For the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed.An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor.A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed.

Face gear drives are special angular gears in which an involute pinion and face gear wheel mesh. They enable high transmission ratios in small construction spaces. The face gear is typically manufactured by gear hobbing or gear shaping using an involute pinion-type cutter. Face gear drives with identical pinion and cutter parameters form a conjugated pairing. Conjugate pairings tend to have unfavourable edge contact, which is usually counteracted by geometric flank modifications during manufacture. A common modification technique is the crowning of the flanks. This usually requires changes to the machine kinematics. Due to their geometry and manufacturing process, face gear drives offer an easy way to achieve a crowned contact pattern in the facewidth direction without changing the machine kinematics, making them promising for multiple applications. Using a pinion with fewer teeth than the cutter results in a crowned contact pattern (lead crowning). The position of the contact point along the facewidth can be adjusted by varying the profile shift coefficient of the pinion or the cutter. This paper presents a straightforward method for selecting proper design parameters depending on the contact distances. The contact distances can be estimated analytically to evaluate the chosen design parameters. Example calculations are given as proof of the developed method presented in this paper. Overall, this study offers a novel evaluation strategy for an ideal cutter/pinion design for manufacturing durable face gear drives with optimised contact patterns.

In many cases, gear and transmission design relies on application of standard calculations combined with comprehensive methods for loaded tooth contact analysis (LTCA). Results like local flank load distribution, transmission error and local mesh efficiency evaluation have been KPIs for detail design. Mostly, the optimization cycle to find an advantageous gear main geometry and the consecutive optimization of microgeometry are separated due to different applied theory and cost of time. The new challenges arising from areas of electromobility, wind energy but also aerospace require much higher power density than in the past and a closer integration of the whole drivetrain. Tighter timelines in development lead to the necessity to handle increasing complexity in theoretical background. New possibilities in computer performance allow for application of advanced gear and transmission analysis tools. Altogether these trends culminate in a new generation of gear design software algorithms which are connecting known system approaches with advanced conclusions to achieve top quality in the desired drivetrain properties. This work outlines the scope and applied algorithms for an advanced gearbox design method within the software suite RIKOR. The method combines a full system approach including gears, shafts and bearing analysis which does not stop at resulting deformations and loads but proceeds beyond to allow capacity ratings, NVH evaluations and efficiency information. Comparative calculations in this work demonstrate the functional scope and applicability of the implemented and documented algorithms. New optimization goals may be tackled with this integrative approach.