摘要
五轴数控铣削过程几何-动力学建模及工艺参数优化是国家重大工程中迫切需求的典型零件实现自主制造的核心技术之一,同时也是解决制造企业五轴数控加工效率、加工质量偏低的行之有效的方法。但是目前五轴数控铣削工艺研究及实际加工中存在如下问题:在刀具路径规划阶段,现有的商用CAM系统仅支持刀位干涉检验、修正与加工误差效验,缺乏对刀具运动扫描体包络面与设计曲面之间整体逼近的分析及相应离散刀位的控制;在工艺参数选取和优化阶段,由于缺乏有效的五轴数控铣削过程建模及仿真手段,同时又缺乏对加工过程不确定性的定量分析,工艺参数优化结果基于确定参数的五轴铣削动力学模型,因此实际加工往往不能取得预期的优化效果。
本文拟针对上述五轴数控铣削工艺研究和实际加工中存在的问题,围绕五轴加工有理运动设计—五轴运动刀具扫描包络面生成—刀具路径整体优化—工艺参数鲁棒优化层层推进的研究思路,结合整体叶轮叶片的五轴加工提出基于几何-动力学模型的工艺参数鲁棒优化方法,从几何层面的刀具路径优化和动力学层面的工艺参数优化两方面提升复杂曲面零件的加工精度和效率。在五轴数控铣削加工几何-动力学建模与工艺参数优化研究中,本论文取得如下创新性成果:
1.从运动学的角度将刀具抽象为点-线刚体,将刀具扫描运动的研究转化为对点-线刚体扫描运动的研究,建立了点-线刚体有理运动与对偶四元数空间超平面曲线之间的映射关系,提出了点-线刚体有理运动设计方法。在此理论框架下,将有理直纹面设计问题转化为对偶四元数空间超平面曲线设计问题,将五轴加工刀具姿态球面NURBS曲线设计和优化问题转化为四元数空间曲线设计及优化问题。整体式叶轮叶片五轴加工实验表明,应用优化后的刀具姿态,明显改善叶片的过切现象,提高了五轴铣削的加工精度。
2.将初始离散刀位视为空间离散点-线刚体,利用点-线刚体有理运动方法生成连续的刀具路径,再由双参数球族包络理论求出典型刀具五轴运动包络面解析表达式,以设计曲面上的离散点-刀具运动包络面距离极大值极小化为准则,通过微调初始的离散刀位,将刀具路径整体优化问题转化为设计曲面和刀具运动包络面之间的曲面比较问题,建立了五轴铣削加工刀具路径整体优化模型,通过序列规划方法优化求解。直纹面侧铣的仿真算例表明,利用本文提出的整体刀位优化方法,曲面的几何精度与国际上目前最好的数值结果(LBM方法)相比,提高20%以上。
3.建立了叶片的壳单元模型,将切削中材料去除过程视为壳单元厚度减小的过程,利用矩阵摄动理论预报高速铣削加工中材料去除对工件的模态的影响,得到时变的工件动力学模型,降低了实验强度。模态测试实验表明铣削加工中不同阶段叶片的模态与理论预测模态非常吻合。考虑工件-刀具中实际存在的不确定参数,利用区间代数,推导带不确定参数的工件-刀具的区间有限元特征矩阵和刀具动态响应的上下界。
4.考虑加工过程中的不确定因素,利用区间代数,基于灵敏度分析,求解铣削颤振稳定图的上下界和刀具动态响应的上下界,将带有不确定参数的多目标优化问题转化为确定参数的单目标优化问题,建立工艺参数鲁棒优化模型并优化求解。在整体式叶轮叶片五轴加工中,考虑刀具系统模态参数的不确定性,以主轴转速最大化和刀具振动位移最小化为优化目标,以切削过程稳定、无颤振为约束条件建立工艺参数鲁棒优化模型,与确定性工艺参数优化模型相比,鲁棒优化模型求解得到的结果保证了叶片五轴铣削的稳定性,改善了叶片的表面质量。
Geometry-dynamics modeling in five-axis numerical control milling with cutting parameters optimization is one of the key technologies to manufacturing the vital parts independently in national projects. It is also an effective way to improving the productivity and precision in manufacturing enterprises. However, some important questions remain as follows. In the stage of tool path generation and optimization, the commercial CAM software in general lack of the analysis of global approximation between the surface enveloped by tool motion and the design surface via fine-tuning of the discrete cutter locations. In the stage of selection and optimization of the cutting parameters, the effective modeling, simulations and the quantitative uncertainty analysis in five-axis machining process are absent. The cutting parameters optimization is traditionally developed based on the deterministic parameter model, thus the obtained nominal optimization results are not the real ones as expected in practical machining.
This thesis aims to solving the problems given above arising from the studies and shop floor. The relationships of the contents of this paper are rational motion design of rigid point-line—swept surface generation of tool spatial motion—tool path optimization—robust cutting parameters optimization. The tool path optimization and cutting parameters optimization in five-axis numerical control machining of complex surfaces are detailed to improve the productivity and precision from a geometry way as well as a dynamics way. In the studies of the model of geometry—dynamics in five numerical control milling and robust cutting parameters optimization, the main content and innovative ideas are presented as follows:
The cutting tool is viewed as the rigid point-line from a respective of kinematics, and then the study of the cutting tool motion can be transformed into that of the rigid point-line. The mapping of the point-line rational motion to the hyper-plane curve in dual quaternions space is constructed. The rational motion design of the rigid point-line is developed. In the frame of rigid point-line motion design, the problem of design of rational ruled surface is transformed into that of hyper-plane curve design in dual quaternions space. The design and optimization of the cutting tool orientation curve, which is a sphere NURBS curve is viewed as the curve design and optimization in quaternion space. The experiment, optimization of cutting tool orientation curve in five-axis machining of blade structures, indicates that the overcuts in the machining are eliminated and the quality is improved after optimizing the tool orientation curve.
The individual cutter locations are viewed as the discrete spatial point-lines and the continuous tool path is generated by using the rational motion method. The analytical swept surface of typical cutting tool used in five-axis motion is developed based on the double parameters envelope theory of sphere congruence. The problem of global tool path optimization is then transformed into that of the comparison of two surfaces, i.e. designed surface and the swept envelop surface. Optimization of five-axis tool path is modeled as fine tuning of initial cutter locations under the minimum zone criterion which requires to minimize the maximum geometrical deviation between the design surface and the envelop surface.
The finite shell element model of workpiece is developed, and the material removal process in milling is treated as the perturbation of the workpiece geometry. The effect of material removal on the modal shapes of blade structure in high-speed machining is predicted by using the matrix perturbation theory, as a result the varying dynamics of workpiece are obtained and the modal shape experiments are reduced. The experiment results validate the theoretical predictions. Considering the uncertainties in workpiece-tool, the interval finite element characteristic matrices of workpiece-tool are obtained using the interval arithmetic. Upper and lower bounds of dynamic responses of the tool are derived based on the interval arithmetic.
Based on the sensitivity analysis, considering the uncertain parameters in five-axis machining, the upper and lower bounds of chatter lobes and the dynamic responses of tool are obtained. The multi-object optimization problem with uncertain parameters is transformed into the single-object optimization one with deterministic parameters. In practical five-axis machining of blade structure, considering the uncertain parameters of modes of tool system, the robust optimization model is developed, in which the optimization object is to maximize the spindle speeds and minimize the tool vibration amplitudes, and the constrained condition is to keep the machining process un-chatter. Comparing with the deterministic model, the results of the robust model guarantee the stability of the milling process and improve the surface quality of the blade structure.
引文
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[3] Rubio, W., Lagarrigue, P., Dessein, G., and Pastor, F., 1998, "Calculation of Tool Paths for a Torus Mill on Free-Form Surfaces on Five-Axis Machines with Detection and Elimination of Interference," The International Journal of Advanced Manufacturing Technology, 14(1), pp. 13-20.
[4] Redonnet, J., Rubio, W., and Dessein, G., 1998, "Side Milling of Ruled Surfaces: Optimum Positioning of the Milling Cutter and Calculation of Interference," The International Journal of Advanced Manufacturing Technology, 14(7), pp. 459-465.
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