# Gear Integrated Error Determination Using the Gaussian Template Convolution-Facet Method
## 6 Conclusions  
Our method, based on the GTC\(-\)Facet algorithm, represents novel technology for obtaining gear integrated errors instantaneously. This approach affords several advantages, including fast measurement speed, high positioning accuracy, and comprehensive error information. Additionally, it holds the potential to enable online full inspection on large-scale and fine-module gear production lines in the future. As follows:  
(1) A GTC\(-\)Facet sub-pixel algorithm is proposed to extract gear contours, achieving a positioning accuracy of 3.6 \(\upmu\)m. This algorithm simplifies polynomial fitting to the Gaussian template convolution operation and utilizes the Canny operator to determine the gear edge transition region, effectively reducing the image convolution area and saving computational time.  
(2) The iterative reweighted least squares method is employed to fit the center point of the gear end face. By calculating the pitch deviation and profile deviation, the gear integrated error curve can be synthesized. From the curve, both analytical and functional measurement results of the gears can be derived. Compared with the measurement results of P26, for gears with 23 teeth and module of 0.5 mm, the maximum error is 2.2 \(\upmu\)m for \(F_{p}\), \(-1.6\)\(\upmu\)m for \(f_{p\text{max}}\), 3.6 \(\upmu\)m for the absolute value of \(F_{a}\), 1.9 \(\upmu\)m for \(f_{fa}\), and 3.9 \(\upmu\)m for \(f_{fa}\).  
(3) The information about each tooth can be measured simultaneously without affecting the overall measurement speed. The average measurement speed of the method is  
Figure 28: Analysis of profile modification using the gear integrated error curve.  
Figure 27: Analysis of gear eccentricity using the SJZ curve.  
approximately 0.35 s/piece, which is much faster than the classic contact measurement method (20 s/piece). There is no need for clamping during measurement, enhancing measurement speed while avoiding the introduction of clamping errors and gear damage. It also allows for the rapid identification and quantitative analysis of tooth face burrs and micro modifications of each profile.  
At present, the method proposed in this article is only applicable to spur gear measurement, and it requires further improvement through the use of a multi-sensor fusion measurement scheme in future research.  
Conceptualization, Z.S., Y.F. and P.Z.; methodology, Z.S. and Y.F.; software, Y.F.; validation, Y.F.; formal analysis, Y.F.; investigation, Y.F.; resources, Z.S.; data curation, Z.S. and Y.F.; writing--original draft preparation, Y.F.; writing--review and editing, Z.S., Y.F. and Y.S.; visualization, Y.F.; supervision, Z.S., Y.F. and Y.S.; project administration, Z.S. and Y.F.; funding acquisition, Z.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation Major Scientific Research Instrument Development Project of China, grant number [52227809].  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the data also form part of an ongoing study.  
The authors declare no conflicts of interest.