Self-Excited Vibration: Internal Hysteresis in Turbomachinery Rotor Assembly - Part I

1. Introduction to Self-Excited Vibrations

Self-excited vibrations are oscillations that are maintained or amplified by energy drawn from the mean flow of the system. Unlike forced vibrations, which are driven by external periodic forces, self-excited vibrations result from feedback mechanisms within the system. These vibrations can lead to significant operational problems, including noise, wear, and even catastrophic failure.

2. Understanding Turbomachinery Rotor Assemblies

Turbomachinery refers to machines that transfer energy between a rotor and a fluid, including both turbines and compressors. The rotor assembly in these machines typically comprises a shaft, blades, disks, and sometimes additional components like seals and bearings. The primary function of the rotor is to convert kinetic energy from the fluid into mechanical energy or vice versa.

3. Internal Hysteresis in Materials

Hysteresis refers to the phenomenon where the response of a material depends on its history of loading and unloading. In the context of turbomachinery, internal hysteresis occurs due to the energy dissipation within the material of the rotor components as they undergo cyclic loading and unloading. This energy dissipation is a result of internal friction and other microstructural mechanisms within the material.

4. Mechanism of Self-Excited Vibration Due to Internal Hysteresis

Internal hysteresis can lead to self-excited vibrations in the following manner:

• Energy Dissipation and Storage: As the rotor rotates, the materials in the rotor undergo cyclic stresses. Due to internal hysteresis, some of the energy from these stresses is not entirely dissipated as heat but stored and released in a cyclic manner.
• Phase Lag: The internal hysteresis causes a phase lag between the applied stress and the resulting strain. This phase lag can lead to a situation where the stored energy is released in a way that reinforces the vibration of the rotor.
• Feedback Mechanism: The cyclic release of stored energy can act as a feedback mechanism, continuously feeding energy into the vibrational mode of the rotor, sustaining or amplifying the vibrations.

5. Factors Influencing Internal Hysteresis

Several factors influence the extent of internal hysteresis in turbomachinery rotors:

• Material Properties: Different materials exhibit different hysteresis characteristics. Metals, composites, and alloys used in rotor construction have unique internal friction properties.
• Temperature: Operating temperatures can affect the material properties, increasing or decreasing internal hysteresis. For instance, higher temperatures might increase the internal friction in metals.
• Cyclic Loading: The magnitude and frequency of cyclic loading impact the amount of energy dissipated and stored. High cyclic loads often increase hysteresis effects.
• Microstructural Features: Grain boundaries, dislocations, and other microstructural features within the material can affect internal hysteresis.

6. Impact of Self-Excited Vibration in Turbomachinery

Self-excited vibrations due to internal hysteresis can have several detrimental effects:

• Increased Wear and Fatigue: Continuous vibrations can lead to increased wear and fatigue of rotor components, reducing their lifespan and leading to unexpected failures.
• Noise: Vibrations can generate unwanted noise, which can be problematic in both industrial and residential settings.
• Operational Instability: Severe vibrations can cause operational instability, leading to inefficient performance or even damage to the machinery.
• Safety Risks: In extreme cases, self-excited vibrations can lead to catastrophic failures, posing significant safety risks.

7. Mitigating Self-Excited Vibrations

To mitigate self-excited vibrations caused by internal hysteresis, several strategies can be employed:

• Material Selection: Choosing materials with lower hysteresis characteristics can help reduce the potential for self-excited vibrations.
• Damping Mechanisms: Incorporating damping mechanisms, such as viscoelastic materials or tuned mass dampers, can help absorb and dissipate vibrational energy.
• Design Optimization: Optimizing the design of rotor components to minimize stress concentrations and cyclic loading can reduce the impact of internal hysteresis.
• Operational Controls: Implementing operational controls, such as varying the speed or load conditions, can help avoid resonance conditions that might exacerbate self-excited vibrations.
• Regular Maintenance: Regular inspection and maintenance can help identify and address early signs of wear and fatigue, preventing the development of severe self-excited vibrations.

8. Conclusion

Self-excited vibrations due to internal hysteresis in turbomachinery rotor assemblies present a complex challenge that requires a deep understanding of material properties, design principles, and operational conditions. By carefully considering these factors and employing appropriate mitigation strategies, it is possible to minimize the impact of these vibrations, ensuring the safe and efficient operation of turbomachinery.

Understanding and controlling self-excited vibrations not only enhance the reliability and longevity of the machinery but also contribute to overall safety and performance efficiency.

References

• Sinha, J. K., & Friswell, M. I. (2001). "The Influence of Internal Damping on the Vibration of Rotating Machines." Vibration Analysis. Discusses the role of internal damping and hysteresis in rotor vibrations.
• "Understanding Rotor Dynamics and Vibration in Turbomachinery" (2018). Bentley Nevada Technical Review. A comprehensive review of rotor dynamics and vibration issues in turbomachinery.
• Rao, S. S. (2011). Mechanical Vibrations (5th ed.). Prentice Hall. This book covers fundamental concepts of vibrations, including self-excited vibrations and their mechanisms.
• Thomson, W. T., & Dahleh, M. D. (1998). Theory of Vibration with Applications (5th ed.). Prentice Hall. Provides insights into the theory of vibrations, including internal hysteresis.
• Blevins, R. D. (2016). Formulas for Natural Frequency and Mode Shape. John Wiley & Sons. Contains useful formulas and explanations for vibration analysis in mechanical systems.