# Design and Analysis of Internal-External Composite Meshing Hy-Vo Chain
## 4 Meshing Characteristics  
Figure 10 shows the ideal state of the internal-external composite meshing between the chain plate and the sprocket. In this case, the distance between the left pitch point of the chain plate and the \(y\)-axis is supposed to be \(x_{\text{p}}\), and the distance between the pitch line of the actual chain and the sprocket rotation center should satisfy \(s_{\text{jmax}}=r_{\text{p}}\). Under the influence of the convexity of the internal meshing profile, the distance between the left  
Figure 9: Design scheme of the internal–external composite meshing Hy-Vo chain.  
pitch point and the left internal meshing profile is \(f_{1}+\delta\). Supposing that the meshing line of the chain and sprocket is M-M, according to the meshing theory, line M-M tangents to the base circle of the sprocket and passes through the intersection point between the \(y\)-axis and the pitch circle of the sprocket. If the internal meshing point between the chain plate and the sprocket is M\({}_{1}\), point M\({}_{1}\) must be on meshing line M-M.  
Supposing that the distance between point M\({}_{1}\) and the actual chain pitch line is \(h\), we obtain the following:  
\[h=x_{\rm p}\sin\alpha\cos\alpha+(f_{1}+\delta)\sin\alpha+(r_{\rm p}-r_{\rm j}) \cos^{2}\alpha, \tag{20}\]  
When \(x_{\rm p}=p\), the internal meshing profile of the chain plate begins to mesh with the sprocket involute tooth profile. At this time, the distance between point M\({}_{1}\) and the pitch line of the actual chain is at maximum, the maximum value is as follows:  
\[h_{\rm max}=p\sin\alpha\cos\alpha+(f_{1}+\delta)\sin\alpha+(r_{\rm p}-r_{\rm j })\cos^{2}\alpha, \tag{21}\]  
Based on the periodic motion characteristics of the chain, when \(x_{\rm p}=0\), the meshing between the internal meshing profile and the involute tooth profile must be finished. At this time, the distance between point M\({}_{1}\) and the actual chain pitch line is at a minimum, which is  
\[h_{\rm min}=(f_{1}+\delta)\sin\alpha+(r_{\rm p}-r_{\rm j})\cos^{2}\alpha, \tag{22}\]  
In the practical meshing process, as Figure 11 shows, when \(x_{\rm p}=0\), the internal meshing profile of the chain plate is already out of contact with the sprocket involute profile; that is, the meshing point M\({}_{1}\) lies on the extending line of the internal meshing profile of the chain plate. This is because, compared with the normal silent chain, the hole of the Hy-Vo chain plate is much bigger than that of the normal silent chain plate. To increase the strength of the plate, the Hy-Vo chain equivalent apothem\(f_{1}\) has to be bigger than the normal silent chain standard apothem \(f\). Based on the silent chain meshing theory, if the apothem is greater, the tooth width of the sprocket will be greater, and the tooth shape of the sprocket will be smaller. Because the tooth shape of the sprocket is smaller, the meshing area in the tooth is smaller, and the meshing point is out of the meshing earlier than the theoretical end time. Therefore, in this research, we hold that the internal-external composite meshing between the Hy-Vo chain and sprocket is continuous but incomplete. It should be pointed out that, as for the meshing between the rigid chain and the sprocket, the meshing is continuous and complete because there is another meshing line that is symmetric with line M-M on the \(y\)-axis. In conclusion, because the internal-external composite meshing of the  
Figure 10: The ideal state of the internal–external composite meshing between chain plate and sprocket.  
Hy-Vo chain is continuous but incomplete, its effect on reducing the polygon action and the meshing impact is limited.