Alignment, Balancing, and Vibration Analysis

Shaft Alignment, Balancing, and Vibration Analysis

Chapter Introduction

This chapter covers three technical areas that are closely related in the practice of the industrial mechanic (millwright) trade: shaft alignment, rotor balancing, and vibration analysis. These skills are essential for ensuring the reliability, service life, and safety of rotating machinery. The Red Seal exam requires mastery of the principles, procedures, and calculations associated with these techniques. You must understand not only how to perform these tasks, but also why they are necessary and how to interpret the results.

Shaft Alignment

Definitions and Fundamental Principles

Alignment is the operation of making the rotational axes of two (or more) coupled shafts collinear. Misalignment is the leading cause of premature failure of couplings, bearings, and seals.

Two types of alignment defects exist:

Parallel (radial) misalignment: the axes of the two shafts are parallel but offset by a distance Δ (delta). This defect is measured in millimetres (mm) or thousandths of an inch (mils).

Angular misalignment: the axes of the two shafts form an angle Ω (omega) between them. This defect is measured in mm/m (millimetres per metre) or mils/inch.

In practice, most misalignments are combined: parallel and angular simultaneously.

Alignment Measurement Methods

Straight Edge and Feeler Gauge Method (Simple Method)

This method is used for rough alignment. A straight edge is placed across both coupling halves to check parallelism, and feeler gauges are used to check the angular gap. This method is not sufficient for high-speed or high-precision machinery.

Dial Indicator Method

This is the most common method for precision alignment. Two dial indicators are mounted on a bracket attached to one coupling half, with the indicator stems bearing against the other coupling half.

Radial indicator: measures radial (parallel) displacement.

Axial indicator: measures axial (angular) displacement.

Standard procedure (two-indicator method):

21.Attach the bracket with the two indicators to the coupling half of the movable machine (usually the motor).

22.Set the indicators to zero at the 12 o'clock position.

23.Rotate the shaft in 90° increments (3 o'clock, 6 o'clock, 9 o'clock positions) and record the readings.

24.Return to the 12 o'clock position to verify return to zero (if not, repeat the measurement).

25.Calculate the necessary corrections.

Calculation formulas (two-indicator method):

For the vertical plane (side view):

Parallel misalignment at the coupling plane: Δ = (bottom reading - top reading) / 2

Angular misalignment: Ω = (bottom axial reading - top axial reading) / diameter of the measurement circle

To correct, you use the similar triangles rule to calculate the shims to add or remove under the feet of the movable machine.

Example of shim calculation:

If the measured angular misalignment is 0.20 mm/m and the distance between the front foot and the coupling centre is 200 mm, the correction at the front foot is:

Correction = 0.20 mm/m × 0.2 m = 0.04 mm

Laser Method (Laser Alignment)

This is the most accurate and fastest method. A laser transmitter is mounted on one shaft and a receiver (detector) on the other. The system automatically calculates the necessary corrections. The Red Seal exam requires you to know the basic principles, but the calculations are performed by the instrument.

Alignment Tolerances

Tolerances depend on rotational speed. The following table gives reference values according to ISO 1940-1 (balancing) and common industry practices (for alignment, the reference standard is often API 686 or manufacturer recommendations).

Rotational Speed (RPM)	Max Parallel Misalignment (mm)	Max Angular Misalignment (mm/m)
< 1000	0.10	0.10
1000 – 2000	0.08	0.08
2000 – 4000	0.05	0.05
> 4000	0.03	0.03

Important: These values are guidelines. Always consult the manufacturer's specifications for the machine and coupling.

Effects of Misalignment

Increased radial forces on bearings.

Abnormal heating of bearings and couplings.

Premature wear of seals.

Increased energy consumption.

Excessive vibration.

Possible catastrophic failure.

Thermal Expansion and Cold Alignment

Machines expand when they heat up during operation. An alignment performed cold must therefore compensate for this expansion. This is referred to as cold alignment with thermal correction. The manufacturer typically provides compensation values (in mm) for each foot. These values are added to or subtracted from the readings to achieve correct alignment at operating temperature.

Rotor Balancing

Balancing Principles

Balancing is the operation of distributing the mass of a rotor so that its rotational axis coincides with its principal inertia axis. An unbalanced rotor generates centrifugal forces that cause vibration, wear, and noise.

The centrifugal force generated by an unbalance is given by:

F = m × r × Ω²

Where:

F = centrifugal force (N)

m = unbalance mass (kg)

r = radius of the mass (m)

Ω = angular velocity (rad/s) = 2π × N / 60 (N in RPM)

Example: A mass of 10 g at a radius of 100 mm on a rotor turning at 3600 RPM generates:

Ω = 2π × 3600 / 60 = 377 rad/s

F = 0.01 × 0.1 × 377² = 142 N

This force of 142 N applied at every revolution can quickly destroy bearings.

Types of Unbalance

Type	Description	Effect
Static	The centre of gravity is displaced from the rotational axis. Detectable at standstill (the rotor rotates to place the heavy spot at the bottom).	Significant radial vibration.
Dynamic (couple)	Two opposing unbalance masses in two different planes. Not detectable at standstill.	Radial and axial vibration.
Combined	A mixture of static and dynamic unbalance.	Complex vibration.

Balancing Quality Grades (ISO 1940-1)

The ISO 1940-1 standard defines balancing quality grades. The key parameter is the allowable residual unbalance per unit mass of the rotor, denoted e (residual eccentricity) in mm/s.

Grade	Rotor Type	e (mm/s)
G 4000	Rigid drive shafts (marine, automotive)	4000
G 1000	Drive shafts with intermediate shafts	1000
G 250	Electric motor rotors, turbines, compressors	250
G 40	Pump rotors, fans, machine tools	40
G 16	Small electric motor rotors, turbines	16
G 6.3	Electric motor rotors, alternators, steam turbines	6.3
G 2.5	Gas turbine rotors, centrifugal compressors, precision machinery	2.5
G 1	Machine tool spindle rotors, gyroscopes	1
G 0.4	High-precision rotors (grinders, centrifuges)	0.4

Calculation of allowable unbalance:

The allowable residual unbalance U (in g·mm) is:

U = e × M / Ω

Where:

e = allowable residual eccentricity (mm/s) according to the grade

M = rotor mass (kg)

Ω = angular velocity (rad/s)

Example: A 50 kg rotor turning at 3000 RPM, grade G 6.3.

Ω = 2π × 3000 / 60 = 314 rad/s

U = 6.3 × 50 / 314 = 1.00 g·mm

If the correction radius is 100 mm, the allowable unbalance mass is:

m = U / r = 1.00 / 100 = 0.01 g = 10 mg

Balancing Methods

Static Balancing

The rotor is placed on perfectly horizontal knives or rollers. The lowest position (heavy spot) is marked. Mass is added on the opposite side or removed from the heavy side. This is repeated until the rotor remains in equilibrium in any position.

Dynamic Balancing (on a Balancing Machine)

The rotor is mounted on a balancing machine that measures vibration in two correction planes. The machine calculates the correction mass and position for each plane. This method is used for long or high-speed rotors.

Field Balancing (in Place)

A vibration analyzer with a phase sensor (laser tachometer or strobe light) is used. The procedure is as follows:

88.Measure the initial vibration (amplitude and phase).

89.Add a known trial mass at a known position.

90.Measure the new vibration.

91.Calculate the correction mass and position using the vector method (force triangle) or trigonometric calculation.

Calculation formula (triangle method):

Let V₀ = initial vibration vector, V₁ = vibration vector with trial mass. The correction vector is:

V_c = V₁ - V₀

The correction mass is:

m_c = m_trial × |V₀| / |V_c|

The correction position is offset by the angle between V₀ and V_c, in the direction of rotation.

Correction Procedures

Adding mass: welding, bolting, riveting of plates or weights.

Removing mass: drilling, milling, grinding.

The correction must be made in the correction planes provided for this purpose on the rotor.

Vibration Analysis

Basic Principles

Vibration analysis is a predictive maintenance technique that involves measuring and interpreting the vibrations of a machine to diagnose its health condition. Vibrations are mechanical oscillations around an equilibrium position.

The fundamental parameters are:

Amplitude: displacement (mm), velocity (mm/s), or acceleration (m/s²).

Frequency: number of oscillations per second (Hz) or per minute (CPM - cycles per minute).

Phase: angular position of the vibration relative to a reference (degrees).

Measurement Transducers

Type	Measurement	Typical Application
Accelerometer	Acceleration	High-speed machinery, bearings, gears
Velocimeter (geophone)	Velocity	Medium-speed machinery, balancing
Proximity probe (eddy current)	Displacement	Machines with sleeve bearings, bare shafts

Measurement Units and Standards

The ISO 10816 standard (evaluation of machine vibration by measurements on non-rotating parts) defines vibration severity zones.

Zone	Machine Condition	RMS Vibration Velocity (mm/s)
A	New machine (good condition)	< 1.8
B	Acceptable for continuous operation	1.8 – 4.5
C	Tolerable for limited operation	4.5 – 11.2
D	Damaging (shutdown required)	> 11.2

Note: These values are for medium-sized machines (15 kW to 300 kW) operating at rated speed.

Frequency Analysis (Vibration Spectrum)

The Fourier transform (FFT) decomposes the vibration signal into its frequency components. Each machine fault generates vibrations at characteristic frequencies.

Characteristic Fault Frequencies

Fault	Characteristic Frequency
Unbalance	1× rotational speed (1× RPM)
Misalignment	1×, 2×, 3× RPM (often 2× predominant)
Mechanical looseness	1×, 2×, sometimes 3× RPM, multiple harmonics
Defective bearing	Ball pass frequencies (BPFO, BPFI, BSF, FTF)
Worn gear	Gear mesh frequency (GMF = number of teeth × RPM) and its harmonics
Cavitation	Random high-frequency noise (broadband)
Resonance	Natural frequency of the structure (independent of speed)
Oil whirl	0.4× to 0.5× RPM (sleeve bearings)

Formulas for Bearings

For a ball bearing with Z rolling elements, ball diameter d, pitch diameter D, contact angle α, and rotational speed N (RPM):

BPFO (Ball Pass Frequency Outer): frequency of ball passage over the outer race

BPFO = (Z × N / 2) × (1 - (d/D) × cos α)

BPFI (Ball Pass Frequency Inner): frequency of ball passage over the inner race

BPFI = (Z × N / 2) × (1 + (d/D) × cos α)

BSF (Ball Spin Frequency): rotational frequency of the balls

BSF = (N × D / (2 × d)) × (1 - (d/D)² × cos² α)

FTF (Fundamental Train Frequency): rotational frequency of the cage

FTF = (N / 2) × (1 - (d/D) × cos α)

Example: Bearing 6205 (Z = 9 balls, d = 7.94 mm, D = 39 mm, α = 0°), N = 1800 RPM.

BPFO = (9 × 1800 / 2) × (1 - 7.94/39) = 8100 × 0.796 = 6448 CPM ≈ 107 Hz

BPFI = (9 × 1800 / 2) × (1 + 7.94/39) = 8100 × 1.204 = 9752 CPM ≈ 163 Hz

Overall Vibration Measurements (Trending)

Overall vibration velocity (mm/s RMS) is measured on each bearing in three directions: horizontal (H), vertical (V), and axial (A). The trend is plotted over time to detect progressive degradation.

Alert rule: An increase of 25% in overall vibration compared to the reference value justifies an investigation. An increase of 100% (doubling) justifies a planned shutdown.

Diagnosis of Common Faults

Unbalance

Spectrum: dominant peak at 1× RPM.

Direction: high radial vibration (H and V), low axial.

Phase: stable, 90° offset between H and V.

Cause: mass not uniformly distributed, product buildup, erosion.

Misalignment

Spectrum: peaks at 1× and 2× RPM (sometimes 3×).

Direction: high axial vibration (often 50% or more of radial).

Phase: unstable, 180° offset between the two sides of the coupling.

Cause: incorrect alignment, uncompensated thermal expansion.

Defective Bearing

Spectrum: peaks at BPFO, BPFI, BSF, FTF frequencies and their harmonics.

Direction: high-frequency vibration (acceleration).

Phase: random.

Cause: wear, fatigue, lack of lubrication, contamination.

Mechanical Looseness

Spectrum: peaks at 1×, 2×, 3× RPM with numerous harmonics (up to 10×).

Direction: radial, often predominantly vertical.

Phase: unstable, non-reproducible.

Cause: loose bolts, clearance in bearings, clearance in coupling.

Envelope Analysis (Accelerometry)

To detect bearing faults at an early stage, envelope analysis (envelope spectrum) is used. This technique filters out low frequencies and demodulates the high-frequency signal to reveal the periodic impacts of bearing faults.

Procedures and Best Practices

Complete Alignment Procedure

162.Preparation: Verify that foundations are clean, bolts are tight, and machine feet are in contact with the base.

163.Soft foot check: Loosen one bolt at a time and measure the dial indicator displacement. Soft foot is present if the displacement exceeds 0.05 mm.

164.Rough alignment: Use the straight edge and feeler gauges for an initial alignment.

165.Precision alignment: Use dial indicators or laser.

166.Correction: Add or remove shims under the feet. Use stainless steel shims, full width, with a minimum number of shims (maximum 4).

167.Final verification: Repeat measurements to confirm alignment is within tolerances.

168.Bolt tightening: Tighten in a cross pattern, progressively, while verifying that the alignment does not change.

Field Balancing Procedure

170.Initial measurement: Measure vibration and phase at operating speed.

171.Correction plane selection: Identify the available correction plane(s).

172.Trial mass: Choose a trial mass (approximately 10% of the rotor mass divided by the radius, or based on experience).

173.Second measurement: Mount the trial mass at a known position (e.g., at 0°), measure again.

174.Calculation: Use the vector method to calculate the correction mass and position.

175.Correction: Add or remove the calculated mass.

176.Verification: Measure again to confirm that vibration is within acceptable limits.

Vibration Analysis: Diagnostic Procedure

178.Data collection: Measure overall vibration (H, V, A) on each bearing.

179.Spectral analysis: Acquire an FFT spectrum at each measurement point.

180.Frequency identification: Compare spectrum peaks to calculated characteristic frequencies (1× RPM, BPFO, GMF, etc.).

181.Phase analysis: Measure phase to confirm the diagnosis.

182.Trending: Compare with previous measurements.

183.Report: Document the results and recommendations.

Applicable Standards and Codes

Standard	Title	Application
ISO 1940-1	Mechanical vibration — Balance quality requirements for rotors in a constant (rigid) state	Rotor balancing
ISO 10816	Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts	Overall vibration measurements
ISO 7919	Mechanical vibration — Evaluation of machine vibration by measurements on rotating shafts	Proximity probes
CSA B149.1	Natural gas and propane installation code	Machinery in classified areas (where applicable)
Canadian Electrical Code, Part I, Chapter V	Rules for electrical installations in classified areas	Electrical equipment in hazardous locations (Rule 8-200 for motors)

Important note: The Canadian Electrical Code, Part I, Chapter V (Rule 8-200) requires that electric motors installed in classified areas be certified for the intended use. When performing alignment or balancing in these areas, you must ensure that the tools used (laser, analyzer) are certified for use in classified areas (intrinsically safe certification).

Common Pitfalls to Avoid

190.Forgetting thermal expansion: A perfect cold alignment can become a misalignment when hot. Always apply the manufacturer's thermal corrections.

191.Ignoring soft foot: Soft foot invalidates all alignment measurements. Always check and correct soft foot before alignment.

192.Using poor-quality shims: Rusted, deformed, or too many shims (more than 4) compromise machine stability.

193.Confusing units: Do not confuse mm/m (angular slope) and mm (parallel displacement). Check the units on the dial indicators (mm or mils).

194.Forgetting to verify return to zero: If the indicator does not return to zero after a full rotation, the measurements are invalid.

195.Neglecting phase in balancing: Balancing is not just about amplitude. Phase is essential for determining the position of the correction mass.

196.Using the wrong balancing grade: Choosing a grade that is too strict (G 0.4 instead of G 6.3) makes balancing impossible or unnecessarily expensive.

197.Confusing BPFO and BPFI: BPFO (outer race) is generally lower than BPFI (inner race). An inversion leads to a wrong diagnosis.

198.Forgetting harmonics: A peak at 2× RPM is not always misalignment. Check the direction (axial vs. radial) and phase.

199.Working in a classified area without certified tools: Using a non-certified laser or analyzer in a classified area can cause an explosion.

200.Not documenting measurements: Trends are essential in vibration analysis. Without history, diagnosis is difficult.

201.Incorrect bolt tightening: Tighten bolts in a cross pattern and progressively. Asymmetric tightening distorts the machine and affects alignment.

Summary

Alignment: Making rotational axes colinear. Two types of defects: parallel and angular. Methods: straight edge, dial indicators, laser. Tolerances depend on speed. Always compensate for thermal expansion.

Balancing: Distributing mass so that the rotational axis coincides with the inertia axis. Types: static, dynamic, combined. ISO 1940-1 grades (G 0.4 to G 4000). Methods: static, balancing machine, field balancing with analyzer.

Vibration analysis: Measuring and interpreting vibrations. Parameters: amplitude, frequency, phase. Transducers: accelerometer, velocimeter, proximity probe. ISO 10816 standard for severity zones. Characteristic frequencies: 1× RPM (unbalance), 2× RPM (alignment), BPFO/BPFI (bearings), GMF (gears).

Key formulas: F = m × r × Ω², U = e × M / Ω, BPFO = (Z × N / 2) × (1 - d/D).

Standards: ISO 1940-1, ISO 10816, CSA B149.1, Canadian Electrical Code Part I Chapter V (Rule 8-200 for classified areas).

Red Seal Exam Tips

Memorize the formulas: F = m × r × Ω² and U = e × M / Ω are frequent questions.

Know the balancing grades: G 6.3 and G 2.5 are the most common in industry.

Understand bearing frequencies: BPFO < BPFI always (for α = 0°).

Know how to interpret a spectrum: A peak at 1× RPM = unbalance, at 2× RPM = alignment, multiple harmonics = looseness.

Review the ISO 10816 zones: The limit values (1.8 / 4.5 / 11.2 mm/s) should be memorized.

Practice alignment calculations: The similar triangles rule for shims is a classic.

Don't forget safety: In classified areas, use certified (intrinsically safe) tools.

This chapter covers the essential knowledge required for the Red Seal exam in alignment, balancing, and vibration analysis. Regular practice with calculations and familiarity with the standards are essential for success.