# Design and Analysis of Internal-External Composite Meshing Hy-Vo Chain
## 5 Multi-Body Dynamics Experiments
### System Center Distance Fluctuation Analysis  
Under the conventional design approach, the maximum fluctuation difference of system center distance is the only index to evaluate the meshing performance of the Hy-Vo chain transmission system, and it is the maximum fluctuation displacement of the driven sprocket rotation center \(O_{2}\)[12, 13]. Supposing that the maximum center distance between the drive sprocket and the driven sprocket is \(S_{\rm{dmax}}\), the minimum center distance is \(S_{\rm{dmin}}\), the maximum fluctuation difference of system center distance is as follows:  
\[\Delta_{\rm{f}}=S_{\rm{dmax}}-S_{\rm{dmin}}, \tag{23}\]  
Under the classical silent chain meshing theory, if the value of \(\Delta_{\rm{f}}\) is lesser, the system polygon action will be lesser, and the system meshing performance will be better, too [4]. Figure 13a-l display the simulation results about the system center distance fluctuations of the three groups. We take the calculation process of the maximum fluctuation difference of system center distance when the speed of the drive sprocket is at 1000 rpm as an example. In Figure 13a, as for the external meshing Hy-Vo chain system, when time is equal to 0.673 s, the value of \(S_{\rm{dmax}}\) is 228.702 mm. When time is equal to 0.226 s,  
Figure 12: Multi-body dynamics model in CAE software. the value of \(S_{\rm{dmin}}\) is 228.685 mm. Based on Equation (23), we can yield the value of the maximum fluctuation difference of 228.702 \(-\) 228.685 = 0.017 mm. As for the mixed assembly Hy-Vo chain system, the maximum value of \(S_{\rm{d}}\) is reached at 228.688 mm when the time is 0.680 s, and its minimum value is reached at 228.671 mm when the time is 0.226 s. Therefore, the value of \(\Delta_{\rm{f}}\) is 228.688 \(-\) 228.671 = 0.017 mm. As for the internal-external composite meshing Hy-Vo chain system, the value of \(S_{\rm{dmax}}\) is 228.694 mm when the time is 0.775 s, and the value of \(S_{\rm{dmin}}\) is 228.683 mm when the time is 0.317 s, so \(\Delta_{\rm{f}}\) should be 228.694 \(-\) 228.683 = 0.011 mm. When the value of \(\Delta_{\rm{f}}\) of the external meshing Hy-Vo chain system when the speed is at 1000 rpm is the benchmark, the maximum fluctuation difference of system center distances for the mixed assembly Hy-Vo chain system is the same as that of the external meshing Hy-Vo chain system, and that of the internal-external composite meshing Hy-Vo chain system is decreased by \((0.017-0.011)/0.017=35.29\%\). In other words, by using the internal-external composite meshing mechanism, the meshing performance of the Hy-Vo chain system can be improved by 35.29% when the speed is at 1000 rpm. By using the same method, based on the simulation results of Figure 13, we can easily obtain all values of the maximum fluctuation difference of system center distances for these three groups at all speeds and the meshing performance improving rates of the different meshing mechanism chain systems at all speeds, as Figure 14 shows. Based on Figure 14a, we know that the system meshing performance can be enhanced to be the best by the internal-external composite meshing mechanism except for when the speed is at 5000 rpm. According to Figure 14b, the average improving rate of meshing performance of the internal-external composite meshing mechanism Hy-Vo chain system reached 42.38%, and that of the mixed assembly Hy-Vo chain is only 13.08%. Therefore, we can obtain the conclusion that the design approach of the internal meshing profile of the internal-external composite meshing Hy-Vo chain proposed in this paper is correct, and the meshing performance of the Hy-Vo chain system can be significantly enhanced by the internal-external composite meshing mechanism. It can also be obtained from Figure 14 that, from the perspective of the average improving rate, although the meshing performance can also be enhanced by the mixed assembly Hy-Vo chain, the improving performance is uncertain.