基于自适应NSGA-Ⅱ算法的变截面涡旋盘优化

Optimization of variable cross-section scroll based on self-adaptive NSGA-Ⅱ algorithm

针对目前对涡旋压缩机涡旋盘的优化设计多以几何性能最佳为优化目标,其力学性能较差这一缺点,提出了基于自适应第二代非支配遗传算法(NSGA-Ⅱ)、综合考虑力学性能和几何性能的变截面涡旋盘多目标优化设计方法.针对由基圆渐开线和高次曲线组成的变截面涡旋盘,确立了以涡旋型线特征参数表示的动涡旋轴向气体力及内容积比数学模型,以轴向力最小和内容积比最大为设计目标进行多目标优化设计,引入了根据种群的进化状态来进行自我调节的交叉算子和变异算子,以提高NSGA-Ⅱ算法的效率和最优解的分布均匀度,并得到了Pareto最优解集.在最优解集中挑选三种优化型涡旋盘与传统型涡旋盘进行对比分析,其最大轴向气体力分别减少了3.20%,1.08%和1.90%,内容积比分别提高了5.37%,6.64%和3.35%,表明提出的优化方法可以得到综合性能较优的变截面涡旋盘.

In the optimization design of scroll, considering merely the geometric performance as an optimization objective often results in the low mechanical performance of the scroll compressors. Therefore, a new multi-objective optimization method was proposed based on self-adaptive second-generation non-dominated sorting genetic algorithm(NSGA-Ⅱ),which balances mechanical and geometric performance of variable cross-section scroll.First,the mathematical model of the axial gas force and compression ratio of the scroll were established based on the analytical characteristic parameters of the scroll profile composed of the base circle involute and higher-ordered curve.Then,the multi-objective optimization design was carried out,which takes the minimum axial force and the maximum compression ratio as the target function.A crossover operator and a mutation operator that can self-adjust according to the evolution state of the population were introduced to improve the efficiency of NSGA-Ⅱ algorithm and the distribution uniformity of the optimal solution.Lastly,the Pareto optimal solution set of variable cross-section scroll was obtained.Three representative scrolls in the optimal solution set are compared with traditional variable cross-section scrolls, and the maximum axial gas force is reduced by 3.20%, 1.08% and 1.90%, the compression ratio is increased by 5.37%, 6.64% and 3.35%,respectively.Results show that the optimization proposed is effective in obtaining both mechanical and geometric optimal design.