A hybrid cooperative-competitive evolutionary algorithm with non-dominated sorting for gear profile dynamic optimization in split-path transmission systems

Abstract

Split-path gear transmission systems (SPGTs) are widely employed in construction machinery, valued for their power-splitting capabilities and high torque density. The dynamic characteristics critically impact overall mechanical performance. This study proposes a hybrid cooperative-competitive evolutionary algorithm with non-dominated sorting (CCNS) for tooth profiles dynamic optimization in SPGTs. A nonlinear dynamic model for multi-gear pair SPGTs is first developed, incorporating time-varying mesh stiffness, damping, backlash, and enabling micro-geometric tooth profile modifications. This model is then integrated within the CCNS algorithm to minimize vibration acceleration RMS and dynamic transmission error peak-to-peak by optimizing modification parameters. The dynamic model’s validity is confirmed experimentally on a self-developed test rig under the constant torque and varying input speeds (450–1800 r/min). Results show predicted acceleration trends closely match measurements, exhibiting RMS errors of 4 % to 11.7 %. Leveraging this validated model, the influence of tooth profile modification parameters on dynamic characteristics is analyzed. This analysis reveals non-monotonic parameter effects, underscoring the necessity of multi-objective optimization. For the high-dimensional design space of SPGTs, CCNS demonstrates faster convergence and delivers superior Pareto solutions compared to other widely used optimization algorithms.