# Pattern Classification and Gear Design of Spatial Noncircular
## 4 Tooth Profile Classification Design of Spatial Noncircular Gear
### Transmission Experiment of the Curve Face Gear Pair  
In order to verify the correctness of the tooth profile classification design of the curve face gear pair, a transmission experiment is needed. Taking the first pair of the curve face gear pairs in class C as an example, the parameters in Tables 4 and 6 were selected to obtain the curve face gear pairs with three different tooth profiles by 5-axis CNC milling. Figure 16: Maximum relative error of overall transmission ratio simulation. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Class**} & **Type I: Addition Method** & **Type II: Multiplication Method** \\ \cline{2-3}  & **A: NG-PBGT** & **B: NG-PCGT** & **C: CFG-BG-PCGT** & **D: CFG** & **E: NG** \\ \hline \multirow{5}{*}{Characteristics} & Simple design; & \multirow{5}{*}{Complex design;} \\ \cline{2-3}  & Larger transmission ratio range; & Smaller transmission ratio range; \\ \cline{2-3}  & Less parameter restrictions; & More parameter restrictions; \\ \cline{2-3}  & Complex structure; & Simple structure; \\ \cline{2-3}  & Large volume & Small volume; \\ \cline{2-3}  & Longer transmission chain & Shorter transmission chain \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CVT mechanism characteristics of types I and II. Figure 17 shows the transmission experiment of the curve face gear pair. The input rotation speed is 200 rpm, and the load is 50 N-m. The rotation speeds of the input shaft and output shaft were measured by torque-speed sensor JN338 (produced by Beijing Sanjing Creation Science and Technology Group Co., Ltd., Beijing, China) and torque-speed sensor DRFL-VI-500-A-K (produced by ETH-MESSTECHNIK), respectively, and the transmission ratios of three kinds of curve face gear pairs were calculated. The experimental transmission ratios were compared with the theoretical transmission ratios, as shown in Figure 18. \(i_{\text{t}}\) is the theoretical curve of transmission ratio. \(i_{\text{s}}\), \(i_{\text{h}}\) and \(i_{\text{c}}\) are the measured curves of transmission ratios of curve face gear pairs with straight tooth, helical tooth, and curvilinear tooth, respectively. As can be seen, when the rotational angle \(\theta_{2}\) varies from 0 to 360\({}^{\circ}\), the transmission ratio \(i_{21}\) varies in the range of 1.6-2.4, and the number of cycles of \(i_{21}\) is 2. Moreover, as can be seen from the total comparison and single comparison, the three measurement curves of the transmission ratio are in good agreement with the theoretical curve, which indicated the correctness of the theoretical method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Cutting Method**} & \multirow{2}{*}{**Material**} & \multicolumn{4}{c}{**Generating Back**} & \multicolumn{4}{c}{**Curve Face Gear Pair**} \\ \cline{3-8}  & & & **Module** & **Addendum Coefficient of Bottom** & **Coefficient of Bottom** & **Pressure Bag** & **Number of Count** & **Gears** & **Circumferential Accuracy** & **Circumferential Accuracy** \\ \hline
5-axis CNC milling & 20 CMnTil & 4 mm & 1 & 0.25 & 20\({}^{\circ}\) & 36/18 & 8 & 0.1 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Specific properties of the curve face gear pair. Figure 17: Transmission experiment of the curve face gear pairs with different tooth profiles. Figure 18: Comparison between the theoretical and experimental transmission ratios of the curve face gear pair. Figure 19 shows the maximum relative error of the transmission ratio experiment. The experimental curves of the transmission ratios of the three curve face gear pairs are close to the theoretical curve, and the matching degree from low to high is the transmission ratio curve of the straight tooth, helical tooth, and curvilinear tooth curve face gear pair, respectively. The maximum relative errors of the corresponding transmission ratios are 5.5%, 4.6%, and 3.9%, respectively. The main reason for this difference is that the tooth profile has an important influence on the transmission stability of the curve face gear pair.