A PERSPECTIVE ON THE NUMERICAL AND EXPERIMENTAL CHARACTERISTICS OF MULTI-MODE DRY-FRICTION WHIP AND WHIRL

The present work investigates the nature of dry-friction whip and whirl through experimental and numerical methods. Efforts of the author, Dyck, Pavalek, and coworkers enabled the design and construction of a test rig that demonstrated and recorded accurately the character of multi-mode dry-friction whip and whirl. These tests examined steady state whip and whirl characteristics for a variety of rub materials and clearances. Results provided by the test rig are unparalleled in quality and nature to those seen in literature and possess several unique characteristics that are presented and discussed. A simulation model is constructed using the Texas A and M University (TAMU) Turbomachinery Laboratory rotordynamic software suite XLTRC2 comprised of tapered Timoshenko beam finite elements to form multiple degree of freedom rotor and stator models. These models are reduced by component mode synthesis to discard highfrequency modes while retaining physical coordinates at locations for nonlinear interactions. The interaction at the rub surface is modeled using a nonlinear Hunt and Crossley contact model with coulomb friction. Dry-friction simulations are performed for specific test cases and compared against experimental data to determine the validity of the model. These comparisons are favorable, capturing accurately the nature of dryfriction whirl. Experimental and numerical analysis reveals the existence of multiple whirl and whip regions spanning the entire range of frequencies excited during whirl, despite claims of previous investigations that these regions are predicted by Black's whirl solution, but are not excited in simulations or experiments. In addition, spectral analysis illustrates the presence of harmonic sidebands that accompany the fundamental whirl solution. These sidebands are more evident in whip, and can excite higher-frequency whirl solutions. Experimental evidence also shows a strong nonlinearity present in the whirl frequency ratio, which is greater than that predicted by the measured radius-toclearance ratio at the rub location. Results include whirl frequencies 250% of that predicted by the measured radius-to-clearance ratio

Reverse first principles: Weber's law and optimality in different senses

The relationship between optimality and evolvability is analyzed through a case study of Weber's law, a common property of many sensory systems across a wide array of species. After demonstrating a variety of senses in which Weber's law is mathematically optimal, we ask whether principled methods exist for evaluating such optimality analyses. We argue that at least one such method exists: examining the evolvability of a trait with respect to each of the different metrics that it happens to optimize. Through evolvability analyses of Weber's law, it is demonstrated that optimality-equivalent measures of phenotypic quality need not be selectively equivalent: a trait that is optimal by two measures may have very different behavior under selection for each. This non-equivalence allows different optimality analyses of the same phenomenon to be assessed by a standard other than intuition, and in a manner requiring fewer degrees of freedom than are needed to model selection from scratch. Two qualitatively different models of selection are explored: phenotypic selection, a basic form in which mutations directly affect the model phenotype, and embryological selection, a more exotic form in which mutations affect the algorithm by which the phenotype is built

Words Alive Standards for Excellence Performance Audit

Student project for LEAD 501: Fundamentals of Nonprofits on Words Alive, a literacy organization that promotes reading for pleasure for children and adolescents through read-aloud programs and book groups. The Executive Director, Jennifer Williamson, and the board agreed that a performance audit will help the organization reach the next level of compliance and professionalism. The evaluation team (the team) suggested the Standard for Excellence (Standards) because of its thoroughness, design, and detail to mission. Standards was preferred by the team because it was more comprehensive than other suggested evaluation tools such as the Better Business Bureau or the Independent Sector. The Standards was also more logically structured and easier to follow. The team felt that it would be easier to present the findings to Words Alive with the comprehensive questions that Standards provided.https://digital.sandiego.edu/npi-bpl-programdesign/1009/thumbnail.jp

Turbomachinery Overview for Supercritical CO2 Power Cycles

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Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing

Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. The thrust of this research is to explain the difference between measured and predicted stiffness and damping coefficients for TPJBs, and to provide some confidence to designers that TPJB dynamic coefficients can be accurately predicted. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming harmonic rotor motion such that the amplitude and phase of pad motions resulting from radial and transverse rotor motions are predicted by rotor-pad transfer functions. In short, these transfer functions specify the amplitude and phase of pad motion (angular, radial, translational, etc.) in response to an input rotor motion. A new pad perturbation model is developed including the effects of angular, radial, and circumferential pad motion and changes in pad clearance due to pad bending compliance. Though all of these pad variables have previously been included in different analyses, there are no publications containing perturbations of all four variables. In addition, previous researchers have only perturbed the journal, while both the bearing and journal motions are perturbed in the present analysis, and the applicability of comparing rotor-perturbed bearing impedance predictions to impedances measured on a bearing-perturbed test rig is discussed. This perturbation model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. Direct measurements of pad motion during test excitation were recorded to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is given. Motion probes were added to the loaded pad (having the static load vector directed through its pivot) of a 5-pad TPJB to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw, and pitch. Strain gages were attached to the side of the loaded pad to measure static and dynamic bending strains, which were then used to determine static and dynamic changes in pad curvature (pad clearance). Good agreement was found between the amplitude of the measured and predicted transfer functions concerning radial and transverse pad motions throughout the range of speeds and loads tested, while pad tilt was moderately underpredicted. For the bearing investigated, radial pad motions resulting from pivot compliance were as large as 60% of the radial component of shaft motion when operating at 4400 rpm under heavily loaded conditions. Hence, if a dynamic load applied to the shaft resulted in a shaft displacement of 25 microns (1 mil), the pad would displace radially 15 microns (0.6 mils), and the fluid film height would only decrease by 10 microns (0.4 mils). The consequence of this pad motion is that fluid film stiffness and damping forces produced by relative rotor-pad motions are significantly reduced, resulting in a bearing having significantly less direct stiffness and damping than predicted. A similar effect occurs when shaft motions produce significant changes in pad clearance due to pad compliance. For the pad tested here, the measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad and pivot compliance will produce large errors, and is not advised. Transverse pad motion was predicted and observed. Based on phase measurements, this motion is lightly damped, and appears to be caused by pivot deflection instead of slipping. Despite observing a lightly damped phase change, an increase in magnitude at this natural frequency was not observed. Predicted direct stiffness and damping for unit loads from 0-3200 kPa (0-450 psi) fit through 1.5× running speed are within 18% of measurements at 4400 rpm, while predictions at 10200 rpm are within 10% of measurements. This is a significant improvement on the accuracy of predictions cited in literature. Comparisons between predictions from the developed bearing model neglecting pad, pivot, and pad and pivot flexibility show that predicted direct stiffness and damping coefficients for a model having a rigid pad and pivot are overestimated, respectively, by 202% and 811% at low speeds and large loads, by 176% and 513% at high speeds and high loads, and by 51% and 182% at high speeds and light loads. While the reader is likely questioning the degree to which these predictions are overestimated in regard to previous comparisons, these predictions are based on measured operating bearing clearances, which are 20-30% smaller than the cold bearing clearances that previous comparisons were based on. The effect of employing a full bearing model (retaining all of the pad degrees of freedom) versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. This overestimation of stability is due to an increase in predicted direct damping at the synchronous frequency over the subsynchronously reduced value. This increase in direct damping with excitation frequency was also seen in highly loaded test data at frequencies below approximately 2×running speed, after which direct damping decreased with increasing excitation frequency. This effect was more pronounced in predictions, occurring at all load and speed combinations. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies at 10200 rpm. It was found that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping. This outcome contrasts with the comparison between models using synchronously and subsynchronously reduced impedance predictions, which showed the subsynchronously reduced model to be the most conservative. This contrast results from a predicted increase in damping with increasing excitation frequency at all speeds and loads, while this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions

Troubleshooting of Sub-synchronous Torsional Interaction Phenomena on an Electric Motor-Driven Centrifugal Compressor

Case StudyThis case study discusses the identification, troubleshooting, and correction of a torsional instability in an electric motor-driven driveline with variable frequency drive (VFD) for a high-pressure gas compressor test facility permanently installed at SwRI. A torsional instability was identified on the gearbox high-speed shaft at speeds when the VFD output (line) frequency met or exceeded the torsional natural frequency of the train. The issue was resolved by changing to sensorless vector control in the VFD instead of voltage/frequency control. In the literature, this change was not observed

Design and Implementation of Swirl Brakes for Enhanced Rotordynamic Stability in an Off-shore Centrifugal Compressor

Technical BriefsRotordynamic stability of gas compressors at high speeds and operating pressures is a significant technical challenge. Dynamic instability must be avoided for the sake of safe, reliable and continuous operation of turbomachinery. Experience and literature have shown that one of the main sources of instability is the swirl within the secondary leakage path in shrouded impellers, especially the swirl entering the shroud seals. The technical brief presents the design and implementation of swirl brakes for centrifugal compressors with Teeth-on-Rotor seal configurations for shrouded impellers. Discussion includes (a) aerodynamic design of swirl brakes with the help of Computational Fluid Dynamics (CFD), (b) sub-scale testing of the swirl brake design in an instrumented single-stage test rig to measure the inlet swirl ratio in a shrouded impeller, (c) full-scale prototype shop-testing and qualification, with and without the swirl brakes in a closedloop test facility, and (d) results of incorporating the swirl brakes at an off-shore compressor installation to improve rotordynamic stability

Turbomachinery Overview for Supercritical CO2 Power Cycles

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Introduction to sCO2 Power Cycles, Applications, Turbomachinery, Heat Exchangers, and Research Programs

Short CourseThe recent interest to use supercritical CO2 (sCO2) in power cycle applications over the past decade has resulted in a large amount of literature that focuses on specific areas related to sCO2 power cycles in great detail. Such focus areas are demonstration test facilities, heat exchangers, turbomachinery, materials, and fluid properties of CO2 and CO2 mixtures, to name a few. As work related to sCO2 power cycles continues, more technical depth will be emphasized in each focus area, whereas those unfamiliar with the topic are left to undertake the large task of understanding fundamentals on their own. This short course aims to remedy this problem by providing an introduction to the following aspects of this new and exciting field. 1. sCO2 Power Cycle Basics and Proposed sCO2 Cycles 2. sCO2 Power Cycle Applications 3. sCO2 Turbomachinery 4. sCO2 Materials 5. sCO2 Heat Exchangers 6. sCO2 Researc

Troubleshooting of Sub-synchronous Torsional Interaction Phenomena on an Electric Motor-Driven Centrifugal Compressor

Case StudyThis case study discusses the identification, troubleshooting, and correction of a torsional instability in an electric motor-driven driveline with variable frequency drive (VFD) for a high-pressure gas compressor test facility permanently installed at SwRI. A torsional instability was identified on the gearbox high-speed shaft at speeds when the VFD output (line) frequency met or exceeded the torsional natural frequency of the train. The issue was resolved by changing to sensorless vector control in the VFD instead of voltage/frequency control. In the literature, this change was not observed