in the same direction as rotation. Backward whirl is when the vibration frequency is lower than the rotational speed and the vibration direction is opposite to rotation. Forward whirl modes are usually stable and damped, while backward whirl modes are usually unstable and amplified. Another key aspect of rotor dynamics is to analyze the stability of the rotor system. Stability is the ability of the rotor system to return to its equilibrium position after a small disturbance. Stability depends on the damping properties of the rotor system and it can be affected by various factors such as rotational speed, bearing characteristics, fluid forces, etc. Stability analysis can be performed using different methods such as root locus method, Nyquist method, Routh-Hurwitz method, etc. These methods involve plotting or calculating certain parameters that indicate whether the rotor system is stable or unstable under different operating conditions. A common parameter used for stability analysis is the logarithmic decrement, which measures the rate of decay or growth of vibration amplitude over one cycle. Malfunctions

Malfunctions are abnormal conditions that affect the performance, reliability, or safety of rotating machinery. Malfunctions can be caused by various factors such as manufacturing defects, wear and tear, improper installation or operation, environmental influences, etc. Malfunctions can result in increased vibration levels, reduced efficiency, increased noise or temperature, or catastrophic failure.

Some of the common malfunctions that affect rotating machinery are:

Unbalance: This is when the mass distribution of a rotating component is not symmetrical about its axis of rotation. Unbalance causes a centrifugal force that acts on the shaft and induces vibration at 1X rotational frequency.

Rotor bow: This is when a shaft or a disk is bent due to thermal or mechanical effects. Rotor bow causes an eccentricity between the shaft axis and the geometric axis and induces vibration at 1X rotational frequency.

the shaft centerline and induce vibration at various frequencies depending on the load distribution.

Misalignment: This is when the axes of two coupled shafts are not collinear or parallel. Misalignment causes a bending moment on the shafts and induces vibration at 1X and 2X rotational frequency.

Rubbing: This is when a rotating component comes in contact with a stationary or another rotating component due to excessive vibration, thermal expansion, or deformation. Rubbing causes a friction force that acts on the shaft and induces vibration at various frequencies depending on the type and severity of rub.

Looseness: This is when a component of the rotor system is not securely fastened or fitted. Looseness causes a relative motion between the components and induces vibration at multiple harmonics of rotational frequency.

Fluid-induced instability: This is when the fluid forces acting on the rotor system cause a destabilizing effect on the rotor motion. Fluid-induced instability can occur due to internal flow (such as in seals, bearings, or impellers) or external flow (such as in cross-coupled forces or aerodynamic forces). Fluid-induced instability causes a negative damping effect that induces vibration at various frequencies depending on the fluid characteristics and operating conditions.

Shaft cracks: This is when a shaft develops a crack due to fatigue, corrosion, overload, or impact. Shaft cracks cause a reduction in stiffness and strength of the shaft and induce vibration at various frequencies depending on the crack location, depth, and orientation.

To diagnose these malfunctions, various techniques can be used such as vibration analysis, modal analysis, spectrum analysis, time-frequency analysis, wavelet analysis, etc. These techniques involve processing and analyzing the vibration data and plots to extract useful features or patterns that indicate the presence and characteristics of malfunctions. Some examples of these techniques are:

Vibration analysis: This technique involves measuring and analyzing the vibration amplitude, frequency, phase, and direction of the rotor system using sensors and data plots. Vibration analysis can reveal the overall condition of the rotor system and identify some common malfunctions such as unbalance, misalignment, looseness, etc.

Modal analysis: This technique involves identifying and characterizing the natural frequencies or modes of vibration of the rotor system using sensors and data plots. Modal analysis can reveal the dynamic behavior of the rotor system and identify some malfunctions that affect the stiffness or damping properties of the rotor system such as rotor bow, high radial loads, fluid-induced instability, shaft cracks, etc.

Spectrum analysis: This technique involves transforming the vibration data from time domain to frequency domain using Fourier transform or other methods. Spectrum analysis can reveal the dominant frequencies or harmonics of vibration and their sources such as rotational speed, imbalance, misalignment, etc.

Time-frequency analysis: This technique involves transforming the vibration data from time domain to time-frequency domain using short-time Fourier transform, Wigner-Ville distribution, or other methods. Time-frequency analysis can reveal the variation of frequency components over time and their sources such as transient events, rubs, resonance, etc.

Wavelet analysis: This technique involves transforming the vibration data from time domain to time-scale domain using wavelet transform or other methods. Wavelet analysis can reveal the localized features or patterns in time and frequency domains and their sources such as impacts, cracks, modulations, etc.

repair, replacement, etc. These techniques involve adjusting or modifying the components or parameters of the rotor system to reduce or eliminate the vibration and improve the performance, reliability, or safety of the rotor system. Some examples of these techniques are:

Balancing: This technique involves adding or removing mass from a rotating component to make its mass distribution symmetrical about its axis of rotation. Balancing can reduce or eliminate the vibration caused by unbalance.

Alignment: This technique involves adjusting the position or orientation of two coupled shafts to make their axes collinear or parallel. Alignment can reduce or eliminate the vibration caused by misalignment.

Lubrication: This technique involves applying a fluid film between two sliding or rolling surfaces to reduce friction and wear. Lubrication can reduce or eliminate the vibration caused by rubbing, fluid-induced instability, or bearing failure.

Repair: This technique involves fixing or restoring a damaged or worn component to its original condition or function. Repair can reduce or eliminate the vibration caused by rotor bow, looseness, rub and looseness, fluid-induced instability, shaft cracks, blade cracks, etc.

Replacement: This technique involves replacing a damaged or worn component with a new or refurbished one. Replacement can reduce or eliminate the vibration caused by any malfunction that cannot be repaired.

## Conclusion

In this article, we have reviewed some of the fundamentals of rotating machinery diagnostics based on the book by Donald E Bently. We have covered the following topics:

Vibration fundamentals: We have learned what vibration is and how it is measured using sensors and data plots. We have also learned what phase and vibration vectors are and how they are used to analyze vibration.

Data plots: We have learned what data plots are and why they are useful for rotating machinery diagnostics. We have also learned what are the different types of data plots and how they are interpreted.

Rotor dynamics: We have learned what rotor dynamics is and how it affects rotating machinery performance. We have also learned what are the basic elements of a rotor system model and what are the different modes of vibration and stability analysis.

Malfunctions: We have learned what are the common malfunctions that affect rotating machinery and how to diagnose them using vibration data and plots. We have also learned how to prevent or correct these malfunctions using appropriate techniques.

We hope that this article has given you a basic understanding of rotating machinery diagnostics and its applications. We also hope that you have learned about some of the valuable contributions made by Donald E Bently to this field. If you want to learn more about this topic, we recommend you to read his book "Fundamentals of Rotating Machinery Diagnostics" which is available from ASME Press.

## FAQs

Here are some frequently asked questions about rotating machinery diagnostics with brief answers:

What is rotating machinery diagnostics?

Rotating machinery diagnostics is the science and art of detecting and identifying malfunctions in rotating machinery using vibration measurements and analysis.

Why is rotating machinery diagnostics important?

Rotating machinery diagnostics is important because it can help to improve the performance, reliability, and safety of rotating machinery by preventing or correcting malfunctions that can cause increased vibration levels, reduced efficiency, increased noise or temperature, or catastrophic failure.

Who is Donald E Bently?

Donald E Bently is one of the pioneers and leading experts in rotating machinery diagnostics. He founded Bently Nevada Corporation in 1961 and developed innovative products and services for rotating machinery diagnostics. He also authored several books and papers on this topic, including his magnum opus "Fundamentals of Rotating Machinery Diagnostics".

What are some common malfunctions in rotating machinery?

Some common malfunctions in rotating machinery are unbalance, rotor bow, high radial loads, misalignment, rub and looseness, fluid-induced instability, and shaft cracks.

How can these malfunctions be diagnosed?

modal analysis, spectrum analysis, time-fr

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