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}\n }\n @media (max-width: 600px) {\n html { font-size: 16px; }\n .hero { padding: 56px 18px 48px; }\n .content section { padding: 24px 18px; }\n }\n <\/style>\n<\/head>\n<body>\n\n<div class=\"progress-bar\" id=\"progressBar\"><\/div>\n\n\n<header class=\"hero\">\n <div class=\"hero-inner\">\n <span class=\"hero-label\">Technical Reference<\/span>\n <h1>Vibration Diagnostics of Marine Equipment<\/h1>\n <p class=\"hero-subtitle\">A practical guide to measurement methods, signal analysis, fault detection, balancing, and condition monitoring for rotating machinery on ships and offshore installations.<\/p>\n <div class=\"hero-meta\">\n <span>By Vibromera Engineering Team<\/span>\n <span>\u00b7<\/span>\n <span>Standards: ISO 10816 \u00b7 ISO 7919 \u00b7 ISO 1940<\/span>\n <\/div>\n <\/div>\n<\/header>\n\n\n<div class=\"layout\">\n\n\n<aside class=\"sidebar\">\n <nav class=\"toc-nav\" aria-label=\"Table of contents\">\n <div class=\"toc-title\">Contents<\/div>\n <ol class=\"toc-list\">\n <li><a href=\"#s1\">1. Technical Diagnostics Fundamentals<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s1-1\">1.1 Diagnostic Principles<\/a><\/li>\n <li><a href=\"#s1-2\">1.2 Maintenance Strategies<\/a><\/li>\n <li><a href=\"#s1-3\">1.3 Vibration as Diagnostic Tool<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s2\">2. Vibration Physics<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s2-1\">2.1 Core Parameters<\/a><\/li>\n <li><a href=\"#s2-2\">2.2 Vibration Types<\/a><\/li>\n <li><a href=\"#s2-3\">2.3 Units & Standards<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s3\">3. Measurement Methods & Sensors<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s3-1\">3.1 Measurement Principles<\/a><\/li>\n <li><a href=\"#s3-2\">3.2 Sensor Technologies<\/a><\/li>\n <li><a href=\"#s3-3\">3.3 Mounting & Calibration<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s4\">4. Signal Analysis<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s4-1\">4.1 Signal Types<\/a><\/li>\n <li><a href=\"#s4-2\">4.2 Time & Frequency Domain<\/a><\/li>\n <li><a href=\"#s4-3\">4.3 Advanced Techniques<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s5\">5. Condition Monitoring Programs<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s5-1\">5.1 Acceptance Testing<\/a><\/li>\n <li><a href=\"#s5-2\">5.2 Monitoring Systems<\/a><\/li>\n <li><a href=\"#s5-3\">5.3 Alarm & Trend Analysis<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s6\">6. Fault Detection & Identification<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s6-1\">6.1 Bearing Diagnostics<\/a><\/li>\n <li><a href=\"#s6-2\">6.2 Gear & Shaft Faults<\/a><\/li>\n <li><a href=\"#s6-3\">6.3 Severity & Prognosis<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s7\">7. Alignment & Balancing<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s7-1\">7.1 Shaft Alignment<\/a><\/li>\n <li><a href=\"#s7-2\">7.2 Balancing Theory<\/a><\/li>\n <li><a href=\"#s7-3\">7.3 Field Balancing<\/a><\/li>\n <li><a href=\"#s7-4\">7.4 Other Vibration Reduction<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s8\">8. Emerging Technologies<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s8-1\">8.1 AI & Machine Learning<\/a><\/li>\n <li><a href=\"#s8-2\">8.2 Wireless & Edge Computing<\/a><\/li>\n <li><a href=\"#s8-3\">8.3 Autonomous Diagnostics<\/a><\/li>\n <\/ul>\n <\/li>\n <\/ol>\n <\/nav>\n<\/aside>\n\n\n<main class=\"content\">\n\n\n<section id=\"s1\">\n <h2>1. Technical Diagnostics Fundamentals<\/h2>\n <p class=\"section-lead\">Why vibration analysis became the dominant approach to monitoring rotating marine machinery \u2014 and what alternatives exist.<\/p>\n\n <h3 id=\"s1-1\">1.1 Diagnostic Principles<\/h3>\n\n <p>Technical diagnostics is the discipline of assessing the current condition of a machine and predicting how that condition will change over time. For marine equipment this task is especially critical: an unplanned failure at sea can endanger crew, cargo, and the vessel itself.<\/p>\n\n <p>The central idea is straightforward. Every piece of rotating machinery produces measurable physical signals \u2014 vibration, heat, acoustic emission, oil contamination, and others. As internal components wear, crack, corrode, or loosen, those signals change in ways that are usually predictable. A systematic monitoring programme detects these changes early, classifies them by type and severity, and feeds recommendations into the maintenance schedule.<\/p>\n\n <h4>Key Terms<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Term<\/th>\n <th>Definition<\/th>\n <th>Marine Example<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Diagnostic parameter<\/strong><\/td>\n <td>A measurable quantity that correlates with equipment condition<\/td>\n <td>Vibration velocity RMS on a pump bearing housing<\/td>\n <\/tr>\n <tr>\n <td><strong>Diagnostic symptom<\/strong><\/td>\n <td>A specific pattern in the measured data<\/td>\n <td>Elevated vibration at blade-passing frequency in a centrifugal pump<\/td>\n <\/tr>\n <tr>\n <td><strong>Diagnostic sign<\/strong><\/td>\n <td>A recognisable indication of a particular condition<\/td>\n <td>Sidebands around gear mesh frequency indicating tooth wear<\/td>\n <\/tr>\n <tr>\n <td><strong>Recognition algorithm<\/strong><\/td>\n <td>A procedure (manual or automatic) that maps measured data to a fault category<\/td>\n <td>An expert-system rule set that flags bearing defect frequencies in an envelope spectrum<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>The General Diagnostic Workflow<\/h4>\n\n <div class=\"flow\">\n <span class=\"flow-step\">Data collection<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Signal processing<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Pattern recognition<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Fault classification<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Severity assessment<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Maintenance action<\/span>\n <\/div>\n\n <p>In practice the pipeline is iterative: if a pattern does not match any known fault, the analyst goes back, refines the processing, adds new measurement points, or correlates with other diagnostic methods (thermography, oil analysis, ultrasonic testing).<\/p>\n\n <h4>Functional vs. Test-Bench Diagnostics<\/h4>\n\n <p><strong>Functional diagnostics<\/strong> collects data while the machine runs under normal load. It reflects realistic operating conditions but limits what tests you can perform \u2014 you cannot, for instance, inject an artificial excitation into a pump that is supplying cooling water to the main engine.<\/p>\n\n <p><strong>Test-bench (tester) diagnostics<\/strong> applies controlled excitation \u2014 impact hammer, swept-sine shaker, or similar \u2014 usually during a shutdown. It reveals natural frequencies, transfer functions, and structural characteristics that functional diagnostics cannot provide. On board a ship the practical difficulty is obvious: shutdowns are expensive and sometimes impossible for essential systems.<\/p>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Practical note<\/div>\n <p>A good shipboard programme combines both approaches. Routine functional monitoring covers 80\u201390 % of the fleet's machinery, while test-bench methods are reserved for commissioning, troubleshooting, and critical systems.<\/p>\n <\/div>\n\n <h4>Choosing What to Monitor<\/h4>\n\n <p>Not every machine on a vessel justifies the same level of attention. Selecting which parameters to track on which equipment requires a trade-off between diagnostic coverage and practical cost. Typical selection criteria include sensitivity to fault development, measurement repeatability, cost of the sensor and installation, and the criticality of the equipment itself.<\/p>\n\n <h3 id=\"s1-2\">1.2 Maintenance Strategies<\/h3>\n\n <p>The maritime industry has moved through four broad maintenance philosophies, each with a different cost\u2013risk profile.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Strategy<\/th>\n <th>Approach<\/th>\n <th>Strengths<\/th>\n <th>Weaknesses<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Reactive<\/strong><\/td>\n <td>Run to failure, repair after breakdown<\/td>\n <td>Minimal upfront investment<\/td>\n <td>Unpredictable downtime, safety risk, secondary damage<\/td>\n <\/tr>\n <tr>\n <td><strong>Preventive (time-based)<\/strong><\/td>\n <td>Fixed-interval overhauls regardless of condition<\/td>\n <td>Predictable schedule<\/td>\n <td>Over-maintenance, unnecessary parts replacement<\/td>\n <\/tr>\n <tr>\n <td><strong>Condition-based (CBM)<\/strong><\/td>\n <td>Maintain when measured parameters exceed thresholds<\/td>\n <td>Interventions timed to actual need<\/td>\n <td>Requires diagnostic competence and equipment<\/td>\n <\/tr>\n <tr>\n <td><strong>Proactive \/ Reliability-centred<\/strong><\/td>\n <td>Identify and eliminate root causes of failure<\/td>\n <td>Highest long-term reliability<\/td>\n <td>High initial investment, cultural change<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Most modern fleets use a combination. Critical propulsion and power-generation machinery gets condition-based or proactive maintenance. Auxiliary equipment may still follow time-based schedules or even run-to-failure where spares are cheap and consequences are minor. Vibration analysis is the backbone of the CBM layer.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Example<\/div>\n <p>A container ship's cooling-water pumps were previously overhauled every 3 000 operating hours. After implementing vibration-based condition monitoring the operator extended intervals to 4 500 hours while reducing unplanned failures by roughly 75 %. The programme paid for itself in under one year.<\/p>\n <\/div>\n\n <h3 id=\"s1-3\">1.3 Vibration as the Primary Diagnostic Signal<\/h3>\n\n <p>Vibration analysis dominates marine condition monitoring for several interconnected reasons:<\/p>\n\n <ul>\n <li>All rotating machinery produces vibration \u2014 no additional excitation is required.<\/li>\n <li>Faults change vibration patterns in well-documented, fault-specific ways.<\/li>\n <li>Measurements are non-intrusive and can be taken while machinery operates normally.<\/li>\n <li>Early warning times are typically measured in weeks or months, not hours.<\/li>\n <li>The technique is quantitative \u2014 results map directly to severity zones defined by international standards.<\/li>\n <\/ul>\n\n <p>The methodology moves through six stages: baseline establishment, trend monitoring, anomaly detection, fault classification, severity assessment, and prognosis (remaining useful life). Each stage draws on a different toolbox \u2014 from simple RMS trending at the first stage to envelope analysis, cepstrum, and machine-learning classifiers at the later ones.<\/p>\n\n <h4>Condition States<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>State<\/th>\n <th>Indicators<\/th>\n <th>Recommended Action<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Good<\/strong><\/td>\n <td>Low, stable vibration; no fault frequencies<\/td>\n <td>Continue normal monitoring schedule<\/td>\n <\/tr>\n <tr>\n <td><strong>Acceptable<\/strong><\/td>\n <td>Elevated but stable levels<\/td>\n <td>Increase monitoring frequency, investigate root cause<\/td>\n <\/tr>\n <tr>\n <td><strong>Unsatisfactory<\/strong><\/td>\n <td>High levels or rising trend<\/td>\n <td>Plan maintenance at next opportunity<\/td>\n <\/tr>\n <tr>\n <td><strong>Unacceptable<\/strong><\/td>\n <td>Very high levels or rapid deterioration<\/td>\n <td>Shut down or reduce load immediately; emergency maintenance<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Economic Perspective<\/h4>\n\n <p>Return on investment for shipboard vibration programmes varies, but ratios of 5:1 to 10:1 are frequently cited in the literature. Most of the savings come from three sources: avoiding catastrophic secondary damage (a failed bearing that wrecks a shaft), extending component life by eliminating unnecessary overhauls, and reducing the cost of port-side emergency repairs versus scheduled dockyard work.<\/p>\n<\/section>\n\n\n<section id=\"s2\">\n <h2>2. Vibration Physics<\/h2>\n <p class=\"section-lead\">Displacement, velocity, acceleration \u2014 the three faces of vibration and when each one matters most.<\/p>\n\n <h3 id=\"s2-1\">2.1 Core Parameters<\/h3>\n\n <p>Vibration is the oscillatory motion of a mechanical system around an equilibrium position. It is described by three interrelated kinematic quantities, each useful in a different frequency range.<\/p>\n\n <div class=\"formula\">\n Displacement: x(t) = A \u00b7 sin(\u03c9t + \u03c6)<br>\n Velocity: v(t) = A\u00b7\u03c9 \u00b7 cos(\u03c9t + \u03c6)<br>\n Acceleration: a(t) = \u2212A\u00b7\u03c9\u00b2 \u00b7 sin(\u03c9t + \u03c6)<br>\n <br>\n A \u2014 amplitude | \u03c9 = 2\u03c0f \u2014 angular frequency | \u03c6 \u2014 phase angle\n <\/div>\n\n <p>Because velocity scales linearly with frequency (the \u03c9 factor) and acceleration scales with \u03c9\u00b2, the three parameters have very different sensitivities across the spectrum. This is the practical reason engineers choose one over another.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Parameter<\/th>\n <th>Unit<\/th>\n <th>Best Frequency Range<\/th>\n <th>Typical Marine Uses<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Displacement<\/strong><\/td>\n <td>\u03bcm (peak-to-peak), mils<\/td>\n <td>Below \u2248 10 Hz<\/td>\n <td>Large slow-speed diesel cranks, shaft-relative motion<\/td>\n <\/tr>\n <tr>\n <td><strong>Velocity<\/strong><\/td>\n <td>mm\/s (RMS)<\/td>\n <td>10 Hz \u2013 1 kHz<\/td>\n <td>General machinery monitoring; ISO 10816 evaluations<\/td>\n <\/tr>\n <tr>\n <td><strong>Acceleration<\/strong><\/td>\n <td>m\/s\u00b2 or g (peak)<\/td>\n <td>Above \u2248 1 kHz<\/td>\n <td>Rolling-element bearing diagnostics, gear mesh, high-speed pumps<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Statistical Measures<\/h4>\n\n <p><strong>RMS<\/strong> (root mean square) represents the effective amplitude and correlates with the energy content of vibration. It is the default metric for ISO-based severity evaluation.<\/p>\n\n <p><strong>Peak value<\/strong> captures maximum instantaneous amplitude \u2014 useful for detecting impacts and transient events.<\/p>\n\n <p><strong>Peak-to-peak value<\/strong> gives the total swing from positive to negative peak. It is commonly used for displacement measurements and clearance analysis.<\/p>\n\n <p><strong>Crest factor<\/strong> is the ratio of peak to RMS. A healthy rotating machine typically shows a crest factor between 3 and 4. Values above 5\u20136 suggest impulsive events such as bearing defects or impacts.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Diagnostic illustration<\/div>\n <p>A cargo pump bearing's crest factor rose from 3.2 to 7.8 over six weeks while overall RMS remained almost unchanged. That divergence \u2014 stable energy, increasing spikiness \u2014 is a classic early bearing-defect signature. Subsequent inspection confirmed an outer-race pit.<\/p>\n <\/div>\n\n <h3 id=\"s2-2\">2.2 Vibration Types in Marine Systems<\/h3>\n\n <p>Marine machinery generates several categories of vibration, each arising from a different physical mechanism.<\/p>\n\n <h4>By Excitation Source<\/h4>\n\n <ul>\n <li><strong>Free vibration<\/strong> \u2014 the system oscillates at its natural frequency after a transient excitation (startup, shutdown, impact).<\/li>\n <li><strong>Forced vibration<\/strong> \u2014 continuous excitation at a frequency related to rotational speed, blade count, or electrical supply. The majority of steady-state vibration is forced.<\/li>\n <li><strong>Self-excited vibration<\/strong> \u2014 the machinery creates its own excitation through an internal feedback mechanism: oil whirl in journal bearings, aerodynamic flutter, stick-slip friction.<\/li>\n <li><strong>Parametric vibration<\/strong> \u2014 system stiffness or damping varies periodically, pumping energy into the response. A cracked gear tooth that changes mesh stiffness once per revolution is a typical example.<\/li>\n <\/ul>\n\n <h4>By Relationship to Speed<\/h4>\n\n <ul>\n <li><strong>Synchronous (order-related)<\/strong> \u2014 frequency is an integer or simple rational multiple of shaft speed. Unbalance (1\u00d7), misalignment (2\u00d7), and looseness (many harmonics) belong here.<\/li>\n <li><strong>Asynchronous<\/strong> \u2014 frequency is independent of shaft speed. Bearing defect frequencies, electrical line-frequency harmonics, and belt-slip vibration fall in this category.<\/li>\n <\/ul>\n\n <h4>By Direction<\/h4>\n\n <p><strong>Radial<\/strong> vibration (perpendicular to the shaft) dominates in most rotating equipment and is the first direction measured. <strong>Axial<\/strong> vibration (parallel to the shaft) flags thrust-bearing problems, coupling issues, and aerodynamic forces. <strong>Torsional<\/strong> vibration (twisting about the shaft axis) requires specialised sensors and is mainly tracked on long propulsion trains where torsional resonance can be destructive.<\/p>\n\n <h4>Natural Frequencies and Resonance<\/h4>\n\n <p>Every mechanical system has natural frequencies determined by its mass, stiffness, and damping. When an excitation frequency approaches a natural frequency the response is amplified \u2014 sometimes by a factor of 10 or more. In rotating machinery these coincidences are called <em>critical speeds<\/em>.<\/p>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Design rule<\/div>\n <p>Operating speed should be separated from all identified critical speeds by at least 15\u201320 %. Running persistently within this margin risks resonance-driven fatigue and rapid failure.<\/p>\n <\/div>\n\n <h4>Vibration Sources<\/h4>\n\n <p><strong>Mechanical<\/strong> \u2014 unbalance, misalignment, bearing defects, looseness, gear problems, shaft bow. Frequencies typically relate to shaft speed and component geometry.<\/p>\n\n <p><strong>Electromagnetic<\/strong> \u2014 rotor-bar defects, stator eccentricity, supply-voltage imbalance. Frequencies concentrate around twice the line frequency (100 Hz for 50 Hz supply, 120 Hz for 60 Hz) and its multiples.<\/p>\n\n <p><strong>Hydraulic \/ aerodynamic<\/strong> \u2014 blade-passing, cavitation, turbulence, recirculation. Blade-passing frequency equals the number of blades multiplied by rotational frequency; cavitation produces broadband random noise concentrated above 1\u20132 kHz.<\/p>\n\n <h3 id=\"s2-3\">2.3 Units and Standards<\/h3>\n\n <p>Vibration measurements use both linear and logarithmic (decibel) scales. The decibel form compresses wide dynamic ranges and emphasises relative changes:<\/p>\n\n <div class=\"formula\">\n dB = 20 \u00b7 log\u2081\u2080(measured value \/ reference value)\n <\/div>\n\n <p>Reference values differ by parameter: 10\u207b\u2076 m for displacement, 10\u207b\u2079 m\/s for velocity (in some standards 1 nm\/s), 10\u207b\u2076 m\/s\u00b2 for acceleration.<\/p>\n\n <h4>ISO 10816 \u2014 Vibration on Non-Rotating Parts<\/h4>\n\n <p>The standard defines four evaluation zones, A through D, based on broadband velocity RMS. Limits depend on machine class (power rating, speed range) and support stiffness (rigid vs. flexible).<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Zone<\/th>\n <th>Condition<\/th>\n <th>Velocity RMS (Group 2, rigid)<\/th>\n <th>Guidance<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>A<\/strong><\/td>\n <td>Good<\/td>\n <td>up to 1.4 mm\/s<\/td>\n <td>Newly commissioned or recently maintained<\/td>\n <\/tr>\n <tr>\n <td><strong>B<\/strong><\/td>\n <td>Acceptable<\/td>\n <td>1.4 \u2013 2.8 mm\/s<\/td>\n <td>Unrestricted long-term operation<\/td>\n <\/tr>\n <tr>\n <td><strong>C<\/strong><\/td>\n <td>Unsatisfactory<\/td>\n <td>2.8 \u2013 7.1 mm\/s<\/td>\n <td>Limited-duration operation; plan remedial work<\/td>\n <\/tr>\n <tr>\n <td><strong>D<\/strong><\/td>\n <td>Unacceptable<\/td>\n <td>> 7.1 mm\/s<\/td>\n <td>Damage likely; immediate action<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Other relevant standards: <strong>ISO 7919<\/strong> (shaft vibration, measured with proximity probes), <strong>ISO 14694<\/strong> (condition monitoring guidance), <strong>ISO 8528-9<\/strong> (generating sets), <strong>API 610<\/strong> (centrifugal pumps). All follow the same four-zone logic but with limits adapted to the equipment type.<\/p>\n\n <h4>Machine Classification<\/h4>\n\n <p>Vibration limits are set per machine class. Classification considers power rating (small < 15 kW, medium 15\u201375 kW, large > 75 kW), speed range, and support stiffness. A machine is <em>rigidly<\/em> mounted if its first support natural frequency is more than twice the operating frequency; <em>flexibly<\/em> mounted if below half the operating frequency. The distinction matters because flexible mounts amplify housing vibration and therefore call for more lenient limits.<\/p>\n\n <h4>Measurement Points<\/h4>\n\n <p>Standards prescribe measurement on bearing housings, as close to the load zone as practical, in three directions: horizontal radial, vertical radial, and axial (usually at the drive-end bearing only). Measurements should be taken under stable operating conditions \u2014 rated speed and at least 75 % of rated load \u2014 and averaged over a period long enough to capture any cyclic variation.<\/p>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Shipboard caveat<\/div>\n <p>Vessel motion, sea state, and cargo loading can influence vibration readings. Good practice includes logging these conditions alongside every measurement and filtering or flagging data collected in rough weather.<\/p>\n <\/div>\n<\/section>\n\n\n<section id=\"s3\">\n <h2>3. Measurement Methods and Sensors<\/h2>\n <p class=\"section-lead\">Sensor selection, mounting, signal conditioning, and the practical realities of collecting good vibration data on board a ship.<\/p>\n\n <h3 id=\"s3-1\">3.1 Measurement Principles<\/h3>\n\n <h4>Kinematic vs. Dynamic<\/h4>\n <p>Most vibration sensors measure <em>motion<\/em> only \u2014 displacement, velocity, or acceleration \u2014 without quantifying the force that produces it. This is kinematic measurement. Dynamic measurement combines motion and force data, typically through paired accelerometers and force transducers, and is used mainly in controlled test-bench situations such as modal analysis or transfer-function measurements.<\/p>\n\n <h4>Absolute vs. Relative<\/h4>\n <p><strong>Absolute vibration<\/strong> is the motion of a point relative to a fixed (earth-based) reference. An accelerometer bolted to a bearing housing gives an absolute measurement. <strong>Relative vibration<\/strong> is the motion between two parts \u2014 typically the shaft and the bearing housing. Proximity probes provide this and are standard on large turbomachinery where shaft orbit information is needed.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Type<\/th>\n <th>Best for<\/th>\n <th>Limitations<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Absolute (accelerometer, velocity sensor)<\/td>\n <td>General machinery, auxiliary equipment, structural vibration<\/td>\n <td>Cannot directly reveal shaft motion inside the bearing<\/td>\n <\/tr>\n <tr>\n <td>Relative (proximity probe)<\/td>\n <td>Large turbomachinery, journal bearings, critical shafts<\/td>\n <td>Expensive installation, requires shaft access<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Contact vs. Non-Contact<\/h4>\n <p>Contact sensors (accelerometers, velocity pickups, strain gauges) are physically attached to the vibrating surface. They offer high sensitivity, broad bandwidth, and well-established procedures. Non-contact sensors (eddy-current probes, laser vibrometers) measure from a distance and are essential for rotating surfaces, high-temperature zones, and locations where mass loading by a contact sensor would alter the measurement.<\/p>\n\n <h3 id=\"s3-2\">3.2 Sensor Technologies<\/h3>\n\n <h4>Piezoelectric Accelerometers<\/h4>\n <p>The workhorse of marine vibration measurement. A piezoelectric element (quartz or ceramic) generates electric charge proportional to applied force. Internal electronics (IEPE \/ ICP standard) convert this to a low-impedance voltage signal that travels reliably over long cables in noisy engine-room environments.<\/p>\n\n <div class=\"kv-grid\">\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Typical bandwidth<\/div>\n <div class=\"kv-card-value\">1 Hz \u2013 10 kHz<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Sensitivity<\/div>\n <div class=\"kv-card-value\">10 \u2013 100 mV\/g<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Operating temperature<\/div>\n <div class=\"kv-card-value\">\u221250 to +120 \u00b0C<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Mass<\/div>\n <div class=\"kv-card-value\">5 \u2013 50 g<\/div>\n <\/div>\n <\/div>\n\n <p>High-frequency models (up to 50 kHz, lower sensitivity) are used for early bearing-defect detection. High-sensitivity models (100\u20131000 mV\/g, bandwidth to ~5 kHz) are chosen for low-level vibration in precision machinery.<\/p>\n\n <h4>MEMS Accelerometers<\/h4>\n <p>Micro-electromechanical accelerometers are smaller, cheaper, and consume less power than piezoelectric units. They have become viable for permanent monitoring of non-critical machinery and wireless sensor networks. Bandwidth and dynamic range have improved substantially in recent years, though piezoelectric sensors still lead in high-frequency performance.<\/p>\n\n <h4>Velocity Sensors (Seismic Transducers)<\/h4>\n <p>A suspended magnetic mass moves relative to a coil, generating a voltage proportional to velocity. These sensors require no external power, have robust construction, and give a direct velocity output \u2014 convenient for ISO 10816 evaluation without integration. Drawbacks include limited low-frequency response (typically above 10 Hz), temperature sensitivity, and relatively large size.<\/p>\n\n <h4>Proximity Probes (Eddy-Current Sensors)<\/h4>\n <p>A high-frequency oscillator creates an electromagnetic field at the probe tip. Eddy currents in the nearby conductive shaft surface alter the impedance, and electronics convert the change to a DC voltage proportional to gap distance. Two probes mounted at 90\u00b0 on each bearing provide X-Y shaft position data for orbit analysis. Resolution is on the order of 0.1 \u03bcm, and the probe has DC response (it can track slow static displacements as well as dynamic vibration).<\/p>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Application note<\/div>\n <p>Proximity probes are standard on large main turbines, turbochargers, and reduction-gear shafts. They are almost never used for auxiliary machinery \u2014 the installation cost is too high relative to the equipment value.<\/p>\n <\/div>\n\n <h3 id=\"s3-3\">3.3 Mounting and Calibration<\/h3>\n\n <h4>Mounting Methods<\/h4>\n <p>The way a sensor is attached to the machine determines the upper usable frequency. Each method introduces a mounting resonance above which the measurement is unreliable.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Method<\/th>\n <th>Usable Upper Frequency<\/th>\n <th>Notes<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Threaded stud<\/td>\n <td>Up to sensor limit (often > 10 kHz)<\/td>\n <td>Best accuracy; permanent or semi-permanent<\/td>\n <\/tr>\n <tr>\n <td>Thin adhesive layer<\/td>\n <td>~5\u20137 kHz<\/td>\n <td>Good for temporary campaigns<\/td>\n <\/tr>\n <tr>\n <td>Magnetic mount<\/td>\n <td>~2\u20133 kHz<\/td>\n <td>Quick; ferromagnetic surfaces only<\/td>\n <\/tr>\n <tr>\n <td>Hand-held probe<\/td>\n <td>~1 kHz<\/td>\n <td>Screening only; poor repeatability<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Common error<\/div>\n <p>Using a magnetic mount for bearing envelope analysis (which relies on frequencies above 2\u20133 kHz) will produce misleading results. A stud or thin adhesive mount is required.<\/p>\n <\/div>\n\n <h4>Signal Conditioning<\/h4>\n <p>IEPE sensors need a constant-current power supply (typically 2\u20134 mA at 18\u201328 V DC). The data acquisition front-end normally provides this. Charge-mode sensors require a separate charge amplifier. In either case the signal path should use shielded, low-noise cables, and cable runs should be kept as short as practical to minimise electromagnetic pickup from engine-room power cables.<\/p>\n\n <h4>Calibration<\/h4>\n <p>Sensors and channels should be checked against a traceable reference at least once a year \u2014 more often in harsh marine environments. A portable calibration exciter producing a known acceleration at a known frequency (commonly 10 m\/s\u00b2 at 159.15 Hz) is the standard field tool. Back-to-back comparison with a reference accelerometer gives higher confidence and can be done aboard.<\/p>\n<\/section>\n\n\n<section id=\"s4\">\n <h2>4. Signal Analysis<\/h2>\n <p class=\"section-lead\">From raw vibration waveform to diagnostic conclusions \u2014 the signal-processing chain that makes fault identification possible.<\/p>\n\n <h3 id=\"s4-1\">4.1 Signal Types<\/h3>\n\n <p>Understanding what kind of signal your machine produces determines which analysis techniques will extract useful information.<\/p>\n\n <h4>Periodic and Harmonic Signals<\/h4>\n <p>A pure sinusoid at a single frequency is the simplest case (rare in practice). Most rotating machinery produces <em>polyharmonic<\/em> signals \u2014 a fundamental frequency plus its integer multiples. A four-stroke diesel produces firing-order harmonics; a gear train produces mesh frequency and its harmonics.<\/p>\n\n <h4>Modulated Signals<\/h4>\n <p><strong>Amplitude modulation (AM)<\/strong> \u2014 the signal envelope varies periodically. A bearing outer-race defect that passes through the load zone once per revolution creates AM of the high-frequency impact response at the shaft speed. <strong>Frequency modulation (FM)<\/strong> \u2014 the instantaneous frequency varies. Speed fluctuation from a reciprocating compressor is a common source.<\/p>\n\n <div class=\"formula\">\n AM: x(t) = A \u00b7 [1 + m \u00b7 cos(2\u03c0\u00b7f<sub>mod<\/sub>\u00b7t)] \u00b7 cos(2\u03c0\u00b7f<sub>carrier<\/sub>\u00b7t)<br>\n m \u2014 modulation depth | f<sub>mod<\/sub> \u2014 modulation frequency | f<sub>carrier<\/sub> \u2014 carrier frequency\n <\/div>\n\n <h4>Impulsive and Transient Signals<\/h4>\n <p>Short-duration, high-amplitude events that excite multiple resonances simultaneously. Rolling-element bearing defects, gear-tooth chips, and loose fasteners all produce impulsive vibration. Characteristic features: high crest factor (> 5), broad frequency content, rapid decay, and periodic repetition at the defect frequency.<\/p>\n\n <h4>Random Signals<\/h4>\n <p>Turbulent flow, cavitation, and advanced surface degradation produce vibration with no dominant periodic component. Statistically it is characterised by its power spectral density (PSD) rather than by individual frequency peaks.<\/p>\n\n <h3 id=\"s4-2\">4.2 Time Domain and Frequency Domain<\/h3>\n\n <h4>Time-Domain Analysis<\/h4>\n <p>Examining the raw waveform reveals information that spectral analysis can obscure: impact timing, modulation patterns, asymmetry (truncation, clipping), and the presence of transient events. Statistical parameters calculated from the waveform \u2014 RMS, crest factor, kurtosis, skewness \u2014 quantify signal character and are often the first indicators of bearing deterioration.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Parameter<\/th>\n <th>What It Detects<\/th>\n <th>Healthy Range<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>RMS<\/strong><\/td>\n <td>Overall energy<\/td>\n <td>Machine-specific (see ISO limits)<\/td>\n <\/tr>\n <tr>\n <td><strong>Crest factor<\/strong><\/td>\n <td>Impulsive content<\/td>\n <td>\u2248 3.0 \u2013 4.0<\/td>\n <\/tr>\n <tr>\n <td><strong>Kurtosis<\/strong><\/td>\n <td>Peakedness \/ impact rate<\/td>\n <td>\u2248 3.0 (Gaussian baseline)<\/td>\n <\/tr>\n <tr>\n <td><strong>Skewness<\/strong><\/td>\n <td>Waveform asymmetry<\/td>\n <td>\u2248 0 (symmetric)<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Kurtosis is especially valuable for bearing diagnostics. A healthy bearing produces roughly Gaussian vibration (kurtosis \u2248 3). Developing defects drive kurtosis well above 4 \u2014 sometimes above 10 \u2014 long before overall RMS rises enough to trigger an alarm.<\/p>\n\n <h4>Frequency-Domain Analysis (FFT)<\/h4>\n\n <p>The Fast Fourier Transform converts a time record into a frequency spectrum, revealing which frequencies carry the most energy. This is the primary diagnostic tool because different fault types produce vibration at different, predictable frequencies.<\/p>\n\n <div class=\"formula\">\n X(k) = \u03a3<sub>n=0<\/sub><sup>N\u22121<\/sup> x(n) \u00b7 e<sup>\u2212j2\u03c0kn\/N<\/sup>\n <\/div>\n\n <h4>Key DSP Considerations<\/h4>\n\n <p><strong>Sampling rate<\/strong> must exceed twice the highest frequency of interest (Nyquist criterion). Anti-aliasing filters attenuate everything above the Nyquist frequency before digitisation. A practical rule: sample at 2.56 \u00d7 the analysis bandwidth (to allow for filter roll-off).<\/p>\n\n <p><strong>Frequency resolution<\/strong> = 1 \/ T, where T is the record length. To separate two close frequencies you need a longer record. For marine applications where speed varies slightly, order tracking (resampling synchronised to a tachometer pulse) maintains constant resolution in the order domain regardless of speed drift.<\/p>\n\n <p><strong>Windowing<\/strong> suppresses spectral leakage caused by finite record length. Hanning is the general-purpose default; flat-top gives the best amplitude accuracy (important when comparing to absolute limits); rectangular is appropriate only for truly transient signals.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Window<\/th>\n <th>Frequency Resolution<\/th>\n <th>Amplitude Accuracy<\/th>\n <th>Use Case<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Rectangular<\/td>\n <td>Best<\/td>\n <td>Moderate<\/td>\n <td>Transient \/ impact<\/td>\n <\/tr>\n <tr>\n <td>Hanning<\/td>\n <td>Good<\/td>\n <td>Good<\/td>\n <td>General purpose<\/td>\n <\/tr>\n <tr>\n <td>Flat-top<\/td>\n <td>Poor<\/td>\n <td>Best<\/td>\n <td>Calibration, amplitude checks<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3 id=\"s4-3\">4.3 Advanced Techniques<\/h3>\n\n <h4>Envelope Analysis (Amplitude Demodulation)<\/h4>\n <p>The method of choice for rolling-element bearing diagnostics. Steps: (1) band-pass filter around a structural resonance excited by bearing impacts (typically 2\u20138 kHz), (2) extract the amplitude envelope via Hilbert transform or rectification + low-pass filter, (3) compute the FFT of the envelope. Bearing defect frequencies (BPFO, BPFI, BSF, FTF) then appear as distinct peaks in the envelope spectrum, clearly separated from shaft-speed harmonics and other sources.<\/p>\n\n <h4>Cepstrum Analysis<\/h4>\n <p>The cepstrum is the inverse FFT of the log-magnitude spectrum. It detects periodic patterns <em>within<\/em> the frequency spectrum \u2014 exactly what sidebands around gear-mesh frequency or harmonic families from looseness produce. The technique is less intuitive than direct FFT but excels when multiple sideband families overlap.<\/p>\n\n <div class=\"formula\">\n Cepstrum = IFFT( log |FFT(x(t))| )\n <\/div>\n\n <h4>Order Tracking<\/h4>\n <p>For variable-speed machinery (common on vessels with variable-frequency drives or during manoeuvring), conventional FFT smears speed-related peaks. Order tracking resamples the time signal using a tachometer or speed reference, converting the analysis from the frequency domain to the order domain. Each order corresponds to a fixed multiple of shaft speed.<\/p>\n\n <h4>Coherence Function<\/h4>\n <p>Measures the linear relationship between two signals as a function of frequency. Coherence close to 1.0 at a given frequency means the vibration at the response point is predominantly caused by the excitation at the reference point. Useful for isolating transmission paths, verifying measurement quality, and assessing how much of a machine's vibration is transmitted to nearby structures.<\/p>\n<\/section>\n\n\n<section id=\"s5\">\n <h2>5. Condition Monitoring Programs<\/h2>\n <p class=\"section-lead\">Building and running a shipboard vibration monitoring programme \u2014 from acceptance testing through trend analysis.<\/p>\n\n <h3 id=\"s5-1\">5.1 Acceptance Testing<\/h3>\n\n <p>Vibration acceptance testing establishes that newly installed or overhauled equipment meets its design specification before entering service. For marine equipment this is typically done in stages: factory acceptance test (FAT) at the manufacturer, harbour acceptance test (HAT) after installation aboard, and sea trial at full load.<\/p>\n\n <h4>What Acceptance Testing Catches<\/h4>\n <ul>\n <li>Residual unbalance exceeding the specified ISO 1940 quality grade<\/li>\n <li>Soft foot \u2014 one or more mounting feet not in proper contact with the foundation<\/li>\n <li>Coupling misalignment introduced during installation<\/li>\n <li>Piping strain transmitted to pump or compressor flanges<\/li>\n <li>Foundation resonances that coincide with operating speed<\/li>\n <\/ul>\n\n <p>Measurements during acceptance testing become the baseline for future condition monitoring. They should be taken at several load levels (typically 25 %, 50 %, 75 %, 100 %) and documented with operating parameters (speed, load, temperatures, sea state).<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Break-in example<\/div>\n <p>A newly installed cargo pump showed 4.2 mm\/s RMS immediately after commissioning. Over 100 hours of service the reading settled to 2.1 mm\/s as bearing surfaces conformed and clearances stabilised. Without acceptance testing the initial high reading might have triggered an unnecessary investigation.<\/p>\n <\/div>\n\n <h3 id=\"s5-2\">5.2 Monitoring Systems<\/h3>\n\n <h4>Portable (Route-Based) Systems<\/h4>\n <p>A technician walks a pre-defined route through the engine room, collecting data at each tagged measurement point using a handheld data collector. Software on a shore or office PC stores, trends, and analyses the data. This is the most cost-effective approach for auxiliary machinery where continuous monitoring is not justified.<\/p>\n\n <h4>Permanent (On-Line) Systems<\/h4>\n <p>Sensors are permanently installed on critical equipment and wired to a central data acquisition system. Measurements are taken automatically at scheduled intervals or continuously. Alarms trigger when thresholds are exceeded. Main engines, generators, propulsion motors, and reduction gears are typical candidates.<\/p>\n\n <h4>Hybrid Approach<\/h4>\n <p>Most modern fleets combine both. Continuous monitoring covers the 10\u201315 most critical machines. Route-based portable measurements cover 50\u2013200 auxiliary items on a weekly to quarterly cycle. Unified software merges both datasets into a single database.<\/p>\n\n <div class=\"kv-grid\">\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Portable system cost<\/div>\n <div class=\"kv-card-value\">Lower per point<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Permanent system cost<\/div>\n <div class=\"kv-card-value\">Higher per point<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Event capture<\/div>\n <div class=\"kv-card-value\">Permanent wins<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Fleet flexibility<\/div>\n <div class=\"kv-card-value\">Portable wins<\/div>\n <\/div>\n <\/div>\n\n <h4>Database and Hierarchy<\/h4>\n <p>The monitoring database organises equipment in a tree: vessel \u2192 department (engine, deck, electrical) \u2192 system (propulsion, auxiliary cooling, fire-fighting) \u2192 machine \u2192 component \u2192 measurement point. Each point has defined sensor type, direction, units, alarm levels, and analysis settings. Good hierarchy design makes fleet-wide benchmarking and reporting practical.<\/p>\n\n <h3 id=\"s5-3\">5.3 Alarm Levels and Trend Analysis<\/h3>\n\n <h4>Setting Alarm Levels<\/h4>\n <p>There are three common approaches, and they can be combined.<\/p>\n\n <ul>\n <li><strong>Standards-based<\/strong> \u2014 use ISO 10816 or API zone boundaries directly. Simple but one-size-fits-all.<\/li>\n <li><strong>Statistical<\/strong> \u2014 set the alert at baseline mean + 2\u20133 standard deviations, the danger threshold at mean + 4\u20136 \u03c3. Tailored to each machine but requires sufficient baseline data.<\/li>\n <li><strong>Experience-based<\/strong> \u2014 derived from the analyst's knowledge of a specific machine type. Often the most effective for unusual or very old equipment not covered well by generic standards.<\/li>\n <\/ul>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Avoid alarm fatigue<\/div>\n <p>On a ship with hundreds of measurement points, poorly calibrated alarms generate dozens of false positives per route. Crews learn to ignore them. Invest time in proper baseline collection and alarm-level tuning \u2014 it is the single highest-leverage activity in a new programme.<\/p>\n <\/div>\n\n <h4>Trend Analysis<\/h4>\n <p>Plotting a parameter over time reveals developing faults before they reach alarm levels. Trending works for overall RMS, individual frequency components, statistical parameters (crest factor, kurtosis), and envelope-derived metrics. The slope of the trend line \u2014 and especially any sudden change in slope \u2014 is the primary decision driver.<\/p>\n\n <p>Methods range from simple visual inspection of time-series plots to statistical process control (CUSUM, EWMA) and regression-based remaining-useful-life models. For critical machinery, combining multiple trended parameters in a single \"health index\" provides a more robust picture than any one parameter alone.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Trend success story<\/div>\n <p>A main-engine cooling pump showed a steady 15 % monthly increase in outer-race defect-frequency amplitude over six months. Bearing replacement was scheduled during a routine port call, preventing an unplanned failure that would have required diverting the vessel.<\/p>\n <\/div>\n<\/section>\n\n\n<section id=\"s6\">\n <h2>6. Fault Detection and Identification<\/h2>\n <p class=\"section-lead\">Translating spectral peaks, waveform shapes, and statistical parameters into specific fault diagnoses.<\/p>\n\n <h3 id=\"s6-1\">6.1 Rolling-Element Bearing Diagnostics<\/h3>\n\n <p>Rolling-element bearings are the most commonly monitored component in marine vibration programmes. Each defect location produces a distinct characteristic frequency determined by bearing geometry and shaft speed.<\/p>\n\n <h4>Defect Frequencies<\/h4>\n\n <div class=\"formula\">\n BPFO = (N\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 \u2212 d\/D \u00b7 cos \u03c6)<br>\n BPFI = (N\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 + d\/D \u00b7 cos \u03c6)<br>\n BSF = (D\/2d) \u00b7 f<sub>shaft<\/sub> \u00b7 [1 \u2212 (d\/D \u00b7 cos \u03c6)\u00b2]<br>\n FTF = (1\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 \u2212 d\/D \u00b7 cos \u03c6)<br>\n <br>\n N \u2014 number of rolling elements | d \u2014 element diameter<br>\n D \u2014 pitch diameter | \u03c6 \u2014 contact angle | f<sub>shaft<\/sub> \u2014 shaft frequency\n <\/div>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Worked example<\/div>\n <p>SKF 6309 bearing (9 balls, d = 12.7 mm, D = 58.5 mm, \u03c6 \u2248 0\u00b0) at 1 750 RPM (29.17 Hz):<br>\n BPFO \u2248 102 Hz \u00b7 BPFI \u2248 158 Hz \u00b7 BSF \u2248 67 Hz \u00b7 FTF \u2248 11.4 Hz<\/p>\n <\/div>\n\n <h4>Fault Progression Stages<\/h4>\n\n <ol class=\"stage-list\">\n <li><strong>Onset<\/strong> \u2014 subtle increase in the high-frequency noise floor (ultrasonic band, > 20 kHz). No discrete peaks yet. Detectable only with specialised high-frequency techniques (acoustic emission, spike energy).<\/li>\n <li><strong>Discrete defect frequencies appear<\/strong> \u2014 bearing-characteristic frequencies (BPFO, BPFI, etc.) become visible in the envelope spectrum or high-frequency-band acceleration spectrum.<\/li>\n <li><strong>Harmonics and sidebands develop<\/strong> \u2014 defect-frequency harmonics grow; modulation sidebands at shaft speed appear around bearing frequencies.<\/li>\n <li><strong>Broadening and increase<\/strong> \u2014 the noise floor rises in the bearing-frequency band; overall acceleration and velocity RMS begin to climb; crest factor may start to decrease as random content grows.<\/li>\n <li><strong>Advanced damage<\/strong> \u2014 broadband random vibration dominates; displacement levels rise; temperatures increase; audible noise. Failure is imminent.<\/li>\n <\/ol>\n\n <h4>Envelope Analysis in Practice<\/h4>\n <p>Band-pass filter the raw acceleration signal in the 2\u20138 kHz range (or around the highest bearing-excited resonance \u2014 identify it from an impact test or from the spectrum itself). Compute the Hilbert-transform envelope. FFT the envelope. If you see peaks at BPFO, BPFI, BSF, or FTF (and their harmonics), you have a positive bearing-defect identification.<\/p>\n\n <h3 id=\"s6-2\">6.2 Gear Faults and Shaft Problems<\/h3>\n\n <h4>Gear Diagnostics<\/h4>\n <p>The fundamental gear-mesh frequency (GMF) equals the number of teeth multiplied by shaft rotational frequency. A healthy gear produces a clean mesh peak with low sidebands. Developing problems manifest as increased mesh amplitude, growing sidebands spaced at the shaft frequency of the damaged gear, and eventually generation of higher harmonics of GMF.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Gear example<\/div>\n <p>23-tooth pinion at 1 200 RPM (20 Hz) meshing with a 67-tooth wheel (6.87 Hz). GMF = 23 \u00d7 20 = 460 Hz. Sidebands at 460 \u00b1 20 Hz indicate a developing pinion defect; sidebands at 460 \u00b1 6.87 Hz point to the wheel.<\/p>\n <\/div>\n\n <h4>Shaft and Coupling Problems<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Fault<\/th>\n <th>Dominant Frequency<\/th>\n <th>Key Indicators<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Mass unbalance<\/td>\n <td>1\u00d7 shaft speed<\/td>\n <td>Radial vibration; stable phase; amplitude \u221d speed\u00b2<\/td>\n <\/tr>\n <tr>\n <td>Parallel misalignment<\/td>\n <td>2\u00d7 (+ 1\u00d7, 3\u00d7)<\/td>\n <td>High radial vibration; 180\u00b0 phase shift across coupling<\/td>\n <\/tr>\n <tr>\n <td>Angular misalignment<\/td>\n <td>1\u00d7 and 2\u00d7<\/td>\n <td>High axial vibration at coupling<\/td>\n <\/tr>\n <tr>\n <td>Bent shaft<\/td>\n <td>1\u00d7 and 2\u00d7<\/td>\n <td>High 1\u00d7 axial; 180\u00b0 phase between bearings<\/td>\n <\/tr>\n <tr>\n <td>Mechanical looseness<\/td>\n <td>Many harmonics of 1\u00d7<\/td>\n <td>Subharmonics (0.5\u00d7); unstable phase; directional<\/td>\n <\/tr>\n <tr>\n <td>Rotor rub<\/td>\n <td>Fractional harmonics<\/td>\n <td>0.5\u00d7, 1.5\u00d7, 2.5\u00d7 etc.; truncated waveform<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Impeller \/ Flow-Related Problems<\/h4>\n <p>Blade-passing frequency (BPF) = number of blades \u00d7 shaft frequency. Elevated BPF and its harmonics indicate impeller damage, diffuser\u2013impeller gap issues, or inlet flow distortion. Cavitation produces broadband high-frequency noise \u2014 a \"crackling\" sound signature above 2 kHz with high kurtosis. Recirculation at low flow creates low-frequency random instability.<\/p>\n\n <h3 id=\"s6-3\">6.3 Severity Assessment and Prognosis<\/h3>\n\n <p>Detecting a fault is only half the job. The maintenance team needs to know <em>how fast<\/em> the fault is progressing and <em>how long<\/em> the machine can continue to operate safely.<\/p>\n\n <h4>Severity Metrics<\/h4>\n <ul>\n <li>Amplitude of the defect-frequency peak relative to its baseline value<\/li>\n <li>Rate of change of that amplitude (slope of the trend)<\/li>\n <li>Number and strength of harmonics and sidebands<\/li>\n <li>Crest factor and kurtosis progression<\/li>\n <li>Overall velocity or acceleration RMS relative to ISO zone boundaries<\/li>\n <\/ul>\n\n <h4>Prognostic Methods<\/h4>\n <p>Simple trending with linear or exponential extrapolation gives a rough remaining-life estimate. More sophisticated approaches include physics-based degradation models (e.g., spalling propagation under Hertzian stress) and data-driven models trained on failure run-to-failure datasets. In either case, predictions should carry explicit confidence intervals \u2014 a point estimate of \"42 days remaining\" is much less useful than \"30\u201360 days at 90 % confidence\".<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Severity Level<\/th>\n <th>Recommended Action<\/th>\n <th>Typical Timeframe<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Good<\/td>\n <td>Continue normal monitoring<\/td>\n <td>Next scheduled measurement<\/td>\n <\/tr>\n <tr>\n <td>Early fault<\/td>\n <td>Increase monitoring frequency<\/td>\n <td>Weekly \u2192 bi-weekly<\/td>\n <\/tr>\n <tr>\n <td>Developing<\/td>\n <td>Plan maintenance intervention<\/td>\n <td>Next port call or planned downtime<\/td>\n <\/tr>\n <tr>\n <td>Advanced<\/td>\n <td>Schedule repair as soon as possible<\/td>\n <td>Within 1\u20132 weeks<\/td>\n <\/tr>\n <tr>\n <td>Critical<\/td>\n <td>Reduce load or shut down; emergency repair<\/td>\n <td>Immediate<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n<\/section>\n\n\n<section id=\"s7\">\n <h2>7. Alignment and Balancing<\/h2>\n <p class=\"section-lead\">The two corrective actions that eliminate the largest share of vibration problems on marine rotating equipment.<\/p>\n\n <h3 id=\"s7-1\">7.1 Shaft Alignment<\/h3>\n\n <p>Misalignment between coupled shafts is one of the top three vibration causes in marine machinery (alongside unbalance and bearing wear). It creates excessive forces on bearings, seals, and couplings, and produces a characteristic vibration signature dominated by 2\u00d7 shaft speed.<\/p>\n\n <h4>Misalignment Types<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Type<\/th>\n <th>Dominant Vibration<\/th>\n <th>Direction<\/th>\n <th>Phase Signature<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Parallel (offset)<\/td>\n <td>2\u00d7 RPM<\/td>\n <td>Radial<\/td>\n <td>180\u00b0 shift across coupling in radial direction<\/td>\n <\/tr>\n <tr>\n <td>Angular<\/td>\n <td>1\u00d7 and 2\u00d7 RPM<\/td>\n <td>Axial<\/td>\n <td>180\u00b0 shift across coupling in axial direction<\/td>\n <\/tr>\n <tr>\n <td>Combined<\/td>\n <td>1\u00d7 + 2\u00d7 + higher<\/td>\n <td>All<\/td>\n <td>Complex; requires multi-point measurement<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Static vs. Dynamic Alignment<\/h4>\n <p>Static alignment is measured when the machine is cold and at rest. Dynamic (operating) alignment can differ substantially because of thermal growth, foundation deflection under load, and piping forces that develop with temperature and pressure. A diesel generator, for instance, may grow 1\u20132 mm vertically at the coupling centre when the engine reaches operating temperature.<\/p>\n\n <div class=\"formula\">\n Thermal growth: \u0394L = L \u00b7 \u03b1 \u00b7 \u0394T<br>\n Example: 2 m steel shaft, \u03b1 = 12 \u00d7 10\u207b\u2076 \/\u00b0C, \u0394T = 50 \u00b0C \u2192 \u0394L = 1.2 mm upward\n <\/div>\n\n <p>Laser alignment systems calculate cold offsets to compensate for expected thermal growth, so that alignment is correct at operating temperature rather than at ambient.<\/p>\n\n <h4>Soft Foot<\/h4>\n <p>If one or more machine feet do not contact the foundation properly, tightening the hold-down bolt distorts the frame, shifts bearing alignment, and changes vibration characteristics in a load-dependent way. Detecting soft foot is the first step before any alignment procedure: loosen each bolt in turn and measure movement with a dial indicator or laser system. Correct with precision shims.<\/p>\n\n <h3 id=\"s7-2\">7.2 Balancing Theory<\/h3>\n\n <p>Mass unbalance creates a centrifugal force that rotates with the shaft, producing vibration at 1\u00d7 RPM. The force is proportional to \u03c9\u00b2, so a rotor that vibrates moderately at low speed may be destructive at high speed.<\/p>\n\n <div class=\"formula\">\n Unbalance force: F = m \u00b7 r \u00b7 \u03c9\u00b2<br>\n m \u2014 unbalance mass | r \u2014 radius | \u03c9 \u2014 angular velocity\n <\/div>\n\n <h4>Unbalance Types<\/h4>\n <ul>\n <li><strong>Static<\/strong> \u2014 a single heavy spot; the rotor would settle with the heavy side down on knife edges. One correction plane is sufficient.<\/li>\n <li><strong>Couple<\/strong> \u2014 two equal masses 180\u00b0 apart in different axial planes. No static imbalance, but the rotor wobbles during rotation. Two correction planes required.<\/li>\n <li><strong>Dynamic<\/strong> \u2014 the general case: combination of static and couple. Always requires two-plane correction for full elimination.<\/li>\n <\/ul>\n\n <h4>Balancing Quality \u2014 ISO 1940<\/h4>\n <p>ISO 1940 defines permissible residual unbalance as a function of rotor mass and operating speed, expressed as a quality grade G (mm\/s). The product e \u00d7 \u03c9 = G, where e is the specific unbalance (displacement of centre of mass from axis) and \u03c9 is the angular velocity.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Grade<\/th>\n <th>e \u00d7 \u03c9 (mm\/s)<\/th>\n <th>Typical Application<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr><td>G 0.4<\/td><td>0.4<\/td><td>Gyroscopes, precision spindles<\/td><\/tr>\n <tr><td>G 1.0<\/td><td>1.0<\/td><td>High-precision drives<\/td><\/tr>\n <tr><td>G 2.5<\/td><td>2.5<\/td><td>High-speed marine equipment, turbochargers<\/td><\/tr>\n <tr><td>G 6.3<\/td><td>6.3<\/td><td>General marine machinery, pumps, fans, motors<\/td><\/tr>\n <tr><td>G 16<\/td><td>16<\/td><td>Large low-speed diesel components<\/td><\/tr>\n <tr><td>G 40<\/td><td>40<\/td><td>Agricultural machinery, crushers<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3 id=\"s7-3\">7.3 Field Balancing<\/h3>\n\n <p>Field balancing corrects unbalance in the machine's own bearings and supports, under real operating conditions. This is almost always preferable to removing a rotor for shop balancing when the unbalance is due to in-service fouling, erosion, or thermal distortion rather than manufacturing defect.<\/p>\n\n <h4>Single-Plane Procedure (Influence-Coefficient Method)<\/h4>\n\n <ol class=\"stage-list\">\n <li>Measure initial vibration amplitude and phase at 1\u00d7 RPM (reference run).<\/li>\n <li>Attach a known trial mass at a known angular position on the rotor.<\/li>\n <li>Run the machine and measure vibration again (trial run).<\/li>\n <li>Calculate the influence coefficient: how much vibration change one unit of mass at that radius produces.<\/li>\n <li>Calculate the correction mass and angle that will drive vibration to zero (vector arithmetic).<\/li>\n <li>Remove the trial mass, install the correction mass, verify with a final run.<\/li>\n <\/ol>\n\n <p>Two-plane balancing follows the same logic but solves a 2\u00d72 system of influence coefficients, allowing simultaneous correction of static and couple components.<\/p>\n\n <div class=\"product-mention\">\n <div class=\"product-mention-body\">\n <h4>Balanset-1A \u2014 Portable Balancing and Vibration Analysis<\/h4>\n <p>Vibromera's Balanset-1A is a portable instrument for single-plane and two-plane field balancing, as well as general vibration measurement and analysis. It can be used on fans, pumps, turbines, grinding wheels, centrifuges, and other rotating equipment commonly found in marine and industrial environments.<\/p>\n <\/div>\n <a href=\"https:\/\/vibromera.eu\/product\/balanset-1\/\">Learn more<\/a>\n <\/div>\n\n <h4>Marine-Specific Challenges<\/h4>\n <ul>\n <li><strong>Vessel motion<\/strong> \u2014 background vibration from waves and engine can mask the 1\u00d7 signal. Mitigation: measurement averaging over many revolutions, scheduling for calm conditions or in port.<\/li>\n <li><strong>Limited access<\/strong> \u2014 correction planes may be inside enclosures. Pre-planning and custom weight-attachment methods are often required.<\/li>\n <li><strong>Thermal effects<\/strong> \u2014 a turbocharger balanced cold may develop thermal unbalance at operating temperature due to differential expansion. Ideally, balance at operating temperature or apply a thermal correction factor.<\/li>\n <\/ul>\n\n <h3 id=\"s7-4\">7.4 Other Vibration Reduction Approaches<\/h3>\n\n <p>When balancing and alignment do not bring vibration to acceptable levels, several other techniques are available.<\/p>\n\n <h4>Source Modification<\/h4>\n <p>Redesign or modify the component to reduce the excitation force \u2014 for example, optimising impeller\u2013diffuser gap in a pump, improving manufacturing tolerances, or selecting an operating speed further from a critical speed.<\/p>\n\n <h4>Stiffness and Damping Changes<\/h4>\n <p>Reinforcing a foundation shifts its natural frequency away from the excitation frequency. Adding damping (constrained-layer treatments, viscoelastic mounts) reduces the amplification at resonance. Both approaches can be applied post-installation, though foundation reinforcement in a ship is constrained by structural weight limits.<\/p>\n\n <h4>Vibration Isolation<\/h4>\n <p>Resilient mounts (rubber, spring, air) decouple the machine from the hull structure. Effective above roughly \u221a2 \u00d7 the mount natural frequency. Marine isolators must also resist seismic loads from vessel motion and tolerate corrosive atmospheres.<\/p>\n\n <h4>Tuned Absorbers and Dampers<\/h4>\n <p>A tuned mass damper (TMD) \u2014 a small secondary mass-spring system tuned to the problem frequency \u2014 absorbs energy from the primary structure at that specific frequency. Effective for narrow-band problems such as a deck resonance excited by a generator. The drawback is that each TMD addresses only one frequency.<\/p>\n<\/section>\n\n\n<section id=\"s8\">\n <h2>8. Emerging Technologies<\/h2>\n <p class=\"section-lead\">Where marine vibration diagnostics is heading \u2014 wireless sensors, edge computing, machine learning, and the path toward autonomous maintenance.<\/p>\n\n <h3 id=\"s8-1\">8.1 AI and Machine Learning<\/h3>\n\n <p>Machine learning is shifting vibration diagnostics from manually defined rule sets toward data-driven pattern recognition. The most immediate applications are automated fault classification and remaining-useful-life prediction.<\/p>\n\n <h4>Classification<\/h4>\n <p>Convolutional neural networks (CNNs) trained on labelled vibration datasets can classify bearing, gear, unbalance, and misalignment faults with accuracy comparable to experienced analysts \u2014 provided the training data covers the actual operating conditions. Transfer learning and domain adaptation address the common problem of limited labelled marine data by starting from models trained on industrial datasets and fine-tuning with shipboard data.<\/p>\n\n <h4>Anomaly Detection<\/h4>\n <p>Autoencoders and variational autoencoders learn a compressed representation of normal vibration. When a new measurement falls outside the learned distribution the system flags it as anomalous \u2014 without needing prior examples of every possible fault type. This is particularly valuable for rare failure modes.<\/p>\n\n <h4>Digital Twins<\/h4>\n <p>A digital twin is a physics-based or hybrid model of a machine that runs in parallel with the real one, continuously updated with sensor data. Deviations between model predictions and real measurements indicate changing internal conditions. Digital twins enable scenario simulation (\"what if we increase speed by 5 %?\") and more reliable prognosis because they incorporate physics rather than relying solely on statistical extrapolation.<\/p>\n\n <h3 id=\"s8-2\">8.2 Wireless Sensors and Edge Computing<\/h3>\n\n <p>Wireless vibration sensors have matured to the point where battery life exceeds five years, communication reliability is sufficient for non-safety-critical monitoring, and on-board processing allows the sensor to compute statistical parameters locally, transmitting only summaries and alarms rather than raw waveforms. This drastically reduces installation cost \u2014 no cabling, no conduit, no junction boxes \u2014 and makes it economical to monitor hundreds of auxiliary machines that were previously unmonitored.<\/p>\n\n <p>Edge computing places processing power at or near the sensor, enabling real-time alarm generation, local FFT, and even neural-network inference without relying on a shore-side cloud connection. This is important for vessels that spend days or weeks with limited satellite bandwidth.<\/p>\n\n <h3 id=\"s8-3\">8.3 Autonomous Diagnostics and Integration<\/h3>\n\n <p>The long-term trajectory points toward systems that detect, diagnose, and act with minimal human intervention:<\/p>\n\n <ul>\n <li><strong>Self-calibrating sensors<\/strong> that verify their own health and compensate for drift.<\/li>\n <li><strong>Automatic fault diagnosis<\/strong> integrated with the vessel's planned maintenance system \u2014 a bearing-defect detection automatically generates a work order, checks spare-parts inventory, and suggests a maintenance window.<\/li>\n <li><strong>Fleet-level analytics<\/strong> \u2014 comparing the same equipment type across an entire fleet identifies systemic problems (a bad batch of bearings, a design-related resonance) that single-vessel monitoring would miss.<\/li>\n <li><strong>Multi-parameter fusion<\/strong> \u2014 combining vibration, oil analysis, thermography, and performance data in a single health index provides more reliable condition assessment than any single technique alone.<\/li>\n <\/ul>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Regulatory note<\/div>\n <p>Classification societies (DNV, Lloyd's, Bureau Veritas) are developing rules that recognise condition-based maintenance as an alternative to fixed-interval surveys. Robust, auditable vibration monitoring programmes are becoming a regulatory enabler, not just a cost-saving tool.<\/p>\n <\/div>\n\n <h4>Preparing for Adoption<\/h4>\n <p>Technology alone is not sufficient. Successful adoption requires workforce development (data-literacy training for engineers accustomed to wrenches, not algorithms), cybersecurity planning (connected monitoring systems are an attack surface), and a phased approach \u2014 pilot on a few vessels, prove the value, then scale.<\/p>\n<\/section>\n\n<\/main>\n<\/div>\n\n\n<footer class=\"article-footer\">\n <div class=\"article-footer-inner\">\n <h2>Summary<\/h2>\n <p>Vibration diagnostics is the primary condition-monitoring technique for rotating marine equipment. It covers the full lifecycle \u2014 from acceptance testing through routine monitoring to end-of-life prognosis \u2014 and its effectiveness depends on proper sensor selection, disciplined data collection, and competent analysis. As AI, wireless sensors, and digital twins enter the maritime space, the technique is becoming more automated and more integrated with vessel management systems, but the underlying physics and engineering judgement remain essential.<\/p>\n <p style=\"margin-top:20px;\">\n <a href=\"https:\/\/vibromera.eu\/\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\">vibromera.eu<\/a> \u00b7 \n <a href=\"https:\/\/www.youtube.com\/@vibromera\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\" target=\"_blank\" rel=\"noopener\">YouTube<\/a> \u00b7 \n <a href=\"https:\/\/www.instagram.com\/vibromera_ou\/\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\" target=\"_blank\" rel=\"noopener\">Instagram<\/a>\n <\/p>\n <\/div>\n<\/footer>\n\n\n<script>\n\/\/ Progress bar\nwindow.addEventListener('scroll', () => {\n const h = document.documentElement;\n const pct = (h.scrollTop \/ (h.scrollHeight - h.clientHeight)) * 100;\n document.getElementById('progressBar').style.width = pct + '%';\n});\n\n\/\/ Active TOC link\nconst sections = document.querySelectorAll('section[id], h3[id]');\nconst tocLinks = document.querySelectorAll('.toc-list a');\nconst observer = new IntersectionObserver(entries => {\n entries.forEach(entry => {\n if (entry.isIntersecting) {\n const id = entry.target.id;\n tocLinks.forEach(a => {\n a.classList.toggle('active', a.getAttribute('href') === '#' + id);\n });\n }\n });\n}, { rootMargin: '-20% 0px -70% 0px' });\nsections.forEach(s => observer.observe(s));\n<\/script>\n\n<\/body>\n<\/html><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Marine Vibration Diagnostics: Complete Technical Guide | Vibromera Technical Reference Vibration Diagnostics of Marine Equipment A practical guide to measurement methods, signal analysis, fault detection, balancing, and condition monitoring for rotating machinery on ships and offshore installations. By Vibromera Engineering Team \u00b7 Standards: ISO 10816 \u00b7 ISO 7919 \u00b7 ISO […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ai_generated_summary":"","footnotes":""},"categories":[54],"tags":[],"class_list":["post-6285","post","type-post","status-publish","format-standard","hentry","category-content"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/comments?post=6285"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285\/revisions"}],"predecessor-version":[{"id":100994,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285\/revisions\/100994"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/media?parent=6285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/categories?post=6285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/tags?post=6285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

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}\n }\n @media (max-width: 600px) {\n html { font-size: 16px; }\n .hero { padding: 56px 18px 48px; }\n .content section { padding: 24px 18px; }\n }\n <\/style>\n<\/head>\n<body>\n\n<div class=\"progress-bar\" id=\"progressBar\"><\/div>\n\n\n<header class=\"hero\">\n <div class=\"hero-inner\">\n <span class=\"hero-label\">Technical Reference<\/span>\n <h1>Vibration Diagnostics of Marine Equipment<\/h1>\n <p class=\"hero-subtitle\">A practical guide to measurement methods, signal analysis, fault detection, balancing, and condition monitoring for rotating machinery on ships and offshore installations.<\/p>\n <div class=\"hero-meta\">\n <span>By Vibromera Engineering Team<\/span>\n <span>\u00b7<\/span>\n <span>Standards: ISO 10816 \u00b7 ISO 7919 \u00b7 ISO 1940<\/span>\n <\/div>\n <\/div>\n<\/header>\n\n\n<div class=\"layout\">\n\n\n<aside class=\"sidebar\">\n <nav class=\"toc-nav\" aria-label=\"Table of contents\">\n <div class=\"toc-title\">Contents<\/div>\n <ol class=\"toc-list\">\n <li><a href=\"#s1\">1. Technical Diagnostics Fundamentals<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s1-1\">1.1 Diagnostic Principles<\/a><\/li>\n <li><a href=\"#s1-2\">1.2 Maintenance Strategies<\/a><\/li>\n <li><a href=\"#s1-3\">1.3 Vibration as Diagnostic Tool<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s2\">2. Vibration Physics<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s2-1\">2.1 Core Parameters<\/a><\/li>\n <li><a href=\"#s2-2\">2.2 Vibration Types<\/a><\/li>\n <li><a href=\"#s2-3\">2.3 Units & Standards<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s3\">3. Measurement Methods & Sensors<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s3-1\">3.1 Measurement Principles<\/a><\/li>\n <li><a href=\"#s3-2\">3.2 Sensor Technologies<\/a><\/li>\n <li><a href=\"#s3-3\">3.3 Mounting & Calibration<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s4\">4. Signal Analysis<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s4-1\">4.1 Signal Types<\/a><\/li>\n <li><a href=\"#s4-2\">4.2 Time & Frequency Domain<\/a><\/li>\n <li><a href=\"#s4-3\">4.3 Advanced Techniques<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s5\">5. Condition Monitoring Programs<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s5-1\">5.1 Acceptance Testing<\/a><\/li>\n <li><a href=\"#s5-2\">5.2 Monitoring Systems<\/a><\/li>\n <li><a href=\"#s5-3\">5.3 Alarm & Trend Analysis<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s6\">6. Fault Detection & Identification<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s6-1\">6.1 Bearing Diagnostics<\/a><\/li>\n <li><a href=\"#s6-2\">6.2 Gear & Shaft Faults<\/a><\/li>\n <li><a href=\"#s6-3\">6.3 Severity & Prognosis<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s7\">7. Alignment & Balancing<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s7-1\">7.1 Shaft Alignment<\/a><\/li>\n <li><a href=\"#s7-2\">7.2 Balancing Theory<\/a><\/li>\n <li><a href=\"#s7-3\">7.3 Field Balancing<\/a><\/li>\n <li><a href=\"#s7-4\">7.4 Other Vibration Reduction<\/a><\/li>\n <\/ul>\n <\/li>\n <li><a href=\"#s8\">8. Emerging Technologies<\/a>\n <ul class=\"toc-sub\">\n <li><a href=\"#s8-1\">8.1 AI & Machine Learning<\/a><\/li>\n <li><a href=\"#s8-2\">8.2 Wireless & Edge Computing<\/a><\/li>\n <li><a href=\"#s8-3\">8.3 Autonomous Diagnostics<\/a><\/li>\n <\/ul>\n <\/li>\n <\/ol>\n <\/nav>\n<\/aside>\n\n\n<main class=\"content\">\n\n\n<section id=\"s1\">\n <h2>1. Technical Diagnostics Fundamentals<\/h2>\n <p class=\"section-lead\">Why vibration analysis became the dominant approach to monitoring rotating marine machinery \u2014 and what alternatives exist.<\/p>\n\n <h3 id=\"s1-1\">1.1 Diagnostic Principles<\/h3>\n\n <p>Technical diagnostics is the discipline of assessing the current condition of a machine and predicting how that condition will change over time. For marine equipment this task is especially critical: an unplanned failure at sea can endanger crew, cargo, and the vessel itself.<\/p>\n\n <p>The central idea is straightforward. Every piece of rotating machinery produces measurable physical signals \u2014 vibration, heat, acoustic emission, oil contamination, and others. As internal components wear, crack, corrode, or loosen, those signals change in ways that are usually predictable. A systematic monitoring programme detects these changes early, classifies them by type and severity, and feeds recommendations into the maintenance schedule.<\/p>\n\n <h4>Key Terms<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Term<\/th>\n <th>Definition<\/th>\n <th>Marine Example<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Diagnostic parameter<\/strong><\/td>\n <td>A measurable quantity that correlates with equipment condition<\/td>\n <td>Vibration velocity RMS on a pump bearing housing<\/td>\n <\/tr>\n <tr>\n <td><strong>Diagnostic symptom<\/strong><\/td>\n <td>A specific pattern in the measured data<\/td>\n <td>Elevated vibration at blade-passing frequency in a centrifugal pump<\/td>\n <\/tr>\n <tr>\n <td><strong>Diagnostic sign<\/strong><\/td>\n <td>A recognisable indication of a particular condition<\/td>\n <td>Sidebands around gear mesh frequency indicating tooth wear<\/td>\n <\/tr>\n <tr>\n <td><strong>Recognition algorithm<\/strong><\/td>\n <td>A procedure (manual or automatic) that maps measured data to a fault category<\/td>\n <td>An expert-system rule set that flags bearing defect frequencies in an envelope spectrum<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>The General Diagnostic Workflow<\/h4>\n\n <div class=\"flow\">\n <span class=\"flow-step\">Data collection<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Signal processing<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Pattern recognition<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Fault classification<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Severity assessment<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-step\">Maintenance action<\/span>\n <\/div>\n\n <p>In practice the pipeline is iterative: if a pattern does not match any known fault, the analyst goes back, refines the processing, adds new measurement points, or correlates with other diagnostic methods (thermography, oil analysis, ultrasonic testing).<\/p>\n\n <h4>Functional vs. Test-Bench Diagnostics<\/h4>\n\n <p><strong>Functional diagnostics<\/strong> collects data while the machine runs under normal load. It reflects realistic operating conditions but limits what tests you can perform \u2014 you cannot, for instance, inject an artificial excitation into a pump that is supplying cooling water to the main engine.<\/p>\n\n <p><strong>Test-bench (tester) diagnostics<\/strong> applies controlled excitation \u2014 impact hammer, swept-sine shaker, or similar \u2014 usually during a shutdown. It reveals natural frequencies, transfer functions, and structural characteristics that functional diagnostics cannot provide. On board a ship the practical difficulty is obvious: shutdowns are expensive and sometimes impossible for essential systems.<\/p>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Practical note<\/div>\n <p>A good shipboard programme combines both approaches. Routine functional monitoring covers 80\u201390 % of the fleet's machinery, while test-bench methods are reserved for commissioning, troubleshooting, and critical systems.<\/p>\n <\/div>\n\n <h4>Choosing What to Monitor<\/h4>\n\n <p>Not every machine on a vessel justifies the same level of attention. Selecting which parameters to track on which equipment requires a trade-off between diagnostic coverage and practical cost. Typical selection criteria include sensitivity to fault development, measurement repeatability, cost of the sensor and installation, and the criticality of the equipment itself.<\/p>\n\n <h3 id=\"s1-2\">1.2 Maintenance Strategies<\/h3>\n\n <p>The maritime industry has moved through four broad maintenance philosophies, each with a different cost\u2013risk profile.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Strategy<\/th>\n <th>Approach<\/th>\n <th>Strengths<\/th>\n <th>Weaknesses<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Reactive<\/strong><\/td>\n <td>Run to failure, repair after breakdown<\/td>\n <td>Minimal upfront investment<\/td>\n <td>Unpredictable downtime, safety risk, secondary damage<\/td>\n <\/tr>\n <tr>\n <td><strong>Preventive (time-based)<\/strong><\/td>\n <td>Fixed-interval overhauls regardless of condition<\/td>\n <td>Predictable schedule<\/td>\n <td>Over-maintenance, unnecessary parts replacement<\/td>\n <\/tr>\n <tr>\n <td><strong>Condition-based (CBM)<\/strong><\/td>\n <td>Maintain when measured parameters exceed thresholds<\/td>\n <td>Interventions timed to actual need<\/td>\n <td>Requires diagnostic competence and equipment<\/td>\n <\/tr>\n <tr>\n <td><strong>Proactive \/ Reliability-centred<\/strong><\/td>\n <td>Identify and eliminate root causes of failure<\/td>\n <td>Highest long-term reliability<\/td>\n <td>High initial investment, cultural change<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Most modern fleets use a combination. Critical propulsion and power-generation machinery gets condition-based or proactive maintenance. Auxiliary equipment may still follow time-based schedules or even run-to-failure where spares are cheap and consequences are minor. Vibration analysis is the backbone of the CBM layer.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Example<\/div>\n <p>A container ship's cooling-water pumps were previously overhauled every 3 000 operating hours. After implementing vibration-based condition monitoring the operator extended intervals to 4 500 hours while reducing unplanned failures by roughly 75 %. The programme paid for itself in under one year.<\/p>\n <\/div>\n\n <h3 id=\"s1-3\">1.3 Vibration as the Primary Diagnostic Signal<\/h3>\n\n <p>Vibration analysis dominates marine condition monitoring for several interconnected reasons:<\/p>\n\n <ul>\n <li>All rotating machinery produces vibration \u2014 no additional excitation is required.<\/li>\n <li>Faults change vibration patterns in well-documented, fault-specific ways.<\/li>\n <li>Measurements are non-intrusive and can be taken while machinery operates normally.<\/li>\n <li>Early warning times are typically measured in weeks or months, not hours.<\/li>\n <li>The technique is quantitative \u2014 results map directly to severity zones defined by international standards.<\/li>\n <\/ul>\n\n <p>The methodology moves through six stages: baseline establishment, trend monitoring, anomaly detection, fault classification, severity assessment, and prognosis (remaining useful life). Each stage draws on a different toolbox \u2014 from simple RMS trending at the first stage to envelope analysis, cepstrum, and machine-learning classifiers at the later ones.<\/p>\n\n <h4>Condition States<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>State<\/th>\n <th>Indicators<\/th>\n <th>Recommended Action<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Good<\/strong><\/td>\n <td>Low, stable vibration; no fault frequencies<\/td>\n <td>Continue normal monitoring schedule<\/td>\n <\/tr>\n <tr>\n <td><strong>Acceptable<\/strong><\/td>\n <td>Elevated but stable levels<\/td>\n <td>Increase monitoring frequency, investigate root cause<\/td>\n <\/tr>\n <tr>\n <td><strong>Unsatisfactory<\/strong><\/td>\n <td>High levels or rising trend<\/td>\n <td>Plan maintenance at next opportunity<\/td>\n <\/tr>\n <tr>\n <td><strong>Unacceptable<\/strong><\/td>\n <td>Very high levels or rapid deterioration<\/td>\n <td>Shut down or reduce load immediately; emergency maintenance<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Economic Perspective<\/h4>\n\n <p>Return on investment for shipboard vibration programmes varies, but ratios of 5:1 to 10:1 are frequently cited in the literature. Most of the savings come from three sources: avoiding catastrophic secondary damage (a failed bearing that wrecks a shaft), extending component life by eliminating unnecessary overhauls, and reducing the cost of port-side emergency repairs versus scheduled dockyard work.<\/p>\n<\/section>\n\n\n<section id=\"s2\">\n <h2>2. Vibration Physics<\/h2>\n <p class=\"section-lead\">Displacement, velocity, acceleration \u2014 the three faces of vibration and when each one matters most.<\/p>\n\n <h3 id=\"s2-1\">2.1 Core Parameters<\/h3>\n\n <p>Vibration is the oscillatory motion of a mechanical system around an equilibrium position. It is described by three interrelated kinematic quantities, each useful in a different frequency range.<\/p>\n\n <div class=\"formula\">\n Displacement: x(t) = A \u00b7 sin(\u03c9t + \u03c6)<br>\n Velocity: v(t) = A\u00b7\u03c9 \u00b7 cos(\u03c9t + \u03c6)<br>\n Acceleration: a(t) = \u2212A\u00b7\u03c9\u00b2 \u00b7 sin(\u03c9t + \u03c6)<br>\n <br>\n A \u2014 amplitude | \u03c9 = 2\u03c0f \u2014 angular frequency | \u03c6 \u2014 phase angle\n <\/div>\n\n <p>Because velocity scales linearly with frequency (the \u03c9 factor) and acceleration scales with \u03c9\u00b2, the three parameters have very different sensitivities across the spectrum. This is the practical reason engineers choose one over another.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Parameter<\/th>\n <th>Unit<\/th>\n <th>Best Frequency Range<\/th>\n <th>Typical Marine Uses<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Displacement<\/strong><\/td>\n <td>\u03bcm (peak-to-peak), mils<\/td>\n <td>Below \u2248 10 Hz<\/td>\n <td>Large slow-speed diesel cranks, shaft-relative motion<\/td>\n <\/tr>\n <tr>\n <td><strong>Velocity<\/strong><\/td>\n <td>mm\/s (RMS)<\/td>\n <td>10 Hz \u2013 1 kHz<\/td>\n <td>General machinery monitoring; ISO 10816 evaluations<\/td>\n <\/tr>\n <tr>\n <td><strong>Acceleration<\/strong><\/td>\n <td>m\/s\u00b2 or g (peak)<\/td>\n <td>Above \u2248 1 kHz<\/td>\n <td>Rolling-element bearing diagnostics, gear mesh, high-speed pumps<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Statistical Measures<\/h4>\n\n <p><strong>RMS<\/strong> (root mean square) represents the effective amplitude and correlates with the energy content of vibration. It is the default metric for ISO-based severity evaluation.<\/p>\n\n <p><strong>Peak value<\/strong> captures maximum instantaneous amplitude \u2014 useful for detecting impacts and transient events.<\/p>\n\n <p><strong>Peak-to-peak value<\/strong> gives the total swing from positive to negative peak. It is commonly used for displacement measurements and clearance analysis.<\/p>\n\n <p><strong>Crest factor<\/strong> is the ratio of peak to RMS. A healthy rotating machine typically shows a crest factor between 3 and 4. Values above 5\u20136 suggest impulsive events such as bearing defects or impacts.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Diagnostic illustration<\/div>\n <p>A cargo pump bearing's crest factor rose from 3.2 to 7.8 over six weeks while overall RMS remained almost unchanged. That divergence \u2014 stable energy, increasing spikiness \u2014 is a classic early bearing-defect signature. Subsequent inspection confirmed an outer-race pit.<\/p>\n <\/div>\n\n <h3 id=\"s2-2\">2.2 Vibration Types in Marine Systems<\/h3>\n\n <p>Marine machinery generates several categories of vibration, each arising from a different physical mechanism.<\/p>\n\n <h4>By Excitation Source<\/h4>\n\n <ul>\n <li><strong>Free vibration<\/strong> \u2014 the system oscillates at its natural frequency after a transient excitation (startup, shutdown, impact).<\/li>\n <li><strong>Forced vibration<\/strong> \u2014 continuous excitation at a frequency related to rotational speed, blade count, or electrical supply. The majority of steady-state vibration is forced.<\/li>\n <li><strong>Self-excited vibration<\/strong> \u2014 the machinery creates its own excitation through an internal feedback mechanism: oil whirl in journal bearings, aerodynamic flutter, stick-slip friction.<\/li>\n <li><strong>Parametric vibration<\/strong> \u2014 system stiffness or damping varies periodically, pumping energy into the response. A cracked gear tooth that changes mesh stiffness once per revolution is a typical example.<\/li>\n <\/ul>\n\n <h4>By Relationship to Speed<\/h4>\n\n <ul>\n <li><strong>Synchronous (order-related)<\/strong> \u2014 frequency is an integer or simple rational multiple of shaft speed. Unbalance (1\u00d7), misalignment (2\u00d7), and looseness (many harmonics) belong here.<\/li>\n <li><strong>Asynchronous<\/strong> \u2014 frequency is independent of shaft speed. Bearing defect frequencies, electrical line-frequency harmonics, and belt-slip vibration fall in this category.<\/li>\n <\/ul>\n\n <h4>By Direction<\/h4>\n\n <p><strong>Radial<\/strong> vibration (perpendicular to the shaft) dominates in most rotating equipment and is the first direction measured. <strong>Axial<\/strong> vibration (parallel to the shaft) flags thrust-bearing problems, coupling issues, and aerodynamic forces. <strong>Torsional<\/strong> vibration (twisting about the shaft axis) requires specialised sensors and is mainly tracked on long propulsion trains where torsional resonance can be destructive.<\/p>\n\n <h4>Natural Frequencies and Resonance<\/h4>\n\n <p>Every mechanical system has natural frequencies determined by its mass, stiffness, and damping. When an excitation frequency approaches a natural frequency the response is amplified \u2014 sometimes by a factor of 10 or more. In rotating machinery these coincidences are called <em>critical speeds<\/em>.<\/p>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Design rule<\/div>\n <p>Operating speed should be separated from all identified critical speeds by at least 15\u201320 %. Running persistently within this margin risks resonance-driven fatigue and rapid failure.<\/p>\n <\/div>\n\n <h4>Vibration Sources<\/h4>\n\n <p><strong>Mechanical<\/strong> \u2014 unbalance, misalignment, bearing defects, looseness, gear problems, shaft bow. Frequencies typically relate to shaft speed and component geometry.<\/p>\n\n <p><strong>Electromagnetic<\/strong> \u2014 rotor-bar defects, stator eccentricity, supply-voltage imbalance. Frequencies concentrate around twice the line frequency (100 Hz for 50 Hz supply, 120 Hz for 60 Hz) and its multiples.<\/p>\n\n <p><strong>Hydraulic \/ aerodynamic<\/strong> \u2014 blade-passing, cavitation, turbulence, recirculation. Blade-passing frequency equals the number of blades multiplied by rotational frequency; cavitation produces broadband random noise concentrated above 1\u20132 kHz.<\/p>\n\n <h3 id=\"s2-3\">2.3 Units and Standards<\/h3>\n\n <p>Vibration measurements use both linear and logarithmic (decibel) scales. The decibel form compresses wide dynamic ranges and emphasises relative changes:<\/p>\n\n <div class=\"formula\">\n dB = 20 \u00b7 log\u2081\u2080(measured value \/ reference value)\n <\/div>\n\n <p>Reference values differ by parameter: 10\u207b\u2076 m for displacement, 10\u207b\u2079 m\/s for velocity (in some standards 1 nm\/s), 10\u207b\u2076 m\/s\u00b2 for acceleration.<\/p>\n\n <h4>ISO 10816 \u2014 Vibration on Non-Rotating Parts<\/h4>\n\n <p>The standard defines four evaluation zones, A through D, based on broadband velocity RMS. Limits depend on machine class (power rating, speed range) and support stiffness (rigid vs. flexible).<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Zone<\/th>\n <th>Condition<\/th>\n <th>Velocity RMS (Group 2, rigid)<\/th>\n <th>Guidance<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>A<\/strong><\/td>\n <td>Good<\/td>\n <td>up to 1.4 mm\/s<\/td>\n <td>Newly commissioned or recently maintained<\/td>\n <\/tr>\n <tr>\n <td><strong>B<\/strong><\/td>\n <td>Acceptable<\/td>\n <td>1.4 \u2013 2.8 mm\/s<\/td>\n <td>Unrestricted long-term operation<\/td>\n <\/tr>\n <tr>\n <td><strong>C<\/strong><\/td>\n <td>Unsatisfactory<\/td>\n <td>2.8 \u2013 7.1 mm\/s<\/td>\n <td>Limited-duration operation; plan remedial work<\/td>\n <\/tr>\n <tr>\n <td><strong>D<\/strong><\/td>\n <td>Unacceptable<\/td>\n <td>> 7.1 mm\/s<\/td>\n <td>Damage likely; immediate action<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Other relevant standards: <strong>ISO 7919<\/strong> (shaft vibration, measured with proximity probes), <strong>ISO 14694<\/strong> (condition monitoring guidance), <strong>ISO 8528-9<\/strong> (generating sets), <strong>API 610<\/strong> (centrifugal pumps). All follow the same four-zone logic but with limits adapted to the equipment type.<\/p>\n\n <h4>Machine Classification<\/h4>\n\n <p>Vibration limits are set per machine class. Classification considers power rating (small < 15 kW, medium 15\u201375 kW, large > 75 kW), speed range, and support stiffness. A machine is <em>rigidly<\/em> mounted if its first support natural frequency is more than twice the operating frequency; <em>flexibly<\/em> mounted if below half the operating frequency. The distinction matters because flexible mounts amplify housing vibration and therefore call for more lenient limits.<\/p>\n\n <h4>Measurement Points<\/h4>\n\n <p>Standards prescribe measurement on bearing housings, as close to the load zone as practical, in three directions: horizontal radial, vertical radial, and axial (usually at the drive-end bearing only). Measurements should be taken under stable operating conditions \u2014 rated speed and at least 75 % of rated load \u2014 and averaged over a period long enough to capture any cyclic variation.<\/p>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Shipboard caveat<\/div>\n <p>Vessel motion, sea state, and cargo loading can influence vibration readings. Good practice includes logging these conditions alongside every measurement and filtering or flagging data collected in rough weather.<\/p>\n <\/div>\n<\/section>\n\n\n<section id=\"s3\">\n <h2>3. Measurement Methods and Sensors<\/h2>\n <p class=\"section-lead\">Sensor selection, mounting, signal conditioning, and the practical realities of collecting good vibration data on board a ship.<\/p>\n\n <h3 id=\"s3-1\">3.1 Measurement Principles<\/h3>\n\n <h4>Kinematic vs. Dynamic<\/h4>\n <p>Most vibration sensors measure <em>motion<\/em> only \u2014 displacement, velocity, or acceleration \u2014 without quantifying the force that produces it. This is kinematic measurement. Dynamic measurement combines motion and force data, typically through paired accelerometers and force transducers, and is used mainly in controlled test-bench situations such as modal analysis or transfer-function measurements.<\/p>\n\n <h4>Absolute vs. Relative<\/h4>\n <p><strong>Absolute vibration<\/strong> is the motion of a point relative to a fixed (earth-based) reference. An accelerometer bolted to a bearing housing gives an absolute measurement. <strong>Relative vibration<\/strong> is the motion between two parts \u2014 typically the shaft and the bearing housing. Proximity probes provide this and are standard on large turbomachinery where shaft orbit information is needed.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Type<\/th>\n <th>Best for<\/th>\n <th>Limitations<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Absolute (accelerometer, velocity sensor)<\/td>\n <td>General machinery, auxiliary equipment, structural vibration<\/td>\n <td>Cannot directly reveal shaft motion inside the bearing<\/td>\n <\/tr>\n <tr>\n <td>Relative (proximity probe)<\/td>\n <td>Large turbomachinery, journal bearings, critical shafts<\/td>\n <td>Expensive installation, requires shaft access<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Contact vs. Non-Contact<\/h4>\n <p>Contact sensors (accelerometers, velocity pickups, strain gauges) are physically attached to the vibrating surface. They offer high sensitivity, broad bandwidth, and well-established procedures. Non-contact sensors (eddy-current probes, laser vibrometers) measure from a distance and are essential for rotating surfaces, high-temperature zones, and locations where mass loading by a contact sensor would alter the measurement.<\/p>\n\n <h3 id=\"s3-2\">3.2 Sensor Technologies<\/h3>\n\n <h4>Piezoelectric Accelerometers<\/h4>\n <p>The workhorse of marine vibration measurement. A piezoelectric element (quartz or ceramic) generates electric charge proportional to applied force. Internal electronics (IEPE \/ ICP standard) convert this to a low-impedance voltage signal that travels reliably over long cables in noisy engine-room environments.<\/p>\n\n <div class=\"kv-grid\">\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Typical bandwidth<\/div>\n <div class=\"kv-card-value\">1 Hz \u2013 10 kHz<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Sensitivity<\/div>\n <div class=\"kv-card-value\">10 \u2013 100 mV\/g<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Operating temperature<\/div>\n <div class=\"kv-card-value\">\u221250 to +120 \u00b0C<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Mass<\/div>\n <div class=\"kv-card-value\">5 \u2013 50 g<\/div>\n <\/div>\n <\/div>\n\n <p>High-frequency models (up to 50 kHz, lower sensitivity) are used for early bearing-defect detection. High-sensitivity models (100\u20131000 mV\/g, bandwidth to ~5 kHz) are chosen for low-level vibration in precision machinery.<\/p>\n\n <h4>MEMS Accelerometers<\/h4>\n <p>Micro-electromechanical accelerometers are smaller, cheaper, and consume less power than piezoelectric units. They have become viable for permanent monitoring of non-critical machinery and wireless sensor networks. Bandwidth and dynamic range have improved substantially in recent years, though piezoelectric sensors still lead in high-frequency performance.<\/p>\n\n <h4>Velocity Sensors (Seismic Transducers)<\/h4>\n <p>A suspended magnetic mass moves relative to a coil, generating a voltage proportional to velocity. These sensors require no external power, have robust construction, and give a direct velocity output \u2014 convenient for ISO 10816 evaluation without integration. Drawbacks include limited low-frequency response (typically above 10 Hz), temperature sensitivity, and relatively large size.<\/p>\n\n <h4>Proximity Probes (Eddy-Current Sensors)<\/h4>\n <p>A high-frequency oscillator creates an electromagnetic field at the probe tip. Eddy currents in the nearby conductive shaft surface alter the impedance, and electronics convert the change to a DC voltage proportional to gap distance. Two probes mounted at 90\u00b0 on each bearing provide X-Y shaft position data for orbit analysis. Resolution is on the order of 0.1 \u03bcm, and the probe has DC response (it can track slow static displacements as well as dynamic vibration).<\/p>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Application note<\/div>\n <p>Proximity probes are standard on large main turbines, turbochargers, and reduction-gear shafts. They are almost never used for auxiliary machinery \u2014 the installation cost is too high relative to the equipment value.<\/p>\n <\/div>\n\n <h3 id=\"s3-3\">3.3 Mounting and Calibration<\/h3>\n\n <h4>Mounting Methods<\/h4>\n <p>The way a sensor is attached to the machine determines the upper usable frequency. Each method introduces a mounting resonance above which the measurement is unreliable.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Method<\/th>\n <th>Usable Upper Frequency<\/th>\n <th>Notes<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Threaded stud<\/td>\n <td>Up to sensor limit (often > 10 kHz)<\/td>\n <td>Best accuracy; permanent or semi-permanent<\/td>\n <\/tr>\n <tr>\n <td>Thin adhesive layer<\/td>\n <td>~5\u20137 kHz<\/td>\n <td>Good for temporary campaigns<\/td>\n <\/tr>\n <tr>\n <td>Magnetic mount<\/td>\n <td>~2\u20133 kHz<\/td>\n <td>Quick; ferromagnetic surfaces only<\/td>\n <\/tr>\n <tr>\n <td>Hand-held probe<\/td>\n <td>~1 kHz<\/td>\n <td>Screening only; poor repeatability<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Common error<\/div>\n <p>Using a magnetic mount for bearing envelope analysis (which relies on frequencies above 2\u20133 kHz) will produce misleading results. A stud or thin adhesive mount is required.<\/p>\n <\/div>\n\n <h4>Signal Conditioning<\/h4>\n <p>IEPE sensors need a constant-current power supply (typically 2\u20134 mA at 18\u201328 V DC). The data acquisition front-end normally provides this. Charge-mode sensors require a separate charge amplifier. In either case the signal path should use shielded, low-noise cables, and cable runs should be kept as short as practical to minimise electromagnetic pickup from engine-room power cables.<\/p>\n\n <h4>Calibration<\/h4>\n <p>Sensors and channels should be checked against a traceable reference at least once a year \u2014 more often in harsh marine environments. A portable calibration exciter producing a known acceleration at a known frequency (commonly 10 m\/s\u00b2 at 159.15 Hz) is the standard field tool. Back-to-back comparison with a reference accelerometer gives higher confidence and can be done aboard.<\/p>\n<\/section>\n\n\n<section id=\"s4\">\n <h2>4. Signal Analysis<\/h2>\n <p class=\"section-lead\">From raw vibration waveform to diagnostic conclusions \u2014 the signal-processing chain that makes fault identification possible.<\/p>\n\n <h3 id=\"s4-1\">4.1 Signal Types<\/h3>\n\n <p>Understanding what kind of signal your machine produces determines which analysis techniques will extract useful information.<\/p>\n\n <h4>Periodic and Harmonic Signals<\/h4>\n <p>A pure sinusoid at a single frequency is the simplest case (rare in practice). Most rotating machinery produces <em>polyharmonic<\/em> signals \u2014 a fundamental frequency plus its integer multiples. A four-stroke diesel produces firing-order harmonics; a gear train produces mesh frequency and its harmonics.<\/p>\n\n <h4>Modulated Signals<\/h4>\n <p><strong>Amplitude modulation (AM)<\/strong> \u2014 the signal envelope varies periodically. A bearing outer-race defect that passes through the load zone once per revolution creates AM of the high-frequency impact response at the shaft speed. <strong>Frequency modulation (FM)<\/strong> \u2014 the instantaneous frequency varies. Speed fluctuation from a reciprocating compressor is a common source.<\/p>\n\n <div class=\"formula\">\n AM: x(t) = A \u00b7 [1 + m \u00b7 cos(2\u03c0\u00b7f<sub>mod<\/sub>\u00b7t)] \u00b7 cos(2\u03c0\u00b7f<sub>carrier<\/sub>\u00b7t)<br>\n m \u2014 modulation depth | f<sub>mod<\/sub> \u2014 modulation frequency | f<sub>carrier<\/sub> \u2014 carrier frequency\n <\/div>\n\n <h4>Impulsive and Transient Signals<\/h4>\n <p>Short-duration, high-amplitude events that excite multiple resonances simultaneously. Rolling-element bearing defects, gear-tooth chips, and loose fasteners all produce impulsive vibration. Characteristic features: high crest factor (> 5), broad frequency content, rapid decay, and periodic repetition at the defect frequency.<\/p>\n\n <h4>Random Signals<\/h4>\n <p>Turbulent flow, cavitation, and advanced surface degradation produce vibration with no dominant periodic component. Statistically it is characterised by its power spectral density (PSD) rather than by individual frequency peaks.<\/p>\n\n <h3 id=\"s4-2\">4.2 Time Domain and Frequency Domain<\/h3>\n\n <h4>Time-Domain Analysis<\/h4>\n <p>Examining the raw waveform reveals information that spectral analysis can obscure: impact timing, modulation patterns, asymmetry (truncation, clipping), and the presence of transient events. Statistical parameters calculated from the waveform \u2014 RMS, crest factor, kurtosis, skewness \u2014 quantify signal character and are often the first indicators of bearing deterioration.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Parameter<\/th>\n <th>What It Detects<\/th>\n <th>Healthy Range<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>RMS<\/strong><\/td>\n <td>Overall energy<\/td>\n <td>Machine-specific (see ISO limits)<\/td>\n <\/tr>\n <tr>\n <td><strong>Crest factor<\/strong><\/td>\n <td>Impulsive content<\/td>\n <td>\u2248 3.0 \u2013 4.0<\/td>\n <\/tr>\n <tr>\n <td><strong>Kurtosis<\/strong><\/td>\n <td>Peakedness \/ impact rate<\/td>\n <td>\u2248 3.0 (Gaussian baseline)<\/td>\n <\/tr>\n <tr>\n <td><strong>Skewness<\/strong><\/td>\n <td>Waveform asymmetry<\/td>\n <td>\u2248 0 (symmetric)<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <p>Kurtosis is especially valuable for bearing diagnostics. A healthy bearing produces roughly Gaussian vibration (kurtosis \u2248 3). Developing defects drive kurtosis well above 4 \u2014 sometimes above 10 \u2014 long before overall RMS rises enough to trigger an alarm.<\/p>\n\n <h4>Frequency-Domain Analysis (FFT)<\/h4>\n\n <p>The Fast Fourier Transform converts a time record into a frequency spectrum, revealing which frequencies carry the most energy. This is the primary diagnostic tool because different fault types produce vibration at different, predictable frequencies.<\/p>\n\n <div class=\"formula\">\n X(k) = \u03a3<sub>n=0<\/sub><sup>N\u22121<\/sup> x(n) \u00b7 e<sup>\u2212j2\u03c0kn\/N<\/sup>\n <\/div>\n\n <h4>Key DSP Considerations<\/h4>\n\n <p><strong>Sampling rate<\/strong> must exceed twice the highest frequency of interest (Nyquist criterion). Anti-aliasing filters attenuate everything above the Nyquist frequency before digitisation. A practical rule: sample at 2.56 \u00d7 the analysis bandwidth (to allow for filter roll-off).<\/p>\n\n <p><strong>Frequency resolution<\/strong> = 1 \/ T, where T is the record length. To separate two close frequencies you need a longer record. For marine applications where speed varies slightly, order tracking (resampling synchronised to a tachometer pulse) maintains constant resolution in the order domain regardless of speed drift.<\/p>\n\n <p><strong>Windowing<\/strong> suppresses spectral leakage caused by finite record length. Hanning is the general-purpose default; flat-top gives the best amplitude accuracy (important when comparing to absolute limits); rectangular is appropriate only for truly transient signals.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Window<\/th>\n <th>Frequency Resolution<\/th>\n <th>Amplitude Accuracy<\/th>\n <th>Use Case<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Rectangular<\/td>\n <td>Best<\/td>\n <td>Moderate<\/td>\n <td>Transient \/ impact<\/td>\n <\/tr>\n <tr>\n <td>Hanning<\/td>\n <td>Good<\/td>\n <td>Good<\/td>\n <td>General purpose<\/td>\n <\/tr>\n <tr>\n <td>Flat-top<\/td>\n <td>Poor<\/td>\n <td>Best<\/td>\n <td>Calibration, amplitude checks<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3 id=\"s4-3\">4.3 Advanced Techniques<\/h3>\n\n <h4>Envelope Analysis (Amplitude Demodulation)<\/h4>\n <p>The method of choice for rolling-element bearing diagnostics. Steps: (1) band-pass filter around a structural resonance excited by bearing impacts (typically 2\u20138 kHz), (2) extract the amplitude envelope via Hilbert transform or rectification + low-pass filter, (3) compute the FFT of the envelope. Bearing defect frequencies (BPFO, BPFI, BSF, FTF) then appear as distinct peaks in the envelope spectrum, clearly separated from shaft-speed harmonics and other sources.<\/p>\n\n <h4>Cepstrum Analysis<\/h4>\n <p>The cepstrum is the inverse FFT of the log-magnitude spectrum. It detects periodic patterns <em>within<\/em> the frequency spectrum \u2014 exactly what sidebands around gear-mesh frequency or harmonic families from looseness produce. The technique is less intuitive than direct FFT but excels when multiple sideband families overlap.<\/p>\n\n <div class=\"formula\">\n Cepstrum = IFFT( log |FFT(x(t))| )\n <\/div>\n\n <h4>Order Tracking<\/h4>\n <p>For variable-speed machinery (common on vessels with variable-frequency drives or during manoeuvring), conventional FFT smears speed-related peaks. Order tracking resamples the time signal using a tachometer or speed reference, converting the analysis from the frequency domain to the order domain. Each order corresponds to a fixed multiple of shaft speed.<\/p>\n\n <h4>Coherence Function<\/h4>\n <p>Measures the linear relationship between two signals as a function of frequency. Coherence close to 1.0 at a given frequency means the vibration at the response point is predominantly caused by the excitation at the reference point. Useful for isolating transmission paths, verifying measurement quality, and assessing how much of a machine's vibration is transmitted to nearby structures.<\/p>\n<\/section>\n\n\n<section id=\"s5\">\n <h2>5. Condition Monitoring Programs<\/h2>\n <p class=\"section-lead\">Building and running a shipboard vibration monitoring programme \u2014 from acceptance testing through trend analysis.<\/p>\n\n <h3 id=\"s5-1\">5.1 Acceptance Testing<\/h3>\n\n <p>Vibration acceptance testing establishes that newly installed or overhauled equipment meets its design specification before entering service. For marine equipment this is typically done in stages: factory acceptance test (FAT) at the manufacturer, harbour acceptance test (HAT) after installation aboard, and sea trial at full load.<\/p>\n\n <h4>What Acceptance Testing Catches<\/h4>\n <ul>\n <li>Residual unbalance exceeding the specified ISO 1940 quality grade<\/li>\n <li>Soft foot \u2014 one or more mounting feet not in proper contact with the foundation<\/li>\n <li>Coupling misalignment introduced during installation<\/li>\n <li>Piping strain transmitted to pump or compressor flanges<\/li>\n <li>Foundation resonances that coincide with operating speed<\/li>\n <\/ul>\n\n <p>Measurements during acceptance testing become the baseline for future condition monitoring. They should be taken at several load levels (typically 25 %, 50 %, 75 %, 100 %) and documented with operating parameters (speed, load, temperatures, sea state).<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Break-in example<\/div>\n <p>A newly installed cargo pump showed 4.2 mm\/s RMS immediately after commissioning. Over 100 hours of service the reading settled to 2.1 mm\/s as bearing surfaces conformed and clearances stabilised. Without acceptance testing the initial high reading might have triggered an unnecessary investigation.<\/p>\n <\/div>\n\n <h3 id=\"s5-2\">5.2 Monitoring Systems<\/h3>\n\n <h4>Portable (Route-Based) Systems<\/h4>\n <p>A technician walks a pre-defined route through the engine room, collecting data at each tagged measurement point using a handheld data collector. Software on a shore or office PC stores, trends, and analyses the data. This is the most cost-effective approach for auxiliary machinery where continuous monitoring is not justified.<\/p>\n\n <h4>Permanent (On-Line) Systems<\/h4>\n <p>Sensors are permanently installed on critical equipment and wired to a central data acquisition system. Measurements are taken automatically at scheduled intervals or continuously. Alarms trigger when thresholds are exceeded. Main engines, generators, propulsion motors, and reduction gears are typical candidates.<\/p>\n\n <h4>Hybrid Approach<\/h4>\n <p>Most modern fleets combine both. Continuous monitoring covers the 10\u201315 most critical machines. Route-based portable measurements cover 50\u2013200 auxiliary items on a weekly to quarterly cycle. Unified software merges both datasets into a single database.<\/p>\n\n <div class=\"kv-grid\">\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Portable system cost<\/div>\n <div class=\"kv-card-value\">Lower per point<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Permanent system cost<\/div>\n <div class=\"kv-card-value\">Higher per point<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Event capture<\/div>\n <div class=\"kv-card-value\">Permanent wins<\/div>\n <\/div>\n <div class=\"kv-card\">\n <div class=\"kv-card-label\">Fleet flexibility<\/div>\n <div class=\"kv-card-value\">Portable wins<\/div>\n <\/div>\n <\/div>\n\n <h4>Database and Hierarchy<\/h4>\n <p>The monitoring database organises equipment in a tree: vessel \u2192 department (engine, deck, electrical) \u2192 system (propulsion, auxiliary cooling, fire-fighting) \u2192 machine \u2192 component \u2192 measurement point. Each point has defined sensor type, direction, units, alarm levels, and analysis settings. Good hierarchy design makes fleet-wide benchmarking and reporting practical.<\/p>\n\n <h3 id=\"s5-3\">5.3 Alarm Levels and Trend Analysis<\/h3>\n\n <h4>Setting Alarm Levels<\/h4>\n <p>There are three common approaches, and they can be combined.<\/p>\n\n <ul>\n <li><strong>Standards-based<\/strong> \u2014 use ISO 10816 or API zone boundaries directly. Simple but one-size-fits-all.<\/li>\n <li><strong>Statistical<\/strong> \u2014 set the alert at baseline mean + 2\u20133 standard deviations, the danger threshold at mean + 4\u20136 \u03c3. Tailored to each machine but requires sufficient baseline data.<\/li>\n <li><strong>Experience-based<\/strong> \u2014 derived from the analyst's knowledge of a specific machine type. Often the most effective for unusual or very old equipment not covered well by generic standards.<\/li>\n <\/ul>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-title\">Avoid alarm fatigue<\/div>\n <p>On a ship with hundreds of measurement points, poorly calibrated alarms generate dozens of false positives per route. Crews learn to ignore them. Invest time in proper baseline collection and alarm-level tuning \u2014 it is the single highest-leverage activity in a new programme.<\/p>\n <\/div>\n\n <h4>Trend Analysis<\/h4>\n <p>Plotting a parameter over time reveals developing faults before they reach alarm levels. Trending works for overall RMS, individual frequency components, statistical parameters (crest factor, kurtosis), and envelope-derived metrics. The slope of the trend line \u2014 and especially any sudden change in slope \u2014 is the primary decision driver.<\/p>\n\n <p>Methods range from simple visual inspection of time-series plots to statistical process control (CUSUM, EWMA) and regression-based remaining-useful-life models. For critical machinery, combining multiple trended parameters in a single \"health index\" provides a more robust picture than any one parameter alone.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Trend success story<\/div>\n <p>A main-engine cooling pump showed a steady 15 % monthly increase in outer-race defect-frequency amplitude over six months. Bearing replacement was scheduled during a routine port call, preventing an unplanned failure that would have required diverting the vessel.<\/p>\n <\/div>\n<\/section>\n\n\n<section id=\"s6\">\n <h2>6. Fault Detection and Identification<\/h2>\n <p class=\"section-lead\">Translating spectral peaks, waveform shapes, and statistical parameters into specific fault diagnoses.<\/p>\n\n <h3 id=\"s6-1\">6.1 Rolling-Element Bearing Diagnostics<\/h3>\n\n <p>Rolling-element bearings are the most commonly monitored component in marine vibration programmes. Each defect location produces a distinct characteristic frequency determined by bearing geometry and shaft speed.<\/p>\n\n <h4>Defect Frequencies<\/h4>\n\n <div class=\"formula\">\n BPFO = (N\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 \u2212 d\/D \u00b7 cos \u03c6)<br>\n BPFI = (N\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 + d\/D \u00b7 cos \u03c6)<br>\n BSF = (D\/2d) \u00b7 f<sub>shaft<\/sub> \u00b7 [1 \u2212 (d\/D \u00b7 cos \u03c6)\u00b2]<br>\n FTF = (1\/2) \u00b7 f<sub>shaft<\/sub> \u00b7 (1 \u2212 d\/D \u00b7 cos \u03c6)<br>\n <br>\n N \u2014 number of rolling elements | d \u2014 element diameter<br>\n D \u2014 pitch diameter | \u03c6 \u2014 contact angle | f<sub>shaft<\/sub> \u2014 shaft frequency\n <\/div>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Worked example<\/div>\n <p>SKF 6309 bearing (9 balls, d = 12.7 mm, D = 58.5 mm, \u03c6 \u2248 0\u00b0) at 1 750 RPM (29.17 Hz):<br>\n BPFO \u2248 102 Hz \u00b7 BPFI \u2248 158 Hz \u00b7 BSF \u2248 67 Hz \u00b7 FTF \u2248 11.4 Hz<\/p>\n <\/div>\n\n <h4>Fault Progression Stages<\/h4>\n\n <ol class=\"stage-list\">\n <li><strong>Onset<\/strong> \u2014 subtle increase in the high-frequency noise floor (ultrasonic band, > 20 kHz). No discrete peaks yet. Detectable only with specialised high-frequency techniques (acoustic emission, spike energy).<\/li>\n <li><strong>Discrete defect frequencies appear<\/strong> \u2014 bearing-characteristic frequencies (BPFO, BPFI, etc.) become visible in the envelope spectrum or high-frequency-band acceleration spectrum.<\/li>\n <li><strong>Harmonics and sidebands develop<\/strong> \u2014 defect-frequency harmonics grow; modulation sidebands at shaft speed appear around bearing frequencies.<\/li>\n <li><strong>Broadening and increase<\/strong> \u2014 the noise floor rises in the bearing-frequency band; overall acceleration and velocity RMS begin to climb; crest factor may start to decrease as random content grows.<\/li>\n <li><strong>Advanced damage<\/strong> \u2014 broadband random vibration dominates; displacement levels rise; temperatures increase; audible noise. Failure is imminent.<\/li>\n <\/ol>\n\n <h4>Envelope Analysis in Practice<\/h4>\n <p>Band-pass filter the raw acceleration signal in the 2\u20138 kHz range (or around the highest bearing-excited resonance \u2014 identify it from an impact test or from the spectrum itself). Compute the Hilbert-transform envelope. FFT the envelope. If you see peaks at BPFO, BPFI, BSF, or FTF (and their harmonics), you have a positive bearing-defect identification.<\/p>\n\n <h3 id=\"s6-2\">6.2 Gear Faults and Shaft Problems<\/h3>\n\n <h4>Gear Diagnostics<\/h4>\n <p>The fundamental gear-mesh frequency (GMF) equals the number of teeth multiplied by shaft rotational frequency. A healthy gear produces a clean mesh peak with low sidebands. Developing problems manifest as increased mesh amplitude, growing sidebands spaced at the shaft frequency of the damaged gear, and eventually generation of higher harmonics of GMF.<\/p>\n\n <div class=\"callout callout-example\">\n <div class=\"callout-title\">Gear example<\/div>\n <p>23-tooth pinion at 1 200 RPM (20 Hz) meshing with a 67-tooth wheel (6.87 Hz). GMF = 23 \u00d7 20 = 460 Hz. Sidebands at 460 \u00b1 20 Hz indicate a developing pinion defect; sidebands at 460 \u00b1 6.87 Hz point to the wheel.<\/p>\n <\/div>\n\n <h4>Shaft and Coupling Problems<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Fault<\/th>\n <th>Dominant Frequency<\/th>\n <th>Key Indicators<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Mass unbalance<\/td>\n <td>1\u00d7 shaft speed<\/td>\n <td>Radial vibration; stable phase; amplitude \u221d speed\u00b2<\/td>\n <\/tr>\n <tr>\n <td>Parallel misalignment<\/td>\n <td>2\u00d7 (+ 1\u00d7, 3\u00d7)<\/td>\n <td>High radial vibration; 180\u00b0 phase shift across coupling<\/td>\n <\/tr>\n <tr>\n <td>Angular misalignment<\/td>\n <td>1\u00d7 and 2\u00d7<\/td>\n <td>High axial vibration at coupling<\/td>\n <\/tr>\n <tr>\n <td>Bent shaft<\/td>\n <td>1\u00d7 and 2\u00d7<\/td>\n <td>High 1\u00d7 axial; 180\u00b0 phase between bearings<\/td>\n <\/tr>\n <tr>\n <td>Mechanical looseness<\/td>\n <td>Many harmonics of 1\u00d7<\/td>\n <td>Subharmonics (0.5\u00d7); unstable phase; directional<\/td>\n <\/tr>\n <tr>\n <td>Rotor rub<\/td>\n <td>Fractional harmonics<\/td>\n <td>0.5\u00d7, 1.5\u00d7, 2.5\u00d7 etc.; truncated waveform<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Impeller \/ Flow-Related Problems<\/h4>\n <p>Blade-passing frequency (BPF) = number of blades \u00d7 shaft frequency. Elevated BPF and its harmonics indicate impeller damage, diffuser\u2013impeller gap issues, or inlet flow distortion. Cavitation produces broadband high-frequency noise \u2014 a \"crackling\" sound signature above 2 kHz with high kurtosis. Recirculation at low flow creates low-frequency random instability.<\/p>\n\n <h3 id=\"s6-3\">6.3 Severity Assessment and Prognosis<\/h3>\n\n <p>Detecting a fault is only half the job. The maintenance team needs to know <em>how fast<\/em> the fault is progressing and <em>how long<\/em> the machine can continue to operate safely.<\/p>\n\n <h4>Severity Metrics<\/h4>\n <ul>\n <li>Amplitude of the defect-frequency peak relative to its baseline value<\/li>\n <li>Rate of change of that amplitude (slope of the trend)<\/li>\n <li>Number and strength of harmonics and sidebands<\/li>\n <li>Crest factor and kurtosis progression<\/li>\n <li>Overall velocity or acceleration RMS relative to ISO zone boundaries<\/li>\n <\/ul>\n\n <h4>Prognostic Methods<\/h4>\n <p>Simple trending with linear or exponential extrapolation gives a rough remaining-life estimate. More sophisticated approaches include physics-based degradation models (e.g., spalling propagation under Hertzian stress) and data-driven models trained on failure run-to-failure datasets. In either case, predictions should carry explicit confidence intervals \u2014 a point estimate of \"42 days remaining\" is much less useful than \"30\u201360 days at 90 % confidence\".<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Severity Level<\/th>\n <th>Recommended Action<\/th>\n <th>Typical Timeframe<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Good<\/td>\n <td>Continue normal monitoring<\/td>\n <td>Next scheduled measurement<\/td>\n <\/tr>\n <tr>\n <td>Early fault<\/td>\n <td>Increase monitoring frequency<\/td>\n <td>Weekly \u2192 bi-weekly<\/td>\n <\/tr>\n <tr>\n <td>Developing<\/td>\n <td>Plan maintenance intervention<\/td>\n <td>Next port call or planned downtime<\/td>\n <\/tr>\n <tr>\n <td>Advanced<\/td>\n <td>Schedule repair as soon as possible<\/td>\n <td>Within 1\u20132 weeks<\/td>\n <\/tr>\n <tr>\n <td>Critical<\/td>\n <td>Reduce load or shut down; emergency repair<\/td>\n <td>Immediate<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n<\/section>\n\n\n<section id=\"s7\">\n <h2>7. Alignment and Balancing<\/h2>\n <p class=\"section-lead\">The two corrective actions that eliminate the largest share of vibration problems on marine rotating equipment.<\/p>\n\n <h3 id=\"s7-1\">7.1 Shaft Alignment<\/h3>\n\n <p>Misalignment between coupled shafts is one of the top three vibration causes in marine machinery (alongside unbalance and bearing wear). It creates excessive forces on bearings, seals, and couplings, and produces a characteristic vibration signature dominated by 2\u00d7 shaft speed.<\/p>\n\n <h4>Misalignment Types<\/h4>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Type<\/th>\n <th>Dominant Vibration<\/th>\n <th>Direction<\/th>\n <th>Phase Signature<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Parallel (offset)<\/td>\n <td>2\u00d7 RPM<\/td>\n <td>Radial<\/td>\n <td>180\u00b0 shift across coupling in radial direction<\/td>\n <\/tr>\n <tr>\n <td>Angular<\/td>\n <td>1\u00d7 and 2\u00d7 RPM<\/td>\n <td>Axial<\/td>\n <td>180\u00b0 shift across coupling in axial direction<\/td>\n <\/tr>\n <tr>\n <td>Combined<\/td>\n <td>1\u00d7 + 2\u00d7 + higher<\/td>\n <td>All<\/td>\n <td>Complex; requires multi-point measurement<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h4>Static vs. Dynamic Alignment<\/h4>\n <p>Static alignment is measured when the machine is cold and at rest. Dynamic (operating) alignment can differ substantially because of thermal growth, foundation deflection under load, and piping forces that develop with temperature and pressure. A diesel generator, for instance, may grow 1\u20132 mm vertically at the coupling centre when the engine reaches operating temperature.<\/p>\n\n <div class=\"formula\">\n Thermal growth: \u0394L = L \u00b7 \u03b1 \u00b7 \u0394T<br>\n Example: 2 m steel shaft, \u03b1 = 12 \u00d7 10\u207b\u2076 \/\u00b0C, \u0394T = 50 \u00b0C \u2192 \u0394L = 1.2 mm upward\n <\/div>\n\n <p>Laser alignment systems calculate cold offsets to compensate for expected thermal growth, so that alignment is correct at operating temperature rather than at ambient.<\/p>\n\n <h4>Soft Foot<\/h4>\n <p>If one or more machine feet do not contact the foundation properly, tightening the hold-down bolt distorts the frame, shifts bearing alignment, and changes vibration characteristics in a load-dependent way. Detecting soft foot is the first step before any alignment procedure: loosen each bolt in turn and measure movement with a dial indicator or laser system. Correct with precision shims.<\/p>\n\n <h3 id=\"s7-2\">7.2 Balancing Theory<\/h3>\n\n <p>Mass unbalance creates a centrifugal force that rotates with the shaft, producing vibration at 1\u00d7 RPM. The force is proportional to \u03c9\u00b2, so a rotor that vibrates moderately at low speed may be destructive at high speed.<\/p>\n\n <div class=\"formula\">\n Unbalance force: F = m \u00b7 r \u00b7 \u03c9\u00b2<br>\n m \u2014 unbalance mass | r \u2014 radius | \u03c9 \u2014 angular velocity\n <\/div>\n\n <h4>Unbalance Types<\/h4>\n <ul>\n <li><strong>Static<\/strong> \u2014 a single heavy spot; the rotor would settle with the heavy side down on knife edges. One correction plane is sufficient.<\/li>\n <li><strong>Couple<\/strong> \u2014 two equal masses 180\u00b0 apart in different axial planes. No static imbalance, but the rotor wobbles during rotation. Two correction planes required.<\/li>\n <li><strong>Dynamic<\/strong> \u2014 the general case: combination of static and couple. Always requires two-plane correction for full elimination.<\/li>\n <\/ul>\n\n <h4>Balancing Quality \u2014 ISO 1940<\/h4>\n <p>ISO 1940 defines permissible residual unbalance as a function of rotor mass and operating speed, expressed as a quality grade G (mm\/s). The product e \u00d7 \u03c9 = G, where e is the specific unbalance (displacement of centre of mass from axis) and \u03c9 is the angular velocity.<\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Grade<\/th>\n <th>e \u00d7 \u03c9 (mm\/s)<\/th>\n <th>Typical Application<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr><td>G 0.4<\/td><td>0.4<\/td><td>Gyroscopes, precision spindles<\/td><\/tr>\n <tr><td>G 1.0<\/td><td>1.0<\/td><td>High-precision drives<\/td><\/tr>\n <tr><td>G 2.5<\/td><td>2.5<\/td><td>High-speed marine equipment, turbochargers<\/td><\/tr>\n <tr><td>G 6.3<\/td><td>6.3<\/td><td>General marine machinery, pumps, fans, motors<\/td><\/tr>\n <tr><td>G 16<\/td><td>16<\/td><td>Large low-speed diesel components<\/td><\/tr>\n <tr><td>G 40<\/td><td>40<\/td><td>Agricultural machinery, crushers<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3 id=\"s7-3\">7.3 Field Balancing<\/h3>\n\n <p>Field balancing corrects unbalance in the machine's own bearings and supports, under real operating conditions. This is almost always preferable to removing a rotor for shop balancing when the unbalance is due to in-service fouling, erosion, or thermal distortion rather than manufacturing defect.<\/p>\n\n <h4>Single-Plane Procedure (Influence-Coefficient Method)<\/h4>\n\n <ol class=\"stage-list\">\n <li>Measure initial vibration amplitude and phase at 1\u00d7 RPM (reference run).<\/li>\n <li>Attach a known trial mass at a known angular position on the rotor.<\/li>\n <li>Run the machine and measure vibration again (trial run).<\/li>\n <li>Calculate the influence coefficient: how much vibration change one unit of mass at that radius produces.<\/li>\n <li>Calculate the correction mass and angle that will drive vibration to zero (vector arithmetic).<\/li>\n <li>Remove the trial mass, install the correction mass, verify with a final run.<\/li>\n <\/ol>\n\n <p>Two-plane balancing follows the same logic but solves a 2\u00d72 system of influence coefficients, allowing simultaneous correction of static and couple components.<\/p>\n\n <div class=\"product-mention\">\n <div class=\"product-mention-body\">\n <h4>Balanset-1A \u2014 Portable Balancing and Vibration Analysis<\/h4>\n <p>Vibromera's Balanset-1A is a portable instrument for single-plane and two-plane field balancing, as well as general vibration measurement and analysis. It can be used on fans, pumps, turbines, grinding wheels, centrifuges, and other rotating equipment commonly found in marine and industrial environments.<\/p>\n <\/div>\n <a href=\"https:\/\/vibromera.eu\/product\/balanset-1\/\">Learn more<\/a>\n <\/div>\n\n <h4>Marine-Specific Challenges<\/h4>\n <ul>\n <li><strong>Vessel motion<\/strong> \u2014 background vibration from waves and engine can mask the 1\u00d7 signal. Mitigation: measurement averaging over many revolutions, scheduling for calm conditions or in port.<\/li>\n <li><strong>Limited access<\/strong> \u2014 correction planes may be inside enclosures. Pre-planning and custom weight-attachment methods are often required.<\/li>\n <li><strong>Thermal effects<\/strong> \u2014 a turbocharger balanced cold may develop thermal unbalance at operating temperature due to differential expansion. Ideally, balance at operating temperature or apply a thermal correction factor.<\/li>\n <\/ul>\n\n <h3 id=\"s7-4\">7.4 Other Vibration Reduction Approaches<\/h3>\n\n <p>When balancing and alignment do not bring vibration to acceptable levels, several other techniques are available.<\/p>\n\n <h4>Source Modification<\/h4>\n <p>Redesign or modify the component to reduce the excitation force \u2014 for example, optimising impeller\u2013diffuser gap in a pump, improving manufacturing tolerances, or selecting an operating speed further from a critical speed.<\/p>\n\n <h4>Stiffness and Damping Changes<\/h4>\n <p>Reinforcing a foundation shifts its natural frequency away from the excitation frequency. Adding damping (constrained-layer treatments, viscoelastic mounts) reduces the amplification at resonance. Both approaches can be applied post-installation, though foundation reinforcement in a ship is constrained by structural weight limits.<\/p>\n\n <h4>Vibration Isolation<\/h4>\n <p>Resilient mounts (rubber, spring, air) decouple the machine from the hull structure. Effective above roughly \u221a2 \u00d7 the mount natural frequency. Marine isolators must also resist seismic loads from vessel motion and tolerate corrosive atmospheres.<\/p>\n\n <h4>Tuned Absorbers and Dampers<\/h4>\n <p>A tuned mass damper (TMD) \u2014 a small secondary mass-spring system tuned to the problem frequency \u2014 absorbs energy from the primary structure at that specific frequency. Effective for narrow-band problems such as a deck resonance excited by a generator. The drawback is that each TMD addresses only one frequency.<\/p>\n<\/section>\n\n\n<section id=\"s8\">\n <h2>8. Emerging Technologies<\/h2>\n <p class=\"section-lead\">Where marine vibration diagnostics is heading \u2014 wireless sensors, edge computing, machine learning, and the path toward autonomous maintenance.<\/p>\n\n <h3 id=\"s8-1\">8.1 AI and Machine Learning<\/h3>\n\n <p>Machine learning is shifting vibration diagnostics from manually defined rule sets toward data-driven pattern recognition. The most immediate applications are automated fault classification and remaining-useful-life prediction.<\/p>\n\n <h4>Classification<\/h4>\n <p>Convolutional neural networks (CNNs) trained on labelled vibration datasets can classify bearing, gear, unbalance, and misalignment faults with accuracy comparable to experienced analysts \u2014 provided the training data covers the actual operating conditions. Transfer learning and domain adaptation address the common problem of limited labelled marine data by starting from models trained on industrial datasets and fine-tuning with shipboard data.<\/p>\n\n <h4>Anomaly Detection<\/h4>\n <p>Autoencoders and variational autoencoders learn a compressed representation of normal vibration. When a new measurement falls outside the learned distribution the system flags it as anomalous \u2014 without needing prior examples of every possible fault type. This is particularly valuable for rare failure modes.<\/p>\n\n <h4>Digital Twins<\/h4>\n <p>A digital twin is a physics-based or hybrid model of a machine that runs in parallel with the real one, continuously updated with sensor data. Deviations between model predictions and real measurements indicate changing internal conditions. Digital twins enable scenario simulation (\"what if we increase speed by 5 %?\") and more reliable prognosis because they incorporate physics rather than relying solely on statistical extrapolation.<\/p>\n\n <h3 id=\"s8-2\">8.2 Wireless Sensors and Edge Computing<\/h3>\n\n <p>Wireless vibration sensors have matured to the point where battery life exceeds five years, communication reliability is sufficient for non-safety-critical monitoring, and on-board processing allows the sensor to compute statistical parameters locally, transmitting only summaries and alarms rather than raw waveforms. This drastically reduces installation cost \u2014 no cabling, no conduit, no junction boxes \u2014 and makes it economical to monitor hundreds of auxiliary machines that were previously unmonitored.<\/p>\n\n <p>Edge computing places processing power at or near the sensor, enabling real-time alarm generation, local FFT, and even neural-network inference without relying on a shore-side cloud connection. This is important for vessels that spend days or weeks with limited satellite bandwidth.<\/p>\n\n <h3 id=\"s8-3\">8.3 Autonomous Diagnostics and Integration<\/h3>\n\n <p>The long-term trajectory points toward systems that detect, diagnose, and act with minimal human intervention:<\/p>\n\n <ul>\n <li><strong>Self-calibrating sensors<\/strong> that verify their own health and compensate for drift.<\/li>\n <li><strong>Automatic fault diagnosis<\/strong> integrated with the vessel's planned maintenance system \u2014 a bearing-defect detection automatically generates a work order, checks spare-parts inventory, and suggests a maintenance window.<\/li>\n <li><strong>Fleet-level analytics<\/strong> \u2014 comparing the same equipment type across an entire fleet identifies systemic problems (a bad batch of bearings, a design-related resonance) that single-vessel monitoring would miss.<\/li>\n <li><strong>Multi-parameter fusion<\/strong> \u2014 combining vibration, oil analysis, thermography, and performance data in a single health index provides more reliable condition assessment than any single technique alone.<\/li>\n <\/ul>\n\n <div class=\"callout callout-info\">\n <div class=\"callout-title\">Regulatory note<\/div>\n <p>Classification societies (DNV, Lloyd's, Bureau Veritas) are developing rules that recognise condition-based maintenance as an alternative to fixed-interval surveys. Robust, auditable vibration monitoring programmes are becoming a regulatory enabler, not just a cost-saving tool.<\/p>\n <\/div>\n\n <h4>Preparing for Adoption<\/h4>\n <p>Technology alone is not sufficient. Successful adoption requires workforce development (data-literacy training for engineers accustomed to wrenches, not algorithms), cybersecurity planning (connected monitoring systems are an attack surface), and a phased approach \u2014 pilot on a few vessels, prove the value, then scale.<\/p>\n<\/section>\n\n<\/main>\n<\/div>\n\n\n<footer class=\"article-footer\">\n <div class=\"article-footer-inner\">\n <h2>Summary<\/h2>\n <p>Vibration diagnostics is the primary condition-monitoring technique for rotating marine equipment. It covers the full lifecycle \u2014 from acceptance testing through routine monitoring to end-of-life prognosis \u2014 and its effectiveness depends on proper sensor selection, disciplined data collection, and competent analysis. As AI, wireless sensors, and digital twins enter the maritime space, the technique is becoming more automated and more integrated with vessel management systems, but the underlying physics and engineering judgement remain essential.<\/p>\n <p style=\"margin-top:20px;\">\n <a href=\"https:\/\/vibromera.eu\/\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\">vibromera.eu<\/a> \u00b7 \n <a href=\"https:\/\/www.youtube.com\/@vibromera\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\" target=\"_blank\" rel=\"noopener\">YouTube<\/a> \u00b7 \n <a href=\"https:\/\/www.instagram.com\/vibromera_ou\/\" style=\"color:var(--color-teal);text-decoration:none;font-weight:600;\" target=\"_blank\" rel=\"noopener\">Instagram<\/a>\n <\/p>\n <\/div>\n<\/footer>\n\n\n<script>\n\/\/ Progress bar\nwindow.addEventListener('scroll', () => {\n const h = document.documentElement;\n const pct = (h.scrollTop \/ (h.scrollHeight - h.clientHeight)) * 100;\n document.getElementById('progressBar').style.width = pct + '%';\n});\n\n\/\/ Active TOC link\nconst sections = document.querySelectorAll('section[id], h3[id]');\nconst tocLinks = document.querySelectorAll('.toc-list a');\nconst observer = new IntersectionObserver(entries => {\n entries.forEach(entry => {\n if (entry.isIntersecting) {\n const id = entry.target.id;\n tocLinks.forEach(a => {\n a.classList.toggle('active', a.getAttribute('href') === '#' + id);\n });\n }\n });\n}, { rootMargin: '-20% 0px -70% 0px' });\nsections.forEach(s => observer.observe(s));\n<\/script>\n\n<\/body>\n<\/html><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Marine Vibration Diagnostics: Complete Technical Guide | Vibromera Technical Reference Vibration Diagnostics of Marine Equipment A practical guide to measurement methods, signal analysis, fault detection, balancing, and condition monitoring for rotating machinery on ships and offshore installations. By Vibromera Engineering Team \u00b7 Standards: ISO 10816 \u00b7 ISO 7919 \u00b7 ISO […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ai_generated_summary":"","footnotes":""},"categories":[54],"tags":[],"class_list":["post-6285","post","type-post","status-publish","format-standard","hentry","category-content"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/comments?post=6285"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285\/revisions"}],"predecessor-version":[{"id":100994,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/posts\/6285\/revisions\/100994"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/media?parent=6285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/categories?post=6285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/pt_br\/wp-json\/wp\/v2\/tags?post=6285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}