# Mechanical Performance Analysis and Experimental Study of Four-Star-Type Crank-Linkage Mechanism
## 3 Simulation of Mechanical Characteristics of Four-Star-Type Crank Linkage
### Non-Ideal Four-Star-Type Crank Linkage  
#### 3.2.1 Dynamic Characteristics of Four-Star-Type Crank Linkage with Clearance  
In order to facilitate the adjustment of the clearance values, the four-star-type crank-linkage structure was simplified. The simplified model is shown in Figure 21. The variation of the main shaft bearing force with the balance mass is shown in Figure 22a. The frequency domain diagram of the force applied to the crankshaft rotating pair in the direction of piston motion with the optimum amount of balance mass obtained is shown in Figure 22b. The simplification process brings about a change in the volume of the structure and the position of the barycenter. To some extent, the second-order inertia forces are excited, but they are still lower than the third-order inertia forces. The air compressor development process also cannot avoid the problem of center of gravity and mass deviation due to the non-uniform density of the casting. Figure 19: Main shaft bearing force situation without friction. Figure 20: Main shaft bearing force situation with friction. In the actual operation of the machinery, the driving torque needs to change with the load in order to ensure the stability of the rotational speed due to the clearance, friction, and external forces. It is difficult to stabilize the rotational speed by controlling the driving force because of the existence of friction, sudden changes in the load, and a certain degree of randomness. In order to reduce the speed fluctuation, a flywheel is usually connected to the crankshaft, whose rotational inertia is relatively large. In the process of flywheel rotation, the surplus power is saved in the form of kinetic energy, and when the load changes, the energy is absorbed or released to achieve the purpose of stabilizing the speed. The simulation process directly constrains the rotational speed to a constant value so that the driving torque will change. The operating condition is 1480 r/min. The clearance between the crankshaft and first-stage linkage is set to 0.1 mm. The speed is set to the rated value within 0.1 s by using the step function. The drive torque power in the ideal connection and clearance kinematic pair state is obtained, as shown in Figure 23. The shorter the start-up time, the larger the start-up torque required. In 0.1 s, the required starting torque is larger, and the driving power is gradually stabilized after starting. In the ideal state, the final value of torque power amplitude is stable at 819 w. When there are clearances and friction in the kinematic pair, the power of the torque fluctuates transiently, far beyond the ideal connection. The torque power amplitude is at 6711 w without considering the transient fluctuation due to the balancing effect of the flywheel. The rated speed of this type of air compressor is 1480 r/min. According to the relevant technical requirements of submarine air compressor, the wear clearance of the kinematic pair generally does not exceed 0.1 mm, and the installation clearance of the crankshaft and linkage is 0.1 mm. Therefore, the values of 0.10 mm, 0.15 mm, and 0.20 mm are taken as the crankshaft, linkage, and kinematic pair clearances, respectively, for simulation calculation. The modified contact-collision force model is embedded into the contact definition of the crankshaft and linkage revolving pair. To control other variables, only the clearance between the first-stage linkage and the crankshaft is considered, and the other kinematic pairs are defined as ideal connections. Take 0.1 mm clearance as an example. Figure 23: Time-domain diagram of driving torque power of crankshaft. Figure 22: Optimization of crank linkage counterweight. (**a**) Change in balance weight. (**b**) Optimal balance weight. The corresponding dynamics model can be established by expanding the radius of the big end of the first-stage linkage by 0.1 mm and reassembling the four-star-type crank-linkage structure.