Linear ball guide design optimization considering stiffness, friction force, and basic dynamic load rating using particle swarm optimization

Linear-motion ball guides are one of the most common supporting elements in machine tools. Their design optimization is highly crucial for engineers and users because it can assist geometric and operating parameter selection and thereby aid in maximizing the stiffness and operating life while minimizing their friction. In this study, a multi-objective linear ball guide optimization process was performed using the particle swarm optimization (PSO). Five design parameters were selected for optimization: ball diameter, number of balls, groove curvature ratios for balls in contact with carriages and with rails, and initial contact angle. The design optimization objectives were radial stiffness, friction force, and basic dynamic load rating. The bearing stiffness and friction force were calculated using the numerical model proposed by the authors. The basic dynamic load rating was determined according to ISO 14728-1:2017. Pare-to-optimal solutions were used to support optimal design parameter selection. The final selection of an optimal point from points satisfying the Pareto optimality was performed using the cooperative equilibrium point method. The simulation results indicated a good performance of the optimized linear ball guide. Finally, the effects of parametric uncertainties in the optimal design on the performance were extensively investigated through a sensitivity analysis.