Understanding Thermal Bow in Rotating Machinery

Devices

Portable balancer & Vibration analyzer Balanset-1A

Parts

Optical Sensor (Laser Tachometer)

Complete vibration diagnostics and balancing kit from Vibromera, including four vibration sensors with cables, a signal interface module, laser tachometer with magnetic stand, digital scale, USB cable, and a carrying case. The system is designed for field rotor balancing and condition monitoring on industrial equipment.

Devices

Dynamic balancer “Balanset-1A” OEM

Definition: What is Thermal Bow?

Thermal bow (also called hot bow, thermal bending, or temperature-induced shaft bow) is a temporary curvature that develops in a rotor shaft due to uneven temperature distribution around the shaft’s circumference. When one side of the shaft is hotter than the opposite side, thermal expansion causes the hot side to become longer, forcing the shaft to bend into a curved shape with the hot side on the convex (outer) side of the curve.

Unlike permanent shaft bow from mechanical damage, thermal bow is reversible—it disappears when the shaft returns to uniform temperature. However, thermal bow creates significant vibration during warm-up and cool-down periods and can cause permanent damage if severe or frequently repeated.

Physical Mechanism

Thermal Expansion Differential

The physics behind thermal bow is straightforward:

Metal expands when heated (coefficient of thermal expansion typically 10-15 µm/m/°C for steel)
If temperature is uniform around circumference, expansion is symmetric (shaft lengthens but stays straight)
If one side is hotter, that side expands more than the cool side
Differential expansion causes curvature
Bow magnitude proportional to temperature difference and shaft length

Typical Temperature Differences

Temperature difference of 10-20°C across diameter can create measurable bow
In large turbines, 30-50°C difference can produce severe vibration
Effect accumulates along shaft length—longer shafts more susceptible

Common Causes of Thermal Bow

1. Startup Conditions (Most Common)

Asymmetric Heating: Hot steam, gas, or process fluid contacts top of shaft while bottom remains cooler
Radiant Heating: Heat from hot casings or piping warming upper portion of shaft
Bearing Friction: One bearing running hotter than others heats local shaft section
Rapid Startup: Insufficient warm-up time allows thermal gradients to develop

2. Shutdown Conditions (Thermal Sag)

Hot Shutdown: Shaft stops rotating while still hot
Gravitational Sag: Heat rises, causing top of horizontal shaft to cool faster than bottom
Thermal Sag Bow: Bottom side stays hotter longer, shaft bows downward
Critical Period: First few hours after shutdown

3. Operational Causes

Rotor-Stator Rub: Friction from contact generates intense local heating
Uneven Cooling: Asymmetric cooling air flow or water spray
Solar Heating: Outdoor equipment with sun exposure on one side
Process Upsets: Sudden temperature changes in working fluid

Symptoms and Detection

Vibration Characteristics

Thermal bow produces distinctive vibration patterns:

Frequency: 1× running speed (synchronous vibration)
Timing: High during warm-up, decreases as thermal equilibrium reached
Phase Changes: Phase angle may shift as bow develops and resolves
Slow Roll Vibration: High vibration even at very low speeds (unlike unbalance)
Appearance: Similar to unbalance but temperature-dependent

Distinguishing Thermal Bow from Unbalance

Characteristic	Unbalance	Thermal Bow
Frequency	1× running speed	1× running speed
Temperature Sensitivity	Relatively stable	High during warm-up/cool-down
Slow Roll (50-200 RPM)	Very low amplitude	High amplitude
Phase vs. Temperature	Constant	Changes as bow develops
Persistence	Constant at all times	Temporary, resolves at thermal equilibrium
Response to Balancing	Vibration reduced	Minimal or no improvement

Diagnostic Tests

1. Slow Roll Vibration Test

Rotate shaft at 5-10% of operating speed
Measure vibration and run-out
High slow roll vibration indicates thermal or mechanical bow, not unbalance

2. Temperature Monitoring

Monitor shaft or bearing temperatures during startup
Measure temperature at multiple locations around bearing circumference
Correlate vibration changes with temperature gradients

3. Startup Vibration Trending

Plot vibration amplitude vs. time during warm-up
Thermal bow: high initially, decreases as equilibrium approached
Unbalance: increases with speed, independent of temperature

Prevention Strategies

Operational Procedures

1. Proper Warm-Up Procedures

Gradual Temperature Increase: Allow shaft to heat uniformly
Extended Warm-Up Time: Large turbines may require 2-4 hours
Temperature Monitoring: Track bearing and casing temperatures
Vibration Monitoring: Monitor during warm-up, delay speed increase if vibration high

2. Turning Gear Operation

For large turbines, operate turning gear (slow rotation, ~3-10 RPM) during warm-up and cool-down
Continuous rotation prevents thermal bow by distributing heat evenly
Industry standard for steam turbines > 50 MW
May operate turning gear for 8-24 hours during cool-down

3. Shutdown Procedures

Gradual Cooldown: Reduce load and temperature slowly before shutdown
Extended Turning Gear: Keep rotor rotating as it cools
Avoid Hot Shutdowns: Emergency stops leave shaft hot and prone to sag bow

Design Measures

Thermal Insulation: Insulate casings to maintain uniform temperature
Heating Jackets: External heaters for uniform pre-warming
Drainage: Prevent hot condensate accumulation on bottom of shaft
Ventilation: Ensure symmetric cooling air flow

Consequences of Thermal Bow

Immediate Effects

High Vibration: Can reach 5-10× normal levels during warm-up
Bearing Loading: Asymmetric bow increases bearing loads
Seal Rubs: Shaft deflection may cause contact with seals or stationary parts
Startup Delays: Must wait for vibration to decrease before increasing speed

Long-Term Damage

Bearing Wear: Repeated high vibration accelerates bearing deterioration
Seal Damage: Repeated rubs destroy seal components
Fatigue: Cyclic bending stresses during each startup contribute to fatigue
Permanent Set: Severe or repeated thermal bow can cause permanent plastic deformation

Correction and Mitigation

For Active Thermal Bow

Allow Time: Wait for thermal equilibrium before increasing speed
Slow Roll: Rotate slowly to distribute heat if possible
Do Not Attempt Balancing: Balancing cannot correct thermal bow and will be ineffective
Address Heat Source: Identify and eliminate asymmetric heating

For Thermal Sag Bow (After Shutdown)

Turning Gear: Keep rotor slowly rotating during cooldown
Extended Roll Time: May need 12-24 hours of turning gear operation
Temperature Monitoring: Continue until shaft temperature uniform
Delayed Restart: If bow has developed, wait for natural straightening before restart

Industry-Specific Considerations

Steam Turbines

Most susceptible to thermal bow due to high temperatures and massive rotors
Elaborate warm-up and cooldown procedures standard practice
Turning gear mandatory for units > 50 MW
May require 2-4 hours warm-up, 12-24 hours cooldown with turning gear

Gas Turbines

Faster thermal response due to smaller mass
Thermal bow during startup less common but still possible
Combustion-side heating can create asymmetries
Typically faster warm-up cycles than steam turbines

Large Electric Motors and Generators

Thermal bow from rotor winding heat or bearing friction
Outdoor installations subject to solar heating
May require pre-startup turning or heating

Monitoring and Alarming

Key Monitoring Parameters

Slow Roll Vibration: Measure at low speed before normal startup
Bearing Temperature Differential: Compare temperatures at top vs. bottom
Vibration vs. Temperature: Plot vibration amplitude vs. bearing temperature
Phase Angle: Track phase changes indicating bow development

Alarm Criteria

Slow roll vibration > 2× baseline triggers alarm
Temperature differential > 15-20°C indicates thermal imbalance
Rapid phase changes (> 30° in 10 minutes) suggest developing bow
Vibration increasing during warm-up rather than decreasing

Advanced Startup Strategies

Controlled Acceleration

Initial Slow Roll: Verify acceptable vibration at 100-200 RPM
Staged Acceleration: Increase to intermediate speeds (e.g., 30%, 50%, 70% of normal) with holds
Thermal Soak Periods: Maintain constant speed for 15-30 minutes at each stage
Vibration Verification: At each stage, confirm vibration decreasing before proceeding
Temperature Monitoring: Ensure thermal gradients reducing throughout process

Automated Startup Systems

Modern control systems can automate thermal bow management:

Programmable warm-up sequences
Automatic hold periods if vibration or temperature limits exceeded
Real-time calculation of thermal bow magnitude from vibration and temperature
Adaptive speed profiles based on measured conditions

Relationship to Other Phenomena

Thermal Bow vs. Permanent Bow

Thermal Bow: Temporary, disappears at thermal equilibrium
Permanent Bow: Plastic deformation, remains even when cold
Risk: Severe repeated thermal bow can eventually cause permanent set

Thermal Bow and Balancing

Attempting to balance during thermal bow is futile
Correction weights calculated for thermal bow condition will be wrong once equilibrium reached
Always allow thermal stabilization before balancing
Thermal bow can mask true unbalance condition

Prevention Best Practices

For New Installations

Design symmetric heating and cooling systems
Install turning gear for equipment > 100 kW or > 2 meter shaft length
Provide adequate drainage to prevent hot fluid accumulation
Insulate to minimize radiant heat transfer

For Existing Equipment

Develop and strictly follow written warm-up procedures
Train operators on thermal bow risks and symptoms
Install temperature monitoring at multiple locations
Use vibration trending during startups to identify thermal issues
Document historical data to optimize procedures

Maintenance Practices

Verify turning gear operation before every shutdown
Check bearing temperature sensors calibration
Inspect drainage systems for blockages
Verify insulation integrity
Check for and eliminate any sources of asymmetric heating

Thermal bow, while temporary and reversible, is a significant operational challenge for large rotating machinery. Understanding its causes, recognizing its symptoms, and implementing proper warm-up and cooldown procedures are essential for reliable operation of steam turbines, gas turbines, and other high-temperature rotating equipment.

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What is Thermal Bow? Temperature-Induced Shaft Bending

Published by admin on October 31, 2025 October 31, 2025