Temperature Gradient Determination with Thermography and Image Correlation in Curved Surfaces with Application to Additively Manufactured Components

Abstract

Abstract Background Thermographic images provide two-dimensional information of the surface temperatures on specific selected component regions. If these components have curved surfaces, there is the question of calculating the surface temperature assigned to the material points concerned on the one hand and determining the associated temperature gradient on the other. Apart from general objects, special problems might occur with additively manufactured components as the surfaces are often rough and rippled. Objectives In this paper, the image information from 2D-thermography as well as 3D-digital image correlation data are combined to determine both the temperature at the material points as well as the temperature gradients concerned. Thus, on the one hand, the basic theoretical equations of the transformations are provided and, on the other hand, the required steps in the experiment are discussed. Methods Since both discrete data sets of thermography and digital image correlation have to be interpolated, radial basis functions are drawn on. In this context, both a consistent presentation of the underlying equations as well as the error propagation of the occurring uncertainties are addressed as well. First, this is demonstrated at a pure verification example to estimate the expected accuracies. Second, the concept is investigated at real samples made of 3D-printed polymer as well as a wire-arc additively manufactured steel specimen. Results It turns out that (a) edge effects can lead to more uncertain data at the boundaries of the evaluated region, and (b) a required oblique tripod attached to the specimen are essential uncertainty factors. However, the uncertainty of the temperature determination due to the projection scheme is in the order of general temperature dispersions. Conclusions Thus, an additional cheap and reliable experimental device in form of a oblique tripod is required which both camera systems have to detect. Then, the evaluation tool can map the 2D-data onto the curvilinear surface. Moreover, the temperature gradient calculation is possible.