Philip Varney

Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results

An increase in the power-to-weight ratio demand on rotordynamic systems causes increased susceptibility to transverse fatigue cracking of the shaft. The ability to detect cracks at an early stage of progression is imperative for minimizing off-line repair time and cost. The vibration monitoring system initially proposed in Part I is employed herein, using the 2X harmonic response component of the rotor tilt as a signature indicating a transverse shaft crack. In addition, the analytic work presented in Part I is expanded to include a new notch crack model to better approximate experimental results. To effectively capture the 2X response, the crack model must include the local nature of the crack, the depth of the crack, and the stiffness asymmetry inducing the gravity-forced 2X harmonic response. The transfer matrix technique is well suited to incorporate these crack attributes due to its modular nature. Two transfer matrix models are proposed to predict the 2X harmonic response. The first model applies local crack flexibility coefficients determined using the strain energy release rate, while the second incorporates the crack as a rectangular notch to emulate a manufactured crack used in the experiments. Analytic results are compared to experimental measurement of the rotor tilt gleaned from an overhung rotor test rig originally designed to monitor seal face dynamics. The test rig is discussed, and experimental angular response orbits and 2X harmonic amplitudes of the rotor tilt are provided for shafts containing manufactured cracks of depths between 0% and 40%. Feasibility of simultaneous multiple-fault detection of transverse shaft cracks and seal face contact is discussed.

Rough Surface Contact of Curved Conformal Surfaces: An Application to Rotor–Stator Rub

Rotating machines and associated triboelements are ubiquitous in industrial society, playing a central role in power generation, transportation, and manufacturing. Unfortunately, these systems are susceptible to undesirable contact (i.e., rub) between the rotor and stator, which is both costly and dangerous. These adverse effects can be alleviated by properly applying accurate real-time diagnostics. The first step toward accurate diagnostics is developing rotor–stator rub models which appropriately emulate reality. Previous rotor–stator rub models disavow the contact physics by reducing the problem to a single esoteric linear contact stiffness occurring only at the point of maximum rotor radial deflection. Further, the contact stiffness is typically chosen arbitrarily, and as such provides no additional insight into the contacting surfaces. Here, a novel rotor–stator rub model is developed by treating the strongly conformal curved surfaces according to their actual nature: a collection of stochastically distributed asperities. Such an approach is advantageous in that it relies on real surface measurements to quantify the contact force rather than a heuristic choice of linear contact stiffness. Specifically, the elastoplastic Jackson–Green (JG) rough surface contact model is used to obtain the quasistatic contact force versus rotor radial deflection; differences and similarities in contact force between the linear elastic contact model (LECM) and JG model are discussed. Furthermore, the linear elastic model’s point contact assumption is assessed and found to be inaccurate for systems with small clearances. Finally, to aid in computational efficiency in future rotordynamic simulation, a simple exponential curve fit is proposed to approximate the JG force–displacement relationship. [DOI: 10.1115/1.4032786]

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

The goal of this work is to establish a condition monitoring regimen capable of diagnosing the depth and location of a transverse fatigue crack in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model used. The model should account for the depth of the crack and the localization of the crack along the shaft. Negating the influence of crack location on system response ignores a crucial component of real cracks. Two gaping crack models are presented; the first simulates a finite-width manufactured notch, while the second models an open fatigue crack. An overhung rotordynamic system is modeled, imitating an available rotordynamic test rig. Four degree-of-freedom equations of motion for both crack models are presented and discussed, along with corresponding transfer matrix techniques. Free and forced response analyses are performed, with emphasis placed on results applicable to condition monitoring. It is demonstrated that two identifiers are necessary to diagnose the crack parameters: the 2X resonance frequency and the magnitude of the 2X component of the rotor angular response at resonance. First, a contour plot of the 2X resonant shaft speed versus crack depth and location is generated. The magnitude of the 2X component of the rotor’s angular response along the desired contour is obtained, narrowing the possible pairs of crack location/depth to either one or two possibilities. Practical aspects of the diagnosis procedure are then discussed.Copyright

Impact Phenomena in a Noncontacting Mechanical Face Seal

Noncontacting mechanical face seals are often described as unpredictable machine elements, gaining this moniker from numerous instances of premature and unexpected failure. Machine faults such as misalignment or imbalance exacerbate seal vibration, leading to undesirable and unforeseen contact between the seal faces. A hypothesis explaining the high probability of failure in noncontacting mechanical face seals is this undesired seal face contact. However, research supporting this hypothesis is heuristic and experiential and lacks the rigor provided by robust simulation incorporating contact into the seal dynamics. Here, recent developments in modeling rotor–stator rub using rough surface contact are employed to simulate impact phenomena in a flexibly mounted stator (FMS) mechanical face seal designed to operate in a noncontacting regime. Specifically, the elastoplastic Jackson–Green rough surface contact model is used to quantify the contact forces using real and measurable surface and material parameters. This method also ensures that the seal face clearance remains positive, thus allowing one to calculate fluid-film forces. The seal equations of motion are simulated to indicate several modes of contacting operation, where contact is identified using waveforms, frequency spectra, and contact force calculations. Interestingly, and for the first time, certain parameters generating contact are shown to induce aperiodic mechanical face seal vibration, which is a useful machine vibration monitoring symptom. Also for the first time, this work analytically shows a mechanism where severe contact precipitates seal failure, which was previously known only through intuition and/or experience. The utility of seal face contact diagnostics is discussed along with directions for future work. [DOI: 10.1115/1.4033366]

Rotordynamic Analysis of Rotor–Stator Rub Using Rough Surface Contact

Undesirable rotor–stator rub is frequently observed in rotordynamic systems, and has been the subject of many investigations. Most of these studies employ a simple piecewise-smooth linear-elastic contact model (LECM), where the rotor switches between noncontacting and contacting operation once the clearance is exceeded (various complications have been incorporated, though the essential model premises endure). Though useful as a first step, the LECM relies on an arcane contact stiffness estimate, and therefore does not emulate the actual contacting surfaces. Consequentially, the LECM fails to elucidate how real surface parameters influence contact severity and surface durability. This work develops a novel model for rotor–stator rub which is commensurate with reality by treating the surfaces as a collection of stochastically distributed asperities. Specifically, the elastoplastic Jackson–Green (JG) rough surface contact model is used to calculate the quasistatic contact force as a function of rotor displacement, where bulk material deformation and surface cumulative damage are ignored. A simple exponential fit of the contact force is proposed to reduce computational burden associated with evaluating the JG rough surface contact model at each simulation time step. The rotors response using the LECM and JG rough surface contact model is compared via shaft speed bifurcations and orbit analysis. Significant differences are observed between the models, though some similarities exist for responses with few contacts per rotor revolution.

A Fractional Calculus Model of Viscoelastic Stator Supports Coupled With Elastic Rotor–Stator Rub

Rotating machinery is inherently susceptible to costly and dangerous faults. One such commonly encountered fault is undesirable dynamic contact between the rotor and stator (i.e., rotor–stator rub). The forces generated during rotor–stator rub are fundamentally tribological, as they are generated by contact and friction and result in wear. These forces are typically found by assuming linear elastic contact and dry Coulomb friction at the rotor–stator interface, where the normal force is a linear function of the interference. For the first time, this work incorporates viscoelasticity into the stator support and investigates its influence on the global dynamics of rotor–stator rub. The viscoelastic stator supports are modeled using fractional calculus, an approach which adeptly and robustly characterizes the viscoelasticity. Specifically, a fractional derivative order of one-half is employed to generate an analytic time-domain form of viscoelastic impedance. This approach directly assimilates viscoelasticity into the system dynamics, since the rotor equations of motion are integrated numerically in the time-domain. The coupled rotor–stator dynamic model incorporating viscoelastic supports is solved numerically to explore the influence of viscoelasticity. This model provides a framework for analysis of dynamic systems where viscoelasticity is included. [DOI: 10.1115/1.4032787]

Rotordynamic Analysis Using the Complex Transfer Matrix

The transfer matrix method is an expedient numerical technique for determining the dynamic behavior of a rotordynamic system (e.g., whirl frequencies, steady-state response to forcing). The typical 8 × 8 transfer matrix suffers from several deficiencies. First, for a system incorporating damping, the method generates a characteristic polynomial of degree 8N for a model of N lumped masses (degree 4N for an undamped model). The high degree of the polynomial results in lengthy computation times and decreased accuracy. Second, as discussed herein, the 8 × 8 formulation fails to distinguish between forward and backward whirl. These deficiencies are overcome by a novel complex-valued state variable redefinition resulting in a 4×4 transfer matrix including external support stiffness and damping. The complex transfer matrix is then modified to account for analysis within a rotating reference frame. Analysis in a rotating reference frame is a judicious means to determine unique system fault characteristics, which serve as a starting point for the development of an on-line fault detection system. Insights into using the complex transfer matrix in a rotating reference frame are discussed. Analytical results in both inertial and rotating reference frames for an overhung rotor model are provided.Copyright

Dynamic modeling of an eccentric face seal including coupled rotordynamics, face contact, and inertial maneuver loads

Mechanical face seals are constitutive components of turbomachines, which in turn can be constitutive to other systems (e.g. aircraft). Furthermore, the rotating element of a face seal is inextricably coupled to the turbomachine via a flexible mount, and the stationary seal element is coupled to the rotating seal element via the fluid film existing between the seal faces. Consequentially, understanding interactions between the seal and turbomachine is important for quantifying seal performance and improving its design. With few exceptions, previous works study the face seal dynamics independent from the rotordynamics. In addition, most prior investigations consider only angular and axial seal dynamics and neglect eccentric (i.e. lateral) deflections of the seal element(s). For the first time, this work develops a comprehensive and novel model of a mechanical face seal in the inertial reference frame including coupled rotordynamics and inertial maneuver loads of the overall system. The model is developed for a general seal geometry where both seal elements, stationary and rotating, are flexibly mounted and allowed to undergo angular, axial, and eccentric deflections. In addition, the seal model presented here accounts for transient operation, fluid shear forces, seal face contact, friction, and thermoelastic deformation. Finally, various faults due to manufacturing imperfections, component flaws, and/or installation errors can be accounted for by incorporating static angular misalignment of both seal elements, dynamic angular misalignment of the rotating seal element, eccentric rotating imbalance, and axial offset of the rotating seal element center of mass. Throughout this work, the equations of motion developed are valid for both steady-state and transient operation. This comprehensive model significantly advances the state of the art in mechanical face seal dynamic modeling and represents a pivotal step towards analyzing seal performance regarding a broad diversity of realistic problems.

Steady-State Response of a Flexibly-Mounted Stator Mechanical Face Seal Subject to Dynamic Forcing of a Flexible Rotor

Mechanical face seals are constitutive components of much larger turbomachines and require consideration of the system dynamics for successful design. The dynamic interplay between the seal and rotor is intensified by recent trends toward reduced clearances, higher speeds, and more flexible rotors. Here, the “rotor” consists of the flexible shaft and the rotating seal seat. The objective here is to, for the first time, determine how the rotor affects the seal performance and vice versa. Thresholds can then be established beyond which the rotor influences the seal but not vice versa (i.e., the rotordynamics can be sent to the seal analysis as an exogenous input). To this end, a model of a flexibly mounted stator face seal is provided including the coupled dynamics of the flexible rotor. The model accounts for axial and angular deflections of the rotor and seal. Coupled rotordynamics are modeled using a lumped-parameter approach including static and dynamic rotor angular misalignments. For expediency, linearized expressions for fluid forces are used, and the resulting steady-state equations of motion are solved analytically to investigate how rotor inertia, speed, and angular misalignment influence the coupled seal dynamics. Importantly, results from the study reveal that in some operating regimes, neglecting the rotordynamics implies healthy seal operation when instead intermittent rub exists between the faces. This work also shows that when the rotor inertia is much larger than the seal inertia, the rotordynamics can be solved separately and used in the seal model as an external input. [DOI: 10.1115/1.4036380]

Crack Detection in a Rotor Dynamic System by Vibration Monitoring: Analysis and Experimental Results

As the power to weight ratio demand on rotordynamic systems increases, susceptibility to transverse fatigue cracking of the shaft increases as well. The ability to detect cracks in an early stage of progression is imperative for minimizing off-line repair time. A vibration monitoring system proposed prior is developed herein, employing the 2X harmonic response component of the rotor tilt as a signature indicating a transverse shaft crack. To effectively capture the 2X response, the crack model must include the local nature of the crack, the depth of the crack, and the stiffness asymmetry inducing the gravity-forced 2X harmonic response. The transfer matrix technique is well-suited to incorporate these crack attributes due to its modular nature. Two transfer matrix models are proposed to predict the 2X harmonic response. The first model applies local crack flexibility coefficients determined using the strain energy release rate, while the second incorporates the crack as a rectangular notch to emulate a manufactured crack used in the experiments. Analytic results are then compared to experimental measurement of the rotor tilt gleaned from an overhung rotor test rig originally designed to test seal face dynamics. The test rig is discussed, and experimental 2X harmonic amplitudes of the rotor tilt are provided for shafts containing manufactured cracks of depths between zero and 40 percent.Copyright