Automated Correction of Sensor Orientation in Experimental Dynamic Substructuring

Abstract

Experimentally modeling the dynamics of substructures in a large assembly is of great benefit. This comes into play, if some components are too complex to model numerically, or certain effects, e.g. friction, within these parts cannot be modeled accurately. In engineering practice, this task also arises when building a product containing multiple supplier parts, with often no numerical models provided. When the dynamics of the substructures shall be assembled, it is well known that modeling the connection between them properly is essential for obtaining good results. For example, when coupling two pieces of a beam the interface between them must not be assumed as a point with only three translational degrees of freedom. Coupling only these, corresponds to a ball joint connection, which is clearly insufficient for coupling the pieces of a beam. For accurate results one needs to consider rotational degrees of freedom as well. One way of doing so is to apply a so called virtual point transformation. It is based on the assumption that a small region around a connection point is locally rigid. Measuring with sensors distributed around this connection point allows to calculate the rigid motions of the interface (including rotations), provided that their position and orientation is known. This paper focuses on the fact that in an actual experiment the sensor positions can only be known up to a certain measurement accuracy. We will show how a wrong estimate of sensor positions deteriorates the quality of the experimental model obtained from the virtual point transformation and thus its usefulness for dynamic substructuring. However, there are some measures for checking the quality of an experimental model. For instance if the assumption of rigidity on the interface is valid, then the sensors should move with negligible flexible motion between each other. The remaining residual in the transformation should thus be minimal. Another well known property from mechanics is the reciprocity principle. When exchanging the input and output on a linear structure one should get the same transfer function. In other words, the frequency response function (FRF) matrix should be symmetric. Those quality indicators can be used to formulate a cost function for an optimization, with the unknown positions as optimization variables. We will show how wrong position estimates of inputs and outputs can be removed to a large extend by the optimization. We will also show how removing these errors improves the quality of the experimental model and thus the results of dynamic substructuring.