Dry friction contact is widely used to reduce vibration in engineering, especially in the vibration reduction of turbine blades, which are major components of aeroengines

Due to the non-smooth characteristics of stick-slip friction, analytical solutions for the Dry Friction Constrained System (DFCS) are generally unavailable. Consequently, numerical simulation has become the most widely used approach for analyzing the DFCS. However, the accuracy and efficiency of the numerical algorithm considering the Coulomb stick-slip motion and determining whether stick-slip motion is considered in engineering design to further improve the computational efficiency remain a critical area of study. In this paper, a single-degree-of-freedom DFCS is introduced to address these issues. The Runge-Kutta method, combined with the dichotomy, is employed to accurately capture the stick-slip transition point. The normal load and dry friction are both symmetrically and evenly distributed at contact surfaces. Firstly, stick-slip motion analyses are performed, and response characteristics of the DFCS are discussed. Then, the convergence characteristics of the numerical algorithm are analyzed, and the optimal iteration step size and the zero-velocity interval are determined. Finally, whether stick-slip motion is considered in numerical simulation in the design of the DFCS in engineering practice is analyzed based on the dimensionless external force and frequency ratio. The criteria for determining whether stick-slip motion is considered in engineering design are established, which can improve both computational accuracy and efficiency.