Novel mathematical modelling method for meshing impact in conjugated straight-line internal gear pairs

Conjugated straight-line internal gear pump is widely employed in electro-hydrostatic actuator (EHA), where frequent speed and directional variations exacerbate meshing impact issues. This study proposes a precise mathematical method for evaluating the meshing impact characteristics of conjugated straight-line internal gear pairs (CSLIGP), distinguishing between three types of impacts: engagement impact, backlash impact, and contact impact. The calculation errors for impact forces and impact duration are less than 6.72% and 8.73%, respectively. The effects of tooth profiles, gear pair parameters, and operating conditions on impacts were systematically investigated. It turns out that the conjugated straight-line tooth profiles exhibit superior performance in startup, speed transition, and directional switching conditions compared to conventional involute tooth profiles, demonstrating enhanced adaptability to variable working conditions. Appropriately reducing tooth width, increasing addendum height, dedendum height, and tooth angle can mitigate meshing impact forces. Prolonging startup duration and adopting incremental speed adjustment strategies effectively reduce meshing impact forces. The proposed computational method enables rapid and accurate assessment of meshing impact in CSLIGP, providing critical theoretical guidance for the design of variable-speed pump in EHA systems.