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Gear wheel
(2020)
The international standard ISO 6336-3 defines a calculation method for the tooth root capacity of standard gears with basic rack profile according to ISO 53. However, the results of this method may become too optimistic for non-standard gears with custom root fillets, large pressure angles or asymmetric teeth, since the effect of general mean stresses on the local tooth root strength are neglected. Therefore, a more generic calculation method is suggested, which considers the mean stress influence by utilizing the Haigh diagram. Both approaches are then used as basis of root fillet shape optimizations. A comparison of results demonstrates significant differences in the safety assessment and the resulting root geometry.
Stegzahnrad
(2019)
Abstract
Strategies for Optimizing the Tooth Root Load Capacity of High-Performance Gears
Keywords: planet gears, high-performance gearbox, tooth root load capacity, tooth root optimization, multi-objective optimization
In order to achieve greater efficiency, many modern applications such as geared turbofans require high-performance gearboxes with excellent reliability and low weight. The tooth root load capacity often is a limiting design criterion driving minimum face widths and hence the weight of gears.
Consequently, strategies for optimizing the tooth root load capacity of gears are explored in this thesis.
Two methods for tooth root load capacity analysis – a maximum tensile stress method derived from ISO 6336 and a local fatigue approach taking into account mean stress infl – are introduced and ompared to each other with respect to their applicability to optimization problems. A study with 2D fi element models of unidirectionally loaded sun gears reveals that the local fatigue analysis method should be preferred over the common approach of minimizing the maximum tooth root stress, since applying both methods as optimization targets results in diff nt tooth root shapes and a vast overestimation of safety gains when only tensile stresses are considered.
Due to alternating loading, planet gears usually have a lower tooth root load capacity than other gears. Additionally, they are often designed with thin rims making the gear body lighter but also
more elastic. Therefore, the tooth root shape of a thin-rimmed planet gear is optimized to explore possible interactions. The results show that overly thin rims negatively affect the maximization of tooth root safety. Hence, it is necessary to conduct multi-objectiveoptimizations of planet gears, which maximize tooth root safety and minimize mass simultaneously by optimizing tooth root shape, rim geometry and face width. The efficacy of this approach is demonstrated for 3D gear simulation models of spur as well as double helical planet gears. Pareto-optimal designs show significant improvements compared to the baseline design. Moreover, investigations demonstrate the opportunity
to vastly decrease the computational cost of multi-objective optimizations by scalarizing them and using the result to approximate parts of the Pareto front.
Planetary gearboxes in highly sophisticated applications such as turbofan engines are required to have a high power-to-weight ratio and excellent reliability. Hence, thin-rimmed gear units need to be designed as compact as possible which, however, is usually limited by the tooth root load capacity. In order to come up with the best design, a tooth root shape optimization process is developed for thin-rimmed planet gears.