Abstract
This study presents a mathematical model of the dynamics of tricone drill bits, which remain widely used in open-pit mining due to their reliability and versatility. Despite their extensive application, improving their efficiency and durability remains a relevant issue. The main operational challenges are identified, including insufficient knowledge of the stress–strain state of rocks in the contact zone and the effect of tooth geometry on kinematics and rock-breaking efficiency. Analytical dependencies are proposed to account for bit geometry, trajectory motion, transmission ratios, and tooth–rock interaction. Based on the principles of theoretical mechanics, performance criteria are formulated through specific contact and volumetric work of rock destruction, enabling an objective assessment of energy consumption. The model demonstrates the potential of analytical methods for optimizing drill bit design and kinematics, reducing energy consumption, increasing productivity, and extending tool life. The results can be applied in the design of next-generation drill bits and in engineering software for selecting rational drilling parameters under specific geological conditions. The proposed approach provides a foundation for further studies in mathematical modeling of rock destruction dynamics and the advancement of open-pit mining technologies.