Mathematical and computer modeling of transmission with non-traditional engagement for mining equipment drive

Abstract

In modern gear mechanics, transmission mechanisms play a crucial role in converting the rotational motion of a driving shaft into the rotational motion of another shaft with varying angular speeds and torque. To achieve optimal designs for the next generation of transmission mechanisms, it is essential to develop mathematical models of their dynamic behavior, conduct computer simulations of the meshing geometry of key components, and visualize the operation of the mechanism. Despite the widespread use of involute gearing in mechanical transmissions, there is ongoing research into new types of gearing that offer advantages over traditional systems. The main challenges facing the industry include increasing the gear ratio in a single stage, enhancing load capacity, and improving efficiency compared to standard gear transmissions. This paper presents the results of mathematical and computer modeling, along with a comparative analysis of the eccentric-cycloid (EC) engagement with the involute gear transmission. Through analytical calculations, the energy-force parameters of the EC gearbox were determined, equivalent stresses and static deflections of transmission shafts were obtained. The paper includes the results of static analysis of elements of the new EC transmission, as well as an algorithm for computer modeling of contact stresses occurring in the engagement. Conclusively, by comparing contact stresses in traditional involute gear transmission, calculated using various analytical methods, with those in EC engagement determined through computer simulation, the advantages of the new transmission type and its potential application in mining equipment transmission mechanisms are highlighted.