基于SVD的超精密工件自寻位加工算法能力评价

杨航; 宋书飘; 黄文; 何建国

doi:10.11884/HPLPB201931.190261

基于SVD的超精密工件自寻位加工算法能力评价

doi: 10.11884/HPLPB201931.190261

1.
遵义师范学院工学院，贵州遵义，563006
2.
中国工程物理研究院机械制造工艺研究所，四川绵阳，621900

基金项目:

教育部重点实验室开放基金项目黔教合KY字[2017]385

贵州省科技计划项目黔科合LH字[2017]7081

贵州省教育厅青年科技人才成长项目黔教合KY字[2017]249

国家科技重大专项项目 2017ZX04022001

详细信息

作者简介:
杨航(1989—)，男，讲师，主要从事机械装备技术与工艺理论研究；yhangde@mail.dlut.edu.cn

中图分类号: TH164
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-09
- 修回日期: 2019-08-28
- 刊出日期: 2019-11-15

Capability evaluation of self-location machining algorithm for ultra-precision workpiece based on SVD

1.
Department of Engineering, Zunyi Normal College, Zunyi 563006, China
2.
Institute of Mechanical Manufacturing Technology, CAEP, Mianyang 621900, China

摘要

摘要: 为进一步改善超精密表面修形的最终精度、效率与成本，优化超精密自寻位加工的工艺方向与工艺决策过程, 开展了对超精密工件的自寻位加工算法点云融合过程的定量评价研究，提出了基于SVD的自寻位加工算法能力评价方法。首先基于运动学方法建立了点云融合的矩阵表示，分别对平动、转动、复合运动等情况建立了自寻位结果的转换矩阵表示，获得自寻位点云融合转换矩阵；进而对转换矩阵进行奇异值分解得到转换矩阵的奇异值列表；最后将列表中最大奇异值用以表征自寻位加工算法的能力。通过对某型超精密叶片在平动、转动和复合运动、共计1078组自由放置状态进行分析，发现所提出的评价指标在独立平动和独立转动两种任意放置情况下能够正确地表征自寻位加工算法的工艺能力。对于独立平动情况，自寻位加工算法能够正常定位加工，其最大奇异值也与预设偏差较小；对于独立转动情况，当旋转角度小于45°时，均能够正确地进行自寻位加工，最大奇异值差值也趋近于零，旋转角度超过45°时，算法的自寻位加工能力恶化，这一特性能够被所提指标正确捕捉。对于由平动和转动构成的复合运动而言，所提指标显示约35%的情况能够正确进行自寻位加工，其余情况无法进行正确的自寻位加工。结果表明本文所提方法建立的指标能够正确表征自寻位加工算法能力。
- 超精密加工 /
- 自寻位工艺 /
- 点云融合算法 /
- 奇异值分解 /
- 叶片加工
Abstract: In order to further improve the final precision, efficiency and cost-effectiveness of ultra-precision surface modification, and optimize the process direction and process decision-making of ultra-precision self-positioning processing, this paper studies the point cloud fusion process of self-positioning processing algorithm for ultra-precision workpieces. Based on the evaluation, it proposes a self-positioning processing algorithm capability evaluation method based on SVD. Firstly, based on the kinematics method, the matrix representation of point cloud fusion is established. The transformation matrix representation of self-positioning results is established for the translation, rotation and compound motion, respectively.Then the self-positioning point cloud fusion transformation matrix is obtained. A singular value decomposition is performed to obtain a singular value list of the transformation matrix.finally, the largest singular value in the list is used to characterize the self-positioning processing algorithm. By analyzing the free-precision states of a certain type of ultra-precision blade (a total of 1078 sets of free-standing state) it is found that the proposed evaluation index can correctly characterize self-positioning under the condition of independent translation and independent rotation. For the independent translation, the self-positioning processing algorithm can be positioned normally, and the maximum singular deviation value is also less than the pre-set value. For the independent rotation, when the angle is less than 45°, the self-positioning machining can be correctly performed. The singular value difference also approaches zero. Above 45°, the algorithm's self-positioning machining capability deteriorates, and this feature can be correctly captured by the proposed indicators. For the composite motion consisting of translation and rotation, the proposed index shows that about 35% of the cases can be correctly self-positioned, and the rest can not be correctly self-homing. It indicates that the indicators established by the proposed method can correctly characterize the self-positioning machining algorithm.
- ultra-precision machining /
- self-positioning technology /
- point cloud fusion algorithm /
- singular value decomposition /
- turbine blade processing

HTML全文

图 1 超精密零件自寻位加工过程

Figure 1. Self-positioning machining process of ultra-precision parts

下载: 全尺寸图片幻灯片

图 2 T_trans的SVD分解

Figure 2. SVD decomposition of T_trans

下载: 全尺寸图片幻灯片

图 3 某型号涡轮叶片点云

Figure 3. Diagram of point cloud of a certain turbine blade

下载: 全尺寸图片幻灯片

图 4 奇异值差值与平动距离的关系

Figure 4. The relation between singular value difference and translation distance

下载: 全尺寸图片幻灯片

图 5 奇异值差值与转动角度的关系

Figure 5. The relationship between singular value difference and rotation angle

下载: 全尺寸图片幻灯片

图 6 复合运动的λ分布及其统计分析

Figure 6. λ distribution of compound motion and its statistical analysis

下载: 全尺寸图片幻灯片

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