速度规划与轨迹轮廓控制均为复杂曲面数控加工研究中的核心问题。为提高复杂曲面加工效率，数控系统需要充分利用进给系统速度与加速度性能，但进给速度提高会引起伺服系统跟随误差增大，因此对速度规划与轮廓精度控制进行综合研究是提高复杂曲面加工效率与质量的重要途径。本文的研究目标是建立数控速度规划中的轮廓精度约束条件模型，提出满足速度规划模型适用、加工时间最优、计算效率高三方面要求的规划算法，提高系统位置环轮廓跟踪性能，建立数控系统软硬件平台以实现高效加工应用。主要研究内容如下：建立进给系统单轴跟随误差预测模型，根据轨迹几何信息提出速度规划轮廓误差约束条件模型；利用动力学模型理论分析与参数正交实验方法，提出速度规划过象限摩擦误差约束条件模型；利用实验证明这两个约束是保证数控加工精度的必要条件；最后提出速度规划动态参数的在线辨识与反馈方法，使速度规划模型参数更加准确。提出数控时间最优速度规划的凸优化方法，将原始模型离散化后，通过数学变换与分析建立速度规划问题的凸优化模型，利用内点法求解此模型；通过数值实验证明规划结果的最优性，验证时间复杂度由一般非线性规划的指数增长显著降低为多项式增长。利用插补输出刀位点信息，提出一种适合数控系统位置环模块的轮廓误差估计方法，具有计算量小、数值误差与模型误差小等特点；基于此方法在数控系统位置控制模块中实现交叉耦合控制，通过实验验证其提高轨迹轮廓精度的有效性。提出了一种基于GPU通用计算的速度规划并行算法，针对各并行线程独立与负载平衡问题提出一种轨迹划分方法，实验表明大规模输入情况下并行算法相比串行算法计算效率显著提高；设计了一种数控系统体系结构，为本文所提出的速度规划与轨迹控制等关键技术建立了应用平台；在此平台上完成口腔修复体加工控制系统与PCD刀具五轴电火花磨削加工控制系统两个系统的开发，并将理论研究成果进行了应用验证，试验结果表明应用本文所提出的速度规划轮廓误差约束条件与轮廓控制方法后，保持加工效率同时加工精度显著提高，达到工艺要求。
Feed-rate scheduling and trajectory tracking control are important topics in the area of complex surface machining. To improve the machining efficiency, CNC systems need to takes full advantage of the feed system performance to achieve high speed and acceleration. Feed-rate increase in high-speed machining leads to the servo system tracking error to increase, thus affect the contour accuracy. So it is necessary to take the contour error constraints into account in feed-rate scheduling. The research goal of this thesis is to establish an accurate constraints model for feed-rate scheduling, and to propose a feed-rate scheduling algorithm to satisfy the optimality, model applicability and high efficiency calculation, also to improve the system contour tracking performance, and to establish a CNC system development platform for these methods application. The major research work is listed as follows:A following error prediction model for uniaxial feed system is established. Combining with the track geometry information, a contour error constraint model for feed-rate scheduling is proposed. The relationship among the curvature, feed rate and quadrant protrusion error is studied with theoretical analysis. Then refer to comparative experiments of multiple sets of parameters, a friction error model in feed-rate planning is proposed. Experimental results show that these two constraints are the necessary conditions to guarantee the machining accuracy. A model parameters identification and feedback architecture is proposed, which improves the modeling accuracy.A time-optimal feed-rate scheduling method based on convex optimization is established. The model is converted into a discret model through parameterization method. The non-convex object function and constraints in the model are transformed into convex through a set of reformulation, and then the model is solved by interior point method. The numerical experimental results show that the optimality of planning, and the time complexity compared with general nonlinear programming decreases from exponential growth to polynomial growth.A contour error estimation method is proposed, which using interpolation output sequence of cutter points and suited for application in position loop module. With a small amount of calculation, the method avoids numerical errors and model errors. The cross-coupling controller in the CNC system position control module is implemented, the comparison experimental results show that the track contour error significantly decreases.A parallel feed-rate planning algorithm based on Graphics Processing Unit (GPU) is presented. The curve is divided into “planning units” which carries out speed planning independently and improves the load balancing of parallel computing. Experimental results show that the proposed parallel algorithm is much faster than the sequential approaches. A CNC development platform is designed and implemented, which is compatible with the feed-rate scheduling, trajectory control, and other key technologies in this thesis. A dental restoration machining system and PCD cutting tool EDG system is implemented in this platform, and the experimental results show that the machining accuracy meets the requirements by using the feed-rate scheduling model and cross-coupling position controller in this thesis.
