## 7 Conclusions  
In this paper, the deformation degree of the flanging lip of the V groove is researched after the roller staking process. Taking the MS14101-9 bearing as an example, numerical analysis and experimental verification of the deformation degree of flanging lip and the loading control method during the roller staking process were carried out. The following conclusions can be drawn:  
(1) Based on the feeding displacement, the push-out load, the starting torque, and the deformation characteristics of the flanging lip, it is proposed to divide the deformation degree of the flanging lip into five states after roller staking. \"State 1\" is the initial state; \"State 2\" is the limit state in which the starting torque is not significantly affected; \"State 3\" is the limit state in which the push-out load meets the quality inspection requirements and the starting torque reaches the maximum value specified in the standard after roller staking process.  
Figure 12: Cross-sectional view and state comparison of specimens under MSCL control and displacement–time control: (**a**) initial deformation controlled by MSCL; (**b**) “State 2” of MSCL; (**c**) “State 3” of MSCL; (**d**) “State 5” of displacement–time control.  
Figure 13: Qualification rates of different quality indexes under three loading control methods.  
staking; \"State 4\" is the limit state in which the starting torque exceeds the requirements and the damage degree of the flanging lip is out at the maximum allowable limit. \"State 5\" is when the push-out load meets the requirements, but the starting torque is too large and the flanging lip is severely damaged.  
(2) The ideal state for the good staking quality and working performance of the bearing is \"State 3\". The aforementioned five states have a timing sequence and a certain overlap. Before the maximum limit state of \"State 3\", the staking loads are almost linear, and the surface quality of the flanging lip is better.  
(3) The control method of \"Multi-Stage Composite Loading (MSCL)\" is proposed by analyzing the displacement-time control and the force-time control, i.e., the rotate speed of the roller tool is constant, and the MSCL control is adopted during the roller staking process. The effectiveness of the MSCL control method was verified by the roller staking test. At the same time, the feeding displacement is proposed as a reference index, and it is suggested that the feeding displacement is 0.5-0.6 times the V groove depth.  
The above research analyzed the mechanical state of the roller staking process, and the revealed deformation mechanism of the flanging lip of the V groove during the roller staking process. In terms of the roller staking technology of SSPBs, a precise process-loading control method and parameter indexes are given, which provides a theoretical reference for further formation about more reliable technical standards, and has been well applied in practice.  
Conceptualization, Q.W.; data curation, Q.W., J.C. and Z.H.; software, X.W. and H.Z.; supervision, J.C., H.Z. and Z.H.; writing--original draft preparation and formal analysis, Q.W.; writing--review and editing, X.W., H.Z. and Z.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the scientific research start-up funding project of Zhejiang SciTech University of China, grant number 11132932612009, Funding projects for the central government to guide the development of local science and technology of China, grant number 206Z100 SG and the Science and Technology Projects of Qinhuangdao, grant number 201901B003.  
Not applicable.  
All data generated or analyzed during this study are included in this article.  
The authors want to thank Aviation Key Laboratory of Science and Technology on Generic Technology of Aviation Self-Lubricating Spherical Plain Bearing.  
The authors declare no conflict of interest.