Effects of Standard Pressure Angle on Tooth Deflection and Root Stresses of Helical Internal Gears.

Abstract

This paper presents a study on tooth deflections and root stresses of helical internal gears with various standard pressure angles. The deflection and root stress of internal gear tooth with various standard normal pressure angles αn due to a concentrated load were calculated by the three-dimensional finite-element method (FEM). On the basis of these caluclated results, approximate equations for the influence function of the tooth deflection and the bending moment factor on the critical section of the gear tooth were derived. The validity of these approximate equations was confirmed by comparing results by these approximate equations with those by the FEM. The load sharing factor, the load distributions on contact lines and the root stresses of helical internal and external gear pairs with various helix angles, face widths and numbers of teeth were calculated using the influence functions of tooth deflection and contact approach, the bending moment factors and the stress concentration factors for various αn. The effects of design parameters on the load sharing factor, the load distribution and the root stress of these gear pairs were determined. Furthermore, the meshing position of maximum root stress of the helical internal gear pair was also determined.