Effect of instrumentation position and direction inaccuracy on the calculation of virtual point transformed FRFs

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This work comprises research in the field of Experimental Dynamics. This technique is currently used in the automotive area and is used to enhances the current state of FEM with the inclusive of test- based models. Building test-based models for EDS (Experimental Dynamic Substructuring) requires very accurate measurement, and this thesis examines how uncertainty on sensors and impacts affects the accuracy of the test-based model. Dynamic Substructuring is the collection of methods to describe large and complex systems by using the models of its substructures. This approach assumes that the dynamics of each substructure is enclosed in a so-called super element at interface DoF. Modeling domains that engage condensed dynamic information, like admittance FRFs in the frequency domain, are therefore particularly suited for substructuring [49]. One of the methods to model the interface between two (or more) substructures, is coupling two sub- structure by a single mutual point, so-called Virtual Point. This single point is a collocated point, a super-element, which has both translational and rotational DoFs., In order to obtain the FRF of the coupling point of each substructure, an experimentally gained in- formation is transforming into the super-element’s admittance (Virtual Point FRF). The experimentally gained information is recorded by sensors and roving impacts. The transformation uses projection ma- trices for both input and output and is called Virtual Points Transformation (VPT). In all experiments, we almost always have some uncertainties, and achieving true experiments is al- most impossible. Making errors while mounting the sensors and roving impacts is very plausible. This mounting errors can be positional as well as directional. Because of these uncertainties, we can never find the true transformation matrices. In this thesis, the propagation of the positional and directional uncertainty of measuring equipment (sen- sors and roving impacts) into the calculation of Virtual Point frequency response function is investigated analytically, as well as numerically. It is shown which error and in what extend is the most dominant er- ror source, and in which frequencies and in which cross-functions of V P we can expect the least precise. Expectations can be made on the inputs’ or outputs’ DOF with dominant effect on error generation for a particular mode shape, based on the local mode shape-motion of measurement area, and by using the Component Mode Synthesized method (CMS). It is shown that the error generation on measurement, and further error propagation into super-element caused by a particular error source is mode shape- and frequency-dependent. Further, an estimation is given for the amount of influence of each dominant error source on the cal- culation of the forces and responses of Virtual Point, on both rotational and translational forces and responses. Since the dominant error generation is depending on the mode shape motion, the V P’s cross-functions with the least precision can also be defined.
It is shown that based on the decomposition of transformation matrices, the rotational/ rotational cross- functions are the most sensitive ones to both positional and directional uncertainties if we are looking to absolute value. Then, base on the numerical results, a comparison is made between all four studied cases; Impacts Positional Uncertainty (IPU), Impacts Directional Uncertainty (IDU), Sensors Positional Uncertainty (SPU), and Sensors Directional Uncertainty (SDU). The possibility of error cancellation and the maximum error propagation is introduced.