Conclusion on the State of the Art and Challenges

Currently, a function-oriented selection of all component tolerances under economic aspects for gear components that influence the operational behavior of the running gears is not state-of-the-art. However, there are only normative approaches in AGMA and ISO that relate individual deviations in the gearing to their effects on the load-carrying capacity (Refs. 23, 24). The preliminary work carried out is not readily suitable for the function-oriented definition of tolerances, taking into account scatter distributions for entire gearboxes. The reason for this is that there may be an unspecified correlation between the individual manufacturing deviations as input variables and the quality parameters as output variables. In addition, previous approaches do not take into account deviations due to tolerance interlinking, but only direct deviations at the gear flanks. Studies that present tolerance optimization about both costs and functionality often refer to simple, linear dimensional chains and are therefore only applicable to complex cylindrical gears to a limited extent. For this reason, only static limit values based on experience or literature are usually used for tolerance optimization. In particular, the aspect that different components and tolerance types have different effects on the overall manufacturing costs is currently only of secondary importance in tolerancing. Objective and Approach The aim of this report is to develop a method that performs a tolerance design for different types of deviation within a cylindrical gearbox. The calculation approach for the tolerance design should take into account that the tolerance-cost correlations are different for different types of deviation. Instead of fixed acoustic limit values, variables from descriptive statistics are used to define the tolerance. To realize the objective, a geometric-analytical model is used to reduce relevant deviations of the surrounding gear components in the tooth contact. This is followed by a variant calculation in the finite element-based tooth contact analysis (Ref. 25), taking into account typical tooth flank and profile deviations. There, the calculation of excitation parameters is carried out in the form of the total transmission error for different orders. The deviation characteristics as input variables are used together with the output values (total transmission error) to train a neural network in order to achieve reasonable calculation times, see Figure 2, left.

A closed-loop optimization process is then implemented, which modifies the tolerances using the metamodel on the basis of tolerance-cost functions for manufacturing processes and the influence of each type of deviation on the total transmission error. In addition to a Particle-Swarm Optimization, a multi-criteria Pareto-Optimization is used, which determines a so-called Pareto-Front (Ref. 26). In addition to tolerance-cost correlations, the excitation statistics are used as input parameters for the evaluation, see Figure 2. Economically optimized tolerance limits are determined as the output of the calculation method, for which compliance with the excitation scatter is ensured, see Figure 2 on the right. Furthermore, the distribution of the acoustic excitation can be determined and compared with the target specifications.