# Mechanical Performance Analysis and Experimental Study of Four-Star-Type Crank-Linkage Mechanism
## 5 Conclusions  
The crank-linkage mechanism is the main moving part in the operation of a reciprocating air compressor. This paper focuses on the kinematic characteristics, stresses, and mechanical behavior of the four-star-type crank-linkage mechanism. The main findings are summarized as follows:  
1. From the viewpoint of the motion relationship, there are two moments in a rotation cycle of the four-star crank linkage where the acceleration of each piston is exactly equal in magnitude. From the point of view of the force, the four-star crank linkage has a good balance of the second-order reciprocating inertia force. The first-order reciprocating inertia force and the second-order reciprocating moment of inertia mainly exist. By calibrating the static strength of the first-order piston, first-order piston pin, second-order linkage, linkage needle roller bearing, and thin-walled bearing liner of the linkage, the stress-concentration areas were found;
2. The modal calculation results of the simplified crankshaft finite element model are closest to the experiments. The computational efficiency of the simplified crankshaft finite element model is greatly improved. However, the error is about two times the original finite element model. Compared with the experimental modal, the modal frequency error before and after simplification can be controlled within 7%. The linkage is a combined part, and the finite element modal analysis treats it as a single part for modal analysis. In addition, the local  
Figure 34: Vibration acceleration levels of the bench.  
Figure 33: Spectrum of vibration acceleration of the bench.  
details are simplified to obtain the finite element modal frequency calculation error, which is significantly increased compared with the crankshaft;
3. The crankshaft is more complex than the linkage in terms of forces. The first-order inherent frequency of the crankshaft is significantly higher than the first-order inherent frequency of the linkage. However, the analysis results of rigid-flexible coupling dynamics model show that the crankshaft is closer to a flexible body compared to a linkage. The rigid-body dynamics analysis can meet the general calculation requirements due to the small axial length of crankshaft, high stiffness, and high inherent frequency;
4. The presence of friction in the revolving pair will suppress some of the resonance peaks. However, it will broaden the excitation frequency band and excite high-frequency vibration. For a power machine with a distinct line spectrum, such as an air compressor, moderate friction can attenuate the vibration acceleration. Friction consumes system energy during the operation of the mechanism, which is beneficial to the attenuation of vibration energy. However, it also generates heat, which has a negative impact on the reliability of the machine operation;
5. The larger the clearance, the higher the excitation force on the main shaft bearing of the four-star-type crank linkage, and the frequency corresponding to the amplitude of the excitation force will be shifted. The greater the clearance, the higher the low-frequency excitation force of the four-star-type crank-linkage main shaft bearing. In the wide frequency band, the clearance of the crankshaft-linkage kinematics pair corresponding to the vertically moving piston can reduce the main bearing excitation force in the horizontal direction to some extent. Therefore, the presence of individual clearances is larger than the periodic excitation force of symmetrical distribution of clearances, which is more likely to excite the vibration mechanism.  
Data curation, Y.Y.; Writing--original draft, K.C.; Writing--review & editing, J.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by National Natural Science Foundation of China (Grant No. 52201389 and 51679245); Natural Science Foundation of Hubei Province (Grant No. 2020 CFB148).  
Data is unavailable due to privacy or ethical restrictions.  
The authors declare no conflict of interest.