考虑粗糙表面特性的驱动轴系统轴向派生力的区间不确定性优化

Interval Optimization for Generated Axial Force of Drive Shaft Systems Considering Rough Surface Characteristics

以一驱动轴系统为研究对象,基于分形理论,首先建立了一种考虑粗糙表面特性的轴向派生力的确定性模型。通过轴向派生力测试,验证了确定性模型的有效性。在考虑粗糙表面特性后,轴向派生力具有较大的不确定性。为了更有效地分析和优化轴向派生力,基于建立的确定性模型和勒让德多项式,提出了一种轴向派生力的区间不确定性模型。在区间模型中,输入参数被视为区间变量。以区间模型的上界和不确定度为优化目标,提出了轴向派生力的多目标区间不确定性优化方法。为了提高优化效率,结合勒让德多项式特点和顶点法,提出了一种快速获取区间模型上界和不确定度的方法。数值算例表明:基于提出的优化方法,不仅可使轴向派生力的上界满足设计要求,还可提高轴向派生力的鲁棒性。

Taking a drive shaft system as the research object, a deterministic model of the generated axial force(GAF) considering rough surface characteristics(RSC) is established based on fractal theory. By measuring the GAF of a drive shaft system, the proposed deterministic model of the GAF is verified. Since there are many factors effecting the GAF after considering RSC, the GAF has greater uncertainty. To study the GAF more effectively, an interval model for the GAF is proposed based on Legendre polynomials and the deterministic model. In the interval model, the influencing factors are considered as interval parameters. Taken the upper bound and the uncertainty level of the GAF as the optimization objectives, a multi-objective interval optimization method for the GAF is proposed. In order to enhance the optimization efficiency, an efficient method for calculating the upper bound and the uncertainty level of the GAF is proposed by combining Legendre polynomials and vertex method. The results of the numerical examples show that through the multi-objective interval optimization, not only the upper bound of the GAF can meet the design requirement, but also the robustness of the GAF is enhanced.