# Design and Analysis of Internal-External Composite Meshing Hy-Vo Chain
## 5 Multi-Body Dynamics Experiments  
### Setting and Calculating  
Considering the Hy-Vo chain is a kind of flexible connecting mechanism that consists of a large number of chain plates and pins, the theoretical transmission performance of the Hy-Vo chain system can only be verified by the CAE software [23]. Moreover, the actual Hy-Vo chain is significantly affected by manufacturing errors and assembly errors, and it is difficult to simulate these errors by setting the simulation parameters in the CAE software. Therefore, the multi-body dynamics simulation results can only be used to verify the correctness of the design method, but cannot represent the experiment results under actual conditions. It should be pointed out that the transmission performance mentioned in this paper mainly refers to the Hy-Vo chain meshing transmission performance and has nothing to do with NVH characteristics and wear resistance characteristics. In this study, we set three groups to simulate and analyze: the external meshing Hy-Vo chain system, the mixed assembly Hy-Vo chain system, and the internal-external composite meshing Hy-Vo chain system, respectively, as shown in Table 3. To obtain the effect of the different meshing mechanisms on the system transmission performance, the basic parameters of these three groups are the same except for the parameters of the internal meshing profile. The basic parameters of these three groups come from an example of widespread use [4; 9; 11; 22]. In this example, the chain pitch is \(p=9.525\) mm, the hole pitch is \(A=8.16\) mm, the basic apothem is \(f=5\) mm, the positioning offsetting angle is \(\gamma=3.8^{\circ}\), the contact radius of the rocker pin is \(r_{\text{r}}=7.4\) mm, the tooth number of the drive sprocket is \(z_{1}=35\), the tooth number of the driven sprocket is \(z_{2}=37\), and the chain link number is \(n=84\). As for the mixed assembly Hy-Vo chain system, the specific setting in Table 3 is mainly derived from the previous studies. These studies have proved that the transmission  
Figure 11: The practical internal-external composite meshing process between chain plate and sprocket. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Meshing Mechanism**} & \multicolumn{2}{c}{**Chain Link Number**} & \multicolumn{2}{c}{**Shape of Internal**} & \multirow{2}{*}{\(\delta\) **(mm)**} \\ \cline{3-3} \cline{5-6}  & & **External Meshing** & & & & \\ \hline
1 & External meshing & 84 & 0 & - & - \\
2 & Mixed assembly & 44 & 40 & Arc & 0.21 \\
3 & Internal–external composite meshing & 0 & 84 & Straight line & 0.108 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Groups setting for simulation. performance of the system will be the best if the Hy-Vo chain is composed of 44 external meshing chain plates and 40 internal meshing chain plates. Moreover, in this case, the curvature center of the internal meshing profile in \(S_{2}(x_{2}O_{2}y_{2})\) is (11.938 mm, 3.380 mm), the radius \(r_{\rm{p}}\) is 16.647 mm, and the convexity \(\delta\) is 0.21 mm [6]. As for the internal-external composite meshing Hy-Vo chain system, according to the design approach introduced in this paper, the internal meshing profile of the internal-external composite meshing Hy-Vo chain should be a straight line. According to the equations of Table 2, we can obtain that the equivalent pitch when the chain is positioned on the drive sprocket is \(p_{\rm{p1}}\)\({}^{\prime\prime}\) = 9.5584 mm, and the equivalent pitch when the chain is positioned on the driven sprocket is \(p_{\rm{p2}}\)\({}^{\prime\prime}\) = 9.5597 mm. When taking the drive sprocket as the basis, according to Equation (19), the convexity of the internal meshing profile is \(\delta_{1}\) = 0.1073 mm. Similarly, we can also obtain the convexity of the internal meshing profile based on the driven sprocket, which is \(\delta_{2}\) = 0.1015 mm. Because \(\delta_{1}\approx\delta_{2}\), we think the value of the actual convexity should be selected from the range [0.10 mm, 0.11 mm].