# Investigation of the Mechanical Properties of Spur Involute Gearing by Infrared Thermography
## 4 Analysis of Measured Data
### Response Amplitude Image Analysis  
The amplitude \(A\) of the response \(s(t)\), Equation (2) corresponds to the amplitude \(A_{1}\) of the first term of the series (4) and expresses the temperature change \(\Delta T\). Knowing the thermal diffusivity \(K\) (Table 1), we can determine the change of the first invariant \(\Delta\sigma_{ii}\), according to the term (2), together with the knowledge of the term. For the given loads of 20 N, the modal exciter was built up by the load, which we evaluated through the IR camera as the I. invariant of the stress.  
Figures 5 and 6 on the left show the field (map) of the first invariant for the wheel made of PLA and PETG material. In the maps, 2 line segments are plotted. The line segment closer to the edge of the tooth (red) passes through the region with the occurrence of contour fibers. The line segment further away from the tooth edge (green color) corresponds to the area of the tooth matrix, without contour filament.  
Figures 5 and 6 on the right are plots showing the progression of the invariant along the line segments plotted in the map. On the horizontal axes of the graphs, the position of a point is expressed by the pixel number of the camera detector in the horizontal direction (the detector is 320 pixels by 256 pixels); the pixel numbers on the horizontal axes of the graphs in Figures 5 and 6 can take values from 1 to 320.  
Figure 4: The phase shift for gears made of (**a**) PLA, (**b**) PETG allows to distinguish the region of compressive and tensile load in the region of the loaded tooth of the gear. The highlighted part (white closed curve) indicates the highlighted concentric contour fibers.  
Figure 5: First stress invariant for the PLA wheel under the force load induced by the modal exciter, and the values of the invariants at the points on the line segments marked in the contour fiber region (red plot) and in the matrix region (green plot).  
If we compare the waveforms of the invariant plots, then in the contour fiber region (red color) the invariants take higher values for both materials than in the matrix.  
Comparison the maximum values of the invariants in the matrix regions (green color), then higher invariant values are obtained for PLA than for PETG.  
When we compare the maximum invariant values in the matrix regions, then higher invariant values are obtained for PLA than for PETG. We assume that the reason for this is the higher compliance of PETG than PLA.  
Qualitatively, we consider the distribution of invariants for both materials to be approximately the same, with higher values of invariants being achieved only in the region of the contour and in the root of the teeth than in the matrix.  
The determined values of the invariants along the used line segments show not a smooth but a \"saw\" signal If the filament was 0.2 mm in diameter and the pixel projected an image from an area on the sample smaller than approximately 0.3 \(\times\) 0.3 mm, then there was uneven coverage of the area by the filaments on that 0.3 \(\times\) 0.3 area. This problem has yet to be addressed.