Made available in DSpace on 2015-03-03T11:52:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-09-02Bitstream added on 2015-03-03T12:06:23Z : No. of bitstreams: 1 000804878.pdf: 2650434 bytes, checksum: ef9e16c1a0c4300c6e8f770cf0a58ed0 (MD5) / Esta tese apresenta o desenvolvimento de uma metodologia de otimização dinâmica e estrutural para rotores com eixos em material compósito. A dinâmica destes rotores difere das análises convencionais devido à existência de amortecimento interno no eixo. As equações de movimento destes rotores apresentam a influencia do amortecimento interno sobre o comportamento dinâmico dos rotores. Materiais compósitos podem ser manufaturados em diferentes sequências de laminação. Para obter as melhores propriedades mecânicas, que possibilitem aos rotores operarem, em condições de estabilidade dinâmica e de esforços estruturais, foi necessário o desenvolvimento de uma metodologia de otimização para obter o melhor projeto. Para a aplicação desta metodologia foi desenvolvido um algoritmo de otimização. Para fundamentar este desenvolvimento foram revisados conceitos da teoria clássica de laminação, dos modelos de amortecimento estrutural, da dinâmica de rotores com amortecimento interno, de elementos finitos e dos métodos de otimização. O método de otimização escolhido foi o genético. Dentro do algoritmo de otimização foram inseridos módulos de análise para calcular as propriedades equivalentes, de avaliação estrutural por critérios de falha e de análise dinâmica de rotores. Diferentes simulações demonstraram a importância da sequência de laminação sobre a dinâmica dos rotores. Dentre os resultados finais estão simulações de otimizações e uma análise dos principais parâmetros que influenciam a obtenção de soluções ótimas pela otimização / This thesis presents a development on dynamic and structural optimization method (multiobjective) for rotors mount on composite shafts. The dynamic analysis of these rotors differs from conventional analysis due to the existence of internal damping in the shaft. The equations of motion for these rotors represent the influence of internal damping on the dynamic behavior of the rotor system. Composite materials can be manufactured using different layups. To obtain the best mechanical properties, which allow rotors to operate in stability dynamic and allowable efforts structural conditions, it was necessary to develop a methodology for design optimizing. For the application of this methodology an optimization algorithm was developed. To support this development were reviewed: the classical lamination theory, models of structural damping, rotor dynamics with internal damping, finite elements and optimization methods. The optimization method chosen was algorithm genetic. Within the optimization algorithm were inserted analysis modules responsible for: calculate the equivalent properties, evaluate structurally by failure criteria and analyze the dynamics of the rotors. Several simulations have demonstrated the importance of the layup for rotor dynamics. Among the final results from optimization simulations, there are discussions about the influence of the each optimization parameters that influence the achievement of optimal solutions

Orientador: Katia Lucchesi Cavalca / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-06T20:31:32Z (GMT). No. of bitstreams: 1 GandaraNeto_Irineu_M.pdf: 5409150 bytes, checksum: 6e56e75e660311a97e894ef966472cd1 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho foi desenvolvido um modelo matemático para mancais hidrodinâmicos com movimento oscilatório. Ao contrário dos mancais convencionais, o eixo não desenvolve um movimento completo de rotação dentro do mancal e passa a pertencer a uma nova classe definida como mancais hidrodinâmicos de movimento oscilatório. A motivação do trabalho veio da tribologia dos motores de combustão interna, na qual procurou-se estudar o problema de lubrificação do mancal que estabelece a conexão entre pistão e biela. Para análise do problema, assumiu-se o escoamento de um fluido viscoso com inércia desprezível dentro de uma folga inclinada formada pelas superfícies do eixo e mancal. A superfície interior é fixa enquanto a superfície exterior desenvolve um movimento oscilatório que resulta num escoamento combinado de Couette e Poiseuille. Usando a mesma abordagem da teoria da lubrificação de Reynolds e a solução na forma complexa conforme sugere o 2º problema de Stokes, as equações de conservação da massa e quantidade de movimento foram integradas analiticamente e forneceram os campos de velocidade, pressão e as forças hidrodinâmicas. Como resultado, pôde-se determinar a espessura do filme de óleo em função do tempo e da freqüência de oscilação que permitiu avaliar as condições de lubrificação do sistema / Abstract: In this work was developed a mathematical model for the hydrodynamic lubrication problem applied to bearings with oscillating motion. In contrast with common bearings, this type of bearing does not perform a complete rotation, belonging to a newly defined class: the bearings with oscillatory movement. The motivation lies in the tribology of internal combustion engines, specifically the lubrication problem at the bearing existing between the connecting rod and the piston pin. For the analysis of lubrication, a viscous fluid flow with negligible inertia inside a narrow gap formed by two surfaces was considered. The surfaces can be considered flat and are inclined to each other. The inner surface is fixed whereas the outer one performs an oscillating motion which generates a combined Couette-Poiseuille flow inside the gap. Using the same assumptions as in classical Reynolds' lubrication equation, the simplified mass and momentum conservation equations were analytically solved to determine the velocity and pressure distributions and hydrodynamic forces. As result it was possible to determine the oil film thickness as function of time and oscillating frequency that allowed to evaluate the lubrication conditions of the system / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Katia Lucchesi Cavalca / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-09T12:41:08Z (GMT). No. of bitstreams: 1 Castro_HelioFioride_D.pdf: 2921981 bytes, checksum: 83a1aae9466f9a33a00043c950bea261 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho, foi realizada a análise e validação de um modelo de sistema rotativo sustentado por mancais hidrodinâmicos. Para isto, considerou-se um modelo não-linear de mancal hidrodinâmico. A parte girante do sistema foi modelada pelo Método dos Elementos Finitos. Este modelo é capaz de simular a resposta do sistema a auto-excitação causada pelo ilme de óleo no mancal hidrodinâmico. Para calibração do modelo, um método de ajuste metaheurístico, baseado em Algoritmo Genético e Recozimento Simulado foi aplicado. Após o ajuste do modelo, compararam-se os resultados da simulação, considerando o resultado do ajuste, e resultados adquiridos na bancada experimental de teste do Laboratório de Máquinas Rotativas (DPM) na Faculdade de Engenharia Mecânica da UNICAMP. Uma especial atenção foi dada na análise dos esforços hidrodinâmicos, pois se buscou levantar os coeficientes dinâmicos lineares (coeficientes de amortecimento e rigidez) dos mancais através dos resultados obtidos experimentalmente e pelas simulações. Além disto, foram estimados coeficientes não-lineares das forças, os quais são relacionados a termos quadráticos de deslocamentos e velocidades e suas combinações, ressaltando o caratê não-linear deste tipo de mancais. Os resultados demonstraram que o modelo não-linear de mancais hidrodinâmicos é capaz de representar a instabilidade fluidoinduzida / Abstract: In this investigation, the analysis and validation of rotative system supported by hydrodynamic journal bearings was accomplished. A non-linear hydrodynamic bearing model was considered. The rotary shaft and rotor mass were modeled by The Finite Element Method. The combination of these models is able to simulate the system response to the auto-excitation caused by the oil film instabilities in the journal bearing. In order to calibrate the model, a metaheuristic method, based in Genetic Algorithm and Simulated Annealing, was applied. After the model fitting, the simulation results, taking into account the fitting results, and experimental results acquired from the experimental set-up at the Rotating Machine Laboratory in the Department of Mechanical Design of the Mechanical Engineering Faculty at UNICAMP. A special attention was directed to the hydrodynamic forces, because the dynamic bearing coefficients (stiffness and damping coefficients) were evaluated through simulated and experimental results. Moreover, non-linear coefficients of the forces were also estimated. These coefficients are related to quadratic terms of displacements and velocities and ççtheir combinations, highlighting the non-linear feature of this kind of bearing. The results showed hat the non-linear journal bearing model is able to represent the fluid-induced instability / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

An analytical technique for determining the damped or undamped critical speeds and generating a critical speed map for a general flexible rotor in isotropic bearings has been developed. Rotordynamics theory related to this research work is studied including synchronous unbalance response, critical speed, gyroscopic effect, critical speed map, and stability. The method of solution is based on the Transfer Matrix approach containing both real and complex variable notations for deriving the overall system matrices. Muller's Method is applied to search for real or complex eigenvalues of the system. The corresponding mode shapes are found by back substitution. An accurate and efficient computer program, BEAM VII, has been designed to perform the analysis. Through the discussion of a series of numerical examples published by other authors, the confirmation of the rotor dynamics theory and precision of the computer code are achieved. / Master of Science

To increase efficiency, shafts are made lighter and more flexible, and are designed to rotate faster to increase the system's power-to-weight ratio. The demand for higher efficiency in rotordynamic systems has led to increased susceptibility to transverse fatigue cracking of the shaft. Shaft cracks are often detected and repaired during scheduled periods of off-line maintenance. Off-line maintenance can be expensive and time consuming; on-line condition monitoring allows maintenance to be performed as-needed. However, inadequate (or a lack of) monitoring can allow rapidly propagating cracks to result in catastrophic shaft failure. It is therefore imperative to develop on-line condition monitoring techniques to detect a crack and diagnose its severity. A particularly useful method for transverse shaft crack detection/diagnosis is vibration monitoring. Detection, and especially diagnosis, of transverse fatigue cracks in rotordynamic systems has proven difficult. Whereas detection assesses only the presence of a crack, diagnosis estimates important crack parameters, such as crack depth and location. Diagnosis can provide the operator with quantitative information to assess further machinery operation. Furthermore, diagnosis provides initial conditions and predictive parameters on which to base prognostic calculations. There is a two-fold challenge for on-line diagnosis of transverse fatigue crack parameters. First, crack characterization involves specifying two important parameters: the crack's depth and location. Second, the nature of rotating machinery permits response measurement at only specific locations. Cracks are typically categorized as breathing or gaping; breathing cracks open and close with shaft rotation, while gaping cracks remain open. This work concerns the diagnosis of gaping crack parameters; the goal is to provide metrics to diagnose a crack's depth and location. To this end, a comprehensive approach is presented for modeling an overhung cracked shaft. Two linear gaping crack models are developed: a notch and a gaping fatigue crack. The notch model best approximates experimentally manufactured cracks, whereas the gaping fatigue crack model is likely more suited for real fatigue cracks. Crack diagnosis routines are established using free and forced response characteristics. Equations of motion are derived for both crack models, including excitation due to gravity and imbalance. Transfer matrix techniques are established to expediently obtain the steady-state system response. A novel transfer matrix technique, the Complex Transfer Matrix, is developed to distinguish forward and backward whirl components. The rotor's angular response is primarily employed in this work for crack detection and diagnosis. The overhung shaft induces an increased sensitivity to variations in crack depth and location. In addition, an available overhung rotordynamic experimental test rig allows for comparison of the current analytic results to previously obtained experimental results. Under the influence of gravity, the steady-state response of the cracked system includes a prominent 2X harmonic component, appearing at a frequency equal to twice the shaft speed. The magnitude of the 2X harmonic is strongly influenced by the shaft speed. A resonant response occurs when the shaft speed reaches half of a system natural frequency. This work demonstrates that the profile of the 2X harmonic versus shaft speed is a capable diagnostic tool. Identification of the 2X resonance frequency restricts the crack parameters to certain pairs of location and depth. Following this limiting process, the magnitude of the 2X harmonic is used to identify the crack's depth and location. Orbital shapes at the rotor are discussed, as are orbital modes of the shaft deflection. Quantitative results and qualitative observations are provided concerning the difficulty of crack detection and diagnosis.

Helicopters in forward flight experience complex aerodynamic phenomena to various degrees. In low speed level flight, the vortex wake remains close to the rotor disk and interacts with the rotor blades to give rise to blade vortex interaction phenomena. In high speed flight, compressibility effects dominate leading to the formation of shocks. If the required thrust is high, the combination of high collective pitch and cyclic pitch variations give rise to three-dimensional dynamic stall phenomena. Maneuvers further exacerbate the unsteady airloads and affect rotor and hub design. The strength and durability of the rotor blades and hub components is dependent on accurate estimates of peak-to-peak structural loads. Accurate knowledge of control loads is important for sizing the expensive swash-plate components and assuring long fatigue life. Over the last two decades, computational tools have been developed for modeling rotorcraft aeromechanics. In spite of this progress, loads prediction in unsteady maneuvers which is critical for peak design loads continues to be a challenging task. The primary goal of this research effort is to investigate important physical phenomena that cause severe loads on the rotor in steady flight and in extreme maneuvers. The present work utilizes a hybrid Navier-Stokes/free-wake CFD methodology coupled to a finite element based multi-body dynamics analysis to systematically study steady level and maneuvering flight conditions. Computational results are presented for the UH-60A rotor for a parametric sweep of speed and thrust conditions and correlated with test data at the NFAC Wind Tunnel. Good agreement with test data has been achieved using the current methodology for trim settings and integrated hub loads, torque, and power. Two severe diving turn maneuvers for the UH-60A recorded in the NASA/Army Airloads Flight Tests Database have also been investigated. These maneuvers are characterized by high load factors and high speed flight. The helicopter experiences significant vibration during these maneuvers. Mean and peak-to-peak structural loads and extensive stall phenomena including an advancing side stall phenomena have been captured by the present analyses.

Rotordynamics is an important area in mechanical engineering. Many machines contain rotating parts. It is well known that rotating components can develop large amplitude lateral vibrations near certain speeds called critical speeds. This large amplitude vibration is called rotor whirl. This thesis is about rotor whirl. Conventional treatments in rotordynamics use what are called gyroscopic terms and treat the rotor as a one-dimensional structure (Euler-Bernoulli or Timoshenko) with or without rigid masses added to them. Gyroscopic terms are macroscopic inertial terms that arise due to tilting of spinning cross-sections. This approach, while applicable to a large class of industrially important rotors, is not applicable to a general rotor geometry. In this thesis we develop a genuine continuum level three dimensional formulation for rotordynamics that can be used for many arbitrarily shaped rotors. The key insight that guides our formulation is that gyroscopic terms are macroscopic manifestations of the prestress induced due to spin of the rotor. Using this insight, we develop two modal projection techniques for calculating the critical speed of arbitrarily shaped rotors. These techniques along with our prestress based formulation are the primary contributions of the thesis. In addition, we also present two different nonlinear finite element based implementations of our formulation. One is a laborious load-stepping based calculation performed using ANSYS (a commercially available finite element package). The other uses our nonlinear finite element code. The latter two techniques are primarily developed to provide us with an accurate answer for comparison with the results obtained using the modal projection methods. Having developed our formulation and the subsequent modal projection approximations, we proceed to validation. First, we analytically study several examples whose solutions can be easily obtained using routine methods. Second, we consider the problem of a rotating cylinder under axial loads. We use a semi-analytical approach for this problem and offer some insights into the role played by the chosen kinematics for our virtual work calculations. The excellent match with known results obtained using Timoshenko theory validates the accuracy of our formulation. Third, we consider several rotors of arbitrary shape in numerical examples and show that our modal projection methods accurately estimate the critical speeds of these rotors. After validation, we consider efficiency. For axisymmetric rotor geometries, we implement our formulation using harmonic elements. This reduces the dimension of our problem from three to two and considerable savings in time are obtained. Finally, we apply our formulation to describe asynchronous whirl and internal viscous damping phenomena in rotors.

Orientador: Robson Pederiva / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T09:02:45Z (GMT). No. of bitstreams: 1 Sanches_FabioDalmazzo_D.pdf: 3111854 bytes, checksum: 7a85cd92fff24bc0ca9170821fb61025 (MD5) Previous issue date: 2015 / Resumo: Este trabalho aborda a identificação simultânea do desbalanceamento e empeno de eixo em rotores a partir do modelo matemático tanto do rotor como das falhas estudadas. Esses dois fenômenos são síncronos à rotação do rotor e, por isso, difíceis de serem separados um do outro. A partir do modelo do rotor representado na forma de espaço de estados, é possível aplicar a definição de matrizes de correlações de modo a gerar um algoritmo que correlaciona os parâmetros de falhas com as respostas do sistema, possibilitando que as falhas sejam identificadas tanto em magnitude como em localização. O estimador é baseado na equação matricial de Lyapunov. Como o número de respostas medidas é inferior ao total de graus de liberdade do rotor, um sistema auxiliar (filtro) é necessário para gerar correlações adicionais que possibilitem a identificação das falhas em estudo. Transformações de coordenadas através da matriz de observabilidade são necessárias para descrever o sistema através das poucas respostas medidas do rotor. Como um modelo matemático confiável é essencial para o sucesso da identificação, grandezas desconhecidas tais como: parâmetros de mancal, rigidez angular do acoplamento e amortecimento do sistema foram identificados através de otimização pelo método Evolução Diferencial, comparando-se as FRF's medidas e simuladas. Técnicas de redução de ordem do modelo ajustado do rotor foram empregadas de modo a reduzir o esforço computacional na determinação da matriz de observabilidade, possibilitando o uso de um filtro de ordem reduzida. Os estudos ocorrem de forma numérica e experimental para dois tipos de rotores: Laval e dois discos. Simulações mostram como o empeno de eixo altera a dinâmica dos rotores quando comparadas com as respostas ao desbalanceamento puro. Na presença do empeno, várias configurações de desbalanceamento foram simuladas e posteriormente introduzidas nas bancadas experimentais. O algoritmo de identificação se mostrou robusto na caracterização dessas duas falhas e o método contribui com o estado da arte na área de detecção de falhas / Abstract: This work is about simultaneous unbalance and shaft bow identification in rotor using the mathematical model of both the rotor and the studied failures. These two phenomena are synchronous with the rotation of the rotor, causing difficulties in separating them from each other. From the rotor model represented in state space form, it is possible to use the definition of correlation matrix in order to generate an algorithm that correlates the fault parameters with the system responses, enabling the faults to be identified in amplitude and phase. The estimator comes form the Lyapunov matrix equation. As the number of measured available responses are lower than total number of rotor degrees of freedom, an auxiliary system (filter) is required to generate additional correlations that enable the studied faults identification. Coordinate transformations though the observability matrix are necessary to describe the system by means of some few measured outputs. As a reliable mathematical model is essential for the success of the identification process, unknown parameters such as: bearing coefficients, coupling angular stiffness and damping systems were identified using the Differential Evolution optimization technique in which the experimental and simulated FRF's were compared and adjusted. Model order reduction techniques were used on the updated rotor model to reduce computational costs in determining the observability matrix, which allows the usage of a lower filter order. The studies were performed numerically and experimentally for two different test rigs: Laval rotor and two disc rotor. Simulations show the shaft bow changes the dynamic behavior of the rotor when compared to the pure unbalanced rotor responses. In the presence of bow, various unbalance configurations were simulated and thereafter introduced in the test rigs. The identification algorithm showed robustness in identifying these two faults and this method contributes with the state of the art in the field of faults identification / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh. / Ph. D.

Thesis (PhD) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: With increasing environmental concerns and the drive for a greener economy comes an increased desire to improve turbine engine fuel efficiency and reduce emissions. Unfortunately weight reduction techniques used increase the blade loading, which in turn increases the losses. Non-axisymmetric endwall contouring is one of several techniques being investigated to reduce loss in a turbine. An investigation at Durham University produced a non-axisymmetric endwall design for a linear cascade. An adaption of the most promising endwall was investigated in an annular rotating test rig at the CSIR using steady state instrumentation. The current investigation extends those investigations into the unsteady time domain. Previous investigations found that a generic rotor endwall contour improved efficiency by controlling the endwall secondary flow vortex system in both a linear cascade and an annular 1½ stage rotating test turbine. The current research was aimed at determining if there were any unsteady effects introduced by the contoured endwall. The approach was unique in that it investigated the unsteady effects of an endwall contour originally designed for a linear cascade both experimentally and numerically at three incidence angles (positive, zero and negative to represent increased load, design load and decreased load respectively), the results of which are openly available. Unsteady experimental hotfilm results showed that the endwall contour made the velocity profile more radially uniform by reducing the strength of the endwall secondary flow vortex system. The fluctuations in the velocity were also reduced producing a more temporally uniform velocity profile. The FFT magnitude of the velocity at the blade passing frequency below midspan was also reduced. It was found that the reduction in the endwall secondary flow vortex system due to the contour increased with increasing loading. Numerical results showed that the oscillations in the flow were small and did not penetrate the boundary layer. The contoured rotor was forward and aft loaded when compared to the annular rotor, resulting in a weaker cross passage pressure gradient which allowed the endwall secondary flow vortex system to be less tightly wrapped. Numerical results did not show a significant difference in the oscillations observed in the annular and contoured rotor. A new objective function for use in the endwall optimisation process was proposed that acts as a proxy for efficiency, but is less prone to uncertainty in the results. When used on the current results it shows the same trend as efficiency. It remains to be used to design an endwall for full validation. / AFRIKAANSE OPSOMMING: Met ’n toenemende omgewingsbesorgdheid en die strewe na ’n groener ekonomie kom ’n toenemende behoefte om turbine enjin brandstofdoeltreffendheid te verbeter en vrystellings te verlaag. Ongelukkig het gewigsbesparingstegnieke wat gebruik is die lemlading verhoog, wat op sy beurt die verliese verhoog. Nie-assimmetriese endwandprofilering is een van verskeie tegnieke wat ondersoek word om verliese in ’n turbine te verminder. ’n Ondersoek by die Universiteit van Durham het ’n nie-assimmetriese endwandontwerp vir ’n lineêre kaskade gelewer. ’n Aanpassing van die mees belowende endwand is in ’n annulêre roterende toetsopstelling by die WNNR getoets, deur gebruik te maak van bestendige toestand instrumentasie. Die huidige ondersoek brei daardie ondersoeke uit na die nie-bestendige verwysingsraamwerk . Vorige ondersoeke het bevind dat die generiese rotor endwandprofiel doeltreffendheid verbeter as gevolg van die beheer van die endwand sekondêre vloei draaikolkstelsel in beide ’n lineêre kaskade sowel as ’n annulêre 1½ stadium roterende toetsturbine. Die huidige navorsing was daarop gemik om vas te stel of die endwandprofiel enige onbestendige effekte tot gevolg gehad het. Die benadering was uniek in die sin dat dit die onbestendige effekte ondersoek het van ’n endwandprofiel wat oorspronklik ontwerp is vir ’n lineêre kaskade beide eksperimenteel en numeries op drie invalsshoeke (positief, nul en negatief om onderskeidelik verhoogde lading, ontwerplading en verlaagde lading te verteenwoordig), waarvan die resultate algemeen beskikbaar is. Onbestendige eksperimentele warmfilm resultate het getoon dat die endwandprofiel die snelheidsprofiel meer radiaal uniform gemaak het deur die vermindering van die sterkte van die endwand sekondêre vloei werwelstelsel. Die skommelinge in die snelheid is ook verminder wat ’n meer tyduniforme snelheidsprofiel gelewer het. Die FFT (Fast Fourier Transform) grootte van die snelheid van die lem verbygaan frekwensie onder lem midbestek het ook verminder. Daar was bevind dat die vermindering in die endwand sekondêre vloei draaikolkstelsel as gevolg van die endwandprofiel toeneem met toenemende lading. Numeriese resultate het getoon dat die ossilasie in die vloei klein was en nie die grenslaag binnegedring het nie. Die rotor met gevormde wand het ’n voor- en agterlading gehad in vergelyking met die rotor met annulêre wand, wat tot ’n laer drukgradient dwarsop die vloeirigting gelei het, die endwand sekondêre vloei draaikolkstelsel minder beperk het. Numeriese resultate het nie ’n beduidende verskil in die ossilasies tussen die annulêre en gevormde rotorwand getoon nie. ’n Nuwe doelwitfunksie vir gebruik in die endwand optimersproses is voorgestel wat dien as ’n plaasvervanger vir doeltreffendheid, maar minder geneig is tot onsekerheid in die resultate. Wanneer dit gebruik word op die huidige resultate toon dit dieselfde tendens as doeltreffendheid. Dit moet nog gebruik word in die ontwerp van ’n endwand vir volledige bevestiging.