In recent years, thanks to their significant advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations, internal gears have been used in automotive and aerospace applications especially in planetary gear drives. Although internal gears have a number of advantages, they have not been studied sufficiently. Internal gears are manufactured by pinion type cutters which are nearly identical with pinion gear except the addendum factor which is 1.25 instead of 1. The tip geometry of a pinion type cutter which determines the fillet of internal gear tooth can be sharp or rounded. In this study, the design of internal gears were investigated by using a traditional approach. Mathematical equations of pinion type cutter were obtained by using differential geometry, then the equations of internal gear tooth were derived accurately by using coordinate transformations and relative motion between the pinion type cutter and internal gear blank. A computer program was generated to attain points of internal gear teeth and three dimensional design of complete gear. 20°-20° were used as pressure angle. To find optimum internal gear geometry, different rim thicknesses and shapes are tried out for finite element analyses. There were several parameters that were shown to effect the performance of the internal gears, with tooth stiffness being the most significant parameter. Tooth stiffness was also vitally influence the dynamic analysis. In order to compute gear tooth stiffness of the internal gear with various rim thicknesses and shapes, finite element analysis was used. A static analysis was performed to assess the gear bending stress and tooth displacement. Tetrahedral element type was selected for meshing. The internal gear outer ring was fixed and the force of 2500 N was applied on the tooth. According to the displacement values from the analysis internal gear tooth stiffness were calculated individually. Additionally, the effect of root bending stress with varying rim thickness, shapes, and root radius were investigated. The bending stresses were calculated according to ISO 6336 and using finite element analysis were shown to be in good agreement. It was shown that when the rim thickness and fillet radius were increased, the maximum bending stresses decreased considerably. As rim thickness was increased, the maximum bending stress decreased nearly 23%. It was also shown that as the fillet radius decreased, the maximum bending stress increased, whereas the rim stresses slightly changed. As the fillet radius was decreased, the maximum bending stress increased nearly 10%. It was also observed that when rim thickness was increased, the stress on the rim was decreased, whereas tooth stiffness was increased. However, fillet radius had no visible effect both on rim stress and tooth stiffness. Furthermore, it was shown that the rim shape had significant effect on rim stress.
Effects of Rim Thickness on Spur Gear Bending Stress
