# A Novel Coaxial Balance Mechanism for Reciprocating Piston Engines
## 1 Introduction
[PERSON] carried out systematic research and software development on the balance schemes of in-line and V-type engines [19]. There are two defects with the existing balancing mechanism. The first is that the structure is not compact enough. The balance mechanism with corresponding auxiliary parts increases the volume and mass of the engine. Generally, one balancing mechanism can only balance the inertial load of the corresponding order. Thus, the current balancing mechanism is not suitable for a compact engine. In general, for a single-cylinder piston engine, only the first-order balance mechanism is installed due to cost, and the second- and higher-order inertia forces are ignored. As a result, the balance effect is not satisfied, leading to significant engine vibration and loud noise. The second-order inertia force has a significant influence on engine vibration. Taking the DK32 single-cylinder engine [20; 21] developed by the author's laboratory as an example, the maximum value of second-order inertia force could reach 4900 N at the rated speed of 2350 r/min, which is unacceptable for an engine with high vibration performance. The second defect with the existing balancing mechanism is an error in calculating the inertial load. Conventional methods [22; 23] employ Taylor expansion of the inertial load function with respect to \(\lambda\) (crank-conrod ratio) and then expand the coefficients of the previous orders into Fourier series with respect to the \(\alpha\) crank angle. Finally, the coefficient of each order in the Fourier series obtained by integration can represent the characteristics of the inertia load. However, we found that the high-order term coefficient of Taylor expansion significantly impacts lower-order terms of the Fourier series, meaning the calculation of second- and higher-order inertia load by conventional methods is not accurate. In this study, we focused on achieving vibration reduction of a single-cylinder engine by reducing the inertia force, aiming to design a mechanism that can eliminate the effect of inertia force as much as possible. Additionally, considering the cost constraints of the engine, the balance mechanism should increase the number and volume of engine parts as little as possible. Firstly, we adopt a novel closed-form method [24] to accurately calculate inertia load, which considers all the orders of \(\lambda\), and only carries out Fourier expansion of the inertia load function. Compared with the conventional methods, the novel closed-form method can accurately calculate the inertia load. Secondly, we designed a balance mechanism to balance many-order inertia forces once to improve space utilization. A set of novel coaxial balance mechanisms [25] that can automatically balance first- and second-order inertia forces was designed in this study by comprehensively considering the manufacturing cost, size limitation, and engine vibration reduction. The principle of the novel mechanism was analyzed and studied in detail. The novel mechanism adopted the idea of a unit-body module without increasing the size of the balance mechanism or changing the main structure and size of the original engine. This could be realized by modifications inside the original first-order balance mechanism in a highly compact form. Additionally, the novel closed-form method was used to accurately calculate the second-order inertia force, and an accurate balance mass was then designed so that the balance mechanism can completely balance the second-order inertia force. Hence, this balance mechanism was able to reduce vibration to a greater extent. In terms of the engine vibration simulation method, research shows that the use of a flexible body model has a greater impact on the simulation accuracy of the whole engine [26; 27; 28; 29; 30]. Because piston engines involve multiple components, it is generally necessary to establish a multi-body dynamic model of the whole engine. This paper is organized as follows.