# Design and Analysis of Internal-External Composite Meshing Hy-Vo Chain
## 5 Multi-Body Dynamics Experiments
### Rotation Velocity of Driven Sprocket Analysis  
In classical theory, the system polygon action and the system meshing performance are consistent, so the system polygon action is also verified by testing the maximum fluctuation difference of the system center distance [12; 13]. However, in this paper, we hold that the most direct expression of the system polygon action is the fluctuations of the rotation velocity of the driven sprocket. If the fluctuation extent of the rotation velocity of the driven sprocket is smaller, the system polygon action will be smaller. Taking the calculation of the fluctuation extent of the driven sprocket velocity at 1000 rpm as an example, based on Figure 19a, the maximum value of the driven sprocket velocity of the external meshing Hy-Vo chain system is \(100.004\) rad/s, and the minimum value of that is \(98.090\) rad/s; thus, the velocity fluctuation extent is \(100.004\) \(-\)\(98.090\) = \(1.914\) rad/s. The maximum value of the driven sprocket velocity of the mixed assembly Hy-Vo chain system is \(99.854\) rad/s, and the minimum value is \(97.997\) rad/s; thus, the velocity fluctuation extent is \(99.854\) \(-\)\(97.997\) = \(1.857\) rad/s. The upper limit of the driven sprocket of the internal-external composite meshing Hy-Vo chain is \(99.840\) rad/s, and the lower limit is \(98.194\) rad/s, so the velocity fluctuation extent is \(99.840\) \(-\)\(98.194\) = \(1.646\) rad/s. Compared with the external meshing Hy-Vo chain system, the velocity fluctuation extent of the mixed assembly Hy-Vo chain system is reduced by \((1.914\) \(-\)\(1.857)/1.914 = \(2.97\%\), and that of the internal-external composite meshing Hy-Vo chain system is the smallest when the speed is at \(1000\) rpm. By using the same method, we can obtain the velocity fluctuation extents of the driven sprocket at all speeds, and we can obtain the improving rates of polygon action for the internal-external composite meshing Hy-Vo chain system and mixed assembly Hy-Vo chain system relative to the external meshing Hy-Vo chain system at all speeds, as Figure 20 demonstrates. Figure 19: _Cont._  
Figure 19: Rotation velocity fluctuation curves of driven sprocket: (**a**) 1000 rpm; (**b**) 1500 rpm; (**c**) 2000 rpm; (**d**) 2500 rpm; (**e**) 3000 rpm; (**f**) 3500 rpm; (**g**) 4000 rpm; (**h**) 4500 rpm; (**i**) 5000 rpm; (**j**) 5500 rpm; (**k**) 6000 rpm; and (**l**) 6500 rpm. Based on Figure 20a, as for the internal-external composite meshing Hy-Vo chain system, the velocity extents of the driven sprocket, except for 3500 rpm, are the smallest. As for the mixed assembly Hy-Vo chain system, the velocity extents of the driven sprocket at most speeds, except for 4500 rpm and 6500 rpm, are lesser than that of the external meshing Hy-Vo chain. Focusing on Figure 20b, when taking the external meshing Hy-Vo chain as the benchmark, the improving rate of polygon action of the internal-external composite meshing Hy-Vo chain system is much bigger than that of the mixed assembly Hy-Vo chain system at most speeds, except for 3500 rpm. Moreover, the average improving rate of polygon action for the internal-external composite meshing Hy-Vo chain system reached 32.72%, but that of the mixed assembly Hy-Vo chain system is only 8.60%. Based on the calculation results, we can obtain that the internal-external composite meshing Hy-Vo chain can effectively reduce the system polygon action, and the effectiveness of the internal meshing profile design proposed in this research is certified to be reliable. Even though the tooth shape of the sprocket in the Hy-Vo chain system is too small to have a complete internal meshing period, the Hy-Vo chain system polygon action can still be reduced further by the internal-external composite meshing mechanism. Moreover, the results also show that the polygon action of the Hy-Vo chain system is not always consistent with its meshing performance.