Benjamin Greiner

Zusammenfassung

During the design and development of mechanical systems, mathematical models are a common tool to analyze, predict and characterize the behavior of a structure. For a model to accurately describe the physical behavior of a system, the model type and structure must be suitable for the analysis type. In structural dynamics, simulations employing finite element models of lightweight structures are used to assess the vibration response due to internal and external loads. With appropriately chosen approximations for the model, the simulation results depend on the values of model parameters. The identification of such parameters, the determination of their role and quantitative contribution towards the behavior of a model, is an important task during the process of modeling. Measurement data from experiments are used as reference values to tune and validate the results from model analyses. Complex structures with a significant number of sub-components tend to require complex models in order to reflect their physical behavior accurately. This increases the number of parameters, which poses difficulties during the identification process due to overlaps in parameter effects. Furthermore the size of associated optimization problems increases prohibitively. This thesis presents a multi-stage approach for identifying model parameters of complex lightweight structures. Instead of identifying model parameters for a fully integrated structure at once, sub-assemblies and individual parts are analyzed separately. Model parameters identified in sub-assembly stages are then incorporated into an assembled model. As measurement data and identified parameters are associated with uncertainty distributions, errors in the identification of parameters of upstream stages propagate into higher assembly models. Accordingly, such propagating errors should be minimized in early stages. Additionally, this effect has to be taken into account during the refinement of existing parameter in later stages and for the assessment of model accuracy at higher assembly levels. The staged identification has been applied to two distinct structures: First, in order to validate the principles of staged identification, a cantilevered truss-like space frame beam structure has been modeled and measured in an laboratory setup. Data from previous studies pertaining the structure as well as new measurements from experimental modal analysis have been used to identify a finite element model. The structure was divided into a cell and a short beam configuration in order to simulate sub-assemblies for the staged approach. A second, more complex, structure which motivated the work on this thesis is the SOFIA Telescope Assembly. A legacy finite element model, constructed during the design and integration phase of the telescope, exists but was modeled with a focus on the qualification regarding flight-worthiness and the fulfillment of specifications using conservative parameter values. The model has been updated through staged parameter identification in order to be suitable for simulations under the environment of operational conditions with a focus on dynamic characteristics affecting the optical path. A multitude of data sources from the project documentation archive as well as new measurements with test benches and flight hardware have been used to update single parts and major assemblies, such as the Primary Mirror Assembly and Secondary Mirror Mechanism of the telescope. Comparisons of modal analyses using the updated integrated Telescope Assembly model with ground-based and in-flight modal surveys show the improvement of accuracy of the model. Together with the reorganization of model structure and handling through program scripts, the new model is suitable for further analyses in support of improving the performance of the observatory through enhanced control systems and the reduction of image jitter.

Zusammenfassung

The Stratospheric Observatory for Infrared Astronomy (SOFIA) employs an airborne telescope with a 2.7m primary mirror. The telescope structure is composed of carbon fibre with major parts of steel for the suspension and balancing components. It is exposed to harsh environmental conditions and subject to vibration excitation due to aircraft motions and turbulence from the airflow coming into the telescope cavity. To meet pointing requirements and improve image stability there are ongoing efforts on various components of the telescope system, one of which is the implementation of an Active Mass Damping (AMD) control system: Based on accelerometer signals, reaction mass actuators impose forces onto the support structure to dampen the vibration of optical components. The system has been designed, implemented and preliminary tested in the early years of SOFIA’s scientific operation, but concerns about the structural integrity of the primary mirror and new requirements regarding software qualification have prevented the activation and further development for several years. These concerns being addressed, we are now in the process of reactivating the AMD system on the support structure of the primary mirror. Recent ground tests and in-flight jitter measurements indicate that the damping system is very efficient at eliminating the excitation of targeted structural modes of the telescope structure at 40 to 80 Hz and the first bending modes of the primary mirror at 175 Hz, resulting in a significantly improved image quality. This paper presents the analysis of those measurements and discusses options for future development.