Master of Science in Engineering (MSEgr), Wright State University, 2010, Mechanical Engineering

Mistuning prediction in integrally bladed rotors is often done with reduced order models that minimize computational expenses. A common model reduction technique used for mistuning applications is the component mode synthesis method. In this work, two modern component mode synthesis methods are used to generate mistuned response distributions that will be used to determine if the two methods are statistically indistinguishable. The first method, nominal mode approximation, assumes an airfoil geometric perturbation alters only the corresponding substructure modal stiffnesses while its mode shapes remain unaffected. The mistuned response is then predicted by a summation of the nominal modes. The second method, non-nominal mode approximation, makes no simplifying assumptions of the dynamic response due to airfoil geometric perturbations, but requires recalculation of substructure matrices and mode shapes with each iteration. The number of retained fixed interface normal modes for the non-nominal method are increased until there is satisfactory accuracy compared to full finite element model results. Each approach is employed for calculating the mistuned response of a simple academic rotor and an advanced rotor with complex geometries. Three different veering regions are investigated in the advanced test case. Results indicate there is minimal difference between response distributions generated by the nominal and non-nominal methods for the academic rotor. Large differences were observed for the advanced rotor, where the nominal method typically predicted conservative response levels larger than non-nominal predictions.

Committee: Joseph C. Slater Ph.D. (Advisor); Jeffrey M. Brown Ph.D. (Committee Member); Ravi C. Penmetsa Ph.D. (Committee Member) Subjects: Engineering; Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2021, Mechanical Engineering

Turbomachinery, like jet engines and industrial gas turbines in power plants, are very advanced and complex machines. Due to the complexity and cost of modern turbomachinery, there is active research in accurately predicting the physical system dynamics using computational models. Two big mechanisms that affect the structural response are the prestress effects from high rotational speeds and mistuning effects from tolerance deviations, wear, or damage. Understanding the role these two mechanisms play in the computational modeling of these systems is an important step toward a complete digital twin of an entire jet engine. There previously existed modeling methods that enabled each to be analyzed independently, but not simultaneously in an efficient manner. This will be one of the focus points of this dissertation. The other focus being an experimental investigation into exciting system resonances of a rotating bladed disk using air jets. These experiments will be used to validate the computational modeling method developed. This dissertation has three primary objectives. The first objective is to present reduced order modeling methods that allow for the efficient modeling of coupled systems and rotating systems, both with small or large mistuning. By efficiently including these mechanisms, more realistic boundary conditions can be used to help validate the reduced order models (ROMs) with experimental data. Both modeling methods create models a fraction of the size of the full model while retaining key dynamic characteristics of the full model. The second objective of this work is to show the capability of air jets in exciting synchronous and non-synchronous vibrations in a rotating bladed disk. Much previous research in this field focused on experiments with stationary systems. These tests can help isolate specific mechanisms that may be present in bladed disks, but may limit the applicability of the results to actual rotating systems. This work presents a method (open full item for complete abstract)

Committee: Kiran D'Souza (Advisor); Randall Mathison (Committee Member); Manoj Srinivasan (Committee Member); Herman Shen (Committee Member) Subjects: Mechanical Engineering

Master of Science in Engineering (MSEgr), Wright State University, 2014, Mechanical Engineering

An improved spatial statistical approach and probabilistic prediction method for mistuned integrally bladed rotors is proposed and validated with a large population of rotors. Prior work utilized blade-alone principal component analysis to model spatial variation arising from geometric deviations contributing to forced response mistuning amplification. Often, these studies considered a single rotor measured by contact probe coordinate measurement machines to assess the predictive capabilities of spatial statistics through principal component analysis. The validity of the approach has not yet been demonstrated on a large population of mistuned rotors representative of operating fleets, a shortcoming addressed in this work. Furthermore, this work improves the existing predictions by applying principal component methods to sets of airfoil (rotor) measurements, thus effectively capturing blade-to-blade spatial correlations. In conjunction with bootstrap sampling, the method is validated with a set of 40 rotors and quantifies the subset size needed to characterize the population. The work combines a novel statistical representation of rotor geometric mistuning with that of probabilistic techniques to predict the known distribution of forced response amplitudes.

Committee: Joseph C. Slater Ph.D., P.E. (Advisor); Jeffrey M. Brown Ph.D. (Committee Member); J. Mitch Wolff Ph.D. (Committee Member); Ha-Rok Bae Ph.D. (Committee Member) Subjects: Aerospace Engineering; Engineering; Mechanical Engineering

Doctor of Philosophy (PhD), Wright State University, 2013, Engineering PhD

This effort seeks to increase the reduced-order model fidelity for mistuned Integrally Bladed Rotor (IBR) and Dual Flow-path Integrally Bladed Rotor (DFIBR) response prediction by explicitly accounting for blade geometric and material property deviations. These methods are formulated in a component mode synthesis (CMS) framework utilizing secondary modal reductions in a cyclic symmetry format. The resulting reduced-order models (ROMs) capture perturbations to both blade natural frequencies and mode shapes resulting from geometric deviations. Furthermore, the secondary modal reductions and cyclic symmetry format offer significant computational savings over traditional component mode synthesis methods that give a further reduction in model size. The first formulation for IBRs assumes a tuned disk-blade connection and presents two methods that explicitly model blade geometry surface deviations by performing a modal analysis on different degrees of freedom of a parent reduced-order model. The parent ROM is formulated with Craig-Bampton component mode synthesis (CB-CMS) in cyclic symmetry coordinates for an IBR with a tuned disk and blade geometric deviations. The first method performs an eigen-analysis on the constraint-mode degrees of freedom (DOFs) that provides a truncated set of Interface modes while the second method includes the disk fixed-interface normal modes in the eigen-analysis to yield a truncated set of Ancillary modes. Both methods can utilize tuned or mistuned modes, where the tuned modes have the computational benefit of being computed in cyclic symmetry coordinates. Furthermore, the tuned modes only need to be calculated once, which offers significant computational savings for subsequent mistuning studies. Each geometric mistuning method relies upon the use of geometrically mistuned blade modes in the component mode framework to provide a very accurate ROM. Free and forced response results are compared to both the full finite element model (FE (open full item for complete abstract)

Committee: Joseph Slater Ph.D. (Advisor); Ramana Grandhi Ph.D. (Committee Member); Jeffrey Brown Ph.D. (Committee Member); Charles Cross Ph.D. (Committee Member); Ha-Rok Bae Ph.D. (Committee Member); Richard Cobb Ph.D. (Committee Member) Subjects: Aerospace Engineering; Mechanical Engineering

Master of Science, The Ohio State University, 2021, Mechanical Engineering

To facilitate experimentation in the field of gas turbine disk dynamics, a new integrally bladed disk, or blisk, was designed and manufactured for use at The Ohio State University (OSU) Gas Turbine Laboratory. The axisymmetric disk portion of the equipment and the blades are manufactured as a single unit in blisks. This new blisk is referred to hereafter as the OSU Rotor 67 Blisk. The OSU Rotor 67 Blisk was designed with traditional airworthy gas turbine rotating hardware standards in mind, although it is not meant for flight. The standards put forth by the Federal Aviation Administration (FAA) are loosely followed to produce a blisk that is similar to hardware that could be used in general aviation. The guidelines put forth by the FAA for rotor design are found in 14 CFR Part 33, and provide requirements for safety aspects of rotor design. The airfoil design and mounting configuration were strongly influenced by the existing NASA Rotor 67 airfoil and disk geometry, with modifications to convert it from a bladed disk to a blisk. Additionally, damper grooves were added to the design to facilitate a variety of damping experiments. After the OSU Rotor 67 Blisk was machined, balanced, and inspected, it was received at OSU, where it was subsequently tested on a non-rotating bench setup to characterize its properties. A roving modal hammer was used along with a calibrated capacitance probe for dynamics measurements. The data generated through the dynamics experiments provided clarity on the natural frequencies and the mistuning of the blisk. These data will be used to design future experiments at the OSU Gas Turbine Laboratory where the blisk will be rotated at different operating speeds and excited by air-jets to evaluate different damping technologies.

Committee: Kiran D'Souza (Advisor); Michael Dunn (Advisor); Randall Mathison (Committee Member) Subjects: Mechanical Engineering

Master of Science in Mechanical Engineering (MSME), Wright State University, 2019, Mechanical Engineering

Integrally Bladed Rotors (IBR) of aircraft turbine engines suffer from fluctuations in the dynamic response that occurs due to blade to blade geometric deviations. The Stochastic Approach for Blade and Rotor Emulation (SABRE) framework has been used to enable a probabilistic study of mistuned blades in which a reduced order modeling technique is applied in conjunction with sets of surrogate models, called emulators, to make predictions of mistuned mode shapes. SABRE has proven useful for non-switching mode shapes. However, switching mode shapes have non-stationary or discontinuous response surfaces which reduce the accuracy of the surrogate models used in SABRE. To improve emulator accuracy, the methodology proposed in this thesis was developed. This methodology improves prediction quality by identifying and eliminating non-stationary and discontinuous portions of the response with the classification decision boundary methodology, efficiently identifying areas of inaccuracy while improving the surrogate as efficiently as possible with adaptive sampling, and alleviating the computational burden associated with large numbers of finite element samples required to build accurate emulators.

Committee: Harok Bae Ph.D. (Advisor); Ahsan Mian Ph.D. (Committee Member); Jeffrey Brown Ph.D. (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy (PhD), Wright State University, 2019, Engineering PhD

As-manufactured rotors behave quite differently than nominal, as-designed rotors due to small geometric and material property deviations in the rotor, referred to as mistuning. Traditional integrally bladed rotor (IBR) modeling approaches assume each blade is identical. State-of-the-art IBR dynamic response predictions can be accomplished using asmanufactured models (AMM) generated via optical topography measurements and mesh morphing. As-manufactured models account for geometric deviations occurring through the machining process, material deviations and field wear, allowing each blade to respond differently. Rotor designs are intended to avoid resonance crossings throughout an engine's operating range, but total avoidance is challenging. This has led to conservative designs as well as heavily instrumented rig and engine testing to attempt to reduce future HCF issues, debiting aircraft performance while increasing development costs. Therefore, it is vital that accurate modeling approaches predict the forced response of resonance crossings to capture mistuning phenomenon and to place safety instrumentation appropriately. Safe engine operation is ensured by setting safety limits on rotor airfoil mounted strain gages that monitor the dynamic response of the component. Traditionally, strain gage limits are generated utilizing geometry obtained from an “as-designed nominal model where finite element analysis is used to compute the static and modal stresses. Predicted modal stresses of the cyclic analysis are used to optimize strain gage locations to ensure modal observational coverage, modal identification, and maximum vibrational stress for each mode. Strain gage limits are then produced for these optimal strain gage locations on the tuned finite element model. The described nominal geometry based process is subject to errors associated with airfoil mode shape variations caused by manufacturing deviations. This work develops a new process based on as-manufactured geo (open full item for complete abstract)

Committee: Joseph C. Slater Ph.D., P.E. (Advisor); J. Mitch Wolff Ph.D. (Committee Member); Harok Bae Ph.D. (Committee Member); Richard G. Cobb Ph.D. (Committee Member); Jeffrey M. Brown Ph.D. (Committee Member) Subjects: Aerospace Engineering; Engineering; Mechanical Engineering

Doctor of Philosophy (PhD), Wright State University, 2008, Engineering PhD

Design of structural components is constrained by both iteration time and prediction uncertainty. Iteration time refers to the computation time each simulation requires and controls how much design space can be explored given a fixed period. A comprehensive search of the space leads to more optimum designs. Prediction uncertainty refers to both irreducible uncertainties, such as those caused by material scatter, and reducible uncertainty, such as physics-based model error. In the presence of uncertainty, conservative safety factors and design margins are used to ensure reliability, but these negatively impact component weight and design life. This research investigates three areas to improve both iteration time and prediction uncertainty for turbomachinery design. The first develops an error-quantified reduced-order model that predicts the effect of geometric deviations on airfoil forced response. This error-quantified approximation shows significant improvements in accuracy compared to existing methods because of its bias correction and description of random error. The second research area develops a Probabilistic Gradient Kriging approach to efficiently model the uncertainty in predicted failure probability caused by small sample statistics. It is shown that the Probabilistic Gradient Kriging approach is significantly more accurate, given a fixed number of training points, compared to conventional Kriging and polynomial regression approaches. It is found that statistical uncertainty from small sample sizes leads to orders of magnitude variation in predicted failure probabilities. The third research area develops non-nominal and nominal mode Component Mode Synthesis methods for reduced-order modeling of the geometric effects on rotor mistuning. Existing reduced-order methods approximate mistuning with a nominal-mode, or design intent, basis and airfoil modal stiffness perturbation. This assumption introduces error that can be quantified when compared to a finite el (open full item for complete abstract)

Committee: Ramana Grandhi PhD (Advisor); Joseph Slater PhD (Committee Member); Ravi Penmetsa PhD (Committee Member); Mo-how Shen PhD (Committee Member); Charles Cross PhD (Committee Member) Subjects: Mechanical Engineering