# Gear Integrated Error Determination Using the Gaussian Template Convolution-Facet Method
## 5 Experiment and Discussion
### GVMS Integrated Measurement Experiment
#### 5.2.2 Measurement Results  
The integrated error curve in the gear section on the right/left flank obtained through GVMS is shown in Figures 14a and 15a. Here, 1-17 teeth are sorted and distinguished by lines of different colors. There are 137-166 sampling points on each profile, with adjacent teeth spaced 360\({}^{\circ}\)/z.  
The gear integrated error curve of the cross-section of the right flank takes the basic circle position of the first right flank as the initial position, where the rolling angle is 0\({}^{\circ}\). The gear integrated error curve of the left flank section rotates 360\({}^{\circ}\)/z/2 more counterclockwise than the right flank, so the curve does not start from the rolling angle of 0\({}^{\circ}\). The termination position of the gear integrated error curve of the left flank section is at the basic circle of the 17 th left flank, and the angle at this position must be greater than 360\({}^{\circ}\). This way, the integrated error curve in the gear section composed of the right and left flanks can fully contain the error information of the gear for one revolution.  
\begin{table}
\begin{tabular}{c c} \hline
**Component** & **Parameters** \\ \hline Camera & CMOS, GigE interface, 5472 \(\times\) 3648 px, 1\({}^{\prime\prime}\) target surface \\ Lens & Magnification: 0.5; distortion: \textless{}0.006\%; resolution: 7.9 \(\upmu\)m \\ Light source & LED surface light source \\ Pixel equivalent & 4.76 \(\upmu\)m/pixel \\ Gear parameters & Powder metallurgy spur gears; number of teeth: 17; modulus: 0.5 mm; pressure angle: 20\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 1: CVMS parameters.  
Figure 14: Gear integrated error curve of gear section (right flank). (**a**) Gear integrated error curve. (**b**) Gear integrated error curve and its outer envelope.  
Figure 13: GVMS. (**a**) System structure. (**b**) Collected gear image.  
ISO\(-\)1328.1:2013 [14] requires low-pass filtering of the original measurement data used for involute evaluation before analyzing and comparing tolerances. This article also applies Gaussian low\(-\)pass filtering to the integrated error curve in the gear section. Figures 14a and 15a show the filtered integrated error curve in the gear section using the Cartesian coordinate system. Figures 14b and 15b show the results of the extracted envelope from the error curve.  
Figures 16 and 17 are the polar coordinate system representations of the gear integrated error curve. The value of polar coordinates is calculated using the distance in the direction of the inscribed or circumscribed circle that contains the error curve. The use of the Cartesian coordinate system to represent the error curve is more in line with people's habits of observation, while the use of polar coordinate representation can more intuitively reflect the integration of the gear corresponding to various angles on the circumference of the gear. Both methods can decompose the individual errors of gears from them.  
Figure 16: Polar coordinate representation of the gear integrated error curve. (right profile). (**a**) Gear integrated error curve. (**b**) Gear integrated error curve and its outer envelope.  
Figure 15: Gear integrated error curve of gear section (left flank). (**a**) Gear integrated error curve. (**b**) Gear integrated error curve and its outer envelope.