Self-Excited Vibration: Internal Hysteresis in Turbo machinery Rotor Assembly - Part II

1. Differentiating Between Hysteresis and Normal Forced-Induced Vibrations

Understanding the differences between hysteresis-induced vibrations and normal forced-induced vibrations is crucial for diagnosing and mitigating issues in turbo machinery.

a. Nature of Excitation

Hysteresis-Induced Vibrations:

• Self-Excited: These vibrations are self-excited, meaning they arise from the internal properties of the material and the feedback mechanisms within the system.
• Internal Energy Dissipation: The vibrations are due to the internal energy dissipation and storage within the material of the rotor components, often characterized by internal friction or material damping.

Forced-Induced Vibrations:

• External Excitation: These vibrations are driven by external periodic forces or disturbances, such as unbalanced rotor forces, aerodynamic forces, or mechanical impacts.
• Harmonic Excitation: Typically, forced vibrations follow the frequency of the external force applied to the system.

b. Frequency Characteristics

Hysteresis-Induced Vibrations:

• Nonlinear Frequency Response: The frequency response can be nonlinear due to the complex nature of hysteresis. The response might not be harmonically related to any driving frequency.
• Multiple Frequencies: These vibrations can manifest at multiple frequencies or as a spectrum, depending on the internal dynamics of the system.

Forced-Induced Vibrations:

• Discrete Frequencies: The system typically vibrates at discrete frequencies corresponding to the external excitation frequencies.
• Resonance Phenomena: Significant amplification of vibrations can occur at the system's natural frequencies when they coincide with the excitation frequencies.

c. Energy Dynamics

Hysteresis-Induced Vibrations:

• Energy Feedback: Energy is fed back into the system from the hysteresis effect, which can sustain or amplify the vibrations.
• Phase Lag: There is a characteristic phase lag between stress and strain due to internal hysteresis, which contributes to the energy feedback mechanism.

Forced-Induced Vibrations:

• Energy Input from External Sources: The system receives energy directly from an external source. The amplitude of vibration depends on the magnitude of the external force.
• Direct Response: The system's response is directly related to the external force's phase and magnitude.

d. Diagnostic Feature

Hysteresis-Induced Vibrations:

• Broad Frequency Spectrum: The vibration spectrum might be broad due to the nonlinear nature of hysteresis.
• Damping Characteristics: Changes in damping characteristics can be observed, which are indicative of material internal friction.

Forced-Induced Vibrations:

• Narrow Frequency Peaks: Clear peaks in the frequency spectrum at the excitation frequencies.
• Harmonic Analysis: Harmonic components corresponding to the excitation force can be detected.

2. Techniques Used to Diagnose Hysteresis Vibration in Turbomachinery

Diagnosing hysteresis vibrations requires a combination of theoretical analysis, experimental techniques, and advanced diagnostics tools. Here are the detailed methodologies:

a. Modal Analysis

Purpose: To identify the natural frequencies, mode shapes, and damping characteristics of the rotor system.

Procedure:

• Excite the rotor system using known input forces (e.g., impact hammer, shaker).
• Measure the response using accelerometers, laser vibrometers, or other sensors.
• Use software to analyze the frequency response functions (FRFs) and extract modal parameters.

Indicators of Hysteresis:

• Nonlinear damping characteristics.
• Variations in natural frequencies with amplitude changes.

b. Frequency Response Analysis

Purpose: To understand the frequency response of the rotor system under operational conditions.

Procedure:

• Apply a range of frequencies to the system using a controlled input.
• Record the output vibration signals.
• Analyze the frequency response and look for nonlinear characteristics or broad frequency bands.

Indicators of Hysteresis:

• Broadening of frequency response peaks.
• Nonlinear amplitude response

c. Time-Domain Analysis

Purpose: To capture transient behaviors and nonlinearities in the vibration signals.

Procedure:

• Measure the time-domain response of the rotor system using high-resolution data acquisition systems.
• Analyze the time-domain signals for any irregularities or phase lags.

Indicators of Hysteresis:

• Phase lag between force and displacement.
• Amplitude-dependent damping effect

d. Hysteresis Loop Analysis

Purpose: To directly measure the hysteresis behavior of the rotor material.

Procedure:

• Perform cyclic loading and unloading tests on the rotor material.
• Plot the stress-strain or force-displacement curves to form hysteresis loops.
• Calculate the energy dissipation from the area within the loops.

Indicators of Hysteresis:

• Shape and size of hysteresis loops.
• Energy dissipation per cycle.

e. Advanced Signal Processing Techniques

Purpose: To extract detailed information from vibration signals using sophisticated algorithms.

Techniques:

• Wavelet Transform: Provides a time-frequency representation of the signal, useful for identifying transient features and nonlinearities.
• Hilbert Transform: Helps analyze the envelope of the signal, which can indicate amplitude modulation due to hysteresis.
• Bispectral Analysis: Detects quadratic phase coupling, which is indicative of nonlinear interactions.

Indicators of Hysteresis:

• Nonlinear features in time-frequency representations.
• Amplitude modulation patterns.

f. Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA)

Purpose: To identify modal parameters under operational conditions without requiring controlled excitation

Procedure:

• EMA: Conduct tests using controlled excitation sources to identify modal parameters.
• OMA: Use ambient or operational forces (e.g., flow-induced forces) to analyze the system's response.

Indicators of Hysteresis:

• Changes in modal damping with varying operational conditions.
• Nonlinear modal interactions.

g. Computational Simulations and Modeling

Purpose: To simulate the rotor system and predict hysteresis-induced vibrations.

Techniques:

• Finite Element Analysis (FEA): Model the rotor components and simulate their dynamic behavior, incorporating material hysteresis models.
• Multi-Body Dynamics (MBD): Simulate the entire rotor system, considering interactions between components.

Indicators of Hysteresis:

• Nonlinear dynamic response in simulations.
• Discrepancies between simulated and experimental damping characteristics.

h. Condition Monitoring and Diagnostics Systems

Purpose: To continuously monitor the rotor system and detect early signs of hysteresis-induced vibrations.

Techniques:

• Vibration Monitoring Systems: Use accelerometers and other sensors to capture real-time vibration data.
• Data Analysis Software: Analyze trends and patterns in the vibration data to detect anomalies.

Indicators of Hysteresis:

• Increasing trends in vibration amplitude without corresponding changes in operational conditions.
• Changes in damping characteristics over time.

3. Conclusion

Diagnosing self-excited vibrations due to internal hysteresis in turbomachinery rotor assemblies requires a multifaceted approach, combining theoretical models, experimental techniques, advanced signal processing, and continuous monitoring. By differentiating between hysteresis-induced and forced-induced vibrations, and employing a range of diagnostic techniques, engineers can effectively identify and mitigate these vibrations, ensuring the reliability and performance of turbomachinery.