Mechanical Transmissions with Convex–Concave Multipair Contact of Teeth in Precessional Gearing

Abstract

In this study, we propose a new toothed gear for mechanical transmissions built from a satellite wheel with two toothed conical crowns, one of which conjugates with a fixed central conical wheel mounted in the transmission housing and the other with a movable conical wheel installed on the flange of the driven shaft. The satellite wheel is mounted on the inclined portion of the crankshaft and performs spherospatial motion around a fixed point. When the crankshaft rotates, the teeth of the wheels engage with spherospatial interaction in two lateral gearings of the satellite wheel, yielding kinematic ratios dependent on the correlation of the number of teeth. The teeth of the satellite wheel are used with circular arc profiles, and the teeth of the central wheel have flank profiles with variable curvatures increasing continuously from the root to the tip, so that, in meshing, the teeth form multipair contacts with convex–concave geometry with a small difference in flank curvatures. The flank profile geometry and pairs of teeth simultaneously engage depending on the configurational parameters of the gearing and can use up to 100% of pairs of simultaneously conjugated teeth.

Keywords

• mechanical precessional transmissions
• multipair gearing
• convex–concave contact
• mathematical modeling
• relative sliding