## 1 Introduction
Historically, research on rock-cutting force has primarily focused on the quasi-static moment when the shear failure surface is formed [22; 27]. However, the actual rock-breaking process is inherently dynamic [12], especially when the cutting state is stable, where the interaction between the cutting teeth and the rock may exhibit cyclic patterns [14]. Therefore, we hypothesize that the cutting force may possess frequency domain characteristics closely associated with the cutting process, such as periodicity. Nevertheless, existing research has predominantly concentrated on the time domain characteristics of cutting force, such as its average and peak values [14], with limited attention given to its frequency domain characteristics. In addition, the wear of cutting teeth is an inevitable phenomenon in drilling and significantly impacts drilling efficiency [36; 37; 38; 39]. In rock cutting, the interaction between the tool and the rock is the fundamental factor driving tool wear. As seen from the previous cutting model, the extrusion zone serves as an intermediary medium for the interaction between the tool and the rock [22; 27]. Its geometric characteristics not only form the basis for analyzing the rock-breaking mechanism, but also directly reflect the contact area between the tool and the rock. However, in previous studies, the longitudinal dimension of the extrusion zone has typically been empirically approximated as the cutting depth [22]. Therefore, to better understand the interaction between the tool and the rock during the cutting process, it is essential to further explore and analyze the geometric characteristics of the extrusion zone. In light of the above analysis, and building upon the previous quasi-static single-tooth cutting model, this paper develops a new dynamic cutting geometry model in which the height of the extrusion zone is not equal to the cutting depth. Through an analysis of the dynamic evolution of the cutting force during the rock-breaking process, it is demonstrated that the cutting force exhibits periodicity. A method for extracting the cutting frequency by applying the fast Fourier transform (FFT) to the cutting force time series signal is proposed. The results are then validated through cutting tests using numerical simulations. Additionally, a series of linear single-tooth rock-breaking simulations were conducted to investigate the influence of cutting parameters such as rake angle, cutting depth, and cutting speed on the cutting frequency. Finally, based on the new dynamic cutting model, the impact mechanism of cutting parameters on the cutting frequency is explored, and the relationship between the height of the extrusion zone and the cutting depth is analyzed. This study provides new insights into the application of cutting force, enhances our understanding of the dynamic cutting rock-breaking process, and offers valuable reference for optimizing cutting models and determining tooth-rock contact range. According to the idea of this study, the chapters in the paper are arranged as follows: Section 1 is the introduction; Section 2 is the theoretical research. The construction of a dynamic cutting model and the theoretical analysis of dynamic cutting characteristics such as cutting frequency are carried out. Section 3 is the research method, which introduces the verification of the theoretical analysis results and the research approach of the cutting dynamic characteristics in detail. Section 4 is the presentation of the research results. Section 5 is the discussion, contains in-depth analysis of the research results, and analyzes the shortcomings of the current research and the prospect of future work. Section 6 is the summary of the research content.