Functional tolerancing of the tooth root geometry of high-pressure angle gears

This research work presents a methodology for the determination of the required manufacturing accuracy of custom, high-pressure angle gears. The gears examined throughout the present work are constructed using involute segments beyond the 25° limit specified in the ISO/TC 60/SC 2 and custom root filet geometries produced with the employment of fourth order Bezier curves. Due to the existence of extensive undercuts in the root region, production of these geometries cannot be practically achieved by conventional machining, for example, hobbing; therefore, production methods such as additive manufacturing or powder metallurgy are required. The root geometry incorporating the fourth order Bezier curves is optimized and described in closed form in terms of the coordinates of the control points. In the context of this study finite element analyses are performed to determine the sensitivity of strength (maximum principal stresses) and functional characteristics (static transmission error—STE) on the surface profile deviations focusing on the root area. Tolerancing of the tooth profile is performed as per ISO 1660:2017, by specifying an unequally disposed tolerance zone with an offset that takes into account the maximum material condition of the theoretically exact feature (TEF) in order to avoid interference at zero backlash nominal tooth geometries and considering nominal center distances. The surface profile tolerance values are calculated using appropriate thresholds for the strength and STE values and can be used as design guidelines for both the production and quality inspection of the gear geometries presented herein. The presented methodology can be applied to any gear pair regardless of the root or flank geometry used. The case studies shown in this work demonstrate very small STE variations (in the order of 5%) for a 10% increase of the resulting maximum principal stress at the tooth root area. At the same time, the asymmetric tolerance zone for the same stress increase threshold is calculated in the order of 0.1 times the normal module.