# A Novel Coaxial Balance Mechanism for Reciprocating Piston Engines
## 4 Conclusions  
To reduce the vibration of piston engines without increasing the engine body size or requiring additional design features, this work proposed a high-order coaxial balancing mechanism solution. In this proposed design, the second-order balance mass block is arranged inside the original first-order balance mass block, and the two balance mass blocks undergo coaxial rotation at different speeds. The novel mechanism was applied to a DK32 single-cylinder engine developed in a laboratory setting as an example. Dynamics simulations of the whole engine using Adams software were carried out in detail. Compared with the first-order balance device, the test point velocity on the cylinder of the single-cylinder engine with the novel coaxial balance mechanism was significantly reduced. The simulation results showed that at 800, 1500, 1800, and 2350 r/min, the percentage decrease in the average velocity (RMS) in the direction of piston motion was 86.25%, 94.81%, 96.19%, and 97.31%, respectively. The support reaction force decreased by 90.62%, 94.98%, 96.12%, and 96.54% at 800, 1500, 1800, and 2350 r/min, respectively. A crankshaft speed of 2350 r/min was taken as an example, and with the first-balance mechanism installed, the average velocity (RMS) of the six test points on the cylinder of the single-cylinder engine was 155.45 mm/s and the support reaction force amplitude was 11,825 N. In comparison, with the novel coaxial balance mechanism installed, the average velocity (RMS) was reduced to 4.18 mm/s and the support reaction force amplitude was reduced to 409 N.  
To summarize, the novel coaxial balance mechanism plays a significant role in vibration reductions. Based on this design concept and, by analogy, the fourth-order balance mechanism could be realized by adding a planetary gear transmission mechanism with a hole inside the second-order balance shaft to balance the fourth-order inertia force. The design retains the original unit body module and does not increase the dimensions of the mechanism. The novel closed-form method used in this study can improve the accuracy of calculating second-order balance mass. By comparing the support reaction force in dynamics simulations, at 800, 1500, 1800, and 2350 r/min, the percentage decrease in the average velocity (RMS) in the direction of piston motion reached 5.75%, 28.68%, 41.12%, and 47.53%, respectively. Additionally, the support reaction force was reduced by 22.45%, 35.26%, 39.73%, and 42.69%, respectively. Using the novel closed-form method, we further enhanced the vibration reduction effect of the coaxial balance mechanism. By adopting a compact unit-body design, the workload and cost of modification could be reduced for all types of single-cylinder or multiple-cylinder engines in service, and the goal of reducing the vibration of the original model could be achieved by adding second- and higher-order  
Figure 15: Support reaction force in the direction of piston motion in the two cases with the novel coaxial balance mechanism based on the closed-form method and conventional method, respectively. balance mechanisms without changing the existing balance mechanism configuration or increasing the dimensions. Future research should expand the scope of the novel coaxial balance mechanism. This mechanism is independent of the engine configuration, and can thus be conveniently used for various engine configurations to balance higher-order inertia loading, including eccentric and single- or multi-cylinder engines, or other mechanisms with a connecting rod and crank. Conceptualization, N.G., Z.X. and M.Z. ; methodology, N.G. and Z.X. ; software, N.G., Z.X., A.W. and Y.G. ; validation, N.G. and Z.X. ; formal analysis, N.G. ; investigation, N.G., Z.X. and Y.G. ; resources, M.Z. ; data curation, N.G. and Z.X. ; writing--original draft preparation, N.G. and Z.X. ; writing--review and editing, N.G., Z.X., Y.G. and M.Z. ; visualization, N.G., A.W., Z.X. and Y.G. ; supervision, M.Z. ; project administration, M.Z.