Comprehensive simulation methods for crossed helical gear sets with the main focus on the calculation of contact patterns

Crossed helical gear sets consist of two helical gears paired at an angle of intersection between Σ > 0° and Σ ≤ 90° and are characterized by point contact. Typical applications of this gear type are actuators, e. g. in automobiles or medical devices. Various materials such as steel, cast iron, bronze or plastic are used for crossed helical gears. Main advantages are easy assembly, quiet operation, variable angles of intersection and high gear ratios in a single gear stage. FZG has developed the FVA-Software SCHRAD2 which serves for the calculation and simulation of crossed helical gears.

SCHRAD2 covers the following basic calculation functions: Main geometry, Tolerances (ISO 1328, DIN 3961, DIN 3974), Load carrying capacity (Niemann-Winter, Wassermann, Wendt, VDI 2736-3, Pech).

Additionally, the program calculates the contact pattern. For this purpose, the program determines the geometry of the gears numerically, based on a manufacturing simulation. A modification of the tooth profile in the area of the tooth tip and tooth root is possible. Subsequently, a meshing simulation of the gears is conducted to calculate the local flank distances for a variety of meshing positions. Misalignments, for example deviations of the center distance or of the angle of intersection, can be considered in the meshing simulation. The local flank distances during meshing are used to analyse the position and size of the contact pattern without load and to check the gear stage for possible transmission errors. Furthermore, a method for calculating the load distribution of crossed helical gears has been developed by FZG. Thereby influences from deformations of the shafts, teeth, bearings and of the housing can be considered. For validation of the contact patterns, comparative worm gear sets were calculated using the FVA program SNETRA. By use of the presented calculation methods, contact patterns in without load and under load can be calculated for the first time within a short processing time. In the future, these results can be used within the design process of crossed helical gear sets. Furthermore, the load distribution forms the basis for the calculation of specific local parameters such as Hertzian stress, thickness of the lubricating film or coefficient of friction.