Jenny Niebsch

Imbalance Estimation Without Test Masses for Wind Turbines

Rotor imbalances of a wind turbine can cause severe damage of the turbine or its components and thus reduce the lifespan and security of the turbine significantly. At present, balancing of the rotor is a time consuming and expensive process due to the necessity of mounting test weights to measure a reference imbalance state. We describe a new method for the detection and reconstruction of imbalances in the rotor of a wind turbine avoiding test weight measurements. The method is based on a wind turbine model, which is derived by the finite element method. In some respect, the model information replaces the information of a reference imbalance state. A mathematical equation linking imbalances and the resulting vibrations is derived using the model. Thus the inverse problem of computing an imbalance from vibration measured at the nacelle is solvable with the usual techniques for ill-posed problems. We show that our model for a wind turbine can be used to predict the vibrations for a given imbalance distribution. In particular, it can be used to reconstruct the imbalance distribution of a wind turbine from noisy measurements in real time, which is verified both for artificial and real data. Also, an optimization strategy is presented in order to adapt the model to the wind turbine at hand. The new method requires a simple model of a wind turbine under consideration but reduces the measuring effort for the computation of balancing weights. It can be implemented into a condition monitoring system (CMS). For the first time, there can be not only an alarm generation but also the actual imbalance and balancing weights and positions can be computed directly from the observed CMS data.

Simultaneous estimation of mass and aerodynamic rotor imbalances for wind turbines

The safe operation of wind turbines requires a well-balanced rotor. The balancing of the rotor requires a method to determine its imbalances. We propose an algorithm for the reconstruction of two types of imbalances, i.e., mass and aerodynamic imbalances from pitch angle deviation. The algorithm is based on the inversion of the (nonlinear) operator equation that links the imbalance distribution of the rotor to its vibrations during operation of the wind turbine. The algorithm requires a simple finite element model of the wind turbine as well as the minimization of a Tikhonov functional with a nonlinear operator. We propose the use of a gradient-based minimization routine. The approach is validated for artificial vibration data from a model of a Nordwind NTK 500 wind turbine.

Mollifier Methods for Aerosol Size Distribution

The ill-posed problem of aerosol size distribution determination from a small number of extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities. The points r where n(r) is evaluated may be freely selected and parallel processing is possible.

Surface Generation Process with Consideration of the Balancing State in Diamond Machining

In order to manufacture optical components or mechanical parts with high requirements regarding surface quality, diamond machining is frequently applied. Nevertheless, to achieve the desired surface quality, the understanding of the surface generation process and its influencing parameters is highly important. One crucial parameter is the residual unbalance of the main spindle. As the residual unbalance affects the process and vice versa, the investigation of the process-machine interaction is necessary. In this paper results of experimental work and mathematical modelling of diamond machining under varying balancing states are presented. The experiments show the connection between unbalances and resulting surface quality; the mathematical model provides the possibility to simulate the surface quality for given unbalances distributions. Furthermore, regularization techniques in order to solve the inverse problem of computing the optimal balancing state for a given or desired surface quality are presented.

Determination of Rotor Imbalances

During operation, rotor imbalances in wind energy converters (WEC) induce a centrifugal force, which is harmonic with respect to the rotating frequency and has an absolute value proportional to the square of the frequency. Imbalance driven forces cause vibrations of the entire WEC. The amplitude of the vibration also depends on the rotating frequency. If it is close to the bending eigenfrequency of the WEC, the vibration amplitudes increase and might even be visible. With the growing size of new WEC, the structure has become more flexible. As a side effect of this higher flexibility it might be necessary to pass through the critical speed in order to reach the operating frequency, which leads to strong vibrations. However, even if the operating frequency is not close to the eigenfrequency, the load from the imbalance still affects the drive train and might cause damage or early fatigue on other components, e.g., in the gear unit. This is one possible reason why in most cases the expected problem-free lifetime of a WEC of 20 years is not achieved. Therefore, reducing vibrations by removing imbalances is getting more and more attention within the WEC community. Present methods to detect imbalances are mainly based on the processing of measured vibration data. In practice, a Condition Monitoring System (CMS) records the development of the vibration amplitude of the so called 1p vibration, which vibrates at the operating frequency. It generates an alarm if a pre-defined threshold is exceeded. In (Caselitz & Giebhardt, 2005), more advanced signal processing methods were developed and a trend analysis to generate an alarm system was presented. Although signal analysis can detect the presence of imbalances, the task of identify its position and magnitude remains. Another critical case arises when different types of imbalances interfere. The two main types of rotor imbalances are mass and aerodynamic imbalances. A mass imbalance occurs if the center of gravitation does not coincides with the center of the hub. This can be due to various factors, e.g., different mass distributions in the blades that can originate in production inaccuracies, or the inclusion of water in one or more blades. Mass imbalances mainly cause vibrations in radial direction, i.e., within the rotor plane, but also smaller torsional vibrations since the rotor has a certain distance from the tower center, acting as a lever for the centrifugal force. Aerodynamic imbalances reflect different aerodynamic behavior of the blades. As a consequence the wind attacks each blade with different force and moments. This also results in vibrations and displacements of the WEC, here mainly in axial and torsional direction, but also in contributions to radial vibrations. There are multiple causes for aerodynamic imbalances, e.g., errors in the pitch angles or profile changes of the blades. The major differences in the impact of mass and aerodynamic imbalances are the main directions of the induced vibrations and the fact that aerodynamic imbalance loads change with the 7

The MICADO first light imager for the ELT: overview, operation, simulation

MICADO will enable the ELT to perform diffraction limited near-infrared observations at first light. The instrument’s capabilities focus on imaging (including astrometric and high contrast) as well as single object spectroscopy. This contribution looks at how requirements from the observing modes have driven the instrument design and functionality. Using examples from specific science cases, and making use of the data simulation tool, an outline is presented of what we can expect the instrument to achieve.

Modelling of Ultra-Precision Turning Processes in Consideration of Unbalances

In order to manufacture optical components or mechanical parts with high surface roughness requirements, diamond machining is used. To achieve the desired surface quality, the understanding of the surface generation process and its influencing parameters is important. Here, the crucial parameter is the residual unbalance of the main spindle. As the residual un-balance affects the process and vice versa, the investigation of the process-machine interaction is necessary. In this paper we present a model describing this interaction between dynamical unbalances that occur during the machining process and the engine-shaft structure at the example of an ultra-precision turning lathe. This model allows the determination of the achievable surface quality of a workpiece for a given balancing state. On the other hand we will present a mathematical method to solve the corresponding inverse problem of computing the necessary residual balancing state and balancing weights for a given desired or given measured surface quality.

Imbalances in High Precision Cutting Machinery

In high precision cutting processes it is very important to have a highly balanced system in order to produce components in optical quality. Achieving the best possible balancing state is a time consuming process. Therefor the prediction of the influence of the balancing state on the surface quality of the component is desirable. On the other hand such a prediction model should enable us to compute an objective necessary balancing state for a desired surface quality and thus save balancing time. In this article we present a model of an high precision cutting experimental platform that describes vibrations of the platform caused by imbalances and forces from the cutting process. To compute imbalances from vibrational measurements, regularizations techniques for the solution of inverse and ill-posed problems are employed and presented.Copyright

Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data

The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new two- dimensional model for the troposphere is proposed.