# Investigation of the Mechanical Properties of Spur Involute Gearing by Infrared Thermography
## 4 Analysis of Measured Data
### Analysis of Measured Phase Shift Images  
For the phase-shift measurements, we based our measurements on theoretical considerations and in most cases measured values that could be expected. A tensile load is applied to part of the tooth and a compressive load to another part of the tooth. The above difference in the method of loading is detectable by the difference in the phase displacements between these parts of the object under analysis. So, if in two parts of the object the values of phase shifts (resp. angles) are detected and the difference of these shifts corresponds to 180\({}^{\circ}\), then the loads in these parts of the object are in the opposite phase, which can be interpreted as the presence of a tensile load in one part of the wheel (I) and a compressive load in the other part (II), respectively, and a compressive load in (I) and a compressive load in (II).  
For gears extruded from PLA material, Figure 4a shows in light green the area of compressive load (representing a phase shift of approximately 0\({}^{\circ}\)) that connects the area from the contact of the teeth of the wheel and the counter to the root of the adjacent tooth of the wheel, or extends up to half of the width of the adjacent tooth. The dark blue area represents a phase shift of approximately \(-180^{\circ}\) and shows the tensile load area, the phase difference is approximately 180\({}^{\circ}\).  
In Figure 4b, the gear is printed from PETG material, the yellow color represents the compressive load region (phase shift of approximately 65\({}^{\circ}\)) and the dark blue region represents the phase shift of approximately \(-140^{\circ}\) and shows the tensile load region. The difference in phase shift between these regions is approximately 205\({}^{\circ}\). The value of 205\({}^{\circ}\) is contained within a tolerance interval of 180\({}^{\circ}\)\(\pm\) 30\({}^{\circ}\). This 180\({}^{\circ}\)\(\pm\) 30\({}^{\circ}\) tolerance interval for the 180\({}^{\circ}\) phase shift assessment is the same as the tolerance interval for the detection of the phase shift value when passing through the resonance in the experimental modal analysis.  
These measurements also highlight the surface and subsurface structure of the gears. In Figure 4a,b, concentric contour filaments in the printed gears are also detectable, for example indicated by the white closed curves. This phenomenon is due to the harmonic excitation of the tooth of the composite gear by the frequency \(f_{lock-in}\) and the processing of the measured response mentioned earlier. This phenomenon is used in the field of non-destructive testing (NDT) [23].  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Mean Peak to Valley Height**} & \multirow{2}{*}{**
\begin{tabular}{} \end{tabular}**} \\  & **[um]** & **[1]** \\ \hline PLA & 97.13 & \(-0.16\) \\ \hline PETG & 61.93 & 0.32 \\ \hline Steel counter-piece & 8.55 & 1.17 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter of roughness of profile determined on a line on the tooth width.