# A Novel Coaxial Balance Mechanism for Reciprocating Piston Engines
## 1 Introduction  
Vibration is one of the most commonly observed phenomena in reciprocating piston engines, and particularly this with a single cylinder. Excessive vibration leads to fatigue damage of engine parts, and affects the stability and mechanical efficiency of the engine's operation. The resulting noise may also cause irreversible hearing loss in operators [1, 2]. Numerous scholars have carried out in-depth research on vibration sources. For an engine system, the vibration is determined by the excitation force and the inherent characteristics of the system structure. The excitation force mainly includes the gas explosion pressure and inertial load, whereas the inherent characteristics depend on the inertia and rigidity of the engine body structure and mounting base. [PERSON] et al. [3] studied the relationship between injection parameters (e.g., injection pressure, injected quantities, and injection timing) and engine block vibration. [PERSON] et al. [4] investigated the effect of coolant temperature on the vibration of a single-cylinder diesel engine by frequency spectrum analysis and noted that piston slap was also the main factor that affected the vibration. [PERSON] et al. [5] further studied the influence of piston slap on engine block vibration. [PERSON] et al. [6] explored the relationship between faults in the valve train and the vibration of a diesel cylinder head, and a fault analysis method of vibration signals using Wigner-Ville distributions and probabilistic neural networks was developed. [PERSON] et al. [7, 8, 9] studied the effects of engine support and installation methods on engine vibration. [PERSON] et al. [10] analyzed the inertia force produced by piston motion in a reciprocating piston engine. This kind of inertia force makes the engine body generate both noise and vibration. To improve the balance of the engine, they designed a balance mechanism to eliminate the influence of inertia force. [PERSON] et al. [11] studied the influence of engine static and dynamic balance on the vibration of the engine. [PERSON] et al. [12] calculated the dynamic responses oftwo support cushions of the engine, which was excited by the inertial forces related to the reciprocating movement of the pistons and connecting rods, and unbalanced crankshaft counterweights. [PERSON] et al. [13] reviewed recent research that was focused on reducing and isolating engine vibration, including the effect of unbalanced reciprocating and rotating parts. The above research showed that the gas pressure curve could be adjusted via the engine electronic control system to reduce vibration; however, reducing the inertial load of the engine must be achieved by designing a balance mechanism. Therefore, optimizing the balance mechanism for engines in which the main configuration had been determined was an economical and effective vibration reduction measure. In 1907, Dr. [PERSON] invented a forward and reverse double balance shaft mechanism for the reciprocating inertial force of the engine. The centrifugal force generated by the mechanism could offset the unbalanced inertial force component for part of the engine [14]. Since 1970, many researchers have continuously improved the above-mentioned traditional balancing mechanism. For example, the height of the two shafts was varied in one mechanism. Because the two shafts are not symmetrical, with respect to the center of the crankshaft, a moment will be generated, offsetting a part of the second moment of inertia based on balancing the secondary reciprocating inertia force [15]. [PERSON] et al. designed a silent crankshaft in the engine to reduce its second-order vibration and improve the NVH performance in cars [16]. [PERSON] et al. developed an in-line four-cylinder engine with a double balance shaft device, which greatly improved the NVH performance [17]. [PERSON] et al. optimized the mass of reciprocating motion and valve train motion, greatly reducing the second-order inertial force [18].