3.1 Virtual Points: a brief overview

Virtual point methodology is an innovative concept at the forefront of DIRAC’s unique capabilities. The concept of the virtual point comes from the need to make test-based models for activities such as substructuring and transfer path analysis. In a computer-based simulation, these models are easily obtained by calculating the dynamics at any discrete location with six degrees of freedom (DoF) information.

 

Experimental coupling point

Within the testing world, this is not so straightforward. Interfaces usually cannot be directly measured at a discrete location because they consist of bolts and holts, as shown in Figure 3‑1. Also, typical measurement equipment is only capable of measuring translational DoF.

The virtual point provides a solution to both of these issues. With the virtual point, sensors and impacts are placed around the virtual point, and Interface Displacement Modes (IDMs) are used to transform the measured FRFs to collocated 6-DoF virtual point FRFs.

Figure 3-1: Graphical depiction of the virtual point methodology

Best practices for placing impacts & sensors

Virtual points can be calculated with up to six degrees of freedom. The choice for which VP DoF to include is completely free, as well as the base orientation of the VP itself. In order to capture six DoF using triaxial accelerometers, a minimum of three sensors is required, as illustrated in Figure 3‑2.

For the excitations, a minimum of six impacts is required to define a six DoF VP. In practice, it is good to define 12-15 impacts per VP, as the impacts are much more prone to errors than the sensors.

Sensors and impacts should be positioned in locations close enough to the virtual points such that all objects move rigidly together within the frequency range of interest. Within  the Prepare module, the conditioning of the resulting virtual points and the contributions of their associated measurement DoF can already be assessed. An innovative VP quality widget is available; see 4.2 Prepare widgets for more information.

Figure 3-2: Sensor placement for measurement of accelerations in an arbitrary structure

Quality: consistency calculations

The sensors and impacts used to describe a virtual point should be placed in a rigid area around the VP. To evaluate this assumption, as well as the accuracy of the positions and orientations of the physical impacts and responses, consistency checks are built into DIRAC.

For evaluation of the sensor consistency, the measured responses $$ \boldsymbol {u} $$ are filtered using the virtual point Interface Displacement Mode (IDM) matrix, essentially filtering out any dynamics that are not captured by the VP. This gives a set of VP-filtered responses $$ \boldsymbol {\tilde{u}} $$. Similarly, for the impacts, the force IDM matrix looks for an equivalent combination of impacts $$ \boldsymbol {\tilde{f}} $$ that produces the same load on the virtual point as the actual impacts $$ \boldsymbol {f} $$.

While these explanations relate to sensors and impacts, the same operations can be applied to the rows and columns of the FRF matrices, either independently or simultaneously. Then, the “filtered” FRFs $$ \boldsymbol {\tilde{Y}} $$ are compared to the measured FRFs $$ \boldsymbol {Y} $$ using metrics that evaluate the similarity of the FRFs in both magnitude and phase. This calculation results in the force consistency and response consistency quality checks available in the Analyze Module.

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