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Vibration Monitoring by the Numbers
Accelerometers, units and severity, spectra, unbalance, misalignment, bearing and gear faults, alarms and running a monitoring program
How to monitor the condition of rotating machines by vibration, from piezoelectric sensors and units to spectra, fault diagnosis, alarms and the economics of a program, worked with numbers.
Start readingAbout this book
Every rotating machine vibrates, and the way it vibrates changes as it wears. An unbalanced fan shakes once per revolution; a misaligned coupling adds twice per revolution; a spalled bearing race rings at a frequency set by its geometry; a chipped gear tooth knocks once each time it meshes. Measured with a small sensor on the bearing housing and analysed by frequency, those changes appear weeks or months before the machine fails, which gives a maintenance team time to plan the repair instead of reacting to a breakdown.
This book shows how to use vibration monitoring with numbers. It starts with why vibration reveals condition and how that sets monitoring intervals, then covers the units of vibration and how to convert between them, the piezoelectric accelerometer that measures it, judging severity and setting alarms, and reading a spectrum. It then works through the common faults, unbalance, misalignment, looseness, resonance, rolling bearing defects and gear faults, and finishes with running a program and judging what it is worth.
It is for maintenance planners, reliability and mechanical engineers, fitters, vibration technicians and operations managers. It assumes engineering or trade training and comfort with basic mechanics; the physics of the sensor and the signal processing are explained as they are used. Each chapter works the running case with real numbers, includes a plausible mistake and how it was found, links the BIZOMAT tools that do the chapter’s calculations, and ends with an exercise and its worked answer.
The running case
Every chapter follows one site. This is an illustration. A timber mill near Mount Gambier, South Australia, runs a sawmill, a chipper and a kiln, and monitors its critical rotating plant on a fortnightly route with a portable data collector, plus two permanently mounted sensors on its most important machine:
- F-2, the dust extraction fan: a 55 kW motor driving an overhung centrifugal impeller at 1,480 r/min through a flexible coupling.
- P-4, the hydraulic power unit for the log carriage: a 37 kW, 1,480 r/min motor whose drive-end bearing is a 6309 deep-groove ball bearing.
- G-3, the log-deck conveyor gearbox: a two-stage helical reducer driven at 1,480 r/min, with a 19-tooth input pinion.
- The chipper: the mill’s largest machine, with permanently mounted accelerometers on its two main bearings.
Speeds, sizes, vibration levels, costs and results are the mill’s working figures or are calculated from stated assumptions. They do not describe BIZOMAT work or any real mill, machine maker or service company. Bearing geometry is typical for illustration and should be taken from the bearing maker’s data for real calculations. Prices are in Australian dollars excluding GST.
How to use the book
Read Chapters 1 to 3 first: they set out why monitoring works, the units and the sensor. Chapters 4 and 5 cover severity, alarms and spectra, which every diagnostic chapter uses. Chapters 6 to 9 cover the faults and can be read in any order. Chapter 10 brings the program and its cost together.
Every calculation in the book was checked by running it, and the BIZOMAT tools linked from each chapter were checked against the calculations they perform. Where a tool was built for a different purpose but does one step of a chapter’s calculation, the chapter says which output is used.
Source limits and professional responsibility
This book is educational. Severity criteria for particular machines come from standards such as the ISO 20816 series and from machine makers, which the book names by number and scope only; their limits are not reproduced. Working near rotating machinery and taking measurements on running plant are hazardous and must follow the site’s safe work procedures, isolation rules and guarding requirements. Decisions to run, repair or stop real machines remain with the competent people responsible for them.
Who this book is for
Maintenance planners, reliability and mechanical engineers, fitters, vibration technicians and operations managers who set up, run, interpret or pay for vibration monitoring of fans, pumps, motors and gearboxes.
What you will learn
- Explain why vibration reveals machine condition, and set monitoring intervals from the time between a fault's first sign and failure.
- Convert between acceleration, velocity and displacement, choose measurement units and judge severity against standards and baselines.
- Explain how a piezoelectric accelerometer works, and mount and select one so that its frequency range covers the faults of interest.
- Read a vibration spectrum and diagnose unbalance, misalignment, looseness, resonance, rolling bearing and gear faults.
- Set alarm limits, run a route or online program, and judge its cost against the failures it prevents.
Inside this book
Chapters
- 01Why vibration reveals conditionHow faults change vibration, the P-F interval between first sign and failure, why time-based replacement fails for random failures, monitoring intervals, and a quarterly route that missed a bearing.
- 02Displacement, velocity and accelerationThe three ways to express vibration and converting between them, RMS, peak and peak-to-peak, overall levels, which unit suits which faults, and a peak reading compared with an RMS alarm.
- 03The piezoelectric accelerometerHow a piezoelectric crystal turns force into charge, the accelerometer as a mass on a spring, sensitivity, mounted resonance, mounting, cables and overload, and a magnet that invented a fault.
- 04Severity, trends and alarm limitsJudging vibration against standards and a machine's own history, alert and danger levels, limits from individuals and EWMA charts, band alarms, and an overall-level alarm that missed a bearing.
- 05Spectra and signal settingsFrom waveform to spectrum: maximum frequency, lines and resolution, windows, averaging, orders and speed, and a low-resolution spectrum that blamed a motor's mechanics for an electrical fault.
- 06Unbalance and balancing in placeHow unbalance makes a 1× vibration, the force on the bearings, balance quality grades, single-plane balancing with a trial weight and vectors, splitting a correction, and a trial weight left on.
- 07Misalignment, looseness and resonanceThe signatures of misalignment, soft foot and looseness, how resonance magnifies an ordinary force, bump tests, the isolator selection tool, and a pump skid that could not be balanced.
- 08Rolling bearing faultsWhere a rolling bearing's defect frequencies come from, calculating them, the stages of bearing damage, envelope analysis, lubrication faults, and a 3× peak taken for an outer-race defect.
- 09Gears, pumps and fansGear mesh frequency and sidebands, shaft speeds through a reducer, wear against a cracked tooth, synchronous averaging, blade and vane pass, cavitation, and sidebands traced to the wrong shaft.
- 10Running a monitoring programChoosing which machines to monitor and how, routes and intervals, people and qualifications, acting on findings, measuring the program's value, and appraising an online system for the chipper.
Apply This in Practice
Use these BIZOMAT tools to try the method from this reading with your own numbers.
Applies this method
Bearing Defect Frequency Check (BPFO, BPFI, Ball Spin, Cage, Match to a Measured Peak)
Calculates a rolling bearing's defect frequencies and harmonics from its geometry and speed, and matches measured spectrum peaks to them within a tolerance.
Used in Rolling bearing faults
Applies this method
Complex Number Calculator
Does the vector division in single-plane balancing with a trial weight, turning the original vibration and the trial weight's effect into the correction weight's size and angle.
Used in Unbalance and balancing in place
Applies this method
Counterbalancing Masses in One Plane
Checks a balance correction split between two fan blades: 5.2 g at 45° and 21.2 g at 90° at 450 mm combine to 11,316 g·mm at 81.6°, matching the required weight.
Used in Unbalance and balancing in place
Applies this method
Equipment Investment Appraisal (NPV, IRR, Payback, B/C, EUAC)
Judges whether online monitoring pays: A$38,000 installed against A$32,000 a year of avoided losses gives an NPV of about A$131,500 and a payback of 1.3 years at 8%.
Used in Running a monitoring program
Applies this method
EWMA Control Chart Check (Weighted Moving Average, Control Limits, Small Shifts)
Catches a small, sustained rise in vibration sooner than fixed limits: with a weighting of 0.2 on a fan's baseline, a slow drift signals at the eighth reading.
Applies this method
Gear Train Output Check (Ratio, Output Speed and Torque, Output Shaft Stress)
Finds a two-stage gearbox's shaft speeds from its tooth counts, giving the shaft and mesh frequencies to look for in its spectrum: 10.009 to 1 and 147.86 r/min output.
Used in Gears, pumps and fans
Applies this method
Individuals Control Chart Check (Moving Range, Control Limits, Points Out of Control)
Sets statistical alert limits from a machine's own route readings: twelve overall velocity readings on a fan give a mean of 4.51 mm/s and an upper limit of about 5.19 mm/s.
Applies this method
Rotor Balancing Check (Grade, Plane Unbalance and Corrections)
Works out the permissible unbalance for a fan rotor from its mass, speed and balance grade: 120 kg at 1,480 r/min and G 6.3 allow 40.65 µm and 2,439 g·mm per plane.
Used in Unbalance and balancing in place
Applies this method
Vibration Isolator Selection
Shows why a pump skid on stiff pads amplified vibration: its natural frequency on the mounts sat near running speed, and the tool finds the softer mounts that isolate it.
Applies this method
Weibull Reliability and B10 Life
Shows why time-based overhauls do little for near-random bearing failures: with a shape of 1.1 and a 45,000 h characteristic life, a fan bearing's reliability after a year is 84.8%.
Used in Why vibration reveals condition
Related Tools and Examples
Useful alongside
Vee Engine Shaking Force, Shaking Moment and Inertia Torque (Shared Crank Throws)
Shows which shaking forces of a vee engine or compressor rotate at constant size, like the unbalance this chapter corrects with weights, and which 2× forces no weight can cancel.
Related to Unbalance and balancing in place
References and source notes
The manuscript and worked examples are original BIZOMAT writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 3 November 2026.
- C. Kittel, John Wiley & Sons. Introduction to Solid State Physics (1996). Seventh edition. Copyright work, used only as a map of ideas: dielectric polarisation, ferroelectric crystals and the piezoelectric effect, and elastic waves in solids. No text, equations as set out there, figures or problems are reproduced, and all cases and calculations are BIZOMAT originals.
- R. B. Randall, John Wiley & Sons. Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications (2011). Background for signal processing, spectrum analysis, envelope analysis and the diagnosis of rolling bearing and gear faults used in Chapters 5, 8 and 9.
- International Organization for Standardization. ISO 20816-3, Mechanical vibration — Measurement and evaluation of machine vibration — Part 3: Industrial machinery with a power rating above 15 kW and operating speeds between 120 r/min and 30 000 r/min (2022). Named by number and scope only: broadband in-situ vibration evaluation of coupled industrial machines. Its zone boundaries and criteria are not reproduced and must be read in full.
- International Organization for Standardization. ISO 18436-2, Condition monitoring and diagnostics of machines — Requirements for qualification and assessment of personnel — Vibration condition monitoring and diagnostics (2014). Named by number and scope only: a four-category scheme for vibration analysts. A revision was in development in 2024–25; check the current edition.
- National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods (2012). Background for the Weibull, control chart and trending methods used in Chapters 1, 4 and 10.