摘要
重型数控机床是由多个部件和子系统组成的复杂系统,相互之间存在不同程度的耦合关系,这给该产品设计带来了很大的困难。将多学科设计优化方法(MDO)应用到该类产品的设计之中,则能充分考虑复杂系统各学科之间的关联,得到满足设计要求的全局优解;这对于提高重型数控机床设计水平和创新能力,具有较大的实际意义。
本课题受国家“863”高技术研究发展计划项目2007AA04Z136、国家自然科学基金项目60573178和60736019支持,对重型数控机床MDO应用中的的若干关键难点进行研究。研究内容包括总体设计的MDO模型建立、学科建模和MDO问题求解。
对多学科设计优化方法与技术进行了较全面的介绍。对重型数控机床设计优化发展情况进行了阐述。以重型数控双柱立式车床为例,对机床总体设计的MDO建模进行了研究,给出了总体设计的MDF、IDF、CO、BLISS模型。
针对空间受力复杂的多油垫静压导轨的静压计算这一静不定问题求解困难甚至无法求解的现状,以静压导轨及其连接部分刚性足够大为前提,提出一种以油腔中心点共面/共线方程为协调条件的新的近似方法。用该近似计算方法建立了某重型数控立车横梁—滑座导轨静压计算的学科分析模型。在此基础上,采用元模型方法,对该横梁—滑座静压导轨系统进行了设计优化。
将导轨静压近似计算新方法用于该重型数控立车刀架系统设计中,建立了刀架系统精加工精度计算模型,进而建立了刀架系统的MDO模型。此优化问题具有高阶、多峰、非线性的特点,且全局优解位于狭窄不规则的区域,导致基于元模型技术和启发式探索的优化迭代困难。对此,提出了基于元模型的设计空间轮换(DSA)策略,即:先在位于该约束边界上的子空间进行试验设计,建立元模型;在随后的每轮优化迭代循环中,以元模型为分析代理,顺序进行子设计空间上的启发式全局探索、整个设计空间上的局部寻优算法搜索、系统分析和更新元模型的操作,直至收敛。采用DSA策略,得到了该多学科优化问题的全局优解。
进行了考虑静压—结构耦合的重型数控立车工作台导轨静压计算的数学建模与工作台MDO研究。在工作台主轴z向浮动情况下,用有限元法求解工作台变形时,它的z向约束较难处理。针对此问题,提出一种计算工作台刚性位移的方法和新的用于静压迭代计算求解的校正改进法,由此求出各油腔的油膜厚度和静压。新的校正改进法还可用于工作台中心卸荷或限制浮升起作用的情况。在此基础上,建立了包括结构和静压两个强耦合学科的工作台优化模型,采用并行子空间设计(CSD)方法求得了该优化模型的全局优解。
Heavy-duty CNC machine tools are complex systems with some coupled components and subsystems, which leads to great difficulties in their design optimizations. This problem may be solved by applying multidisciplinary design optimization (MDO) methods that can consider the interactions between coupled disciplines. Using MDO approaches in Heavy-duty CNC machine tool design has real significance in promoting the designers' capabilities in design and creation.
Supported by the National "863" High-Tech Development Project of China under the grant No. 2007AA04Z136 and National Natural Science Fund under the grant No. 60573178 and 60736019, some key problems are studied in the MDO applications to heavy-duty CNC machine tool designs. The researches involve establishment of MDO model of the overall design, disciplinary mathematical modeling and MDO problem solving.
The MDO methods and technologies are reviewed. The development situation of heavy-duty CNC machine tools is also discussed. Taking heavy duty CNC vertical turning mill as the research object, MDO modeling problem of the overall design is introduced and studied, and its MDF, IDF, CO and BLISS models are given subsequently.
Aiming at the difficulty of statically indeterminate problem, i.e., the hydrostatic pressure calculation of multipad hydrostatic guideways sustained complex spatial forces, under an assumption that stiffnesses of guideways and their jointing structure are sufficiently large, a new approximation method is presented by taking co-planarity/co-linearity equations that constrains pocket centers as compatibility conditions. Then, the disciplinary analytical model is constructed by the approximation method for hydrostatic pressure calculation of beam & slide-rest guideways in a heavy duty CNC vertical turning mill. Based on this, hydrostatic system of the beam & slide-rest guideways is optimized by metamodeling technology.
The new approximation method of hydrostatic pressure calculation is also used for tool head system design of the machine tool, and an accuracy calculation model of finish machining is constructed for the tool head. On the basis of this, MDO model of the tool head system is set up. The MDO problem is high-order, multimodal and nonlinear whose global optimum is only located in such a narrow and irregular area that it is difficult to find the solution using metamodeling technology and heuristic methods. To solve this problem, a metamodel-based design space alternation (DSA) strategy is proposed. In this strategy, metamodels are created in the narrow area of interest; then, heuristic exploration in the narrow area and local search in global design space with metamodels, system analysis and metamodel updating are sequentially executed in every iteration cycle until the convergence criterion is met. The DSA strategy is applied successfully to the tool head MDO problem and its global solution is obtained.
Mathematical modeling of hydrostatic pressure calculation for worktable guideway considering fluid-structure coupling and MDO of worktable in a heavy duty CNC vertical turning mill are studied. In the case that the worktable spindle is in a state of floating in z direction, it is difficult to set the constraint of the spindle part in z direction when finite element methods are used to analyze its deformations. To address this issue, a new method is proposed to predict the rigid displacement of the worktable and a novel correction-improvement method is presented to iteratively calculate hydrostatic pressures. Thus, the oil film thickness and hydrostatic pressure in each pocket are obtained. The new correction-improvement method is also suitable for the case that central unloading device or floating restriction device is active. Then, an optimization model is built including structural analysis and hydrostatic pressure calculation disciplines which are coupled bi-directionally. The optimization problem is solved using the concurrent subspace design (CSD) method and its global optimum is attained.
引文
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