Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration最新文献

{"title":"Measured and Predicted Temperature Differentials Within a Rotor at a Tilting-Pad-Journal Bearing Associated With the Morton Effect","authors":"Chris D. Kulhanek, S. Cunningham, H. Delgado, Jeff Moore, Justin R. Hollingsworth","doi":"10.1115/gt2022-83237","DOIUrl":"https://doi.org/10.1115/gt2022-83237","url":null,"abstract":"\u0000 The current work shows the implementation of a high-speed turbomachinery test rig to measure vibration and internal shaft temperature differentials at a journal bearing for a rotor system designed to induce the Morton effect rotordynamic phenomenon. The vibration and shaft temperature measurements are compared to predictions using an analytical code described by Tong and Palazzolo [6,7]. An existing high-speed test rig was adapted, including a new rotor with six equally-spaced RTDs embedded at the journal bearing centerline. The rotor configuration included an overhung rotor design with a 58 mm (2.3 inch) diameter, 5-pad tilting-pad journal bearing. The in-rotor temperature measurements were conditioned using a custom on-board amplifier and extracted with a high-speed commercial slip ring. Test conditions included various levels of unbalance, bearing oil inlet temperature, and operating speed. Test measurements show that the temperature differential across the shaft is dependent upon operating speed, as well as vibration amplitude. Operating conditions included rotational speeds up to 19.5 krpm and vibration levels approaching the magnitude of the bearing clearance. Testing near the rotor first lateral natural frequency (or critical speed) with a high level of initial unbalance resulted in the highest temperature differentials across the shaft of approximately 11 °C (20 °F) plus. Vibration measurements show hysteresis in the synchronous vibration response in the Bode and polar plots. This measured vibration hysteresis is consistent with the rotor hot spot or temperature differential changing the unbalance level of the rotor. Overall, both the test measurements and predictions show notable temperature differentials and hysteresis behavior in the vibration response that are believed to be associated with the Morton Effect. These conditions are considered precursors to the spiral vibration or fully developed synchronous instability typically associated with the Morton Effect.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115459923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient Enhanced Kriging Using Modal Sensitivity Approximations in a Reduced Basis Space for As-Manufactured Airfoil Analysis","authors":"Jeffrey M. Brown, Emily B. Carper, A. Kaszynski, Daniel L. Gillaugh, Joseph A. Beck","doi":"10.1115/gt2022-83402","DOIUrl":"https://doi.org/10.1115/gt2022-83402","url":null,"abstract":"\u0000 This work develops a new process to efficiently predict the effect of as-manufactured geometry variations on airfoil modal response. A gradient enhanced kriging approach is formulated that uses two sets of results at the training model sites in order to reduce the total number of models required. The first set of results are the frequency or mode shape values and the second are their respective gradients. Computational efficiency is achieved through analytical calculations of eigenvalue and eigenvector sensitivities. This approach avoids the need to recompute full eigensolutions for finite difference sensitivity approximation. Efficiency in mode shape approximation is further enabled through transformation of displacement variations into a principal component reduced-basis space. This allows prediction of the full mode shape variation without emulating each degree of freedom independently. In order to perform gradient enhanced kriging with this space, a novel approach is developed to calculate reduced basis space gradients. The process projects the modal displacement principal component vectors onto first-order Taylor series expansions of the physical mode shape variation at each training site. The resulting perturbed principal component coordinates are used in finite difference estimates of sensitivity that make gradient enhanced kriging in this space possible. This new process is demonstrated on three cases, and it is shown that the new approach provides significant improvements in accuracy and efficiency compared to traditional kriging methods.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115482371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Investigation on HCF Weak Link Locations of a Wide-Chord Laminated Composite Fan Blade With Coupled Modal Vibrations","authors":"Xue-Yan Tang, Yong Chen, Jiguo Zhang","doi":"10.1115/gt2022-83613","DOIUrl":"https://doi.org/10.1115/gt2022-83613","url":null,"abstract":"\u0000 High cycle fatigue (HCF) of laminated composite fan blade (LCFB) caused by vibration is important content within airworthiness certification. This paper proposed a method suitable for LCFB to evaluate its HCF failure location under complex excitations. First, a high-fidelity finite element model (FEM) of LCFB was built and the classification of modal shapes was carried out. By setting the resonance margin threshold on the campbell diagram, the modal superposition vibration that may be excited at the common rotation speed was found out. Then, a postprocessing strategy was proposed to evaluate HCF weak link locations. Constant life diagrams (CLD) for the unidirectional lamina were employed to determine the HCF weak link location of LCFB in combination with the steady and vibratory stresses along the corresponding material principal directions. For the coupled mode vibration, the HCF weak link locations with different stress components were calculated and the critical failure stress component was identified. For the coupled mode vibrations, the HCF weak link locations with the resultant stresses were calculated with different combination of modal participating coefficients. The results indicated that the HCF weak link locations may change to locations different from that in single mode vibration. Furthermore, the critical failure stress components may be transferred to directions with larger vibratory stress margins. This work presented a useful numerical technique to study the effect of mode coupling on LCFB HCF characteristics under complex operating conditions.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128259718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gas Turbine Rotor Damper Lift-Off Study","authors":"S. Manoharan, S. Abhimanyu, S. Babu, L. Tognarelli, G. Peano","doi":"10.1115/gt2022-82960","DOIUrl":"https://doi.org/10.1115/gt2022-82960","url":null,"abstract":"\u0000 Gas turbine rotor system is subjected to vibratory stresses due to excitations caused by various excitation sources at varying energy levels. To dissipate the energy that occurs in the rotating system, damping is induced internally or externally. Damping is achieved by having damper at the appropriate location in the rotor system. The damper needs to have a provision to assemble in the rotor assembly, which is typically a split, facilitating the damper to wind and unwind in circumferential direction. The damper used in the rotating system needs to be axisymmetric with a suitable cross-section, to achieve the required level of damping. As the damper is used at the interior location of the rotor system, it needs to build necessary preloading by itself in such a way that the damper rotates with the rotor system during operation. Damper design study is very vital in deciding the shape of the damper in such a way that it provides efficient damping and minimizing the vibratory stress. At some vibrating condition, damper tends to detach from its supporting feature which is referred to as damper lift-off. The magnitude of this lift-off is expected to be higher at the split regions compared to other circumferential location of the damper, which makes the damper design very complex. When the damper split region passes through the maximum lobe and minimum lobe position of any nodal diameter, the region near the split tends to lift-off from its support and behaves like a simply supported beam and cantilever beam respectively. A careful consideration of this damper lift-off phenomenon in damper design is key towards achieving a robust damper design. Various types of simulation techniques using finite element analysis are followed in performing necessary design assessments. This paper is intended to describe the steps followed in performing damper design study to help achieving design robustness.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130071627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust Probabilistic Analysis of Deterioration-Induced Aeroelasticity in an Axial Turbine","authors":"Lennart Stania, J. Seume","doi":"10.1115/gt2022-82628","DOIUrl":"https://doi.org/10.1115/gt2022-82628","url":null,"abstract":"\u0000 The surface of a real-world turbine blade differs from the geometry of its model. Manufacturing tolerances, wear, and regeneration during the turbine’s lifetime impact the aerodynamic behaviour, stage efficiency, and parameters as previous probabilistic studies have shown. Aerodynamic changes lead to aeroelastic variances in downstream rows that can have a significant impact on high-cycle fatigue due to a possible increase of a blade’s vibration amplitude. The present study expands an existing tool chain to uni-directional aeroelastic full three dimensional simulations. The test object is the last stage of a low-pressure five-stage axial turbine; the geometric variances are applied to characteristic airfoil parameters of the vane by Latin hypercube sampling. A required sample size for an accurate sensitivity analysis is estimated a-priori and verified by computational simulations. The aerodynamic analysis identified the stagger angle, trailing-edge thickness, maximum thickness, and maximum camber as the most important parameters among the characteristic blade parameters. For large deviation in the stagger angle a non-monotonous influence on isentropic efficiency was found, which shows limitations of a sensitivity analysis based on the Spearman rank correlation coefficients. A variance-based sensitivity analysis was used for a more detailed analysis, which is capable to detect such non-monotonous relationships. In the aeroelastic simulations, the chord length, maximum camber, and the trailing-edge angle have the highest influence on aerodynamic forcing and damping on a downstream rotor blade of the changed stator blade. Furthermore, direct correlations between aerodynamic stage parameters and aerodynamic damping are shown, which allows reduced order modelling. The correlation between work coefficient and vibration amplitude was overlooked by the Spearman’s coefficient but identified by the variance-based approach. A maximum vibration amplitude is identified, indicating a potential of using probabilistic studies for adjusting the safety factors for high-cycle fatigue during the design process of blades.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132528586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interface Reduction in an Equivalent Linearization Algorithm for Nonlinearly Coupled Systems Under Random Excitation","authors":"Alwin Förster, Lars Panning‐von Scheidt","doi":"10.1115/gt2022-78367","DOIUrl":"https://doi.org/10.1115/gt2022-78367","url":null,"abstract":"\u0000 Stochastic excitation is a rarely discussed topic regarding the vibrational behavior of turbine blades. While the calculation of stochastic quantities describing the stochastic steady-state vibration response is comparatively straightforward in the linear case, it becomes much more challenging in the case of nonlinear couplings. A method suitable for calculating approximations of the stochastic steady-state vibration response is the equivalent linearization method. However, the efficiency of this method decreases with an increasing number of degrees of freedom. This is especially challenging if the number of nonlinearly coupled degrees of freedom is large, as in the case of an extended contact interface, such as a shroud contact. While the uncoupled part of the system can be reduced using a component mode synthesis, the remaining nonlinear interface degrees of freedom have to remain unreduced to evaluate the nonlinear forces. To address this problem, this paper presents an approach to reduce the interface degrees of freedom within the framework of the equivalent linearization method. The presented method is based on a representation of the dynamics of the contact interface by means of a reduced set of Legendre polynomials. However, the evaluation of the nonlinear force still takes place in physical coordinates. The presented procedure is demonstrated using a beam model with different contact pairings as well as a more realistic model of a bladed disk assembly.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"5 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127107513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Dynamic Response of a Two-Degree-of-Freedom System With Dry Friction and Elastic Stop","authors":"Liming Jiang, Zhi-bin Su, Jie Hong, Yanhong Ma","doi":"10.1115/gt2022-82779","DOIUrl":"https://doi.org/10.1115/gt2022-82779","url":null,"abstract":"\u0000 The contact interface is one of the essential components of structural systems, introducing friction and non-smooth constraints, which will cause nonlinear dynamic behavior. This survey provides an insight into the dynamic response of a simplified model with two moving parts in detail. The proposed model can be applied to analyze the dynamic behavior of a rotor system with pedestal looseness fault. First, a two-degree-of-freedom system is established, and the nonlinear force caused by friction and elastic stop is introduced between the two moving parts. Dimensionless governing equations are derived, and the harmonic balance method and the shooting method are used to obtain the periodic solution. Floquet theory and Poincaré mapping are applied to analyze stability. The amplitude-frequency curves obtained by the two methods are compared considering friction merely, and the accuracy of the harmonic balance method is verified by the numerical integration method. Then, the features of energy dissipation versus excitation frequency are present, and influences of friction force amplitudes on the dynamic response are studied. The periodic solution is unstable considering friction and elastic stop in some excitation frequency ranges, and Hopf bifurcations exist correspondingly, indicating quasi-periodic motion occurs. The frequency domain of periodic motion contains super-harmonic components merely, while the frequency domain of quasi-periodic signal is composed of combined frequencies. Since Hopf bifurcation indicates a new periodic solution whose frequency is incommensurable with the original one, a formula for explaining combined frequencies is presented. Meanwhile, there are multiple collisions phenomena per cycle in time history. Finally, the influences of parameters on the dynamic response are studied. Note that the model in this survey may be regarded as a single-degree-of-freedom system with a friction-impact damper, which is beneficial to design nonlinear vibration absorbers based on friction and impact for vibration suppression.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126644328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}