# Mechanical Performance Analysis and Experimental Study of Four-Star-Type Crank-Linkage Mechanism
## 1 Introduction  
The marine air compressor mainly provides compressed air for starting diesel engines, pneumatic machinery manipulation, weapon firing, and underwater vehicle diving and floating. It is an indispensable piece of equipment for a pneumatic system. The main focuses of recent air compressor research have primarily been on fault detection and diagnosis, strength verification of the structure, and thermodynamic analysis. However, there has been relatively little research on the vibration control of large air compressors, particularly a systematic study on the vibration characteristics of four-star air compressors, which remain largely unexplored [1]. Four-star air compressors, with their compact layout, high exhaust pressure, excellent self-balancing properties, and relatively low vibration, have become the preferred system for submarines in military superpowers. Yet, the vibration of compressors is caused by numerous factors including imbalance forces and torques, friction excitation, valve shocks, airflow pulsation, and motor vibration. A thorough analysis of these vibration sources will substantially increase the workload for the overall vibrationresearch on the machine. The main moving part of the air compressor is the crank-linkage mechanism. Only considering the crank-linkage excitation force to predict the vibration response of the whole machine has become the mainstream of air compressor vibration analysis [2]. The different lubrication and wear states of the crank-linkage mechanism kinematic pair will cause changes in mechanical characteristics. The crank-linkage dynamic balance condition also has a large impact on the mechanical characteristics. During the operation of the crank-linkage mechanism, the kinematic pair is inevitably subjected to a certain clearance due to lubrication needs and later wear, which has a certain impact on the piston motion state [3]. When the clearance value exceeds the permissible limit, it will not only consume the system energy sharply but also produce large amounts of vibration. In severe cases, this can lead to system instability and even accidents [4]. A one-dimensional shock model of the crank-linkage mechanism was proposed by [PERSON] et al. [5]. Subsequently, many researchers and scholars have explored the modeling of kinematics pairs with clearance. In recent years, the modeling of kinematic pairs with clearance has been continuously developed and improved. Three types of representative clearance kinematics pairs have been developed, namely the continuous contact model, \"contact-separation\" two-state model, and \"contact-separation-collision\" three-state model. After clarifying the motion states of the kinematic pair with clearance, the specific analysis needs to be implemented into the mechanical analysis of the contact surface. There are two main methods for modeling and analyzing the contact-collision problem: the discrete analysis method and continuous analysis method [6]. The discrete analysis method, also known as the non-smooth rigid-body analysis method, assumes that impacts occur instantaneously, primarily using linear complementarity and differential variation inequalities. The former prevents mutual penetration of the kinematic pair elements, while the latter uses plain integrators for direct calculation [7]. The continuous analysis method refines the collision process, expressing it as a continuous function of collision force and deformation. The emphasis of studying the dynamic characteristics of motion pairs with a gap lies in establishing relatively accurate contact-collision force models. Current research levels can consider non-linearity, friction, and energy losses during the contact-collision process. As mechanical manufacturing evolves, kinematic pair mechanisms are leaning towards high-speed and heavy-load directions, increasingly amplifying the effects of gap motion pairs [8].