Analytical Calculation of the Gear Body Stiffness of Face Gears

Due to the constantly increasing requirements, more and more transmissions are being adapted and developed for their specific application. It is of paramount importance to optimally exploit the potential of the gears to meet the design objectives. Target criteria can be the NVH behavior and/or the maximum carrying capacity. To evaluate these objectives, it is crucial to know the load distribution in the meshing. The load distribution can be determined using numerical or analytical models. Despite the constant development of finite element contact simulation, analytical methods are still a subject of research and an important cornerstone in gear calculation, as they enable fast calculations. They are easy to use and allow different variants to be compared quickly. The basis of analytical tooth contact simulation (LTCA) is the accurate representation of tooth and gear body stiffness. The calculation of these has been sufficiently researched and validated for cylindrical gears. The approaches for calculating tooth stiffness can be used for angular gears as well. However, the wheel in this case does not have a cylindrical gear body. Instead, the gear body is like a flat circular disk. Available analytical methods for LTCA do not cover this special geometry. This poses a serious drawback in their applicability to angular gearboxes. This paper presents and discusses a novel approach to determine the wheel body stiffness for disk-like gears based on an analytical calculation method. The partial deformation components are calculated using plate/disk formulations and the work integral is determined. Balancing with the external work results in the deformation in force direction, with which the gear body stiffness is finally derived slice by slice over the tooth width. The face gear drive serves as a demonstrator, whereby the approach can be transferred to other angular gears (e.g. bevel gears) without any difficulty.