## 1 Introduction  
A threaded joint is one of the weakest and most critical components of a core drilling tool [1]. A threaded joint is a typical thin-walled structure that operates in a harsh working environment and is mainly subjected to tensile loads and torsional loads. During core drilling, downhole accidents often occur as a result of thread breakage. The most common reason for joint failure is fatigue, which is affected by the maximum stress [2]. Ensuring the joint strength and airtightness of the thread is the key to the success of the coring process; however, due to limited radial dimensions, it has always been difficult to achieve such goals in the study of core drilling tools [3; 4; 5]. At present, research on joint threads mainly focuses on oil drill strings [6; 7; 8], which have a large wall thickness and a large thread design margin; hence, these structures cannot provide a direct reference for the core drilling thread design [9; 10; 11]. Wireline core drill strings are thin-walled structures that can be used as a reference for the thread design of core drilling tools. Many researchers have used model parameterization to study the mechanical characteristics of rotary shouldered connections (RSCs). Studies have shown that the 2D finite element method (FEM) is a powerful numerical method for solving this particular problem [12; 13; 14]. [PERSON] [15] studied the relationship between the thread taper and strength and the corresponding stress distributions through a range of lab tensile, torsional and optical-elastic stress tests. [PERSON] [16] optimized the pitch and length parameters of the thread for diamond wireline core drilling tools. Their results showed that an appropriate increase in the pitch and length of a thread could effectively improve the stress distribution inside a joint thread. Owing to the complex structure, finite element simulation is the most effective method for studying threads. [PERSON] et al. (2017) established the finite element modeling of fatigue loaded bolted flange joints and analyzed the mechanism of bolt fracture. Owing to the complex structure, finite element simulations are the most effective method for studying threads. [PERSON] et al. (2018) established finite element modeling of fatigue-loaded bolted flange joints and analyzed the mechanism of bolt fracture. Based on the nonlinear finite element theory, [PERSON] (2019) carried out a simulation analysis to assess problems involving a threaded joint in a drill pipe joint and the pull-out of a rod during deep-hole drilling. They used finite element software to analyze the pull-out ability of a thread with different wireline core drill strings under different parameters. [PERSON] (2019) used ANSYS software to carry out a 3D simulation of a \(\Phi\)71 mm wireline core drill string and joint and determined that the thread root had the highest stress. [PERSON] (2019) established a quasi-three-dimensional model for a \(\Phi\)89 mm wireline core string joint. Under the condition of neglecting the influence of the helix angle, ANSYS was used to analyze the nonlinear mechanical dynamics of a thread. Finally, the stress nephogram and the deformation nephogram at a joint thread were obtained; however, other loads and boundary conditions were ignored, making the results irregular. [PERSON] (2019) used static mechanics to analyze the stress state of the negative angle thread of a \(\Phi\)74 mm wireline core drill string and calculated the torsional resistance of the thread. Moreover, theoretical calculations and static torsion tests were performed on negative angle threads with different taper and thread heights. [PERSON] (2019) calculated the force in a thread from the influence of the thread structure and the drilling parameters on the thread of the joint. ANSYS/Workbench software was used to simulate the stress and fatigue of a joint thread, and the fatigue life of a drill pipe joint was predicted. Current core drilling tools mostly use American Petroleum Institute (API) standards (2019).