Abstract
In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein, deep-groove ball bearings have been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have a minimum effect on the objective function, i.e., its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, manufacturing accuracy, and material quality, and thus, the dynamic capacity and elasto-hydrodynamic minimum film thickness have been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter, and bearing width for the case of deep-groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients, and the number of rolling elements. These five internal geometrical parameters are taken as design variables; moreover, five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometry and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). Nondominated sorting genetic algorithm (NSGA-II) has been used as the optimization tool. Pareto-optimal fronts are obtained for one of the bearings. Of many points on the Pareto-front, only the knee solutions have been presented . This paper shows that geometrically feasible bearings can be designed by optimizing multiple-objective functions simultaneously and by also incorporating the variations in dimensions, which occur due to manufacturing tolerance.
