基于成本函数与精度稳定性的机械系统精度多目标优化分配

Multi-objective Optimization Allocation of Mechanical System Accuracy Based on Cost Function and Precision Stability

目前在研究机械传动系统运动精度分配时,仅考虑成本因素,而忽视了系统运动精度稳定性因素对精度分配的影响。为此,提出一种基于成本函数与系统运动精度稳定性的机械系统精度多目标优化分配方法。通过引入元动作理论,建立元动作单元的精度-成本函数模型,利用综合复杂度系数表示元动作单元精度提升与成本的关系。以机械传动系统运动误差传递模型为基础,建立机械系统运动精度稳定性分析模型。以机械系统综合成本和系统运动精度稳定性为目标,建立机械系统运动精度多目标优化分配模型。利用模糊集合方法对Pareto非支配解集进行分析,确定最优解。最后,以数控转台系统运动精度分配为例,将所提的多目标优化分配方法与单目标优化分配方法进行对比,验证了文中所述方法的有效性。

At present,when studying the motion precision allocation of mechanical transmission system,only the cost factor is considered,and the influence of the system motion precision stability on the precision allocation is ignored.Therefore,a multi-objective optimization allocation method of mechanical system based on cost function and precision stability was proposed.The meta-action theory was introduced and a precision cost function model for meta-action unit was established,and the comprehensive complexity coefficient was used to represent the relationship between meta-action unit precision improvement and the cost.Based on the motion error transmission model of the mechanical transmission system,the stability analysis model for the motion precision of the mechanical system was established.With the comprehensive cost and the system motion accuracy stability of mechanical system as the goal,a multi-objective optimization allocation model for mechanical system motion precision was established.The fuzzy set method was used to analyze the Pareto non-dominated solution set and to determine the optimal solution.Finally,taking the motion precision allocation of the NC rotary worktable system as an example,the proposed multi-objective optimal distribution method was compared with the single objective optimization allocation method,and the effectiveness of the proposed method was verified.