# Why We Made GageMap

#### Posted on August 9th, 2017

Historically, the finite element method did a pretty decent job of predicting natural frequencies which were useful for predicting rotation speed where resonances might occur. Subjective comparison of mode-shapes was often done using holography to correlate predicted eigenvectors with operational deflection shapes (ODS). However, direct comparison of measured strains with strains from the finite element model were rarely made. Why?

A normal modes analysis using the finite element method produces a group of eigenvalues and eigenvectors which can be correlated to natural frequencies and mode shapes. The output from the model is always nodal displacements for each eigenvector. These displacements are almost always output in the global coordinate system – although local coordinate systems can be created with some additional effort. Strains are, of course, the partial derivatives of the displacements, but for the finite element method, these are computed at so-called integration points within each element. These results are extrapolated to the nodes (or interpolated to the element centroid). Because elements share adjoining nodes, nodal strains are averaged. Output is again, typically in the global coordinate system.

So, computed strains are point values, linked to the nodes, and output in some kind of coordinate system – most often the global coordinate system. In general, stains in isotropic materials have six unique components (they are tensor quantities), so to compare the computed value to a measurement, you need to know the plane on which the measurement is made and a direction. All this depends on a coordinate system too.

Strain measurements, on the other hand, are scaler quantities. Of course, they are made at some location on a part and in some direction, but this knowledge needs to be converted to the coordinate reference frame of the finite element model if you want to compare the results. Then there is the issue of averaging. Strain gages make an average strain measurement over the area of the strain gage. Once all this information is known, it is a fairly simple mathematical computation to resolve the analytical strain – at the nodes – to the direction of the strain gage for comparison with the measurement. Whew. There had to be a better way.

We just released version 2017.3 of GageMap in August of this year, built upon more than 17 years of development. Since the original formulation, GageMap has been expanded to enable users to find optimum sensor locations, handle HCF computations, perform model validation, assess gage misplacement uncertainty, and much more. There is even a scripting version so you can do mode superposition, hot/cold geometry corrections, or any kind of advanced data analysis you can imagine. If you are responsible for comparing analysis and test – particularly strains – there is simply no better finite element post processor out there.GageMap works with three of the most popular finite element packages; Ansys, Abaqus, and Nastran. It supports a large array of element types, simple or complex material properties, non-linear solutions, and cyclic symmetry.

Since we began more than seventeen years ago comparing analytical and experimental strains, we’ve learned a lot about modeling practices, as well as test practices. The HCF problems of the mid-1990’s are now pretty rare because of products like GageMap. This makes for even better propulsion systems and more reliable power generation plants, and that benefits us all.

#### Author: Kurt Nichol, President/CEO of Apex Turbine Testing Technologies

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