摘要
立柱是决定精密数控机床性能的关键部件之一,为实现立柱质量、沿主轴方向变形和低阶固有频率的综合优化,提出了一种结合拓扑结构和尺寸优化的多级优化设计方法。在第丨级优化设计中,通过有限元拓扑结构分析,得到部件结构的优化方向,确定了立柱的内部结构方式。第2级优化中,针对高敏感性参数进行优化,以立柱内部肋板的厚度为例确定其最佳尺寸。在第3级优化中,针对决定立柱的重心尺寸和减重孔尺寸等敏感性相对较低的多个参数,采用中心复合设计的试验方法在设计空间内选取合适的分析样本点,并由有限元分析软件计算样本点响应值,运用最小二乘法建立设计输入与响应输出之间的二阶响应面模型,根据该模型进行设计空间内的优化求解。以某型号卧式加工中心的立柱为例,采用文中方法进行优化设计,得到Pareto最优解集。结果表明:经过该方法优化后得到最优的肋板布置方式及其他相关结构尺寸,与初始结构相比,立柱总体质量减少了47.98%,沿主轴方向的变形和低阶固有频率均在允许范围内,且减小了计算量,结果证明了该方法的可行性。
Vertical column is one of the key components that determine the performance of precision NC machine tools.In this article,the multi-level optimization method in combination with the topology structure and dimension optimization is proposed,in order to identify the comprehensive optimization of column mass,deformation along the spindle direction and low-order natural frequency.At the first-level,the optimization direction of the component is identified based on the finite-element topology analysis;the topology shape of the column and the layout of the rib inside the column structure are determined.At the second-level,the high-sensitive parameters such as the thickness of the rib are optimized.At the third-level,the comparative low-sensitive parameters such as the dimensions which determined the center of gravity of the column and the dimension of the mass-reduced hole are identified.The test method of center composite is adopted to select the appropriate analytical sample points in the design space,and the response value of the sample points is calculated by the finite element software.A secondorder response-surface model between the design input and the response output is worked out with the aid of the Least Square method.The method is applied in the design of the horizontal machining center's vertical column and the optimal Pareto solution set is obtained.The results show that the optimum arrangement of the rib and other dimensions of the structure are identified by means of the optimized method.Compared with that of the initial structure,the overall mass of the vertical column is reduced by 47.98%,the deformation along the spindle direction and the low-order natural frequency are both within the allowable range,and the computing cost is saved.Therefore,the method is feasible.
作者
李源
黄华
郭润兰
LI Yuan;HUANG Hua;G URun-lan(School of Mechanical&Electrical Engineering,Lanzhou University of Technology,Lanzhou 730000)
出处
《机械设计》
CSCD
北大核心
2019年第11期44-49,共6页
Journal of Machine Design
基金
国家自然科学基金资助项目（51565030）
关键词
立柱
二阶响应面
多级优化
多目标优化
vertical column
second-order response surface
multi-level optimization
multi-objective optimization
