Vibration Analysis Fundamentals

1. Overview

Vibration analysis is the primary condition monitoring technique for rotating and reciprocating equipment in the midstream industry. By measuring and analyzing the vibration signature of compressors, pumps, motors, and turbines, engineers can detect developing faults before catastrophic failure, plan maintenance interventions, and verify that newly installed or repaired machinery meets acceptance criteria.

Every rotating machine vibrates. The goal is not to eliminate vibration entirely but to keep it within acceptable limits defined by international standards. When vibration exceeds those limits, it indicates a mechanical problem that will worsen over time if left uncorrected.

Condition Monitoring

Predictive Maintenance

Detect faults 3-6 months before failure

Acceptance Testing

New/Repaired Equipment

Verify compliance before commissioning

Root Cause Analysis

Fault Identification

Distinguish unbalance, misalignment, bearing wear

Protection Systems

Alarm & Trip

Continuous online monitoring for critical machines

Why vibration matters: Unplanned compressor failure can cost $50,000–$500,000+ in repair costs plus $10,000–$100,000 per day in lost production. Vibration monitoring typically provides 2–6 months advance warning of bearing failure and 1–3 months warning of other mechanical faults.

Common Vibration Sources in Midstream Equipment

Source	Frequency	Typical Machines	Severity
Unbalance	1× RPM	All rotating	Most common fault
Misalignment	1×, 2× RPM (axial)	Coupled machines	Second most common
Mechanical looseness	0.5×, 1×, 2×, harmonics	All	Progresses rapidly
Bearing defects	BPFO, BPFI, BSF, FTF	Rolling element	Early detection critical
Oil whirl/whip	0.42–0.48× RPM	Sleeve bearings	Can be catastrophic
Vane/blade pass	N × RPM (N = vane count)	Centrifugal compressors, pumps	Usually normal
Gear mesh	Teeth × RPM	Gearboxes	Sidebands indicate wear
Electrical	2× line frequency (120 Hz)	Motors, generators	Rotor bar / stator issues
Gas forces	1×, 2× RPM + harmonics	Reciprocating compressors	Inherent; higher limits

2. Vibration Parameters

Vibration is characterized by three interrelated parameters: displacement, velocity, and acceleration. Each is best suited for detecting different types of faults at different frequency ranges.

Displacement (mils peak-to-peak)

Displacement measures the total travel of the vibrating surface. One mil equals 0.001 inch. Displacement is most useful for low-frequency vibration below about 600 RPM and for shaft vibration measurements using proximity probes on sleeve bearings. It is the parameter specified by API 617 for centrifugal compressor shaft vibration limits.

Velocity (in/s peak or mm/s RMS)

Velocity is proportional to the energy of vibration and provides a relatively flat frequency response across the 10–1000 Hz range. This makes it the best single parameter for overall severity assessment. ISO 10816 uses velocity in mm/s RMS as the primary evaluation criterion. In U.S. practice, in/s peak is commonly used.

Acceleration (g's peak)

Acceleration emphasizes high-frequency components and is ideal for detecting early-stage rolling element bearing defects, gear tooth damage, and other high-frequency impacts. Measured with piezoelectric accelerometers, acceleration is the native measurement parameter from which velocity and displacement are derived by integration.

Vibration Unit Conversions (sinusoidal at frequency f Hz): Velocity from displacement: v (in/s pk) = π × f × d (mils pk-pk) / 1000 Displacement from velocity: d (mils pk-pk) = v (in/s pk) × 1000 / (π × f) Acceleration from velocity: a (g's pk) = 2πf × v (in/s pk) / 386.4 Velocity unit conversion: v (mm/s RMS) = v (in/s pk) × 25.4 / √2 Where: f = Frequency in Hz = RPM / 60 1 mil = 0.001 inch 1 g = 386.4 in/s² RMS = Peak / √2 (for sinusoidal signals)

Which Parameter to Use?

Parameter	Best Frequency Range	Primary Use	Standard
Displacement	<10 Hz (<600 RPM)	Shaft vibration, low-speed machines	API 617, ISO 7919
Velocity	10–1000 Hz	Overall severity, general machinery	ISO 10816, API 618
Acceleration	>1000 Hz	Bearing defects, gear mesh	ISO 15242

Practical tip: Always record the overall broadband velocity for severity assessment, then examine the frequency spectrum (FFT) to identify specific fault frequencies. Trending the overall level detects deterioration; spectral analysis identifies the cause.

3. ISO 10816 Vibration Severity

ISO 10816 is the international standard for evaluating machinery vibration measured on non-rotating parts (bearing housings, machine casing). It classifies machines into four groups and defines four severity zones based on broadband velocity in mm/s RMS.

Machine Classification

Class	Description	Power Range	Examples
Class I	Small machines	<15 kW (<20 HP)	Fractional HP motors, small fans
Class II	Medium machines, no special foundation	15–75 kW (20–100 HP)	Shop floor motors, small pumps
Class III	Large machines on rigid foundation	>75 kW (>100 HP)	Pipeline compressors, large pumps
Class IV	Large machines on flexible foundation	>75 kW (>100 HP)	Turbines, large centrifugal compressors

Severity Zone Boundaries

Zone boundaries are defined in mm/s RMS velocity. Zone A represents newly commissioned equipment. Zone B is acceptable for long-term unrestricted operation. Zone C requires restricted operation and planned investigation. Zone D is unacceptable and may cause damage.

Zone Boundary	Class I	Class II	Class III	Class IV	Action
A/B	0.71	1.12	1.8	2.8	Good → Satisfactory
B/C	1.8	2.8	4.5	7.1	Satisfactory → Unsatisfactory
C/D	4.5	7.1	11.2	18.0	Unsatisfactory → Unacceptable

All values in mm/s RMS. To convert: mm/s RMS = in/s peak × 25.4 / √2 = in/s peak × 17.96

Severity Zone Definitions

Zone A

Good

Vibration of newly commissioned machines. Baseline reference level.

Zone B

Satisfactory

Acceptable for unrestricted long-term operation. No action needed.

Zone C

Unsatisfactory

Not suitable for long-term continuous operation. Investigate and plan corrective action.

Zone D

Unacceptable

Sufficient to cause damage. Immediate remedial action required.

ISO 10816 vs. ISO 20816: ISO 10816 has been superseded by ISO 20816, which reorganizes the standard into machine-type-specific parts. However, the fundamental zone concept and many numerical limits remain the same. ISO 10816-1 limits are still widely referenced in the field and by equipment vendors.

4. API Vibration Standards

The American Petroleum Institute (API) publishes machinery-specific standards with vibration acceptance criteria for oil and gas industry equipment. These are more prescriptive than ISO 10816 for specific machine types.

API 617 — Centrifugal Compressors

API 617 (8th Edition) specifies shaft vibration limits for centrifugal compressors measured by proximity probes mounted near each radial bearing. The limits are speed-dependent to account for the physics of rotor response.

API 617 Shaft Vibration Limit (8th Ed., Section 4.9): Alert (alarm) level: A_max = √(12,000 / N) mils peak-to-peak Trip (shutdown) level: A_trip = 1.5 × A_max mils peak-to-peak Where: N = Operating speed (RPM) A_max is capped at a minimum of 1.0 mil pk-pk Examples: 3,600 RPM: A_max = √(12000/3600) = 1.83 mils, Trip = 2.74 mils 7,200 RPM: A_max = √(12000/7200) = 1.29 mils, Trip = 1.94 mils 10,000 RPM: A_max = √(12000/10000) = 1.10 mils, Trip = 1.64 mils 13,000 RPM: A_max = √(12000/13000) = 0.96 → use 1.0 mil, Trip = 1.5 mils

API 618 — Reciprocating Compressors

API 618 (6th Edition) addresses reciprocating compressors, which have inherently higher vibration than rotating equipment due to unbalanced reciprocating forces and gas pulsation. Vibration is measured on bearing housings with velocity transducers.

API 618 Vibration Limits (6th Ed., Section 3.9): Bearing housing (unfiltered overall): v_max = 0.5 in/s peak (12.7 mm/s peak) Frame and crosshead guide: Vendor-specific, typically 0.3–0.5 in/s peak Important notes: • Measurements are unfiltered broadband overall • Gas forces contribute 30–60% of total vibration • Pulsation dampener adequacy affects frame vibration • API 618 Design Approach 2 or 3 required for critical service

API 684 — Rotordynamics & Critical Speeds

API 684 provides a tutorial on lateral and torsional critical speed analysis. The key requirement for vibration analysis is the separation margin: operating speed must be at least 20% away from any lateral critical speed.

Critical Speed Separation Margin (API 684): For undamped critical speeds: Operating speed must NOT fall within: 0.8 × N_critical to 1.2 × N_critical This means: Min operating speed > 1.2 × N_cr1 (operate above first critical) or Max operating speed < 0.8 × N_cr1 (operate below first critical) Example: If first critical = 5,000 RPM: Exclusion zone = 4,000 to 6,000 RPM Operating speed must be <4,000 or >6,000 RPM

Comparison of API Vibration Standards

Standard	Equipment	Parameter	Location	Typical Limit
API 617	Centrifugal compressor	Displacement (mils pk-pk)	Shaft (prox. probe)	√(12000/N)
API 618	Recip. compressor	Velocity (in/s pk)	Bearing housing	0.5 in/s
API 610	Centrifugal pump	Velocity (in/s pk)	Bearing housing	0.15–0.30 in/s
API 541	Electric motor	Velocity (in/s pk)	Bearing housing	0.15 in/s (unfiltered)
API 616	Gas turbine	Displacement (mils pk-pk)	Shaft / bearing	1.0–2.0 mils

5. Vibration Diagnostics

The frequency spectrum (FFT) is the primary diagnostic tool. By examining which frequencies dominate the vibration signature, the analyst can identify the fault type. Each mechanical fault produces vibration at characteristic frequencies related to the running speed.

Diagnostic Frequency Chart

Fault	Dominant Frequency	Direction	Key Indicators
Mass unbalance	1× RPM	Radial	Proportional to speed²; phase stable; responds to balance correction
Parallel misalignment	2× RPM dominant	Radial	High 2× relative to 1×; high axial vibration
Angular misalignment	1× RPM (axial)	Axial	High axial at 1×; 180° phase across coupling
Bent shaft	1× RPM (axial)	Axial + radial	High 1× axial; phase difference between bearings
Mechanical looseness	0.5×, 1×, 2×, 3×+	Radial	Many harmonics; sub-harmonics; noisy spectrum
Oil whirl	0.42–0.48× RPM	Radial	Sleeve bearings; subsynchronous; speed-dependent
Oil whip	Locked at critical speed	Radial	Severe sleeve bearing instability; does not track speed
Rolling element bearing	BPFO, BPFI, BSF, FTF	Radial	Non-synchronous; modulated by 1× RPM; envelope analysis
Gear mesh	Teeth × RPM	Radial + axial	Sidebands at 1× RPM spacing indicate wear
Electrical (motor)	2× line freq (120 Hz)	Radial	Disappears instantly when power is removed
Vane pass	Vanes × RPM	Radial	Normal; high amplitude indicates clearance issue
Resonance	Natural frequency	Any	Amplifies forcing frequency when coincident; high Q factor

Phase Analysis

Phase angle is the timing relationship between the vibration signal and a once-per-revolution reference pulse (keyphasor). Phase is essential for:

Distinguishing unbalance from misalignment: Unbalance shows stable phase at 1× RPM. Misalignment shows 180° phase difference across the coupling at 1× and/or 2×.
Field balancing: Phase indicates the angular location of the heavy spot on the rotor, guiding weight placement.
Bode and polar plots: Track amplitude and phase through speed changes to identify critical speeds during startup/shutdown.

Quick diagnostic rule of thumb: If 1× RPM is dominant (>80% of overall), suspect unbalance. If 2× is high or axial vibration is high, suspect misalignment. If many harmonics are present, suspect looseness. If non-synchronous peaks appear, suspect bearing defects or oil instability.

Spectrum Analysis Techniques

The frequency spectrum (Fast Fourier Transform, FFT) decomposes the complex time waveform into individual frequency components. Proper analyzer setup is essential for accurate diagnostics:

Parameter	Typical Setting	Purpose
Frequency range (F_max)	10–40 × RPM	Capture harmonics and bearing defect frequencies
Lines of resolution	800 or 1600	Separate closely spaced peaks (higher = better resolution)
Averaging	4–8 averages	Reduce random noise; improve repeatability
Window function	Hanning	Best general-purpose window for continuous signals
Overlap	50%	Faster data collection with proper averaging

Vibration Trending

Trending is the comparison of vibration levels over time. It is the most effective technique for detecting gradual deterioration that might not trigger absolute alarm limits. Key trending practices include:

Overall level trend: Plot broadband velocity vs. time. A consistent upward trend indicates developing problems.
Band trending: Monitor specific frequency bands (e.g., 1×, 2×, bearing frequencies) independently. A single band increasing while overall stays flat helps identify the specific fault.
Alert threshold: A 25–50% increase from the established baseline warrants investigation. A 100% (2×) increase warrants expedited investigation.
Rate of change: Rapid acceleration in vibration increase indicates fast-developing fault (bearing spalling, coupling failure). Schedule immediate inspection.

6. Rolling Element Bearing Analysis

Rolling element bearings produce vibration at specific defect frequencies determined by bearing geometry and operating speed. These frequencies are non-synchronous (not multiples of RPM) and can be used to identify which component of the bearing is damaged.

Bearing Defect Frequencies

Bearing Defect Frequency Equations: Ball Pass Frequency, Outer Race (BPFO): BPFO = (n/2) × f × (1 - B_d/P_d × cos α) Ball Pass Frequency, Inner Race (BPFI): BPFI = (n/2) × f × (1 + B_d/P_d × cos α) Ball Spin Frequency (BSF): BSF = (P_d / (2 × B_d)) × f × (1 - (B_d/P_d)² × cos² α) Fundamental Train Frequency (FTF / cage frequency): FTF = (1/2) × f × (1 - B_d/P_d × cos α) Where: n = Number of rolling elements f = Shaft rotational frequency (Hz) = RPM / 60 B_d = Ball or roller diameter P_d = Pitch diameter (bearing center-to-center) α = Contact angle (0° for radial bearings, 15–40° for angular contact)

Bearing Failure Stages

Stage	Detection Method	Spectrum Signature	Remaining Life
Stage 1	Ultrasonic / Spike energy	High-frequency noise (20–60 kHz)	6–12 months
Stage 2	Envelope (demodulation)	Bearing defect frequencies appear	3–6 months
Stage 3	Velocity spectrum	Defect frequencies + sidebands	1–3 months
Stage 4	Overall vibration increase	Broadband noise floor rises; random peaks	Days to weeks

Sleeve (Journal) Bearing Issues

Sleeve bearings do not produce discrete defect frequencies. Instead, they are susceptible to fluid-film instabilities:

Oil whirl: Subsynchronous vibration at 0.42–0.48× RPM. Occurs when the shaft operates at less than 50% eccentricity in the bearing clearance. Light loads and high speeds promote oil whirl.
Oil whip: When oil whirl frequency coincides with a rotor natural frequency, it locks onto that frequency regardless of speed changes. This is a severe instability that can cause catastrophic failure.
Remedies: Increase bearing loading, use tilting-pad bearings (inherently stable), reduce clearance, change oil viscosity.

Bearing analysis best practice: When bearing defect frequencies are detected in the envelope spectrum, confirm by checking for sidebands at 1× RPM spacing around the defect frequency. The number and amplitude of sidebands indicates defect severity.

7. Balancing & ISO 1940

Unbalance is the most common cause of excessive vibration in rotating machinery. It occurs when the mass center of the rotor does not coincide with the geometric center of rotation. ISO 1940 defines balance quality grades for different rotor types.

ISO 1940 Balance Quality Grades

The G grade represents the permissible residual specific unbalance × angular velocity, in mm/s. Lower G values mean tighter balance requirements.

Grade	e × ω (mm/s)	Typical Applications
G0.4	0.4	Gyroscopes, precision spindles
G1.0	1.0	Grinding machine drives, high-speed turbines
G2.5	2.5	Gas turbines, compressors, electric motors >80 kW
G6.3	6.3	Pumps, fans, general machinery, reciprocating compressors
G16	16	Agricultural equipment, crushing machinery
G40	40	Automobile wheels, crankshaft assemblies (initial)

Allowable Residual Unbalance (ISO 1940): U_perm = (G × W × 16) / N (oz-in) Where: G = Balance quality grade (mm/s) W = Rotor weight (lbs) N = Operating speed (RPM) 16 = Conversion factor for oz-in from mm/s and lbs Alternative (metric): U_perm = (G × M × 1000) / (2π × N/60) (g-mm) Where: M = Rotor mass (kg) N = Operating speed (RPM) Example: Centrifugal compressor rotor: W = 2000 lbs, N = 3600 RPM, G2.5 U_perm = (2.5 × 2000 × 16) / 3600 = 22.2 oz-in Per correction plane (2-plane balance): U_per_plane = 22.2 / 2 = 11.1 oz-in per plane

Field Balancing Procedure

Single-plane field balancing using the trial weight method:

Original run: Record amplitude (A₀) and phase (φ₀) at 1× RPM.
Trial weight run: Attach a known trial weight (TW) at a known angle. Record new amplitude (A₁) and phase (φ₁).
Calculate influence coefficient: Determine the vector change caused by the trial weight.
Calculate correction weight: Determine the weight and angle needed to cancel the original unbalance.
Verify: Install correction weight, run machine, confirm vibration is within acceptable limits.

Trial weight sizing rule of thumb: The trial weight should produce a 20–50% change in 1× RPM vibration amplitude. For a rough starting point: TW (oz) = 56.4 × W (lbs) / (N (RPM))² × desired force (lbs). Too small a trial weight gives unreliable data; too large risks damage.

8. Measurement Practice

Consistent and accurate vibration measurements require proper sensor selection, mounting, and data collection procedures.

Sensor Types

Sensor	Measures	Frequency Range	Mounting	Application
Accelerometer	Acceleration	1 Hz – 20 kHz	Stud, magnet, handheld	General purpose; bearing housing
Velocity transducer	Velocity	10 Hz – 1 kHz	Stud, magnet	Older systems; direct velocity reading
Proximity probe	Displacement	DC – 10 kHz	Permanently installed	Shaft vibration; sleeve bearings

Mounting Methods (ranked by accuracy)

Stud mount: Best accuracy. Flat machined pad, threaded stud. Required for permanent monitoring and acceptance testing. Frequency response to 10 kHz+.
Adhesive/epoxy mount: Good accuracy. Permanent or semi-permanent. Frequency response to 5–7 kHz.
Flat magnet: Good for route-based data collection. Frequency response to 2–3 kHz. Clean, flat surface required.
Handheld: Lowest accuracy. Only acceptable for screening. Frequency response limited to 500–1000 Hz. Introduces operator variability.

Measurement Locations

Standard practice is to measure vibration in three orthogonal directions at each bearing:

Vertical (V): Top of bearing housing, perpendicular to shaft axis
Horizontal (H): Side of bearing housing, perpendicular to shaft axis
Axial (A): Parallel to shaft axis, typically on bearing housing

Data Collection Best Practices

Measure at steady-state operating conditions (same load, speed, temperature)
Allow machine to reach thermal equilibrium (minimum 20 minutes after startup)
Use the same measurement point and sensor orientation every time
Record operating conditions (speed, load, temperature) with each measurement
Collect time waveform, spectrum, and overall levels
Trend data monthly for general machinery, weekly for critical machines
Use alarm levels at 2× baseline and trip levels at 4× baseline

Data quality: More than 90% of vibration analysis errors come from poor data quality, not poor analysis. Consistent mounting, proper sensor selection, and stable operating conditions are far more important than sophisticated analysis algorithms.

Setting Alarm and Trip Levels

Alarm (alert) and trip (shutdown) vibration levels protect equipment from damage. They can be set using absolute limits from standards or relative limits from baseline data.

Method	Alarm Level	Trip Level	Applicability
Absolute (ISO/API)	B/C zone boundary	C/D zone boundary	New equipment, no baseline
Relative (baseline)	2.0–2.5 × baseline	4.0–5.0 × baseline	Established equipment with history
Statistical	Mean + 2σ	Mean + 3σ	Large fleet with population data
Vendor-specified	Per datasheet	Per datasheet	OEM-defined limits for warranty

For critical unspared equipment (pipeline compressors, charge gas compressors), continuous online monitoring with automatic trip is recommended. For general-purpose spared equipment, periodic route-based monitoring with manual alert review is typically sufficient.

Reciprocating Machine Considerations

Reciprocating compressors require special measurement considerations because their vibration signature is fundamentally different from rotating equipment:

Inherent vibration: Unbalanced reciprocating forces and gas pulsation create inherent vibration at 1×, 2×, and higher multiples of running speed. This is normal and unavoidable.
Higher limits: API 618 permits 0.5 in/s peak on bearing housings, significantly higher than typical rotating equipment limits (0.15–0.30 in/s).
Crosshead and frame: Measure on frame, crosshead guide, and bearing housing. Each location has different normal levels.
Pulsation interaction: Inadequate pulsation dampening (API 618 Design Approach) causes excessive frame vibration through unbalanced shaking forces on piping.
Looseness detection: Foundation bolt looseness and cracked frame are detected by increases in vibration at 0.5×, 1×, and sub-harmonic frequencies.
Rod drop monitoring: For crosshead-guided machines, rod drop (rider band wear) is monitored via proximity probes measuring piston rod position in the packing area.

9. Worked Examples

Example 1: Pipeline Centrifugal Compressor

Given: Centrifugal compressor, 2000 HP, 7200 RPM Shaft vibration measured: 1.5 mils pk-pk at DE bearing Bearing type: Sleeve (tilting pad) Step 1: Convert to velocity f = 7200/60 = 120 Hz v = π × 120 × 1.5 / 1000 = 0.565 in/s peak Step 2: API 617 check A_max = √(12000/7200) = 1.29 mils pk-pk 1.5 > 1.29 → EXCEEDS alert level Trip = 1.5 × 1.29 = 1.94 mils 1.5 < 1.94 → Below trip level Step 3: ISO 10816 check Power = 2000 HP = 1491 kW → Class IV (centrifugal, flexible) v_mm = 0.565 × 25.4 / √2 = 10.15 mm/s RMS Zone boundary: B/C = 7.1, C/D = 18.0 10.15 > 7.1 → Zone C (Unsatisfactory) Result: • API 617: FAIL (exceeds alert, below trip) • ISO 10816: Zone C - Unsatisfactory • Action: Investigate root cause. Check balance, alignment, and bearing condition. Plan corrective maintenance within 30 days.

Example 2: Reciprocating Compressor

Given: Reciprocating compressor, 800 HP, 900 RPM Bearing housing velocity: 0.35 in/s peak Rolling element bearings Step 1: API 618 check Limit = 0.5 in/s peak (unfiltered) 0.35 < 0.5 → PASS % of allowable = 0.35/0.5 = 70% Step 2: ISO 10816 check Power = 800 HP = 597 kW → Class III (large, rigid) v_mm = 0.35 × 25.4 / √2 = 6.29 mm/s RMS Zone: B/C = 4.5, so 6.29 > 4.5 → Zone C Note: For recip compressors, API 618 is the governing standard. ISO 10816 zones were designed for rotating machines and may be overly restrictive for reciprocating equipment. Result: • API 618: PASS at 70% of allowable • Action: Acceptable for continued operation per API 618. Monitor trend for any upward changes.

Example 3: Balance Quality

Given: Gas turbine rotor: 500 lbs, 10,000 RPM Required grade: G2.5 (per ISO 1940) Allowable residual unbalance: U_perm = (2.5 × 500 × 16) / 10,000 = 2.0 oz-in For 2-plane balance: U_per_plane = 2.0 / 2 = 1.0 oz-in per plane Check: If rotor has 1.5 oz-in total measured unbalance on the balance machine, it DOES NOT meet G2.5. Correction is needed to bring it below 2.0 oz-in total.

Example 4: Bearing Defect Frequencies

Given: SKF 6310 bearing, 10 balls, B_d = 0.625 in, P_d = 2.854 in, α = 0°, shaft at 1800 RPM Calculations: f = 1800/60 = 30 Hz cos(0) = 1.0 B_d/P_d = 0.625/2.854 = 0.2190 BPFO = (10/2) × 30 × (1 - 0.2190) = 117.1 Hz BPFI = (10/2) × 30 × (1 + 0.2190) = 182.9 Hz BSF = (2.854/(2×0.625)) × 30 × (1 - 0.2190²) = 65.6 Hz FTF = (1/2) × 30 × (1 - 0.2190) = 11.71 Hz If a peak appears at 117 Hz with sidebands at ±30 Hz (1× RPM), suspect outer race defect.