# Analytical Modeling of Particle Scratching Process
## 4 Conclusions  
The physical and analytical models of the scratching process have been presented. The workpiece material deformation during the scratching process has been divided into the elastic and plastic deformation zones, and the mechanical expression of cutting forces in the elastic and plastic deformation zones has been presented, respectively.  
The coefficient of elastic rebounds \(k_{1}\) and the coefficient of plastic upheaval \(k_{2}\) have been defined to describe the degree of elastic rebounds back and plastic upheaval, respectively.  
The stress distribution on the plastic deformation zone according to the analytical model has also been given and was studied further.  
This study systematically analyzed all parameters influencing the force ratio, conducting simulation experiments using MATLAB. Simulation results were quantitatively analyzed, and the model's validity was further corroborated by referencing findings from published literature. Key observations include: the force ratio increases with an increase in the elastic rebound coefficient, plastic upheaval coefficient, nominal cut depth, and strain-strengthening coefficient, but decreases as particle radius grows. Notably, the nominal cut depth may underestimate the actual indentation depth due to elastic rebound, directly impacting material removal efficiency. A higher \(k_{1}\) (elastic rebound coefficient) amplifies elastic recovery, reducing the effective cut depth; a higher \(k_{2}\) (plastic upheaval coefficient) enhances material bulging along scratch edges, potentially degrading surface quality. Balancing machining efficiency (favored by higher nominal depths) and surface quality (favored by lower nominal depths) can be achieved through strategic adjustment of nominal cut depth. The strain-to-force ratio, which links force-displacement curves during plastic deformation, serves as a critical parameter for modeling cutting forces. Importantly, yield stress was found to have no discernible effect on the force ratio, distinguishing it from other analyzed parameters. Finally, although this paper proposes a physical model and an analytical model of a single abrasive grain in the grinding process, this paper makes relevant assumptions and simplifications to the relevant models; for example, this paper assumes the irregular geometry of the abrasive grain as a perfect sphere for the relevant research, which may lead to result in the insufficient adaptability of the model to complex working conditions. This paper also simplifies the sliding friction process to Hertzian contact and homogenises the material, and these simplifications can limit the applicability of the model in extreme conditions. In addition, the model proposed in this paper does not consider the relevant situation of high temperature and high speed.  
In the future, scholars can consider the actual shape of the particles for related research, and the analysis of the slipping and rubbing process of multilayer structural materials is also one of the future research directions; in addition, a thermally coupled high temperature and high-speed model can be established to study the behaviour of abrasive particles under high temperature and high-speed conditions.  
Conceptualization, S.C., F.Y. and J.H.; Methodology, J.H.; Validation, S.C., F.Y. and S.H.; Writing--review & editing, M.S., Y.F. and S.H.; Funding acquisition, M.S., F.Y. and S.H. All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge financial support by Fujian Science and Technology Project (Grant No. 2022H0018), Fujian Province's Major Science and Technology Special Projects (Grant No. 2024 HZ025008) and the seventh batch of high-level talent team projects introduced in Quanzhou City (Grant No. 2024 CT005).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.