No description available.

[pt] Este trabalho possibilita o desenvolvimento de um protótipo para uma bancada de rotação em escada reduzida pela modelagem, simulação e variação dos parâmetros usando o método analítico e o método dos elementos finitos. A estrutura da bancada é composta por duas seções, cada uma delas com três discos (rotores), unidas por um acoplamento. A bancada está ancorada numa base (estrutura), e foi montada sobre uma mesa isolada. As seções são acionadas por um motor elétrico (CA)monitorado por um inversor de frequência. A avaliação da sensibilidade dos parâmetros do sistema tais como características de eixo, dos rotores (massas e inércias) e mancais, forneceram um melhor entendimento do comportamento dinâmico. Os parâmetros do sistema foram escolhidos de tal forma a poder medir o desbalanceamento, empenamento do eixo, anisotropia dos mancais. Com este protótipo de bancada, será possível estudar as influências do acoplamento e desalinhamento nos mancais em sua operação, procurando-se obter dados experimentais que permitam conhecer o desenvolvimento dinâmico deste tipo de máquinas rotativas (sistemas multirotor-mancais). / [en] This work reports the modeling, simulation of the dynamics and assemblage of a reduced scale prototype of a Multi-span Rotor. Modeling and simulation were performed using both analytical and finite element approaches. The Multi-span Rotor is a two stage rotor, each stage with three disks (rotors). The two stages are joined by a coupler. An electric motor (CA), wich is controlled by frequency inversor supplies the power to the system. Results from simulation oriented the prototype design, guiding the choices of parameters that control the system response. These parameters were chosen in order to measure umbalancing, shaft bow, and anisotropy of bearing. This prototype allows the experimental study of the influences on the system response of couplings and bearing misalignment in operation, and may be helpful fordwards a better understanting of the dynamic behavior of this type of rotative machines (multirotorbearing system).

<p>The world we are living in today is pushing the technology harder and harder. The products need to get better and today they also need to be friendlier to the environment. To get better products we need better analysis tools to optimize them and to get closer to the limit what the material can withstand. Siemens industrial Turbomachinery AB, at which thesis work is made, is constructing gas and steam turbines. Gas and steam turbines are important in producing power and electricity. Electricity is our most important invention we have and most of the people are just taking electricity for granted. One way to produce electricity is to use a gas turbine which is connected to a generator and by combing the turbine with a steam turbine the efficiency can be up to 60 %. That is not good enough and everybody want to get better efficiency for the turbines, meaning less fuel consumption and less impact on the environment.</p><p>The purpose of this thesis work is to analyze a tool for rotor dynamics calculations. Rotor dynamics is important in designing a gas turbine rotor because bad dynamics can easily lead to disaster. Ansys Classic version 11 is the analyze program that is going to be evaluated for the rotor dynamic applications. Nowadays rotor dynamics is done with beam elements i.e. 1D models, but in this thesis work the beam elementsare going to be changed to solid elements. With solid elements a 3D model can be built and thanks to that more complex calculations and simulations can be made. For example, with a 3D model 3D effects can be shown and e.g. simulations with blade loss can be done. 3D effects are not any problem today but in the future the gas turbines have to get better and maybe also the rotational speed will increase.</p><p>Ansys isn’t working perfectly yet, there are some problems. However Ansys have a good potential to be an additional tool for calculations of rotor dynamics, because more complex calculations and simulations can be done. More knowledge and time needs to form the rules to modeled a rotor and developing the analysis methods. Today the calculated lateral critical speeds are lower than the ones obtained from the in-house program Ardas version 2.9.3 which is used in Siemens Industrial Turbomachinery AB today. The difference between the programs are not so big for the four first lateral modes, only 3-8 %, but the next three lateral modes have a difference of 10-20 %. The torsion frequencies from Ansys are the same as the ones from Ardas, when the Solid186 elements are used to model the blades.</p>

No description available.

Vibrações em coluna de perfuração de poços de petróleo têm sido extensivamente estudadas, principalmente devido aos efeitos danosos causados aos elementos da coluna. Os altos custos envolvidos nas operações têm levado cientistas e empresas a buscarem os melhores resultados, seja no projeto ou na execução do poço. Este trabalho apresenta um modelo matemático não linear para estudo de vibrações em coluna de perfuração em operações de backreaming, ou seja, em operações de retirada da coluna de perfuração de dentro do poço com rotação e bombeamento de fluido simultaneamente. O modelo proposto visa estudar os efeitos das vibrações laterais no conjunto de fundo da coluna, conhecido como Bottom Hole Assembly (BHA). Trata-se de um modelo analítico, não linear com parâmetros concentrados, onde são considerados os efeitos de amortecimento devido ao fluido de perfuração, contato entre estabilizador e comando de perfuração contra a parede do poço e rigidez torcional do tubo de perfuração, com implementação da solução numérica do sistema de equações diferenciais através da criação de uma rotina computacional em ambiente MATLAB®. Para calibração do modelo matemático proposto, foi construída uma bancada experimental, em escala com uma coluna de perfuração, simulando a condição dinâmica da coluna. Os resultados mostram boa correlação entre o modelo matemático, bancada experimental e dados reais de campo. Análises paramétricas foram realizadas para estudo da influência do movimento de precessão, aceleração lateral e dano acumulado na coluna. Um modelo probabilístico foi proposto para estudo das vibrações da coluna em conjunto com o modelo matemático ajustado experimentalmente. O trabalho discute os resultados estatísticos para análise de vibração da coluna utilizando o método de Monte Carlo, considerando as incertezas no diâmetro do poço e coeficiente de atrito. Os resultados mostram que a aceleração lateral é menor em poços com diâmetro próximo ao da broca e com baixo coeficiente de atrito, além de não sofrerem influência significativa devido à velocidade de backreaming. Para poços com maior incerteza no diâmetro do poço e elevada velocidade de rotação da coluna, observou-se maiores valores de aceleração lateral. / Oil well drill string vibrations have been studied extensively throughout the world, mainly due to the highly damaging effects caused by these vibrations in the drill string elements. The high costs involved in the operations have led scientists and companies to seek the best results, whether in wellbore project or during real time construction. This thesis presents a non-linear mathematical model for drill string vibrations analysis during backreaming operations, that is, pulling out drill string with pumping and rotation simultaneously. The model proposed aims to study the effects of lateral vibrations on the lower portion of the drill string, commonly known as Bottom Hole Assembly (BHA). The modeling approach is based on analytical, nonlinear and lumped parameters, which considers the effects of drilling fluid damping, stabilizer and drill collar contact with the borehole wall and drill pipe torsional stiffness, with MATLAB® numerical routine implementation to solve the system of differential equations. To setup of the proposed mathematical model, an experimental test rig was built in scale with a real drill string, simulating the dynamic condition of the drill string. The results show good correlation between the mathematical model, experimental test rig and real field data. Parametric analysis were performed to study the influence of backward whirl, lateral acceleration and accumulated damage in the drill string. A probabilistic model was proposed for the study of drill string vibrations with mathematical model experimentally calibrated. The work discusses the statistical results for the drill string vibration using Monte Carlo approach, considering the uncertainties in borehole diameter and friction coefficient. The results show that the lateral acceleration is smaller in borehole diameter closer to the drill bit diameter with low friction coefficient, besides not being significant influence due to the backreaming speed. For wellbore with greater uncertainty in the borehole diameter and for drill string with high speed rotation, a higher lateral acceleration value was observed.

Vibrações em coluna de perfuração de poços de petróleo têm sido extensivamente estudadas, principalmente devido aos efeitos danosos causados aos elementos da coluna. Os altos custos envolvidos nas operações têm levado cientistas e empresas a buscarem os melhores resultados, seja no projeto ou na execução do poço. Este trabalho apresenta um modelo matemático não linear para estudo de vibrações em coluna de perfuração em operações de backreaming, ou seja, em operações de retirada da coluna de perfuração de dentro do poço com rotação e bombeamento de fluido simultaneamente. O modelo proposto visa estudar os efeitos das vibrações laterais no conjunto de fundo da coluna, conhecido como Bottom Hole Assembly (BHA). Trata-se de um modelo analítico, não linear com parâmetros concentrados, onde são considerados os efeitos de amortecimento devido ao fluido de perfuração, contato entre estabilizador e comando de perfuração contra a parede do poço e rigidez torcional do tubo de perfuração, com implementação da solução numérica do sistema de equações diferenciais através da criação de uma rotina computacional em ambiente MATLAB®. Para calibração do modelo matemático proposto, foi construída uma bancada experimental, em escala com uma coluna de perfuração, simulando a condição dinâmica da coluna. Os resultados mostram boa correlação entre o modelo matemático, bancada experimental e dados reais de campo. Análises paramétricas foram realizadas para estudo da influência do movimento de precessão, aceleração lateral e dano acumulado na coluna. Um modelo probabilístico foi proposto para estudo das vibrações da coluna em conjunto com o modelo matemático ajustado experimentalmente. O trabalho discute os resultados estatísticos para análise de vibração da coluna utilizando o método de Monte Carlo, considerando as incertezas no diâmetro do poço e coeficiente de atrito. Os resultados mostram que a aceleração lateral é menor em poços com diâmetro próximo ao da broca e com baixo coeficiente de atrito, além de não sofrerem influência significativa devido à velocidade de backreaming. Para poços com maior incerteza no diâmetro do poço e elevada velocidade de rotação da coluna, observou-se maiores valores de aceleração lateral. / Oil well drill string vibrations have been studied extensively throughout the world, mainly due to the highly damaging effects caused by these vibrations in the drill string elements. The high costs involved in the operations have led scientists and companies to seek the best results, whether in wellbore project or during real time construction. This thesis presents a non-linear mathematical model for drill string vibrations analysis during backreaming operations, that is, pulling out drill string with pumping and rotation simultaneously. The model proposed aims to study the effects of lateral vibrations on the lower portion of the drill string, commonly known as Bottom Hole Assembly (BHA). The modeling approach is based on analytical, nonlinear and lumped parameters, which considers the effects of drilling fluid damping, stabilizer and drill collar contact with the borehole wall and drill pipe torsional stiffness, with MATLAB® numerical routine implementation to solve the system of differential equations. To setup of the proposed mathematical model, an experimental test rig was built in scale with a real drill string, simulating the dynamic condition of the drill string. The results show good correlation between the mathematical model, experimental test rig and real field data. Parametric analysis were performed to study the influence of backward whirl, lateral acceleration and accumulated damage in the drill string. A probabilistic model was proposed for the study of drill string vibrations with mathematical model experimentally calibrated. The work discusses the statistical results for the drill string vibration using Monte Carlo approach, considering the uncertainties in borehole diameter and friction coefficient. The results show that the lateral acceleration is smaller in borehole diameter closer to the drill bit diameter with low friction coefficient, besides not being significant influence due to the backreaming speed. For wellbore with greater uncertainty in the borehole diameter and for drill string with high speed rotation, a higher lateral acceleration value was observed.

The world we are living in today is pushing the technology harder and harder. The products need to get better and today they also need to be friendlier to the environment. To get better products we need better analysis tools to optimize them and to get closer to the limit what the material can withstand. Siemens industrial Turbomachinery AB, at which thesis work is made, is constructing gas and steam turbines. Gas and steam turbines are important in producing power and electricity. Electricity is our most important invention we have and most of the people are just taking electricity for granted. One way to produce electricity is to use a gas turbine which is connected to a generator and by combing the turbine with a steam turbine the efficiency can be up to 60 %. That is not good enough and everybody want to get better efficiency for the turbines, meaning less fuel consumption and less impact on the environment. The purpose of this thesis work is to analyze a tool for rotor dynamics calculations. Rotor dynamics is important in designing a gas turbine rotor because bad dynamics can easily lead to disaster. Ansys Classic version 11 is the analyze program that is going to be evaluated for the rotor dynamic applications. Nowadays rotor dynamics is done with beam elements i.e. 1D models, but in this thesis work the beam elementsare going to be changed to solid elements. With solid elements a 3D model can be built and thanks to that more complex calculations and simulations can be made. For example, with a 3D model 3D effects can be shown and e.g. simulations with blade loss can be done. 3D effects are not any problem today but in the future the gas turbines have to get better and maybe also the rotational speed will increase. Ansys isn’t working perfectly yet, there are some problems. However Ansys have a good potential to be an additional tool for calculations of rotor dynamics, because more complex calculations and simulations can be done. More knowledge and time needs to form the rules to modeled a rotor and developing the analysis methods. Today the calculated lateral critical speeds are lower than the ones obtained from the in-house program Ardas version 2.9.3 which is used in Siemens Industrial Turbomachinery AB today. The difference between the programs are not so big for the four first lateral modes, only 3-8 %, but the next three lateral modes have a difference of 10-20 %. The torsion frequencies from Ansys are the same as the ones from Ardas, when the Solid186 elements are used to model the blades.

This dissertation describes the design, analysis and testing of an unconventional rotor featuring extremely flexible, retractable blades. These rotor blades are composed of a flexible matrix composite material; they are so flexible that they can be rolled up and stowed in the rotor hub. The motivation for this study is to equip the next generation of unmanned rotary-wing vehicles with morphing rotors that can change their diameter in flight, based on mission requirements. Due to their negligible structural stiffness, the static and dynamic behavior of these blades is dominated by centrifugal effects. Passive stabilization of the flexible blades is achieved by centrifugal stiffening in conjunction with an appropriate spanwise and chordwise mass distribution. In particular, such blades are susceptible to large deformations. For example, a combination of the trapeze effect and the tennis racquet effect induces a large negative twist that results in decreased efficiency. Additionally, the rotor blades are prone to aeroelastic instabilities due to their low rotating torsional frequency, and it is seen that without careful design the blades experience coupled pitch-flap limit cycle oscillations. The primary focus of this research is to develop analytical and experimental tools to predict and measure the deformations of an extremely flexible rotor blade with non-uniform mass distribution. A novel aeroelastic analysis tailored towards unconventional blades with negligible structural stiffness is developed. In contrast to conventional analyses developed for rigid rotor blades, the present analysis assumes very large elastic twist. The nonlinear coupled equations of motion for the flap bending, lead-lag bending and torsion of an elastic rotating blade are derived using Hamilton's principle. The virtual work associated with unsteady aerodynamic forces in hover is included in the analysis. An ordering scheme consistent with the relevant physical quantities is defined and terms up to second order are retained in the Hamiltonian. The equations of motion are solved using a nonlinear finite element analysis. The steady-state deformation of the rotor blade is obtained from the time invariant part of the solution. The rotating flap, lag and torsional frequencies are found by solving the eigenvalue problem associated with the homogeneous system of equations. Finally, stability boundaries are computed for various operating conditions and the influence of parameters such as rotational velocity and collective pitch angle is discussed. The analytical predictions are validated by experimental measurements of the blade deformation in hover. These measurements are obtained by a novel, non-contact optical technique called three-dimensional Digital Image Correlation (3D DIC). The use of this technique is demonstrated for the first time to obtain full-field deformation measurements of a rotating blade. In addition, stability boundaries are extracted from experimental observations and correlated with predictions. / text

The McTronX Research group at the Potchefstroom campus of the North-West University, aims to establish a knowledge base on active magnetic bearing (AMB) systems. Up to date, the group has established a firm knowledge base on various topics related to AMB systems. A recent focus was the design and development of a high speed AMB supported rotor system called the rotor delevitation system (RDS) to analyse rotor drops. During the testing phase of the RDS, the machine exhibited vibrations, of which the origins were unknown. The research presented in this dissertation sets out to characterize the vibrations of the RDS, which is the group’s first attempt to fulfil the need for characterizing vibrations in an AMB supported rotor. Emphasis is placed on characterizing the natural response of the RDS rotor, stator and integrated system. The research project is defined in terms of four main objectives: rotor and stator characterization, modelling, system characterization and rotor dynamic diagnostics. A comprehensive literature study introduces the fundamental concepts regarding vibrations of single and multiple degree of freedom systems. These concepts include; natural frequencies, damping, machine vibrations, rotor dynamics and modelling techniques. These modelling techniques are introduced to verify the experimental methodology used to determine the natural frequencies. A critical overview of the literature contextualises the theory with the research investigation. For the RDS rotor and stator characterization, a modal analysis process also known as the “bump test” is implemented in order to validate the bending natural frequencies of the rotor and stator. A simulation model of the RDS is constructed in the finite element (FE) package DyRoBeS®. The model is verified with a numerical and an analytical model and validated with the measured bending natural frequencies of the RDS rotor. For the system characterization, a number of modal analysis processes are implemented, which validates the rigid body natural frequencies of the RDS. These frequencies are also used to validate the FE simulation. The origins of the synchronous vibration harmonics are verified by formulating and evaluating hypotheses according to different modal analysis processes. From the RDS rotor modal analysis it was identified that a bending natural frequency of the rotor is situated at approximately 443.33 Hz. This was verified using the FE simulation model. During the system modal analyses, it was identified that only one rigid body natural frequency, situated at approximately 62 Hz, is excited. This frequency increases with the differential gain control parameter of the system up to approximately 140 Hz. After evaluating two hypotheses regarding the origins of the synchronous vibrations harmonics, it was verified that non-circularity of the rotor at the measuring positions is the cause. Overall the objectives of the study were addressed by characterizing the natural frequencies of the rotor, stator and RDS system. This include the mode forms of the rigid body and bending natural frequencies of the system. The results of the verification and validation methods correlated, which imply these methods are reliable to identify the origins of vibrations in rotor-bearing systems. The differential gain control parameter of the AMBs control the equivalent damping in the RDS. An increase in this parameter should lead to a decrease in amplitude and frequency of the maximum vibration, and vice versa. However, it was noted that an increase in this parameter caused a linear increase in the rigid body natural frequency. The literature indicates that this effect can only be caused by an increase in system stiffness. It is therefore recommended to evaluate the stiffness of the system as a function of the differential gain control parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012.

The McTronX Research group at the Potchefstroom campus of the North-West University, aims to establish a knowledge base on active magnetic bearing (AMB) systems. Up to date, the group has established a firm knowledge base on various topics related to AMB systems. A recent focus was the design and development of a high speed AMB supported rotor system called the rotor delevitation system (RDS) to analyse rotor drops. During the testing phase of the RDS, the machine exhibited vibrations, of which the origins were unknown. The research presented in this dissertation sets out to characterize the vibrations of the RDS, which is the group’s first attempt to fulfil the need for characterizing vibrations in an AMB supported rotor. Emphasis is placed on characterizing the natural response of the RDS rotor, stator and integrated system. The research project is defined in terms of four main objectives: rotor and stator characterization, modelling, system characterization and rotor dynamic diagnostics. A comprehensive literature study introduces the fundamental concepts regarding vibrations of single and multiple degree of freedom systems. These concepts include; natural frequencies, damping, machine vibrations, rotor dynamics and modelling techniques. These modelling techniques are introduced to verify the experimental methodology used to determine the natural frequencies. A critical overview of the literature contextualises the theory with the research investigation. For the RDS rotor and stator characterization, a modal analysis process also known as the “bump test” is implemented in order to validate the bending natural frequencies of the rotor and stator. A simulation model of the RDS is constructed in the finite element (FE) package DyRoBeS®. The model is verified with a numerical and an analytical model and validated with the measured bending natural frequencies of the RDS rotor. For the system characterization, a number of modal analysis processes are implemented, which validates the rigid body natural frequencies of the RDS. These frequencies are also used to validate the FE simulation. The origins of the synchronous vibration harmonics are verified by formulating and evaluating hypotheses according to different modal analysis processes. From the RDS rotor modal analysis it was identified that a bending natural frequency of the rotor is situated at approximately 443.33 Hz. This was verified using the FE simulation model. During the system modal analyses, it was identified that only one rigid body natural frequency, situated at approximately 62 Hz, is excited. This frequency increases with the differential gain control parameter of the system up to approximately 140 Hz. After evaluating two hypotheses regarding the origins of the synchronous vibrations harmonics, it was verified that non-circularity of the rotor at the measuring positions is the cause. Overall the objectives of the study were addressed by characterizing the natural frequencies of the rotor, stator and RDS system. This include the mode forms of the rigid body and bending natural frequencies of the system. The results of the verification and validation methods correlated, which imply these methods are reliable to identify the origins of vibrations in rotor-bearing systems. The differential gain control parameter of the AMBs control the equivalent damping in the RDS. An increase in this parameter should lead to a decrease in amplitude and frequency of the maximum vibration, and vice versa. However, it was noted that an increase in this parameter caused a linear increase in the rigid body natural frequency. The literature indicates that this effect can only be caused by an increase in system stiffness. It is therefore recommended to evaluate the stiffness of the system as a function of the differential gain control parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012.