In S-shaped specimens which are frequently used to reflect the machining ability of machine tools, the surface error refers to the distance between the points on the actual machining surface to their relevant points on the design surface. The proper measurement of this error is crucial for evaluating the machining quality of S-shaped specimens. During the process of error measurement, improper registration between the measurement coordinate system and the design coordinate system, as well as neglected uncertainty remain the main obstacles for the quality evaluation of S-shaped specimens. This study proposes a general method for the high-precision machining quality evaluation of S-shaped specimens that overcomes both problems. By applying the non-uniform rational B-spline (NURBS) surface molding technology, the surface of S-shaped specimen was reconstructed. Based on the minimum area principle and the particle swarm optimization-sequential quadratic programming (POS-SQP) algorithm, a surface error model of S-shaped specimen was developed. This model minimizes the maximum distance of the transacted measurement points to the design surface. It can be used to obtain the optimal registration matrix of the measurement coordinate system, with minimal surface error of S-shaped specimen. Additional common algorithms were also adopted to search the optimal registration matrix for comparison. Accounting for the random characteristics of basic parameters and the nonlinearity of surface error model, an uncertainty model of the surface error of S-shaped specimen was established based on the Monte Carlo method. This could obtain the actual tolerance zone of the surface error, according to which, the allowable tolerance zone of the surface error was optimized and a defined evaluation result of machining quality of S-shaped specimen was obtained. Then, a general approach for the evaluation of the machining quality of S-shaped specimen was developed based on POS-SQP algorithm and Monte Carlo method. This approach was implemented in a case study though a series of experiments. The experimental results identified the proposed approach as effective in improving the measurement quality and the evaluation of the machining quality of S-shaped specimens can thus be performed within an allowable tolerance zone.

在经常用来反映机床加工能力的S形试样中，表面误差是指实际加工面上的点与其设计面上相关点之间的距离。正确测量此误差对于评估 S 形试样的加工质量至关重要。在误差测量过程中，测量坐标系与设计坐标系的配准不当，以及被忽视的不确定性仍然是S形试件质量评价的主要障碍。本研究提出了一种通用的 S 形试样高精度加工质量评估方法，该方法克服了这两个问题。通过应用非均匀有理 B 样条 (NURBS) 曲面成型技术，S形试样表面重建。基于最小面积原理和粒子群优化-序列二次规划(POS-SQP)算法，建立了S形试样的表面误差模型。该模型最小化了交易测量点到设计表面的最大距离。它可用于获得测量坐标系的最佳配准矩阵，S形试样的表面误差最小。还采用了其他常用算法来搜索最佳配准矩阵进行比较。考虑到基本参数的随机性和表面误差模型的非线性，基于蒙特卡罗方法建立了S形试样表面误差的不确定性模型。从而得到表面误差的实际公差带，据此优化表面误差的允许公差带，得到S形试样加工质量的明确评价结果。然后，基于POS-SQP算法和Monte Carlo方法开发了一种通用的S形试样加工质量评价方法。这种方法是通过一系列实验在案例研究中实现的。实验结果表明，所提出的方法在提高测量质量方面是有效的，因此可以在允许的公差带内对 S 形试样的加工质量进行评估。优化了表面误差的允许公差带，得到了明确的S形试样加工质量评价结果。然后，基于POS-SQP算法和Monte Carlo方法开发了一种通用的S形试样加工质量评价方法。这种方法是通过一系列实验在案例研究中实现的。实验结果表明，所提出的方法在提高测量质量方面是有效的，因此可以在允许的公差带内对 S 形试样的加工质量进行评估。优化了表面误差的允许公差带，得到了明确的S形试样加工质量评价结果。然后，基于POS-SQP算法和Monte Carlo方法开发了一种通用的S形试样加工质量评价方法。这种方法是通过一系列实验在案例研究中实现的。实验结果表明，所提出的方法在提高测量质量方面是有效的，因此可以在允许的公差带内对 S 形试样的加工质量进行评估。这种方法是通过一系列实验在案例研究中实现的。实验结果表明，所提出的方法在提高测量质量方面是有效的，因此可以在允许的公差带内对 S 形试样的加工质量进行评估。这种方法是通过一系列实验在案例研究中实现的。实验结果表明，所提出的方法在提高测量质量方面是有效的，因此可以在允许的公差带内对 S 形试样的加工质量进行评估。