Robust multi-objective optimization of gear microgeometry design

Journal article, 2022

Gear microgeometry is important as it can change the tooth flank contact pattern effectively. In gear design, it is important to minimize the peak-peak transmission error (PPTE) for lower Noise, Vibration and Harshness (NVH), and to minimize the generated stresses for higher durability that can help to avoid tooth failure. In the current article, a structured approach is developed that combines the advantages of applying meta-models and robust optimization. For the Design of Experiments (DOE), the LDP software tool was used to obtain the objective functions of PPTE, contact stress, and root stresses at all design points. Probability distribution and worst-case scenario measures were applied to weigh the objective functions and make them robust against torque. The generated data were used in MATLAB to build meta-models for each objective function using squared exponential Gaussian regression. The generated meta-models were then used in a multi-objective optimization algorithm to obtain a Pareto set of solutions. These solutions were examined and ranked from the highest to the lowest, based on the weights of the PPTE and stress safety factors. Using Rank 1 design, the gains of -25, -7, +3 and -5% for the PPTE, contact stress, gear 1 root stress and gear 2 root stress respectively were obtained. However, these gains can be different in other design cases because these gains were calculated using Rank 1 design as compared to the manually selected benchmarked design which mainly depends on the engineer's experience. The developed approach can save time and help to obtain a unique optimal design solution in a structured format.