M. R Homaeinezhad - Associated Prof. at Faculty of Mechanical Engineering, K. N. Toosi University of Technology
S Adineh - Mechanical Engineering BSc Graduated from K. N. Toosi University of Technology

The main objective of this paper is to render the required procedure for the determination of the inherent mathematical model of a worm-gearbox under external disturbance loading. The obtained mathematical model gives enough insight into the internal forces interacting between worm helix curvature and gear teeth/threads during assistive, resistive and quasiresistive output shaft loading. By application of this model, an explicit relation between input shaft loading and output torque is obtained which can be used in the structure of a feedback control system for precise angular positioning of the output shaft. Toward this objective, several free-bodydiagrams of worm and gear in three modes of operation are illustrated based on them, the mechanics of reaction and friction forces produced between worm helix and gear teeth are estimated. The obtained mathematical model is validated based on a vigorous experimental assessment. The proposed mathematical model of the worm-gear reducer is applicable for cases where open-loop controllers are implemented such as CNC machines.

Worm-Gear Modeling، Kinetic Motion،Friction Modeling ، Disturbance Torque Estimation ، Coefficient of Friction Analysis.