Berechnung der Zahnfußspannungen von Beveloidverzahnungen

Sammanfattning: Beveloid gears are conical gears which are derived from cylindrical involute gears to transmit torque and rotation for parallel, intersecting or skew axes. While defined by the same data as cylindrical involute gears, the addendum modification factor, however, changes linearly to the tooth width. This results in the characteristic conical geometry of beveloid gears. Therefore, beveloid gears are also referred to as conical involute gears.Typical applications for beveloid gears are marine transmissions and automotive four-wheel drives. For marine transmissions beveloid gears are used to transmit power from a horizontally mounted motor positioned above the water surface to the propeller below the water surface. For this, propeller shaft and motor shaft are mounted with a moderate axis angle. For automotive four-wheel drives, beveloid gears transmit power from the transmission output shaft to the front axis differential. The use of a beveloid gear enables the transmission design to have the front axle shaft mounted inside the transmission tunnel. This leads to reduced space requirements compared to conventional four-wheel drive concepts. Another application for beveloid gears are robot gears. Here, the beveloid gears are mounted with parallel axes, meaning that the cones have the same angle and the gears are mounted with opposite orientations. This concept allows a precise adjustment of the backlash by shifting the gears axially.Generally, beveloid gears are used when small crossing angles are to be realized. For smaller crossing angles beveloid gears should be used due to advantages in the manufacturing technology. For bigger crossing angels, bevel gears are preferred as beveloid gears tend to unfavorable contact conditions in these cases.Unlike bevel gears or cylindrical gears, there are no existing calculation methods for the tooth root load carrying capacity of beveloid gears. This, however, is an essential requirement for ensuring the beveloid gear does not suffer any root damage during operation without over dimensioning it in the design stage.Therefore, two methods for calculating the tooth root load carrying capacity for beveloid gears are developed in this thesis. First, a calculation method based on local calculation methods is presented and validated by fatigue tests. By means of this calculation method, an analytic-empiric calculation method for tooth root load carrying capacity of beveloid gears with parallel axes and an explanatory model for the tooth root load carrying capacity for beveloid gears with intersecting axes are developed.