A Tolerance Design Method for the Entire Gearbox

The clever selection of manufacturing tolerances is crucial for reducing production costs while maintaining excitation quality. Tolerancing is often based on experience from previous designs. In this report, a tolerance design method for the entire gearbox was proposed based on metaheuristic methods using cost-tolerance functions (C-T functions) for different manufacturing processes. In addition to micro geometric gear tolerances, this also includes deviations on bearing seats of housings, shafts, roller bearings and gear bodies. The aim of the method is to achieve cost savings while maintaining or even optimizing the transmission error. C-T functions for conventional manufacturing processes were first parameterized on the basis of experience and assumptions regarding primary process time, auxiliary time, tool costs, machine costs, wages and space costs. These are used to determine the manufacturing costs compared to a reference design. However, the data for modelling the C-T curves have to be taken from experience or assumptions to apply the described method. Based on n = 200 individual variants per iteration, for which statistical descriptive variables of the total transmission error scatter are determined, a metaheuristic algorithm searches for tolerance combinations that promise lower costs at same or better acoustic behavior. A deep neural network is used for this purpose, which shortens the calculation time per iteration and determines the transmission error in the rotational and gear mesh orders from the tolerance inputs. For a reference tolerance design of the gears in quality class A 5, basic tolerances of A 7 and roller bearings in accuracy class PN, the fictitious geometry-determining total costs for the pinion and wheel shaft, the gears, the bearing seats and fitting bores as well as the roller bearings amounted to C = 3.4627 fC (fictitious currency). For the deviations in the form of normal or magnitude-normal distribution, reference transmission errors in various dominating orders were obtained, which were used as a standard of assessment. In a subsequent multi-criteria particle swarm optimization (MOPSO), a Pareto-Front was determined, which shows tolerance designs that perform better in terms of production and acoustic grading. Variants could be determined that have lower costs of up to pF = -7.5 percent according to the cost modeling implemented here, while almost maintaining the excitation behavior, whereby the reference design was already optimized in terms of process costs. This was mainly achieved by extending the tolerance limits on the gears, which allowed a change to the finish hobbing process for one gear, for example, which contributed to the cost reduction. Further processes and their chains can be considered in future studies. Furthermore, the cost determination for the parameterization of the C-T functions can be further detailed in order to achieve an increased precision of results. So far, the interpretation algorithm assumes that the distribution forms of the deviations remain constant. In future work, this could be extended so that the scattering form of the deviation variables is determined under the specification of a desired excitation distribution and additionally the produced part amount is considered.