Improvement of loading capacity of internal spur gear with using asymmetric trochoid profile

Abstract

Today, with numerous advantages such as reduced sliding velocity and wear, higher transmission ratio, higher running efficiency etc., internal spur gears are used in several industrial applications. An internal gear is generated by pinion cutters towards inside of gear blank opposite of external gear. In this study, bending stress of internal spur gear with the asymmetric trochoid profile is investigated. Asymmetry is ensured by using pinion cutter has different tip radius value on its right and left side. This situation is allowed to use larger tip radius on one side. The limit value of tip radius is defined with taking into account cutter addendum height and interference possibility for the given pinion gear parameters. On the other side, asymmetry on the involute region is also examined. Firstly, a mathematical equation of pinion cutter is derived then points of internal gear are obtained by using coordinate transformation, differential geometry and gearing theory in MATLAB. Points of internal gear are exported to CATIA to realize the 3D design. Case studies are conducted for determining the relation between tip radius and pressure angle on bending stress separately with ANSYS program. According to preliminary results, using asymmetric trochoid profile reduces approximately 16% bending stress of internal spur gear.