Optimizing the Partial Gear Ratios of the Two-Stage Worm Gearbox for Minimizing Total Gearbox Cost

Abstract

Optimizing the design of a worm gearbox is complex to get due to considering multiple objectives and numerous main design parameters. Hence, a more consistent and robust optimization technique will be considered in obtaining the optimized results. This paper presents the optimization process of the Two-Stage Worm Gearbox with the objective function of minimizing total gearbox cost. Ten main design parameters are chosen as input parameters for evaluating their impacts on the response of the partial gear ratio u2. In this study, the simulation experiments were used, which do not need cost to perform all potential tests. In order to do this, a 2^(10-3) model and using 1/16 fractional model were selected due to the limitation of the built-in function in Minitab@18. Moreover, the screening experiments are purposely used to determine the number of parameters, which has a minor influence on the response. Compared to using the Taguchi technique, the model of 2^11 corresponding to L32 or 32 tests is a simple method to achieve the objectives.

The results show that Total gearbox ratio exhibits the biggest effect on the response compared to others. Furthermore, the interactions between these factors to the remaining are significant. The high reliability of the proposed model is verified by simulation experiments. The random tendency of data shows that u2 is not crucially influenced by other than the input parameters. The data in versus order prove that the response is not varied to the time factor. Moreover, the coefficients of adjusted R2 and R2 are both greater than 99 %, it can be concluded that the proposed regression model is appropriate. The proposed optimization process in this study is reliable and the optimal design method can provide a useful reference on performance improvement of other worm gears.

Keywords: bearing cost, gearbox cost, screen experiment, two-stage worm gearbox