A formulation of tooth deformation and its error compensation for worm gear transmission mechanisms

Abstract

Milling head and rotary table are the key components in five-axis CNC machine tools. However, tracking and positioning precision of these rotary axes based on worm gear mechanisms are affected by the backlash, friction, elastic deformation, and other nonlinearities. Therefore, finding out a simple and universal principle to predict the tooth deformation in an initial design is quite significant. A novel deformation calculation and compensation method with finite element analysis and circular plate theory is proposed for the worm gear transmissions. When the relationship (form factor) between the solutions of circular plate theory and finite element analysis is derived, deformation calculation with finite element analysis can be replaced by multiplying the solution of circular plate theory and the form factor. Analysis and calculation results show that the presented method can provide a reference for the compensation control of the positioning errors.