## 5 A Case of Comparative Study between HCR and Involute Internal Spur Gear Drive
### Experimental Details  
The layout and composition of the test setup are shown in Figure 16, which mainly includes the gear pair to be tested, a test gearbox, conductive slip ring, drive motor, load motor, input and output couplings, torque and speed sensor, control cabinet, data acquisition system, and a computer installed with data acquisition software. The drive motor is adjusted to the set rotational speed, and the output torque of the load motor is adjusted to a specific value so that the input torque of the drive motor reaches the set value (\(T_{\text{input torque}}\)). The test procedure is a continuous process, and the conversion between working conditions is completed without stopping. To obtain a stable signal, the sampling time under each working condition is set to 2 min, and the sampling frequency is set  
Figure 15: Test gear dive: (**a**) HCR pinion; (**b**) involute pinion.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Module (m\({}_{2}\)/mm) & 2.5 \\ Pinion tooth number (z\({}_{3}\)) & 37 \\ Internal gear tooth number (z\({}_{4}\)) & 47 \\ Pressure angle (\(\alpha\)/\({}^{\circ}\)) & 20\({}^{\circ}\) \\ Addendum coefficient (h\({}_{4}^{*}\)) & 1 \\ Addendum modification coefficient (x) & \(-\)0.3 \\ Tooth width (b/mm) & 26 \\ Center distance (a/mm) & 12.96 \\ Material & 20 CrNiMo \\ \hline \hline \end{tabular}
\end{table}
Table 3: Design parameters for involute internal spur gear drive.  
to 10,000 Hz. Rotational speeds are 360, 420, 540, 660, and 780 r/min and input torque increases in increments of 100 Nm from 100 to 1200 Nm.  
Strain gauges are attached to the adjacent bottom of tooth space for the involute pinion and HCR pinion. Every strain gauge is located on the middle of the tooth root along the tooth width, and the position in the tooth depth direction is shown in Figure 17. The file stress is given by \(\sigma=E\epsilon\), where \(E\) represents the elastic modulus of the gear material and \(\epsilon\) is the file strain measured by the strain gauge.  
For non-standard gear drives, the contact ratio calculation method is defined as  
\[\epsilon=\frac{T_{tol1}}{T_{stat2}-T_{stat1}} \tag{6}\]  
where \(\epsilon\) is contact ratio, \(T_{tol1}\) is the total mesh time of gear tooth 1, \(T_{stat1}\) is the starting mesh moment of gear tooth 1, \(T_{stat2}\) is the starting mesh moment of gear tooth 2. Furthermore, gear tooth 1 and gear tooth 2 are two adjacent teeth, and gear tooth 2 enters into the mesh after gear tooth 1. The starting point and ending point of a certain gear tooth in a mesh  
Figure 16: Main test setup: (**a**) transmission system; (**b**) gearbox assembly; (**c**) HCR internal spur gear drive attached by strain gauges; (**d**) involute internal spur gear drive attached by strain gauges.  
Figure 17: Schematic diagram of strain gauge attachment.  
cycle are obtained by using the strain signal denoise method based on a low-pass filter. The judgment basis is given below,  
1. Starting moment in a mesh cycle: the strain value is greater than the set threshold (75 \(\upmu\)m/m) and the strain value at the previous moment is less than the set threshold.
2. Ending moment in mesh cycle: the strain value is less than the set threshold (75 \(\upmu\)m/m) and the strain value at the previous moment is greater than the set threshold, and the total meshing time is longer than 40 sampling points (namely 0.004 s).