The Thermal Unbalance Effect Induced by a Journal Bearing in Rigid and Flexible Rotors: Experimental Analysis

This study experimentally analyzes the thermal unbalance effects induced by differential heating in journal bearings on both rigid and flexible rotors, revealing that while rigid rotors exhibit increased synchronous amplitudes with hysteresis, flexible rotors can experience instability and bearing contact depending on the rotor start-up time.

The Gist

The Big Picture: The "Hot Spot" Spiral

Imagine you have a spinning top (a rotor) resting on a cushion of oil (a journal bearing). Usually, this spins smoothly. But sometimes, a strange thing happens: the top starts to wobble more and more violently, not because something broke, but because it got unevenly hot.

This paper is about a phenomenon called the Morton Effect. It's a bit like a feedback loop where the wobble makes the top hot, and the heat makes the top wobble even more. The researchers wanted to see exactly how this happens and why sometimes it's harmless, while other times it causes a crash.

The Experiment: Two Different Tops

To test this, the scientists built a test rig with two different "tops" (rotors):

1. The Short, Stiff Rotor: Think of this like a solid, short wooden dowel. It's rigid and doesn't bend easily.
2. The Long, Flexible Rotor: Think of this like a long, thin fishing rod. It's much more flexible and can bend or bow.

Both were spun up to high speeds (about 7,000 revolutions per minute) and watched closely with cameras and temperature sensors.

What Happened with the Short Rotor? (The "Stable" Wobble)

When they spun the short, stiff rotor, something interesting happened:

• The Wobble Grew: As it spun, the vibration amplitude (how much it shook) slowly got bigger.
• The Heat: The side of the rotor touching the oil film got hotter than the other side. This created a "hot spot."
• The Result: Because one side was hotter, the metal expanded slightly, making the rotor bend a tiny bit. This bend made it wobble more, which created more heat, which made it bend more.
• The Outcome: However, the short rotor was stiff enough that it eventually stabilized. It found a new, slightly larger wobble size and stayed there. It was like a car that hits a bump, swerves a bit, but then the driver corrects the steering and drives straight again.

Key Finding: Even though the vibration grew, the short rotor didn't crash. It just settled into a "stable" but larger wobble.

What Happened with the Long Rotor? (The "Unstable" Crash)

The long, flexible rotor told a different story, and it depended entirely on how fast they started it up.

Scenario A: The Slow Start (The Safe Way)

• They spun the long rotor up slowly over 3 minutes (180 seconds).
• Result: Just like the short rotor, the wobble grew a bit, the heat built up, but then it stabilized. It found a safe rhythm.

Scenario B: The Fast Start (The Dangerous Way)

• They spun the long rotor up very quickly, in just 1 minute and 20 seconds (80 seconds).
• Result: Disaster. The wobble grew rapidly and uncontrollably.
• Why? Because the rotor was flexible (like a fishing rod), the sudden heat didn't have time to spread out evenly. Instead, it caused a sharp bend right near the heavy weight hanging off the end (the overhung disk).
• The Spiral: The vibration didn't just get bigger; it started spinning in a spiral pattern. The researchers saw the vibration vector (the direction of the shake) start to rotate with the spin, which is a sign of trouble.
• The Crash: The wobble got so big that the spinning shaft actually touched the bearing housing. This is like a car tire rubbing against the wheel well because the suspension collapsed.

The "Hot Spot" vs. The "High Spot"

To understand why this happens, the researchers tracked two specific points on the rotor:

1. The High Spot: The point on the rotor that is physically closest to the bearing (the point of maximum wobble).
2. The Hot Spot: The point on the rotor that is the hottest.

The Magic Rule: In a healthy machine, these two spots are far apart. But in the Morton Effect, the friction creates heat before the high spot.

• Imagine a runner (the rotor) running on a track. The "High Spot" is where they stumble. The "Hot Spot" is where they sweat the most.
• The paper found that the "Hot Spot" is always slightly ahead of the "High Spot." This lag causes the runner to stumble in a way that makes them sweat more, which makes them stumble even harder.

The "Start-Up" Analogy

The most important lesson from this paper is about patience.

Think of the flexible rotor like a wet towel hanging on a line.

• If you spin it up slowly, the water (heat) has time to drip down and spread out evenly. The towel spins smoothly.
• If you spin it up instantly, the water doesn't have time to move. It stays in one heavy clump, throwing the towel off balance, causing it to whip around violently and snap.

The researchers found that if you start the machine too fast, the heat gets "trapped" in one spot, causing a dangerous bend. If you start it slowly, the heat distributes, and the machine stays safe.

Conclusion

This study proves that thermal unbalance (wobbling caused by uneven heat) is a real and dangerous thing.

• Stiff machines can handle it; they just wobble a bit more.
• Flexible machines are dangerous if you start them too fast.
• The Solution: You have to be careful with your start-up procedure. Sometimes, slowing down the acceleration is the only way to prevent a catastrophic crash.

The paper ends by saying this is just the first part of the story; the next step is to build computer models to predict exactly when and where this will happen so engineers can design better, safer machines.

Technical Summary

1. Problem Statement

The paper addresses the Morton effect, a thermal unbalance phenomenon in rotor dynamics where heat generated in a lubricated journal bearing causes differential heating of the rotor shaft. This non-uniform temperature distribution creates a thermal bow (bending), which increases the mechanical unbalance, leading to growing synchronous vibrations.

• The Challenge: While the Morton effect is known to cause instability, it is difficult to predict and diagnose because it involves a coupling between rotordynamics and thermal transfer with vastly different time scales (rotation speed vs. heat diffusion).
• The Gap: Existing numerical tools lack validation due to a scarcity of high-quality experimental data from industrial settings. The paper aims to provide clear experimental evidence distinguishing between "stable" thermal responses (where vibrations increase but stabilize) and "unstable" responses (leading to contact or seizure), specifically comparing rigid and flexible rotor configurations.

2. Methodology

The authors conducted experiments on a custom-built test rig featuring two distinct rotor configurations supported by a ball bearing and a cylindrical journal bearing (Teflon-incrusted bronze, L/D ratio < 1, lubricated with ISO VG 32 oil).

• Test Rig Configuration:
  • Short (Rigid) Rotor: 430 mm long, 2.2 kg mass. Operating speed: 7 krpm (far from the first critical speed).
  • Long (Flexible) Rotor: 700 mm long, equipped with heavy overhung disks (10.4 kg) and a central disk. Operating speed: 6.6 krpm (close to the first flexible critical speed).
• Instrumentation:
  • Vibration: Inductive proximity probes (X and Y axes) at Drive End (DE) and Non-Drive End (NDE).
  • Temperature: 10 thermocouples in the bearing mid-plane and 5 thermocouples on the journal (via slip ring) to measure circumferential temperature distribution.
  • Phase Reference: Optical sensor for speed and phase.
• Experimental Procedure:
  • Tests were performed at constant speeds (7 krpm for short, 6.6 krpm for long).
  • Start-up/Coast-down: Varied start-up durations (180 s vs. 80 s) to test the influence of thermal transients.
  • Data Analysis: Synchronous amplitudes, phases, temperature differences ($\Delta T$), and the phase lag between the "hot spot" (max temperature) and "high spot" (min film thickness) were analyzed.

3. Key Contributions

• Differentiation of Rotor Stiffness: The study explicitly compares the Morton effect on a rigid rotor versus a flexible rotor, demonstrating that rotor flexibility and proximity to critical speeds significantly alter the instability threshold.
• Start-up Scenario Sensitivity: The paper provides experimental proof that the start-up time is a critical parameter. A faster start-up (80 s) on a flexible rotor triggered instability, whereas a slower start-up (180 s) resulted in a stable thermal response at the same operating speed.
• Phase Lag Evolution: The authors developed a rigorous methodology to calculate the phase lag between the hot spot and high spot, showing how this lag evolves from a stable state to zero (coincidence) as contact occurs, marking the transition from Morton to Newkirk effect.
• Hysteresis Verification: The use of run-up and coast-down tests clearly demonstrated hysteresis loops in vibration amplitude and temperature, confirming the thermal nature of the unbalance.

4. Key Results

A. Short (Rigid) Rotor at 7 krpm

• Behavior: Exhibited a stable thermal response.
• Vibrations: Synchronous amplitudes increased from ~14–19 µm to ~26–40 µm over 2 hours but eventually stabilized.
• Thermal Correlation: A strong linear correlation ($R^2 = 0.91$) was found between the journal temperature difference and vibration amplitude.
• Phase Lag: The phase lag between the hot spot and high spot decreased from 46° to 26° before stabilizing.
• Hysteresis: Pronounced hysteresis was observed during coast-down, confirming the thermal origin of the unbalance.

B. Long (Flexible) Rotor at 6.6 krpm

• Scenario 1: Slow Start-up (180 s):
  • Resulted in a stable response similar to the short rotor. Amplitudes increased and then asymptotically stabilized.
  • Vibration vectors rotated opposite to the rotation speed (negative phase shift).
• Scenario 2: Fast Start-up (80 s):
  • Triggered an unstable response. Amplitudes grew rapidly, requiring a coast-down after only 23 seconds to prevent contact.
  • Vector Rotation: The vibration vectors began rotating in the direction of the rotation speed (positive phase shift), indicating a shift in the thermal deformation mode.
  • Temperature: The journal temperature difference increased sharply (6°C to 12°C) correlating with vibration growth, while bearing temperatures became more homogeneous.
• Scenario 3: Contact Event:
  • When the rotor was held at speed long enough to induce contact, the phase lag between the hot spot and high spot dropped to zero.
  • This confirmed the transition from the Morton effect (lubricant shear heating) to the Newkirk effect (rubbing contact heating), where the hot spot and high spot coincide.

5. Significance and Conclusions

• Mechanism Confirmation: The experiments validate that the Morton effect is driven by the coupling of bearing shear heating and rotor thermal bending. The instability is not solely dependent on speed or unbalance but is highly sensitive to the thermal transient history (start-up time).
• Flexibility Factor: Flexible rotors operating near critical speeds are significantly more prone to thermal instability than rigid rotors. The overhung mass in the flexible rotor was identified as the primary source of the thermal bending moment causing instability.
• Diagnostic Indicators:
  • Hysteresis in amplitude vs. speed is a definitive signature of thermal unbalance.
  • Phase Lag Evolution: A decreasing phase lag between the hot spot and high spot, eventually reaching zero, signals the onset of contact.
  • Start-up Strategy: Slower start-ups allow the rotor to thermally equilibrate, potentially avoiding the instability threshold even at high speeds.
• Future Work: This experimental data serves as the foundation for Part 2 of the study, which will focus on theoretical predictions and stability analyses using full numerical simulations.

In summary, the paper provides critical experimental evidence that the Morton effect can be managed or triggered by operational strategies (like start-up time) and that the rotor's flexibility plays a decisive role in the severity of the instability.